BEGIN:VCALENDAR VERSION:2.0 PRODID:-//MSP//MSP101 v1.0//EN X-WR-CALNAME: MSP101 X-WR-CALDESC: MSP101 seminar series BEGIN:VTIMEZONE TZID:Europe/London LAST-MODIFIED:20230407T050750Z TZURL:https://www.tzurl.org/zoneinfo-outlook/Europe/London X-LIC-LOCATION:Europe/London BEGIN:DAYLIGHT TZNAME:BST TZOFFSETFROM:+0000 TZOFFSETTO:+0100 DTSTART:19700329T010000 RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU END:DAYLIGHT BEGIN:STANDARD TZNAME:GMT TZOFFSETFROM:+0100 TZOFFSETTO:+0000 DTSTART:19701025T020000 RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU END:STANDARD END:VTIMEZONE BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260212T160000 DTEND;TZID=Europe/London:20260212T170000 LOCATION:LT1414a SUMMARY:Resugaring: Lifting Semantic Features through Syntactic Sugar DESCRIPTION:Speaker: Shriram Krishnamurthi (Brown University)\nTitle: Resugaring: Lifting Semantic Features through Syntactic Sugar\n\nSyntactic sugar is pervasive in language technology. It is used to shrink the size of a core language\; to define domain-specific languages\; and even to let programmers extend their language. Unfortunately\, syntactic sugar is eliminated by transformation\, so when the system provides feedback\, it is in terms of a program that is unfamiliar to the authors. Thus\, tool authors are forced to choose between their convenience and that of the programmer.\n\nWe address this conflict by showing how to lift core language features to present them in terms of the surface syntax. We have performed this research over three different features: execution traces\, binding\, and type rules. In each case we identify properties expected of the lifting and prove that our techniques satisfy these.\n\nMore broadly\, though syntactic sugar is a central area of programming languages\, it remains under-represented in the research literature. We briefly examine some other elements of a research agenda for this area.\n\n UID:469 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260330T130000 DTEND;TZID=Europe/London:20260330T140000 LOCATION:LT711 SUMMARY:Categorical Quantum Nonlocality DESCRIPTION:Speaker: Sam Fish (MSP)\nTitle: Categorical Quantum Nonlocality\n\nAfter decades of being embroiled in political skirmishes\, quantum physicists find themselves presented with a mathematical framework which predicts behaviour contrary to our reasonable intuitive leaning towards locality. Despite powerful attempts to quell the movement ensuing upon this realisation and to force it into irrelevance - even in the face of an incredibly successful experimental verification which no campaign can possibly diminish or sugar-coat - researchers now see no option but to accept the findings and to seek to understand their far reaches\, along with anything they might reveal about quantum theory's relationship with relativity via Einstein's requirement of local causality. \n\nOn Monday I intend to present this timeline of escalation as faithfully as I can\, along with some investigative findings\, and some underlying categorical actors.\n\n UID:468 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260323T130000 DTEND;TZID=Europe/London:20260323T140000 LOCATION:LT711 SUMMARY:(A very belated) Advert for POPL'26 DESCRIPTION:Speaker: Emma Tye (MSP)\nTitle: (A very belated) Advert for POPL'26\n\nSo POPL'26 was 2 months ago. I went as a student volunteer\, with my attendance funded by SIGPLAN and my travel funded by MSP. But what do I actually remember from it? What stood out? Did I see anything I think my fellow PhDs and professors would like?\n\nI plan to give an overview of my first experience at a major conference as a student\, as well as a whirlwind tour of some papers that caught my interest\, or I think might catch yours!\n\n UID:467 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260316T130000 DTEND;TZID=Europe/London:20260316T140000 LOCATION:LT711 SUMMARY:Thin behaviours\, (co)algebraically (Part I) DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Thin behaviours\, (co)algebraically (Part I)\n\nIn this talk I'll provide an update on our project on thin structures. Thin trees as introduced by Bojanczyk\, Idziaszek and Skrzypczak are infinite trees with at most countably many infinite paths. While the theory of (top-down) automata operating on infinite trees is considerably less well-behaved than the one of automata on infinite words\, thin trees provide a convenient setting where one can study tree-shaped data that behaves in some ways like words. In this talk I will recall the notion of a thin tree. I will then explain how thin trees generalise to the level of coalgebras for an analytic functor and how those thin "behaviours" can be seen as the quotient of an initial algebra of representants (terms of finite depth\, but involving an infinitary operation). We axiomatize that quotient with a single equation. Underlying our result is a normal form theorem for thin behaviours. I will then sketch how thin behaviours might be useful in verification and/or model learning. The details of the latter will\, however\, most likely be the content for another 101.\n\nThis is joint work with Anton Chernev\, Corina Cirstea and Helle Hvid Hansen.\n\n UID:466 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260302T130000 DTEND;TZID=Europe/London:20260302T140000 LOCATION:LT711 SUMMARY:Inceptions DESCRIPTION:Speaker: Vikraman Choudhury (MSP)\nTitle: Inceptions\n\nWe can program with continuations using the continuation monad\, which gives us control operators\, control effects\, and classical logic. But\, it is not an algebraic effect\, and corresponds to a large algebraic theory. Is there a monad for non-local control effects\, which is still algebraic?\n\nThis is work-in-progress\, and based on joint work with Gregor Feierabend and Marcelo Fiore.\n\n UID:464 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260223T130000 DTEND;TZID=Europe/London:20260223T140000 LOCATION:LT711 SUMMARY:Introduction to setoids DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Introduction to setoids\n\nA setoid is a type X together with an equivalence relation ≅_X : X → X → Prop\, i.e. ≅_X is reflexive\, symmetric\, and transitive. Setoids are widely used in (pre-HoTT) type theory based approaches to constructive mathematics\, where quotients might not be available\, or better avoided for computational reasons. Even though setoids have a bad reputation ("setoid hell") due to a quickly leading to a lot of boilerplate\, I'll argue that they are quite nice to work with as a model construction\, as setoids validate many convenient axioms such as function extensionality and countable choice.\n\n UID:463 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260216T130000 DTEND;TZID=Europe/London:20260216T140000 LOCATION:LT307 SUMMARY:Finitary testing DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Finitary testing\n\n\n UID:462 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260209T130000 DTEND;TZID=Europe/London:20260209T140000 LOCATION:LT209 SUMMARY:Structural Set Theory DESCRIPTION:Speaker: Rin Liu (MSP)\nTitle: Structural Set Theory\n\nSuppose you were asked\, "is 3 ∈ ℕ?" Being a natural number\, 3 is indeed a member of ℕ\, so the answer is “yes”. On the other hand\, the question\, “is π ∈ ℚ?”\, would quickly receive an answer of “no”. Now\, suppose you were then asked\, “is π ∈ log?”\n\nYou’d might pause for a moment\, before again answering in the negative\, but for a different reason than before. After all\, π is a number\, and log is a function\, so π being a member of log -- whatever that means -- would be ridiculous! A better answer might be to declare the question as meaningless.\n\nAs computer scientists and/or type theorists\, the problem here is obvious. But in the foundations used in most mathematics outside of (higher) category theory\, the issue is less clear-cut. In most common presentations of set-theoretic foundations -- for our purposes\, ZFC\; Zermelo–Fraenkel set theory with Choice -- everything is a set\, so the question “is π ∈ log?” should have a yes-or-no answer.\n\nMany of these kinds of quirks arise from the "global" nature of the set membership relation: it is always valid to compare any two arbitrary sets for membership and equality. However\, in most practical contexts\, sets are often stratified\, in the sense that we usually don’t have very long chains of membership containment\, and sets from different strata are very rarely compared or combined. This talk aims to present the structuralist's approach to this problem: a categorical way of constructing "structural" sets connected together via only local set membership relations between them that avoids these kinds of problems. This talk is intended to be accessible and expository\, and requires only basic exposure to category theory.\n\n UID:461 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260202T130000 DTEND;TZID=Europe/London:20260202T140000 LOCATION:LT209 SUMMARY:Trees for Concurrency DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Trees for Concurrency\n\nLooking at Claessen's 1999 functional pearl "A poor man's concurrency monad"\, we will see how we can simulate a limited form of concurrency in purely functional terms. We will then go on to see how to modify the setup to return a value from that computation as well as introduce join points.\n\n UID:460 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260126T130000 DTEND;TZID=Europe/London:20260126T140000 LOCATION:LT209 SUMMARY:Species of Trees DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: Species of Trees\n\nMathematicians and computer scientists both enjoy trees very much. I know I certainly do\, and I wish to share my enthusiasm. This talk will be a theory-light tour of various interesting phenomena relating to species of trees. We will discuss what makes a species\, what makes a tree\, and look at a range of particularly interesting examples of species of trees. In the interest of managing expectations: you're not likely to learn all that much about combinatorial species from this talk. It's more of an excuse to have a fun and relaxed time exploring ways trees can occur 'in the wild'.\n\n UID:459 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20260119T130000 DTEND;TZID=Europe/London:20260119T140000 LOCATION:LT210 SUMMARY:Wiggle It (Just a Little Bit) DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Wiggle It (Just a Little Bit)\n\nTesting can reveal the absence of bugs in situations where we can show that the test data expose all the possible variations. This is straightforward when the domain is finite\, but one can also achieve test coverage for large domains by restricting the ways in which the program may process its input. For example\, the fact that the sum of the numbers less than n is n choose 2 can be proven by testing for n in {0\, 1\, 2} because both calculations are inherently quadratic. I have\, on and off\, been thinking about how to deliver similar results for other inductive data structures. For example\, one can generate particularly well behaved folds on unlabelled binary trees by giving (i) the tree which is the image of the leaf\, and (ii) a tree with two variables showing how the ouptut for a node is computed from the outputs for its two subtrees. I claim that if two such folds agree at the four smallest trees\, then they agree for all trees. Clearly\, we recover (i) by testing at a leaf. We recover (ii) by testing at a node with leaves for subtrees\, then perturbing each of those subtrees in turn\, to see where the output changes. That is to say\, we use perturbation to recover abstraction. I am currently working on a proof of this claim in Agda and will share my progress (and my prospectus) in this talk.\n\n UID:458 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251215T130000 DTEND;TZID=Europe/London:20251215T140000 LOCATION:TBD SUMMARY:Duality DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: Duality\n\n\n UID:457 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251211T150000 DTEND;TZID=Europe/London:20251211T160000 LOCATION:LT310 and online SUMMARY:The free bifibration on a functor DESCRIPTION:Speaker: Noam Zeilberger (Laboratoire d'informatique de l'École Polytechnique)\nTitle: The free bifibration on a functor\n\nJoint work with Bryce Clarke and Gabriel Scherer.\n\nPreprint: https://arxiv.org/abs/2511.07314\n\nA functor p : D → C is a bifibration if\, loosely speaking\, one can push and pull objects of D along arrows of C. The talk will begin by recalling the formal definition together with some motivation\, and then explain how the free bifibration generated by a functor p may be constructed using a simple sequent calculus. This sequent calculus is closely related to a certain "zigzag double category" ℤC constructed as the free bifibration on the identity functor id : C → C\, and which is also the free fibrant double category on C. The double category perspective leads to a nice string diagram calculus\, while proof-theoretic techniques allow us to derive a canonicity result for free bifibrations\, and to analyze some examples of a combinatorial nature.\n\n UID:456 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251209T140000 DTEND;TZID=Europe/London:20251209T150000 LOCATION:LT1414a SUMMARY:An Introduction to Design-by-Contract with Dafny DESCRIPTION:Speaker: Jan de Muijnck-Hughes (MSP/StrathCyber)\nTitle: An Introduction to Design-by-Contract with Dafny\n\nDafny is a multi-paradigm language with deep integration of *design-by-contract* style verification: Hoare Triples. What makes Dafny interesting from a language design perspective is that\, although\, there is a clear separation between a specification and the code it reasons about\, specifications are nonetheless made from code. For this 101\, I am going to introduce everyone to Dafny and show how one can write and reason about simple imperative and object-oriented programs and their behaviour.\n\nWhat excites me about Dafny is its potential to act as a *bridging language* that guides students\, who are ostensibly rooted in imperative programming\, through to the world of verification without having to introduce them to the world of dependently-typed functional programming. I hope you will be excited about Dafny too.\n\n UID:454 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251124T130000 DTEND;TZID=Europe/London:20251124T140000 LOCATION:LT310 and online SUMMARY:Semantic analysis of Polarization DESCRIPTION:Speaker: Vikraman Choudhury (MSP)\nTitle: Semantic analysis of Polarization\n\nPolarization is a proof-theoretic technique used to study various kinds of logics with classical dualities. I will give a model-theoretic explanation of polarization in the context of classical logic and classical linear logic (Girard and Laurent). Finally\, I will show a higher-dimensional generalisation of these ideas to generalised species.\n UID:453 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251117T130000 DTEND;TZID=Europe/London:20251117T140000 LOCATION:LT1414a and Online SUMMARY:Graph Games with Infinite Plays DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Graph Games with Infinite Plays\n\nIn this 101 I am planning to discuss 2-player graph games with infinite plays. At first we will focus on games with "trivial" acceptance conditions where a player either loses or wins all infinite plays. As motivating example I will present the games that characterize least and greatest fixpoints of monotone operators. After that we will explore why those games are too simple for reasoning about alternating fixpoints and move to parity games\, a type of graph game that captures the full expressive power of the modal mu calculus. Time permitting I will explain how to prove that parity games are (memoryless) determined and how one can compute winning regions of a given parity game.\n UID:452 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251110T130000 DTEND;TZID=Europe/London:20251110T140000 LOCATION:LT1414a and Online SUMMARY:Modular abstract syntax trees (MAST) – substitution tensors with second-class sorts DESCRIPTION:Speaker: Ohad Kammar (University of Edinburgh)\nTitle: Modular abstract syntax trees (MAST) – substitution tensors with second-class sorts\n\nWe adapt Fiore\, Plotkin\, and Turi's treatment of abstract syntax with binding\, substitution\, and holes to account for languages with second-class sorts. These situations include programming calculi such as the Call-by-Value λ-calculus (CBV) and Levy's Call-by-Push-Value (CBPV). Prohibiting second-class sorts from appearing in variable contexts means the presheaf of variables is no longer a left-unit for Fiore et al's substitution tensor product. We generalised their development to associative and right-unital skew monoidal categories. We reuse much of the development through skew bicategorical arguments. In ongoing work\, we replace the skew monoidal structure with ordinary monoidal structure by recourse to substitution modules instead of substitution monoids.\n\nWe apply the resulting theory in two scenarios. We employ the mathematical theory to circumvent the expression problem when proving substitution lemmata for varieties of CBV denotational semantics modularly. We employ a computational implementation of the theory to circumvent the expression problem when implementing intrinsically-typed foreign-function interfaces for the 29 theories of SMTLIB.\n\nJoint work with Marcelo Fiore\, Kajetan Granops\, Mihail-Codrin Iftode\, Georg Moser\, and Sam Staton.\n\n UID:451 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251104T160000 DTEND;TZID=Europe/London:20251104T170000 LOCATION:LT1414a and Online SUMMARY:Matrix Type Theory DESCRIPTION:Speaker: Georgi Nakov (MSP)\nTitle: Matrix Type Theory\n\nWhat is an appropriate type for a matrix\, and what are the accompanying typing rules? Depending on your mileage\, the answer might seem obvious or dull -- can't we start with a humble Matrix A m n? I would argue that better candidates exist\, and that suitable typing rules are far from obvious\, at least if we aim at actually implementing the said rules. In this talk\, I will embark on the long journey of turning something that looks good on paper into something that works in code. We try to abolish any implicit assumptions\, hidden computation and blind guessing from the initial typing rules\, and refine them until they can guide a precise implementation. With guest occurrences of the usual suspects -- bidirectional typing\, thinnings\, and typecheckers-that-get-to-know-monoid-laws.\n\n UID:450 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251027T130000 DTEND;TZID=Europe/London:20251027T140000 LOCATION:LT310 and Online SUMMARY:What I did in my PhD DESCRIPTION:Speaker: Sean Watters (MSP)\nTitle: What I did in my PhD\n\nThe modal μ-calculus is a modal logic that type theorists don't usually spare much thought for\; it's usually treated classically\, and its main application is as a specification language for model checking\, where it subsumes weaker but more commonly used logics like LTL\, CTL\, and PDL. Meanwhile\, modal logicians study the μ-calculus using very "1930s" concepts like explicitly named variables. Most of my efforts during my PhD have been spent trying to pull the theory of the modal μ-calculus into this century (AKA into Agda) using the tools of type theory\, but my real interest is in what we type theorists might glean from the exchange. For example\, the modal μ-calculus is a fixpoint logic\, with a very mature account of fixpoint alternation - something that every proof assistant (to my knowledge) is lacking.\nIn this talk\, I'll be using the μ-calculus and some of my recent work on it as a motivating example to give a slightly non-standard introduction to some important MSP ideas - syntaxes with binding\, and data types as fixpoints. I'll cover the least fixpoint (which computer scientists love)\, the greatest fixpoint (which we sometimes tolerate)\, and the rational fixpoint (which many forget exists\, but plays a key role in my work). If time permits\, I'd also like to open the door to the terrifying world of arbitrary fixpoint alternation\, and some (very very early) ideas for taming it.\n UID:449 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251020T130000 DTEND;TZID=Europe/London:20251020T140000 LOCATION:LT310 and online SUMMARY:Capucci Logic DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Capucci Logic\n\nFor some applications\, it is useful for the truth of a logical statement to be approximate instead of merely true or false. Fuzzy Logics are a famous example of such logics\, where statements are valued in the interval [0,1]\, where 1 represents "definitely true" and 0 represents "definitely false".\n\nIn this talk\, I'll talk about a logic which is valued in [0,∞] where implication is interpreted as a ratio between premises and conclusion. The main feature of this logic is that we can formulate a logic where the "sharp" lattice connectives are replaced by smooth ones. Our hope is that this will allow such logics to be used in situations where satisfiability can be learned\, or where non-satisfaction is treated as a cost during training.\n\n UID:448 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251013T130000 DTEND;TZID=Europe/London:20251013T140000 LOCATION:LT1414a and Online SUMMARY:Introduction to Persistent Homology DESCRIPTION:Speaker: Fiona Blackett (MSP)\nTitle: Introduction to Persistent Homology\n\n\n UID:447 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251010T160000 DTEND;TZID=Europe/London:20251010T170000 LOCATION:LT210 and online SUMMARY:An introduction to constructive logic DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: An introduction to constructive logic\n\nConstructive logic (also known as intuitionistic logic) is logic without the Law of the Excluded Middle\, which states that P or ¬ P holds for every proposition P. Hilbert famously said that denying mathematicians the use of the Law of the Excluded Middle is "the same as denying the boxer the use of his fists". I will try to convince you that there sometimes is merit in not trying to punch people in the head. For example\, constructive logic is the internal logic of toposes\, and so a constructive proof can often be reinterpreted to show a much stronger result than a classical one\, e.g.\, a constructed proof of the existence of a function might in fact automatically yield the existence of a <*ontinuous<*or <*omputable<*function. Constructive logic often leads to interesting mathematics\, as it allows for finer distinctions than classical logic. I will also discuss how and when\, despite appearances\, constructive logic can be seen as an extension of classical logic\, rather than as a restriction.\n UID:446 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20251003T160000 DTEND;TZID=Europe/London:20251003T170000 LOCATION:LT1414a and Online SUMMARY:Let's Take Esoteric Programming Languages Seriously DESCRIPTION:Speaker: Jeremy Singer (University of Glasgow)\nTitle: Let's Take Esoteric Programming Languages Seriously\n\nEsoteric programming languages are challenging to learn\, but their unusual features and constraints may serve to improve programming ability. From languages designed to be intentionally obtuse (e.g. INTERCAL) to others targeting artistic expression (e.g. Piet) or exploring the nature of computation (e.g. Fractan)\, there is rich variety in the realm of esoteric programming languages. This essay examines the counterintuitive appeal of esoteric languages and seeks to analyse reasons for this popularity. We will explore why people are attracted to esoteric languages in terms of (a) program comprehension and construction\, as well as (b) language design and implementation. Our assertion is that esoteric languages can improve general PL awareness\, at the same time as enabling the esoteric programmer to impress their peers with obscure knowledge. We will also consider pedagogic principles and the use of AI\, in relation to esoteric languages. Emerging from the specific discussion\, we identify a general set of "good" reasons for designing new programming languages. It may not be possible to be exhaustive on this topic\, and it is certain we have not achieved that goal here. However we believe our most important contribution is to draw attention to the varied and often implicit motivations involved in programming language design.\n UID:445 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250922T130000 DTEND;TZID=Europe/London:20250922T140000 LOCATION:LT1310 and Online SUMMARY:Leftovers\, Rightunders: Typechecking Thinnings Compositionally DESCRIPTION:Speaker: Conor Mc Bride (MSP)\nTitle: Leftovers\, Rightunders: Typechecking Thinnings Compositionally\n\nIn the interests of sharing MSP lore\, I came up with a way to talk about both the "Input Subject Output" approach to typechecking and the Category of Thinnings in the same talk\, making the latter an interesting example of the former.\n\nThe Input Subject Output approach\, like most bidirectional approaches to problem decomposition\, tracks whether signals go from parent to child or vice versa\, but it also acknowledges a signal has a guarantor as well as a sender\, responsible for the meaningfulness of the signal. Meanwhile\, thinnings are order-preserving embeddings between ordered sequences\, or dually\, selections of elements from sequences (their resemblance to binomial coffecients is no accident)\, and are thus a fine example of a monoidal category.\n\nI won't assume that any of you know know any of this: many of us do\; more of us should. And I'll try to tell the story with pictures\, drawn on a whiteboard\, rather than jargon.\n\nI often use thinnings to talk about embeddings between scopes\, the latter seen as sequences which grow on the right (because of prejudices about time). A compositional way to typecheck a thinning is to start with the available stuff "over" the thinning\, together with a thinning that will start choosing from the newest stuff on the right. If all is well\, we shall learn which "leftovers" have not yet been considered\, and which "rightunders" have been not only considered but also selected. There is a healthy story about both the monoidal/parallel/spatial/tensor structure of thinnings and their categorical/sequential/temporal/composition structure\, yielding an algorithm which never has to guess where to chop sequences in two.\n UID:444 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250918T160500 DTEND;TZID=Europe/London:20250918T170000 LOCATION:LT1414a and Online SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:443 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250530T140000 DTEND;TZID=Europe/London:20250530T150000 LOCATION:LT210 and Online SUMMARY:A formal treatment of bidirectional typing DESCRIPTION:Speaker: Liang-Ting Chen (Institute of Information Science\, Academia Sinica\, Taiwan)\nTitle: A formal treatment of bidirectional typing\n\nIn this talks\, we consider a general and formal theory of bidirectional typing for simply typed languages: for every signature that specifies a mode-correct bidirectionally typed language\, there exists a proof-relevant type synthesiser which\, given an input abstract syntax tree\, constructs a typing derivation if any\, gives its refutation if not\, or reports that the input does not have enough type annotations.\nSufficient conditions for deriving a type synthesiser such as soundness\, completeness\, and mode-correctness are established for all signatures. We propose a preprocessing step\, which helps the user to deal with missing type annotations. The entire theory is implemented in Agda\, serving as a verified generator of proof-relevant type synthesisers as a by-product.\n UID:442 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250528T110000 DTEND;TZID=Europe/London:20250528T120000 LOCATION:LT1414a SUMMARY:Event: ADR/Promotion Information Meeting DESCRIPTION: UID:441 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250319T160000 DTEND;TZID=Europe/London:20250319T170000 LOCATION:LT210 and Online SUMMARY:Generalisation in LLMs DESCRIPTION:Speaker: Petar Veličković (Google DeepMind)\nTitle: Generalisation in LLMs\n\nA general talk about our recent works on generalisation in llms\n UID:440 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250422T150000 DTEND;TZID=Europe/London:20250422T160000 LOCATION:LT210 and Online SUMMARY:A quick & dirty look at at abstract syntax with binders and metavariables DESCRIPTION:Speaker: April Gonçalves (MSP)\nTitle: A quick & dirty look at at abstract syntax with binders and metavariables\n\nIn this talk\, I will show the (categorical) semantics of Fiore and collaborators’ “Second-Order Abstract Syntax with Binders” and of McBride and collaborators’ “Universe of Syntaxes with Bindings”. I will also compare them under multiple criteria (literature\, usage\, meta theory and implementation/formalisation)\, with special focus on how both approaches handle metavariables by using System F as our main example. (Please beware it’s a work in progress\, and many details haven’t been worked out yet\n UID:437 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250407T150000 DTEND;TZID=Europe/London:20250407T160000 LOCATION:LT412 and Online SUMMARY:Modelling cybersecurity games with compositional game theory DESCRIPTION:Speaker: Aven Dauz (MSP)\nTitle: Modelling cybersecurity games with compositional game theory\n\nCompositional game theory and its corresponding Haskell DSL "open-games-engine"\, have been used for modelling microeconomic games\, auctions\, and smart contracts. Some advantages of this compositional approach are leveraging modularity and code-reuse to construct larger games. Incidentally\, game theory has been used to model complex attack-defense scenarios in cybersecurity\, with the simplest case modelling the strategic interaction between a single attacker and defender. Scaling these models to accurately reflect real-world attacks and extrapolate data to improve the performance of systems remains an active area of research. In this talk I'll present a honeypot allocation game and design choices that allow a modeller to easily extend the construction to represent defensive strategies such as deception.\n UID:436 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250317T150000 DTEND;TZID=Europe/London:20250317T160000 LOCATION:LT412 and Online SUMMARY:Additives without Weakening DESCRIPTION:Speaker: Ross Horne (MSP)\nTitle: Additives without Weakening\n\nAs we know\, in linear logic\, conjunction and disjunction decompose into separate multiplicative and additive forms. Only additives are idempotent in general (A + A --o A). The additives also have some properties such as weakening (A & B --o A). By dropping weakening\, the additives further decompose into infinitely many "sub-additive" operators. I explain how I spotted these sub-additive operators when studying nominal quantifiers that can similarly be decomposed into new nominal quantifiers. I found these new additives curious since the resulting operators have properties that are sound with respect to probability distributions\, effectively internalising probability distributions in logic. I end by giving a taste of the proof theory of the sub-additives. A novelty is that\, due to how sub-additives control certain distributivity properties that play an essential role in established cut elimination techniques\, a new proof technique must be invented.\n\n\n UID:434 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250310T150000 DTEND;TZID=Europe/London:20250310T160000 LOCATION:LT412 and Online SUMMARY:A canonical bidirectional typing discipline through polarised System L DESCRIPTION:Speaker: Zanzi Mihejevs (GlAiVe Research)\nTitle: A canonical bidirectional typing discipline through polarised System L\n\nWhat is the relationship between polarity and bidirectional typing? It has long been observed that there is a connection between the two\, but the precise relationship has remained unclear. Moreover\, it has been argued that the link itself is a red herring\, and that bidirectional typing is better explained not by polarity but by chirality - the duality between producers and consumers. In this talk we will look at Polarised System L\, a type theory that combines both dualities - the positive fragment is driven by a cut between a primitive producer and a pattern\, and the negative fragment is driven by a cut between a primitive consumer and a co-pattern.\n\n Remarkably\, linear System L admits a canonical bidirectional typing discipline based on a combination of ideas from both standard and co-contextual typing\, giving us a "bi-contextual" typing algorithm.\n\n We will see how this lets us equip a type system based on full classical linear logic - containing all four connectives and derivable implication and co-implication - with a bidirectional discipline where all typing annotations are exclusively limited to shifts between sythesisable and checkable expressions.\n\n\n UID:433 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250303T150000 DTEND;TZID=Europe/London:20250303T160000 LOCATION:LT412 and Online SUMMARY:Representing type theory in type theory DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Representing type theory in type theory\n\nIt is often claimed that type theory can act as a foundation of mathematics. If that is so\, then type theory should in particular be able to reason about type theory itself. Of course\, Dr Gödel points out that this cannot work\, in general\, but we would expect that type theory could still reason about a slightly weaker version of itself. This turns out to be true\, but messy\, because type theory is quite complicated as a theory. After heroic attempts by Danielsson (2006) and Chapman (2009) to represent type theory internally in type theory\, Altenkirch and Kaposi (2016) made a breakthrough in using so-called quotient inductive-inductive types to represent the well typed terms of type theory\, where quotient constructors are used to encode beta and eta laws as equalities in the type. Being able to treat such laws as actual equalities is a major improvement\, but quickly leads into so-called <"ransport hell<" where explicit transports along equalities show up in terms and needs to be reasoned about. I will report on some recent work together with Liang-Ting Chen and Tzu-Chun Tsai on how one can use experimental (and hopefully future) features of Agda to improve on the quotient inductive-inductive representation and remove most uses of transport.\n UID:432 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250224T150000 DTEND;TZID=Europe/London:20250224T160000 LOCATION:LT412 and Online SUMMARY:Semantic proofs of Cut-elimination for Deep Infererence DESCRIPTION:Speaker: Robert Atkey (MSP)\nTitle: Semantic proofs of Cut-elimination for Deep Infererence\n\nDeep Inference systems are a kind of proof calculus that allow inference rules to be applied anywhere in a formula. Cut-elimination for these systems is similar to that for Sequent calculi: rules that introduce intermediate formulas can be removed from proofs. Prior proofs of cut-elimination relied on intricate syntactic method. I'll talk about a semantic approach that builds a model of the whole calculus from cut-free proofs\, such that every proof constructed in this model can be read back as a cut-free proof. This is a similar technique to the one used in Normalisation by Evaluation (NbE). The technique is very flexible and extends to many extensions of Multiplicative Linear Logic\, including BV's self-dual non-commutative "before" connective\, additives\, and exponentials. This is joint work with Wen Kokke and was published at MFPS last year: https://bentnib.org/sem-cut-elim-mfps.html\n\n\n UID:431 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250217T150000 DTEND;TZID=Europe/London:20250217T160000 LOCATION:LT1414a and Online SUMMARY:Weakest Precondition of Open Coalgebras DESCRIPTION:Speaker: Clovis Eberhart (MSP)\nTitle: Weakest Precondition of Open Coalgebras\n\nCoalgebras are a categorical framework that have proved useful to describe and reason about different types of systems. We define open coalgebras\, a compositional framework where coalgebras can be composed as string diagrams. We give them a semantics in terms of weakest precondition predicate transformers computed as a fixed point and link it to previous work on weakest precondition predicate transformers by Aguirre\, Katsumara\, and Kura. We give several examples of verification problems this semantics can compute\, showing its practical usefulness. We give conditions under which this semantics is compositional for the string diagram structure of open coalgebras. Finally\, we give a syntactic precomputation of open coalgebras that removes their internal states while preserving their semantics.\n UID:430 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250210T150000 DTEND;TZID=Europe/London:20250210T160000 LOCATION:LT209 and Online SUMMARY:Coequations via proof systems DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: Coequations via proof systems\n\n*What even is a coequation?* While Universal Algebra enjoys a set-in-stone consensus on both the correct syntax of equations\, as well as what an equation even is\, Universal Coalgebra is in no such position. There are many attempts at definitions and syntaxes of coequations\, but it is hard to say which one is 'the correct one'.\n\n Rather than sorting out this mess\, why not add yet another proposal? If we squint\, we can see proof systems for modal logic as coequations. This then leads to some fun\, natural questions. Which coequations can be captured by what kind of proof systems? If we restrict our attention to a class of 'simple' systems\, can we specify "every" coequation?\n\n As this is work in progress\, I have a fewer answers than questions. The aim of this talk is to introduce coequations in all their colours\, and to get the audience to a point where the questions may be appreciated.\n\n\n UID:429 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20250203T150000 DTEND;TZID=Europe/London:20250203T160000 LOCATION:LT209 and Online SUMMARY:We solved dependent optics! DESCRIPTION:Speaker: Jules Hedges (MSP)\nTitle: We solved dependent optics!\n\nThere are two major generalisations of lenses. First there are optics\, which require almost nothing of their base category and give you something in return. And then there are dependent lenses (aka container morphisms\, aka natural transformations of polynomials)\, which require a lot of their base category but give you even more in return. One day several years ago I innocently twote the question of how to unify these two constructions\, which is motivated for mathematical\, computational and sociological reasons. The problem ended up occupying us (joint work with Dylan Braithwaite\, Matteo Capucci\, Bruno Gavranović\, Eigil Rischel and André Videla) for several years\, and its difficulty became a meme. Indeed\nntly Shulman has proposed a nearly identical structure under the name ‘LNL-polycategories’. Shulman shows that by asking that different collections of universal properties be present\, LNL-polycategories may be used as a model for the LNL calculus\, CBPV\, and other models of effectful calculi. Inspired by this I will survey the universal properties required for implementing the basic communication primitives in a process calculus. With this framework\, we can compare process models with the structures present in linear logic models\, or effectful models\, offering an additional perspective into the existing connections between the pi-calculus and linear logic or algebraic effects.\n UID:398 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240405T150000 DTEND;TZID=Europe/London:20240405T160000 LOCATION:LT209 and Online SUMMARY:I Think Indexed Enriched Categories are Nice. DESCRIPTION:Speaker: Jade Master (MSP)\nTitle: I Think Indexed Enriched Categories are Nice.\n\nFirst proposed by Lawvere in 1973\, indexed enriched categories are a very complicated mathematical structure studied in only the most privileged ivory towers. In this talk I intend to bring them down to earth by exploring their viability as a data structure. I will cheat by only considering enrichments where the axioms are satisfied trivially. I will explain how these 'trivial' enriched categories are nice data structures for holding solutions to algebraic path problems. Then I will explain how making them indexed allows us to work with distributed\, concurrent\, and compositional algebraic path problems. This talk will be in line with the research programme I started to develop before I quit and left for industry. Namely\, that indexed categories and Grothendieck constructions may be used to develop a general theory of compositional computation. This talk will feature Idris2 code and categorical terminology side-by-side so that those familiar with either language will be able to follow along.\n UID:397 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240322T150000 DTEND;TZID=Europe/London:20240322T160000 LOCATION:LT209 and Online SUMMARY:Softmax is Argmax\, and the Logic of the Reals DESCRIPTION:Speaker: Matteo Capucci (MSP)\nTitle: Softmax is Argmax\, and the Logic of the Reals\n\nI will report some work in progress on the semiotics of softmax. This is an operator used in machine learning (but familiar to physicists way before that) to normalize a log-distribution\, turning a vector of (thus\, a function valued in) logits (i.e. additive reals) into a probability distribution. Its name is due to the fact it acts as a 'probabilistic argmax'\, since the modes of a softmax distribution reflects the minima (by an accident of duality) of the function. I will show an attempt to make this statement precise\, by exhibiting the semantics of a 'very linear logic' on the *-autonomous quantale of extended multiplicative reals. In this logic\, additive connectives are also linear\, but are still in the same algebraic relation with the multiplicative ones. I will show how to define quantifiers\, and thus softmax. If time permits\, I'll show a construction of an enriched equipment of relations in which softmax should be characterizable as a Kan lift\, in the same way argmax is characterized as a Kan lift in relations.\n UID:396 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240308T150000 DTEND;TZID=Europe/London:20240308T160000 LOCATION:LT209 and Online SUMMARY:TBD DESCRIPTION:Speaker: Paulo Torrens (University of Kent)\nTitle: TBD\n\nThe continuation-passing style (CPS) translation employed within compilers gives rise to a class of target calculi where direct style functions don't exist anymore. While those may be studied using the lambda calculus\, this might not be desired if the language should not be closed under beta-reduction\, such as in the intermediate representation (IR) of Appel's compiler. The purpose of this talk is to introduce ongoing work on the metatheory of Thielecke's CPS-calculus\, a small theory of continuations based on production IRs\, how it relates to actual implementations\, and how this allows us to have a strong theoretical background on the study of name-passing IRs in a similar way that the lambda calculus works as a theoretical foundation for functional programming.\n UID:395 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240301T150000 DTEND;TZID=Europe/London:20240301T160000 LOCATION:LT209 and Online SUMMARY:Type-Logical Grammar\, Controlled Substructure\, and Display Calculus DESCRIPTION:Speaker: Wen Kokke (MSP)\nTitle: Type-Logical Grammar\, Controlled Substructure\, and Display Calculus\n\n\n UID:394 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240223T150000 DTEND;TZID=Europe/London:20240223T160000 LOCATION:LT209 and Online SUMMARY:Containers for compiler architecture DESCRIPTION:Speaker: Andre Videla (MSP)\nTitle: Containers for compiler architecture\n\nCompiler architecture sucks. It's been left behind by years of software engineering development that have been very successful in developing software past the command-line age. Today\, applications are meant to be responsive\, accessible from a web browser\, enable collaboration\, be multi-platform\, include some generative AI. Some of those ideas are good\, some are bad\, but most compilers do not include any of them. In this presentation\, I aim to showcase how we can revisit the classical "compiler as a function" architecture using containers to bring the idea of compiler architecture to the XXI century.\n UID:393 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240216T150000 DTEND;TZID=Europe/London:20240216T160000 LOCATION:LT209 and Online SUMMARY:Making lenses less pointless DESCRIPTION:Speaker: Jules Hedges (MSP)\nTitle: Making lenses less pointless\n\nThis talk contains two ideas. The first is a small trick for programming with lenses in a not-pointfree way\, without using macros or other brittle hacks. The key is something I call a "dialectic"\, which is a value that carries around a delimited continuation with it. The second idea is realising that the central construction of Matteo's "Diegetic Open Games" paper amounts to a monad on the category of lenses that arises as the Kleisli dual of the linear ! comonad in a Dialectica category. By putting these two ideas together we get a shallow DSL for open games\, differentiable programming\, and other applications of categorical cybernetics. This will be a live coding talk using Haskell\, although I think the same ideas should work in any language with first class functions.\n UID:392 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240209T150000 DTEND;TZID=Europe/London:20240209T160000 LOCATION:LT209 and Online SUMMARY:Stable domain theory\, Program slicing\, and Automatic Differentiation DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Stable domain theory\, Program slicing\, and Automatic Differentiation\n\nI'll talk about a connection I think I've discovered between stable domain theory and program slicing by Galois Connections. Stable domain theory considers a refinement of continuous functions between domains that captures the intuitive idea that a "nice" computable functions that produce values must do so by only looking at part of their input\, and that part must be uniquely determined. The same idea turns up in Perera et al.'s formulation of program slicing as Galois connections. I'll try to connect the two via ideas from Automatic Differentiation.\n UID:391 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240202T110000 DTEND;TZID=Europe/London:20240202T120000 LOCATION:LT401 and Online SUMMARY:Presheaves on Purpose DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Presheaves on Purpose\n\nDependently typed programming languages allow us to define indexed families of datatypes\, e.g. Term (n : Nat) : Set as the type of lambda-terms with n variables free. As declared\, Term is functorial only on the discrete structure of Nat\, which is to say that it respects equality and nobody will faint with amazement. But by an outrageous coincidence (which I learned from Altenkirch\, Hofmann and Streicher)\, such terms can be acted on by *thinnings* from n to some larger scope m\, allowing us to carry terms under binders. That is\, we can demonstrate by honest toil that Term is a functor from Thin to Set. I dislike honest toil\, and will show you how to design it away in this and similar situations. To that end\, I present a universe construction for descriptions of datatypes indexed over the objects of some category C which\, by construction\, extend to a functors from C to Set\, a.k.a. presheaves on Cop.\n UID:390 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20240126T150000 DTEND;TZID=Europe/London:20240126T160000 LOCATION:LT209 and Online SUMMARY:Plane Graphs\, (Co-)Operads\, and Pattern Matching DESCRIPTION:Speaker: Malin Altenmüller (MSP)\nTitle: Plane Graphs\, (Co-)Operads\, and Pattern Matching\n\nI will present work on open surface-embedded graphs as representations of string diagrams. The key feature of these graphs' definition are distinguished boundary vertices which represent their (outer and inner) boundaries. These special vertices make it possible to define surface-embeddings of graphs using a rotation system which specifies an ordering of incident edges at each vertex. We can then also express graph rewrite rules by their action on boundary vertices. Additionally\, boundary vertices are a convenient structure to define planar graphs as operads\, similar to Spivak's Operad of Wiring Diagrams [1]. I will explain this construction\, as well as a dual "co-operad" version of it\, and finally the operad-cooperad interaction which yields a notion of graph pattern matching.\n\n[1] https://arxiv.org/abs/1305.0297\n UID:389 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231204T103000 DTEND;TZID=Europe/London:20231204T170000 LOCATION:University of Strathclyde (MC301) SUMMARY:Event: CATNIP DESCRIPTION:The second Categories Network Project (CATNIP) meeting. UID:388 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231123T150000 DTEND;TZID=Europe/London:20231123T160000 LOCATION:LT210 and Online SUMMARY:What do bidirected containers (co-)interpret into? DESCRIPTION:Speaker: Danel Ahman (University of Ljubljana)\nTitle: What do bidirected containers (co-)interpret into?\n\nDirected containers are a neat specialisation of containers that fully faithfully interpret into comonad structures on the polynomial functor interpretation of the underlying containers. In terms of shapes and positions\, a directed container requires the family of positions to form a certain kind of dependently typed monoid acting on the shapes. In terms of data types\, directed containers capture structures where every position in a shape determines a subshape rooted at that position\, e.g.\, positions in a non-empty list determine sublists rooted at those positions.\n\nIn this talk I will discuss bidirected containers and what they interpret into. Bidirected containers specialise directed containers further by asking the positions to form a certain kind of dependently typed group acting on the positions. In terms of data types\, this corresponds to every sub data structure having a position in it that takes one back to the parent data structure\, i.e.\, data types that behave like zippers. I will also discuss what we need to seem to ask from comonads to get a similarly tight correspondence as we have for directed containers. I will end by wondering whether an analogous story also applies to the cointerpretation of directed containers as update monads.\n UID:387 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230929T140000 DTEND;TZID=Europe/London:20230929T150000 LOCATION:LT711 and Online SUMMARY:An Introduction to Bricks DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: An Introduction to Bricks\n\n\n UID:386 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231207T110000 DTEND;TZID=Europe/London:20231207T120000 LOCATION:LT210 and Online SUMMARY:LabMate --- your faithful and type-safe Matlab assistant DESCRIPTION:Speaker: Georgi Nakov (MSP)\nTitle: LabMate --- your faithful and type-safe Matlab assistant\n\nCan you write type-safe Matlab code? And what can we do to help you write type-safe Matlab?\n\nThis talk is a report on our progress on LabMate --- an interactive system designed to improve on current best practices of writing Matlab code. Our key proposition can be eloquently described as "add types\, all the types".\n\nI will give a brief tour of the various features in LabMate and the rationale behind including them. We will also recall the basics of bidirectional type checking\, what to do to incorporate dimension and unit checking\, and how to represent matrices with high degree of generality in our type system. Some of the non-trivial challenges with Matlab's permissive syntax and elaborating operator overloading will become apparent in the process.\n\nThis is joint work with Fred and Conor.\n UID:384 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231201T140000 DTEND;TZID=Europe/London:20231201T150000 LOCATION:LT711 and Online SUMMARY:MSP 101: Non-standard analysis DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: MSP 101: Non-standard analysis\n\nI will give a basic 101-style introduction to the first-order logic concept of non-standard models. Intuitively\, a non-standard model of say Peano Arithmetic PA is a model which contains infinitely large numbers. Yet\, by virtue of being a model of PA\, such a model still validates all the axioms of PA\, including the induction axiom schema! It is an interesting and beautiful feature/bug of first-order classical logic that such models exist.\n UID:383 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231122T120000 DTEND;TZID=Europe/London:20231122T170000 LOCATION:University of Strathclyde / Online SUMMARY:Event: SPLS DESCRIPTION: UID:381 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231117T140000 DTEND;TZID=Europe/London:20231117T150000 LOCATION:LT210 and Online SUMMARY:Categorical cybernetics for Markov decision processes DESCRIPTION:Speaker: Riu Rodríguez Sakamoto (MSP)\nTitle: Categorical cybernetics for Markov decision processes\n\nI will introduce two ingredients to MSPs 'categorical cybernetics':\n- "open game"-like categories for backward-filtering problems\n- semiring valuations to formalize softmax as a *preference* relation (generalizing selection relations)\n\nThis will allow us to fit Markov decission processes and certain estimation problems to the existing framework\, clearing our path towards connecting control and estimation problems.\n UID:380 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231103T140000 DTEND;TZID=Europe/London:20231103T150000 LOCATION:LT210 and Online SUMMARY:Hopf-Frobenius Algebras DESCRIPTION:Speaker: Joe Collins (MSP)\nTitle: Hopf-Frobenius Algebras\n\nHopf algebras and Frobenius algebras are two fairly common algebraic structures. They even look pretty similar if you squint your eyes - both consist of a monoid/ comonoid pair\, and some algebraic rule that tells you how they interact. There are a few instances where a single object in a category has the properties of both a Hopf algebra and a Frobenius algebra\, called a Hopf-Frobenius algebra. In particular\, ZX calculus\, a way of modelling quantum circuits using symmetric monoidal categories\, has this property. Why? And where else does this occur?\n\nIn this talk\, I will be talking about what a Hopf-Frobenius algebra is and where it comes from.\n UID:378 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231027T140000 DTEND;TZID=Europe/London:20231027T150000 LOCATION:LT210 and Online SUMMARY:Category Theory ∩ Deep Learning : Where are we\, and where can we go? DESCRIPTION:Speaker: Bruno Gavranović (MSP)\nTitle: Category Theory ∩ Deep Learning : Where are we\, and where can we go?\n\nFour years ago I embarked on my PhD with the goal of exploring the landscape of category theory\, and its application to artificial neural networks. Specifically\, I aimed to understand at which level of generality can we express components of artificial neural networks\, and still meaningfully capture learning.\n\nIn this talk I will give a progress report on this goal\, and outline future directions for improvement.\n UID:377 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231020T140000 DTEND;TZID=Europe/London:20231020T150000 LOCATION:LT210 and Online SUMMARY:The double category of adjunctions DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: The double category of adjunctions\n\nThere's a particular double category which I've noticed floating around for a while. The purpose of this talk is to explicitly describe this double category\, play around in it and see if we can leverage it to get some `theorems for free'. I'll only be assuming prior familiarity with 1-categories\, so it should be of general interest. In fact\, part of the purpose behind this talk is demonstrating that even for staunch 1-category theorists\, having some higher categories `in the back pocket' may help in getting a clear picture of what's `really going on'.\n UID:376 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231013T140000 DTEND;TZID=Europe/London:20231013T150000 LOCATION:LT711 and Online SUMMARY:(Reflexive) Partial Monoids 101 DESCRIPTION:Speaker: Sean Watters (MSP)\nTitle: (Reflexive) Partial Monoids 101\n\nPartial monoids came up in my work recently\, and I found them quite interesting. The main goal of this talk is to introduce the notion into our local sphere of consciousness. After going over the basics I'll focus mostly on reflexive partial monoids\, the suprisingly tricky problem of defining exponentiation for them\, and the free reflexive partial monoid. I'll finish by outlining some remaining questions that I'm still wondering about.\n UID:375 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20231006T140000 DTEND;TZID=Europe/London:20231006T150000 LOCATION:Online SUMMARY:Writing interactive programs using containers DESCRIPTION:Speaker: Andre Videla (MSP)\nTitle: Writing interactive programs using containers\n\nContainers and their morphisms provide a bidirectional structure that matches a lot of programs that are interactive in nature (databases\, servers\, compilers). In this presentation I will show how to build such programs using containers\, container morphisms and their algebra.\n UID:374 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230922T140000 DTEND;TZID=Europe/London:20230922T150000 LOCATION:LT210 and Online SUMMARY:Staging by Evaluation DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Staging by Evaluation\n\nI will present an Agda implementation of a simply typed version of András Kovács' Staged compilation with two-level type theory. Starting from an intrinsically typed language mixing static and dynamic parts using quotes and splices\, we perform a model construction à la normalisation by evaluation and obtain a staging by evaluation algorithm.\n UID:373 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230705T110000 DTEND;TZID=Europe/London:20230705T120000 LOCATION:GH 513 and Online SUMMARY:A dual adjunction between Ω-automata and Wilke algebras DESCRIPTION:Speaker: Anton Chernev (University of Groningen)\nTitle: A dual adjunction between Ω-automata and Wilke algebras\n\nThe notion of ω-regular language captures the idea of a regular language that consists of infinite words. The most standard type of automata for ω-regular languages are called Büchi automata. Ω-automata are another type of automata for ω-regular languages that\, instead of infinite words\, read pairs of finite words\, called lassos\, that represent ultimately periodic words. We study the categorical relationship between Ω-automata and Wilke algebras – the latter are algebraic structures recognising ω-regular languages. We present a chain of adjunctions starting from the category of Ω-automata without initial states and ending with the dual of the category of quotients of the free Wilke algebra. This is joint work with Helle Hvid Hansen (University of Groningen) and Clemens Kupke (University of Strathclyde).\n UID:372 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230627T160000 DTEND;TZID=Europe/London:20230627T170000 LOCATION:GH 513 and Online SUMMARY:A Shiny Hammer and Many Nails to Hit – Bidirectional typing is not only an implementation technique DESCRIPTION:Speaker: Meven Lennon-Bertrand (University of Cambridge)\nTitle: A Shiny Hammer and Many Nails to Hit – Bidirectional typing is not only an implementation technique\n\nIn 2000\, Pierce and Turner introduced a new technique to perform type inference for ML-like languages\, whose main idea was to carefully understand the local flow of information in the algorithm. This technique\, which came to be referred to as bidirectional typing\, did not come out of a void: similar ideas had appeared independently in many other contexts. In particular\, bidirectional typing has been a part of the folklore of dependently typed languages implementers since the dawn of time.\n\n But even in that context where it has a long history\, bidirectional typing was for a long time mostly confined to implementations. Yet\, its type-theoretic structure turns out to be a very versatile and powerful tool when studying (dependent) type systems and their meta-theory.\n\n In this talk\, I will try and give some of my understanding of bidirectional typing\, how it is rooted in type-checker implementations but is more than just this\, and how it can be used to make many facets of the infamously painful meta-theory of dependent type systems a bit less painful.\n UID:371 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230630T150000 DTEND;TZID=Europe/London:20230630T160000 LOCATION:GH 513 and Online SUMMARY:On The Design of a Gradual Dependently Typed Language for Programming DESCRIPTION:Speaker: Joey Eremondi (University of Edinburgh)\nTitle: On The Design of a Gradual Dependently Typed Language for Programming\n\nI describe a design for gradual dependent types\, a system by which dependently typed programs can be run when missing parts of types\, proofs\, or programs. This serves a dual purpose. First\, it reduces the barrier to entry for dependent types\, making it easier to migrate code to use dependently typed languages\, and allowing indexed types to be safely used even when type or proof information is missing. Second\, it gives dynamic semantics to the typed holes that are already found in modern languages\, so programs can be safely run when holes are missing\, providing the programmer with useful information of what terms should fill the holes. In the talk\, I present a vision for what programming with gradual dependent types could look like\, along with technical challenges that arise with it and solutions to some of these challenges.\n UID:370 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230616T150000 DTEND;TZID=Europe/London:20230616T160000 LOCATION:LT310 and Online SUMMARY:Session Types & Imperative Languages & Observations\, Oh My! DESCRIPTION:Speaker: Jan de Muijnck-Hughes (MSP)\nTitle: Session Types & Imperative Languages & Observations\, Oh My!\n\nSession Types are a neat typing discipline to reason both statically and dynamically about program behaviour. An interesting question is how best we can incorporate session types into our programming languages and reach the fabled Emerald City of Type-Driven Validation of Communicating Systems!\n\n Earlier this year\, I gave a talk at PLUG that discussed the dependently-typed mechanics that pushed me along the yellow brick road to create Capable\, a featherweight imperative language that supports Multi-Party Session-Types (MPSTs). Capable has been mechanised within Idris2 to ensure that including MPSTs is done honestly as the Good Witch Glinda would appreciate.\n\n In this talk I intend to step away from the keyboard and take a detour along a yellow-ish cobbled street to look at some of the theoretical observations that arise from mechanisation. Specifically\, I will discuss the design decisions that the Wicked Dependent-Type Checker of the East has requested I do to ensure unification and execution\, but more importantly the trade-offs that come with those decisions.\n\n This work is\, slowly\, getting ready for publication (we do in fact run our session-typed programs) and I am certain that I don't need to return that brain\, yet....\n UID:369 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230621T140000 DTEND;TZID=Europe/London:20230621T150000 LOCATION:MC319 and Online SUMMARY:Computational Effects in Mathematical Perspective DESCRIPTION:Speaker: John Power (University of Bath)\nTitle: Computational Effects in Mathematical Perspective\n\nIn the late 1980's\, Eugenio Moggi introduced the idea of "monads as notions of computation"\, the latter more recently called computational effects\, supported by several impressive examples. He used the definition of monad but did not make substantial use of mathematics that gives rise to monads. In category theory\, monads systematically arise from universal algebra. But universal algebra can also be understood\, from a category theoretic perspective\, in terms of Lawvere theories\, this fact shedding considerable light on computational effects\, in particular the operations that give rise to effects. That observation has been fundamental to a deep\, further development\, giving rise to the notion of algebraic effect. I shall try to explain the conceptual line of thought that gives rise to algebraic effects\, modelled by Lawvere theories and thence my monads. It was joint work primarily with Gordon Plotkin but also with others\, notably Martin Hyland.\n UID:367 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230512T150000 DTEND;TZID=Europe/London:20230512T160000 LOCATION:LT711 and Online SUMMARY:Just when I thought I was out\, they pull me back in. DESCRIPTION:Speaker: Ethel Morgan (MSP)\nTitle: Just when I thought I was out\, they pull me back in.\n\nExperiences from industrial academia & academic industry.\n UID:366 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230505T150000 DTEND;TZID=Europe/London:20230505T160000 LOCATION:LT711 and Online SUMMARY:Modal unification and graph homomorphisms DESCRIPTION:Speaker: Johannes Marti (Oxford)\nTitle: Modal unification and graph homomorphisms\n\nThe problem of unifiability in a modal logic L asks\, whether for a given formula phi there exists a substitution such that applying the substitution to phi turns it into a theorem of L. For the many non-transitive modal logics\, most notably the modal logic K\, it is not known whether this problem is decidable. I present joint work with Sam van Gool\, where we reformulate unifiability relative to some modal logics L as a problem about the existence of a graph homomorphism for some generalised notion of graph that depends on a coalgebra functor T.\n UID:365 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230428T150000 DTEND;TZID=Europe/London:20230428T160000 LOCATION:LT711 and Online SUMMARY:Continuations and co-exponentials DESCRIPTION:Speaker: Vikraman Choudhury (University of Glasgow)\nTitle: Continuations and co-exponentials\n\nGrowing up in Indiana\, I learned about corn-mazes and continuations\, but I found them very confusing\, often getting lost and struggling to get back on track. Now that I’m living far away in Scotland\, I find myself reminiscing about my midwestern roots.\n\n In this talk\, I will present a different perspective on continuations: just as higher-order functions give you exponentials\, higher-order continuations give you co-exponentials. On this motif\, I will develop the theory of co-exponentials and some applications. I will show how to: (1) combine exponentials and co-exponentials in the same language without degeneracy\, (2) give a computational interpretation for bi-intuitionistic logic\, (3) recover classical control operators and the computational interpretation of classical logic using Faustian sums\, (4) use co-exponential combinators to do speculative execution\, backtracking\, and encode effect handlers\, (5) add co-exponentials to a first-order programming language\, with a computational interpretation. I will develop these ideas both in syntax and semantics.\n\n The main idea occurred to me while studying linear logic and star-autonomous categories\, from Mellies’ micrological study of negation. The rest of the work builds upon old ideas of Hofmann\, Streicher\, Reus on models of lambda-mu calculus\, Moggi’s computational lambda calculus\, Thielecke’s ⊗¬ categories\, Freyd categories of Power\, Thielecke\, Führmann and others\, and Hasegawa’s contextual calculus. This work is situated as part of a bigger research programme on trying to understand the foundations of quantum programming languages\, starting from first-order reversibility\, instead of linearity.\n UID:364 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230414T150000 DTEND;TZID=Europe/London:20230414T160000 LOCATION:LT711 and Online SUMMARY:What are higher categories and groupoids? DESCRIPTION:Speaker: Thorsten Altenkirch (University of Nottingham)\nTitle: What are higher categories and groupoids?\n\nCategories are like drugs: once you get addicted to one\, your dealer comes up with something stronger and you aquire a new addiction. This is the games with higher categories.\n\n I want to look at the definition of higher cats\, actually w,1-cats in HoTT using semi-simplicial types and the directed replacement of simplicial types. Also I may discuss the globular approach (which works for higher groupoids but could also made to work for higher cats) I am wondering how these are related. This may help to address some open problems.\n UID:363 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230314T150000 DTEND;TZID=Europe/London:20230314T160000 LOCATION:LT310 and Online SUMMARY:Systems that model their environments\, and systems that plan. DESCRIPTION:Speaker: Nathaniel Virgo (Earth-Life Science Institute (Tokyo))\nTitle: Systems that model their environments\, and systems that plan.\n\n Consider a system interacting with its environment\, perhaps in pursuit of some goal. We might want to ask whether the system has a model of its environment\, especially in POMDP-like cases where the environment is partially observable and the system must make inferences about the environment's state in order to pursue its goal.\n\n But where does the model live in relation to the system? A simple answer is that the system's state parametrises a probability distribtion over environment states. This distribution isn't part of the system but is imposed upon it by an external observer. I will talk about how to model this observer-dependence via notion of 'interpretation' of a sytem\, in which a system's internal states are interpreted as being 'about' a hidden environment state and as being updated using Bayes' theorem. A given system may have many interpretations\, so that interpretations form a fibration over systems.\n\n A more interesting case is where a system uses a model not just to keep track of its environment but to reason about how to influence it. This is a lot harder to model\, and I will talk about various pieces of work in progress towards understanding the relationships between systems\, models and goals\, with an emphasis on a category-theoretic perspective.\n UID:362 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230519T150000 DTEND;TZID=Europe/London:20230519T160000 LOCATION:LT711 and Online SUMMARY:How to be a real™ (C) programmer for beginner type theorists DESCRIPTION:Speaker: Andre Videla (MSP)\nTitle: How to be a real™ (C) programmer for beginner type theorists\n\nFeeling impostor syndrome from writing proof trees yet never executing any programs? Tired of being marginalized from online communities because you've never dereferenced raw memory? Finally\, you can become a C-programmer neckbeard with this one crazy trick without leaving the comfort of your pen&paper. By extending QTT with pointer operations one can finally achieve their dream of submitting a patch to the linux kernel and have it be rejected for naming conventions. At least the program would be correct by construction since you can inherit all your inductive proofs inside your imperative program.\n UID:361 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230609T150000 DTEND;TZID=Europe/London:20230609T160000 LOCATION:LT711 and Online SUMMARY:Control Flow as a Contour of Data Flow DESCRIPTION:Speaker: Malin Altenmüller (MSP)\nTitle: Control Flow as a Contour of Data Flow\n\nI will be talking about some ongoing work on a compositional graph data structure for encoding control flow information of a program. At the centre of this definition is the notion of contour for a given tree-like structure. The notion of contour category was introduced by Melliès and Zeilberger [1]\, who use it in the context of representing derivations in context-free grammars as functors. I will give an overview over their constructions\, and present how we generalise the notion of contour\, moving to a non-linear\, non-deterministic version. We use these generalised contours to express control flow information of a program on top of its abstract syntax tree. I will discuss how normal flow as well as exceptional program behaviour is represented in this framework. This is joint work with Dan Ghica.\n\n [1] UID:360 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230526T150000 DTEND;TZID=Europe/London:20230526T160000 LOCATION:LT711 and Online SUMMARY:From Lenses to Composable Continuations\, and what lies between DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: From Lenses to Composable Continuations\, and what lies between\n\nContinuation-Passing Style (CPS) is a programming discipline that parametrises programs by "the thing that happens next" - the continuation. Programs in CPS gain superpowers by being able to directly manipulate the continuation and use it as many times as they want. In this talk\, I'll try to convince you that lenses are a restricted form of CPS where the continuation must be used exactly once. In fact\, lenses and CPS form a category with lenses as the initial object and CPS as the terminal object. But what lies between them?\n UID:359 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230331T150000 DTEND;TZID=Europe/London:20230331T160000 LOCATION:LT711 and Online SUMMARY:Towards a categorical representation of thin trees DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Towards a categorical representation of thin trees\n\nDeterministic Automata on infinite trees lack expressivity. The situation is different when restricting one’s attention to so-called thin trees where every regular language can be seen as the language of a so-called unambiguous automaton. In my talk I will explain our motivation for why we are interested in unambiguous tree automata and I will present work in progress that aims to understand thin trees more abstractly. This is based on ongoing joint work with Corina Cirstea\, Jade Master and Alexandre Goy.\n UID:358 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230324T150000 DTEND;TZID=Europe/London:20230324T160000 LOCATION:LT711 and Online SUMMARY:From discounted value to discounted state DESCRIPTION:Speaker: Riu Rodríguez Sakamoto \nTitle: From discounted value to discounted state\n\nThe discounted value is a concept in Reinforcement Learning methods such as Value Iteration that allows to aggregate expected future rewards. It can be formalized as lens precomposition with a value function (which is a counit). We give some progress towards another class of RL methods that are based on parametrized policies\, where this composition happens without the need of a counit\, leading to a "discounted state" of a dynamical system. This has some resemblance to a List algebra\, taken over a bicategory of linear relations of a vector space instead of over Set. The discounted state is used in the literature to prove the Policy Gradient Theorem\, which we interpret as an Euler integration for noncommutative operators.\n UID:357 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230310T150000 DTEND;TZID=Europe/London:20230310T160000 LOCATION:LT711 and Online SUMMARY:String Diagrams for Actegories DESCRIPTION:Speaker: Dylan Braithwaite (MSP)\nTitle: String Diagrams for Actegories\n\nActions of monoidal categories are structures useful for modelling interacting systems. They are central to the definition of optics\, but have also found use elsewhere\, for example in the semantics of message-passing. When working in categorical cybernetics we often depict monoidal actions using string diagrams with multiple categories juxtaposed\, but this steps away from the formally specified semantics of string diagrams for monoidal categories which have coherence and completeness results making their manipulation valid for proving equalities. I will discuss how diagrams for actegories can be modelled more formally by considering them as certain bicategories using the construction of the collage of a bimodule.\n\n By depicting actegories as bicategories we obtain satisfying visual representations for actegory structures. We will see that the lax compositional structure of the collage gives rise to useful visualisations for the emergent behaviour between categories interacting via the action of a common monoidal category. This gets represented as coloured string diagrams glued together along certain shared boundaries. As a special case we can depict optics as diagrams with several regions which neatly frame the “forward”\, “backward”\, and “residual passing” stages of their morphisms.\n UID:356 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230303T150000 DTEND;TZID=Europe/London:20230303T160000 LOCATION:LT711 and Online SUMMARY:Chemoids: a rewrite approach to general compositionality DESCRIPTION:Speaker: Carlos Zapata-Carratalá (Society for Multidisciplinary and Fundamental Research)\nTitle: Chemoids: a rewrite approach to general compositionality\n\nIn this talk I will motivate and introduce the notion of 'chemoid'\, a compositional structure generalizing many diagram-based formal systems such as algebras\, categories\, operads\, tensor networks\, etc. I will then present some newly found\, somewhat exotic\, compositional structures that relate to chemical and biological computing (hence the name 'chemoid'). I will be using some of the functionality that I am currently developing with other colleagues at the Wolfram Institute.\n UID:355 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230224T150000 DTEND;TZID=Europe/London:20230224T160000 LOCATION:LT711 and Online SUMMARY:Type theory vs set theory: whose ordinals are better? DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Type theory vs set theory: whose ordinals are better?\n\nIn constructive set theory\, an ordinal is a hereditarily transitive set. In homotopy type theory\, an ordinal is a type with a transitive\, wellfounded\, and extensional binary relation. Which notion is more expressive? We can tackle this question if we first interpret set theory into type theory\, using Peter Aczel's sets as trees interpretation (recast in homotopy type theory using higher inductive types)\, and then compare the notions directly in type theory. With more work\, it is possible to generalise the comparison to capture all sets in Aczel's interpretation rather than only the ordinals. This leads to a natural class of ordered structures which contains the type-theoretic ordinals and realises the higher inductive interpretation of set theory.\n\n This is joint work with Tom de Jong\, Nicolai Kraus\, and Chuangjie Xu.\n UID:354 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230217T150000 DTEND;TZID=Europe/London:20230217T160000 LOCATION:LT711 and Online SUMMARY:Why Fibrations are your Friend DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: Why Fibrations are your Friend\n\nI'll tell you why fibrations should be your friends.\n UID:353 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230203T150000 DTEND;TZID=Europe/London:20230203T160000 LOCATION:LT711 and Online SUMMARY:Contexts and emergent effects in categorical systems theory DESCRIPTION:Speaker: Jules Hedges (MSP)\nTitle: Contexts and emergent effects in categorical systems theory\n\nOne of the most exciting ideas in categorical systems theory is being able to give a clean definition to “emergent effects”\, namely failure of a lax functor to be a functor. But there is a lack of theoretical tools to do useful things after identifying this common situation. I will present work in progress towards a “theory of contexts”\, talking formally about the idea that an open system’s behaviour can depend on what other systems are nearby\, by isolating 1 of the 3 key theoretical ingredients of open games. This hopefully allows situations with emergent effects to be seen as an ordinary functor\, although working out examples is irritatingly difficult.\n UID:351 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230127T150000 DTEND;TZID=Europe/London:20230127T160000 LOCATION:LT1310 and Online SUMMARY:Sorted Lists and Free Idempotent Commutative Monoids (over strict total orders) DESCRIPTION:Speaker: Sean Watters (MSP)\nTitle: Sorted Lists and Free Idempotent Commutative Monoids (over strict total orders)\n\nFree monoids are very well-understood and widely used\, both on paper and in code. However\, their commutative cousins are slightly trickier to pin down a neat data type for. There is a well-established mathematical story involving finite multisets\, but they are notoriously tricky to implement sensibly in code.\n\n Instead\, I want to focus on a datatype for sorted lists which turns out to be nearly the same thing if you squint the right way. I'll first demonstrate how we can construct and work with these things\, and then the squinting shall begin! We can easily show it to be a commutative monoid\, but thinking of it as the free one will require adopting the correct perspective. Specifically\, we'll need to work in the land of total orders rather than sets.\n\n I'm actually interested in finite subsets rather than finite multisets\, and that pleasingly only requires adding idempotency to the monoid multiplication\, and strictness to the total order. Although\, this actually leads to some interesting wrinkles when we try to prove freeness.\n UID:350 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230120T150000 DTEND;TZID=Europe/London:20230120T160000 LOCATION:LT1310 and Online SUMMARY:On a fibrational construction for optics\, lenses\, and Dialectica categories DESCRIPTION:Speaker: Matteo Capucci (MSP)\nTitle: On a fibrational construction for optics\, lenses\, and Dialectica categories\n\nCategories of lenses/optics and Dialectica categories are both comprised of bidirectional morphisms of basically the same form. In this talk I’m going to introduce both and show how they can be considered a special case of an overarching fibrational construction\, generalizing Hofstra’s construction of Dialectica fibrations. At its highest level of generality\, it’s a construction that turns a tower of fibrations into another tower of fibrations by twisting each of the components using the opposite fibration construction.\n UID:349 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20230111T150000 DTEND;TZID=Europe/London:20230111T160000 LOCATION:LT1310 and Online SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:348 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221130T110000 DTEND;TZID=Europe/London:20221130T120000 LOCATION:LT1310 and Online SUMMARY:Brouwerian counterexamples: being a know-it-all 101 DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Brouwerian counterexamples: being a know-it-all 101\n\nSome statements are not provable\, in the sense that they imply falsity (for example: "every inhabited subset of real numbers has a least upper bound"). Other statements are not provable constructively\, even though they are true when using classical logic (for example: "every bounded inhabited subset of real numbers has a least upper bound"). How can we convince ourselves of this fact\, so that we do not waste time and effort looking for a constructive proof? We can construct a so-called Brouwerian counterexample by showing that the claimed statement implies a known non-constructive principle. Brouwer called such principles omniscience principles\, because only an all-knowing being can hope to for example decide if P or not P holds for every proposition P. I will give an introduction to some of the more common omniscience principles such as LPO\, LLPO and Markov's Principle\, and try to give some intuition for when one should expect a statement to not have a constructive proof\; an important skill in order to avoid heartbreak when working in a constructive setting such as type theory or the internal logic of a category. \n UID:345 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221123T110000 DTEND;TZID=Europe/London:20221123T120000 LOCATION:LT1310 and Online SUMMARY: How I stopped worrying and learned to love triple categories (of cybernetic systems) DESCRIPTION:Speaker: Matteo Capucci (MSP)\nTitle: How I stopped worrying and learned to love triple categories (of cybernetic systems)\n\nA good chunk of MSP is busy trying to come up with convincing applications of category theory in 'cybernetics'\, which is an umbrella term for game theory\, learning theory\, control theory\, and more. I'm busy trying to understand what all these people (including me) are doing. What do the systems we are interested in have in common? What does it mean to say game theory and gradient-based learning look alike? How do we study the behaviour of cybernetic systems? Inspired by Myers' categorical system theory I formulated some tentative answers to these questions. Alas\, they require the full breadth of spatial dimensions this universe provides. In this talk I will quickly introduce the ideas behind my version of 'categorical cybernetic system theory'\, including recent developments regarding the definition of a theory of cybernetic systems. The hope is that conceptual motivation will defuse some fear in the higher structures involved.\n UID:344 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221116T093000 DTEND;TZID=Europe/London:20221116T160000 LOCATION:University of Edinburgh SUMMARY:Event: Agda Implementors' Meeting XXXI DESCRIPTION: UID:343 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221109T110000 DTEND;TZID=Europe/London:20221109T120000 LOCATION:LT1310 and Online SUMMARY:Hylomorphism complexity DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: Hylomorphism complexity\n\nAlgebra and coalgebra morphisms are well-known and widely applied. They have a more niche cousin in coalgebra-to-algebra morphisms\, also known as hylomorphisms. These are occasionally used to formalize divide-and-conquer algorithms. They can also be used in defining semantics for coalgebraic logics\, as well as solving certain sets of recursive equations. Taking the perspective of 'solving recursive equations'\, it is natural to ask for the computational complexity of deciding the existence of solutions. This turns out to depend essentially on the type functor for the (co)algebras. In this talk\, I will give a simple classification of (polynomial) functors by the complexity of their corresponding decision problem. On the way\, we will take in a few different intuitions towards (co)algebras and hylomorphisms.\n UID:342 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221102T110000 DTEND;TZID=Europe/London:20221102T120000 LOCATION:LT1310 and Online SUMMARY:Fixed points and recursion in quantitative reasoning DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Fixed points and recursion in quantitative reasoning\n\nThis talk summarizes a series of results regarding the extension of quantitative algebraic reasoning with fixed points and recursion. The work extends the quantitative algebras (which are universal algebras on metric spaces) with syntactic constructs that allow us to encode Banach fixed points on complete metric spaces. In effect\, one gets (a generalization of) a Conway and an iteration theory. I will demonstrate that most of the results known about classic iteration theories on ordered structures remain true in the metric context. And\, in fact\, that the metric settings generalize the results for ordered structures.\n UID:341 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221026T120000 DTEND;TZID=Europe/London:20221026T170000 LOCATION:University of Stirling / Online SUMMARY:Event: SPLS DESCRIPTION: UID:340 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221019T110000 DTEND;TZID=Europe/London:20221019T120000 LOCATION:LT1310 and Online SUMMARY:Tools of the Dependently Typed Compiler Trade DESCRIPTION:Speaker: Guillaume Allais (University of St Andrews)\nTitle: Tools of the Dependently Typed Compiler Trade\n\nVélo is a tiny language to explore the implementation of compilers for functional languages in a dependently typed host. I will highlight some of the design choices striking a balance between enforcing invariants\, getting work done\, and compiling to relatively efficient code. Features include support for well-scoped typed holes\, constant folding\, and common sub-expression elimination.\n UID:339 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20221005T110000 DTEND;TZID=Europe/London:20221005T120000 LOCATION:LT1310 and Online SUMMARY:A guided tour through my work DESCRIPTION:Speaker: Jacques Carette (McMaster University)\nTitle: A guided tour through my work\n\nI will attempt to do something that's generally ill-advised: give a shallow talk with many components without diving in to any part too deeply. Why? The wrong reason to give such a talk is to impress people with all you're doing. A potentially viable reason is to cover that work which might be of interest to the audience\, cause discussion and\, hopefully\, collaboration.\n\n I was tempted to call this a "meander through my work"\, but that really would be ill-advised. There are patterns to the madness\, and indeed the tour will be organized around those patterns.\n UID:337 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220928T110000 DTEND;TZID=Europe/London:20220928T120000 LOCATION:LT1310 and Online SUMMARY:The Topology of Knowledge: Simplicial Models for Epistemic Logic DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: The Topology of Knowledge: Simplicial Models for Epistemic Logic\n\nMulti-agent Epistemic Logic is a modal logic of knowledge. It allows to reason about a finite set of agents who may know facts about the world\, and about each other. In this talk\, I will present a new semantics for epistemic logic\, based on simplicial complexes. In this approach\, the knowledge of the agents is modeled by a higher-dimensional space called a simplicial model\; and the truth of an epistemic logic formula can be evaluated by inspecting the various possible paths in this space. I will illustrate these ideas using examples from the theory of distributed computing\, where the agents correspond to individual processes who can exchange information in order to solve a task. Both topological invariants and logical invariants can be leveraged to prove that some distributed computing tasks are impossible to solve.\n UID:336 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220921T110000 DTEND;TZID=Europe/London:20220921T120000 LOCATION:LT1310 and Online SUMMARY:Citizens and Subjects DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Citizens and Subjects\n\nI'll explore a distinction which emerges from my reimagining of type systems in terms of client-server interaction. A typing rule is a server for its conclusion and a client for its premises. Every signal in a typing interaction has a sender\, transmitting the signal as a syntactic object\, but also a guarantor\, promising that the signal is in some way meaningful. We are thus in a position to distinguish "citizens" (signals whose guarantor is their sender) from "subjects" (signals whose guarantor is their receiver). The two can and should be treated rather differently. Citizens should be free from the relitigation of their status and judged according to their semantics. Subjects should be investigated syntactically in order to establish their status. Like caterpillars and butterflies\, every subject should aspire to citizenship\, but when they achieve it\, they will not be who they were.\n UID:335 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220630T140000 DTEND;TZID=Europe/London:20220630T150000 LOCATION:Online SUMMARY:Can we compose Dependent Lenses as Optics? DESCRIPTION:Speaker: Bruno Gavranović (MSP)\nTitle: Can we compose Dependent Lenses as Optics?\n\nIn this talk\, I'll use Idris 2 to live code work in progress thoughts related to lenses and optics. I'll focus on the relatively unknown fact that\, even though lenses and optics are denotationally equivalent\, operationally they have a different composition rule\, with a different space-time complexity. In the case of optics this composition uses up more space\, but less time. While in the non-dependent case it is well understood how to take a bidirectional gadget and switch between a lens-like and an optic-like composition\, in the dependent case it not. In this talk\, I won't answer the question in the title\, but am instead hoping to frame it in proper context. I'll do type-directed programming\, and at points invoke linear types\, hoping to be guided by the compiler in search of an answer.\n UID:334 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220616T140000 DTEND;TZID=Europe/London:20220616T150000 LOCATION:Online SUMMARY:A unified visual language for games DESCRIPTION:Speaker: Jules Hedges (MSP)\nTitle: A unified visual language for games\n\nThe starting point of this talk is the observation that string diagrams for open games have more in common with extensive form trees than first appears. I will introduce a 3-dimensional syntax that has usual string diagrams and extensive form as 2 orthogonal projections. But first\, we need to talk about parallel universes…\n\n This talk summarises a paper I’ve had brewing for a couple of years and want to actually write soon\, that clarifies and expands on a tweet I wrote in October 2019. It is the secret thread connecting a couple of bits of my research in that time: dependent optics (joint work with half of MSP) and sheet diagrams (joint work with Antonin Delpeuch and Cole Comfort). In short: We define a bimonoidal category of dependent open games with tensor product and external choice\, and then equip it with the natural 3d syntax for bimonoidal categories.\n UID:333 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220609T140000 DTEND;TZID=Europe/London:20220609T150000 LOCATION:Online SUMMARY:Filtrations in modal logic DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: Filtrations in modal logic\n\nFiltration is a common technique in modal logic. The central idea is to consider a (large or even infinite) model M satisfying a property P of interest. By identifying states in a controlled way\, one may (greatly) reduce the size of the M — in fact\, one has an upper bound depending only on P. Filtration for basic modal logic is quite straightforward\, but may be more difficult for extensions\, particularly those involving fixpoint operators. PDL (propositional dynamic logic) is a much-studied such extension of modal logic\, used for reasoning about properties of programs.\n\n I will introduce filtration for basic modal logic\, and prove preservation of the desired properties. I will do the same for PDL\, highlighting the difficulty introduced by the fixpoint operator.\n\n If there is enough time and interest\, I will also discuss filtrations for monotone PDL\, which is PDL interpreted on a more general class of models (namely monotone neighborhood models).\n UID:332 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220526T140000 DTEND;TZID=Europe/London:20220526T150000 LOCATION:Online SUMMARY:Constructive Ordinal Theory in Homotopy Type Theory DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Constructive Ordinal Theory in Homotopy Type Theory\n\nMany constructions proceed in stages: we give a base case\, a step case showing how to go from stage n to stage n+1\, and then the desired result is achieved in the limit. In more complicated situations\, we have to go beyond stages indexed by natural numbers to stages indexed by larger structures — ordinals\, a cornerstone of modern mathematics. These are well understood classically\, but less so in a constructive setting\, where different equivalent classical notions split apart\, with different advantages and disadvantages for each. I will show how a theory of different ordinals can be developed constructively in the setting of homotopy type theory\, and how modern type-theoretic features such as higher inductive types and inductive-inductive definitions can be used to construct ordinal notation systems that truly behave like ordinals\, with extensional and wellfounded order relations.\n\n Joint work with Nicolai Kraus and Chuangjie Xu.\n UID:331 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220519T130000 DTEND;TZID=Europe/London:20220519T140000 LOCATION:Online SUMMARY:How to Compose Shortest Paths DESCRIPTION:Speaker: Jade Master (MSP)\nTitle: How to Compose Shortest Paths\n\nThe magic of the min-plus semiring allows one to express the shortest path problem as an exponential. A weighted graph is represented by a matrix M whose shortest paths are found as F(M) = Sum_{n >=0} M^n. Weighted graphs may be joined along a common boundary via pushout and the composition problem for F asks how the values of F on a pushout may be obtained from the values of F on its components. In this talk I will show how this abstract nonsense may be turned into an actual algorithm which computes shortest paths compositionally. Optimistically\, this algorithm and the relevant results may be adapted to the more general setting of the algebraic path problem.\n UID:330 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220512T130000 DTEND;TZID=Europe/London:20220512T140000 LOCATION:Online SUMMARY:Everybody Used To Be Somewhere DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Everybody Used To Be Somewhere\n\nI will report work in progress on my marking-disrupted incomplete formalisation of the action of relevant substitutions on relevant terms\, indexed over their variable support. A relevant term uses every variable in its support at least once\; a relevant substitution uses every variable in its target support in the image of at least one variable in its source support\; relevant substitutions thus map terms relevant in their source support to terms relevant in their target support.\n\n The "codeBruijn" machinery that makes my treatment of relevant terms work is based on the semisimplicial category: its objects are variable supports and its hom-sets are binomial coefficients seen as types of bit vectors representing selections. There are deep connections between the structure exhibited by this category and the Good Old Boolean Logic of the bits in the vectors. Meanwhile\, relevant substitutions themselves constitute the morphisms of a category whose objects are also variable supports. What keeps the roof up is the double category whose squares tell you what happens to the target scope of a relevant substitution when you select some particular variables from its source.\n UID:329 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220505T140000 DTEND;TZID=Europe/London:20220505T150000 LOCATION:Online SUMMARY:Some more constructions on containers DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Some more constructions on containers\n\nThe category of containers (~ polynomials) contains a wealth of structure for building structures representing question / answer type patterns. I'll discuss these and a few more that I think are novel. I'll try to relate them to ideas about data accessors like prisms and traversals.\n UID:328 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220428T140000 DTEND;TZID=Europe/London:20220428T150000 LOCATION:Online SUMMARY:Strategic games as cybernetic systems DESCRIPTION:Speaker: Matteo Capucci (MSP)\nTitle: Strategic games as cybernetic systems\n\nThis talk I will show how to correct a conceptual shortcoming in open games by showing how Nash equilibria can be described locally\, internally and dynamically instead of relying on external devices. Doing so homogenizes compositional game theory with the general yoga of categorical cybernetics. In order to do so\, we show how feedback in cybernetic systems is handled in a more structured way than previously considered\, which abstracts the formal properties of backpropagation of gradients and gradient descent.\n UID:327 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220421T140000 DTEND;TZID=Europe/London:20220421T150000 LOCATION:Online SUMMARY:Flexible presentations of graded monads DESCRIPTION:Speaker: Dylan McDermott (ICE-TCS\, Reykjavik University)\nTitle: Flexible presentations of graded monads\n\nGraded monads are a generalization of monads that are used\, for example\, to track quantitative information in models of effects. There is an existing notion of presentation (by operations and equations) for graded monads\, which has the problem that many examples of interest fail to admit natural presentations. I will talk about a more general notion of presentation for graded monads\, which resolves this problem by permitting more flexible forms of operation and equation. Every such presentation induces a canonical graded monad equipped with interpretations of these operations. As part of this work\, we reformulate graded monads and related concepts in terms of locally graded categories\, which provide a useful setting for working with grading.\n\n This is joint work with Shin-ya Katsumata\, Tarmo Uustalu and Nicolas Wu.\n UID:326 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220414T140000 DTEND;TZID=Europe/London:20220414T150000 LOCATION:Online SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:325 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220407T140000 DTEND;TZID=Europe/London:20220407T150000 LOCATION:Online SUMMARY:Beyond Epidemics (ACT version) DESCRIPTION:Speaker: William Waites (MSP)\nTitle: Beyond Epidemics (ACT version)\n\nI’ll speak about some of the material from a short talk I recently gave at the “Insights from the RAMP project” and will point out where I see some connections to category theory (mainly lens-like objects\, but also some graph rewriting) where some useful applications might be found. This will be a very informal talk\; expect digressions and no small amount of hand-waving.\n UID:324 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220331T140000 DTEND;TZID=Europe/London:20220331T150000 LOCATION:Online SUMMARY:Game Theory & Semi-Algebraic Geometry: A Symbiotic Relationship DESCRIPTION:Speaker: Yehuda "John" Levy (University of Glasgow\, Adam Smith Business School)\nTitle: Game Theory & Semi-Algebraic Geometry: A Symbiotic Relationship\n\nThis talk will present some of the main results from the long and symbiotic history between game theory and semi-algebraic (s.a.) geometry. On the one hand\, tools from s.a. geometry have been used to characterize sets of Nash equilibria\, study stability properties of equilibria\, and have had applications to equilibrium selection and stochastic games\, among others. On the other hand\, a series of results developed in particular in the past decade have shown that Nash equilibria are\, in certain senses\, universal for s.a. sets\, and that the Nash equilibrium correspondence contains\, in a certain sense\, all s.a. functions as well as some classes of correspondences. Relations to some problems concerning complexity of finding Nash equilibria will be mentioned. No prior knowledge of semi-algebraic geometry is assumed.\n UID:323 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220317T140000 DTEND;TZID=Europe/London:20220317T150000 LOCATION:Online SUMMARY:Practical dependent lenses for backend architecture DESCRIPTION:Speaker: Andre Videla (MSP)\nTitle: Practical dependent lenses for backend architecture\n\n Backend architecture is hard\, requirements change\, databases migrate\, authentication systems evolve\, but our strategy to tackle those problems have remained the same: Employ humans to perform all the necessary changes in the code\, until the next product needs to ship.\n\n To help with this\, I will show how we can leverage dependent lenses and different lens composition operators in order to represent common operations on servers\, including managing server resources\, updating endpoints and their routing\, and even swapping in and out middleware as necessary\, without affecting the operation of the server\, and preserving its typing.\n UID:321 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220309T110000 DTEND;TZID=Europe/London:20220309T170000 LOCATION:University of Edinburgh / Online SUMMARY:Event: SPLS DESCRIPTION: UID:320 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220303T140000 DTEND;TZID=Europe/London:20220303T150000 LOCATION:Online SUMMARY:On the differential structure of containers DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: On the differential structure of containers\n\nAbout twenty years ago\, Conor noticed a curious connection between rules for computing the type of `one-hole contexts' for algebraic data types\, and Leibniz's calculus differentiation rules: they are exactly the same! Together with Neil and Conor\, I've had some fun recently trying to put this result in Blute\, Cockett and Seely's categorical framework of differentiation\, by constructing a so-called Cartesian differential category of containers. Of course\, I will explain what these are during the talk.\n UID:319 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220224T140000 DTEND;TZID=Europe/London:20220224T150000 LOCATION:Online SUMMARY:An introduction to Non-idempotent Intersection Types DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: An introduction to Non-idempotent Intersection Types\n\nAre types for telling us what to program\, or for telling us what we have programed? MSP dogma leans to the former\, but it is worth looking at the latter too.\n\n If we take types to be explanations of programs' behaviour\, then it is only natural that they can have multiple types\, since programs may have multiple behaviours. Intersection types are the basic tool that allows the assignment of multiple behavioural descriptions to a single program.\n\n Traditional intersection types are idempotent: if we know that a term has some behaviour\, then it is of no interest to know this twice. Inspired by linear logic\, however\, we can start to wonder what happens if we record how many times we will need a program to have some behaviour -- non-idempotent intersection types.\n\n When we start counting behaviours\, something remarkable happens. In a result due to Daniel de Carvalho\, it turns out that the size of the typing derivation is equal to the number of steps taken to evaluate the program in the Krivine Abstract Machine.\n\n I'll describe the non-idempotent intersection type system for a CBN untyped lambda-calculus\, and how to prove de Carvalho's result. If here is time\, I'll also discuss how non-idempotent intersection types relate to the relational semantics of Linear Logic.\n\n An Agda formalisation of de Carvalho's result is written up here: https://bentnib.org/posts/2020-08-13-non-idempotent-intersection-types.ht ml\n UID:318 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220217T140000 DTEND;TZID=Europe/London:20220217T150000 LOCATION:Online SUMMARY:Operational view on Optics DESCRIPTION:Speaker: Bruno Gavranović (MSP)\nTitle: Operational view on Optics\n\n Optics\, lenses\, prisms\, and similar abstract gadgets are our best friends when it comes to modelling bidirectional processes. While optics are more general than lenses\, it's understood that they're equivalent in the special setting of a cartesian monoidal category. Fixing the setting of a cartesian monoidal category\, in this talk I'll explore how this equivalence is denotational in nature\, and the result of erasure of important operational data. I'll advocate that the operational aspect is not optional\, but rather crucial in understanding what these systems are doing.\n UID:317 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20220210T140000 DTEND;TZID=Europe/London:20220210T150000 LOCATION:Online SUMMARY:An informal introduction to Game Semantics DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: An informal introduction to Game Semantics\n\nDenotational semantics specifies the meaning of a computer program by associating it with an abstract mathematical object (its play talk\, we look at all three constructions and contemplate their equivalence.\n UID:307 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20211110T150000 DTEND;TZID=Europe/London:20211110T160000 LOCATION:Online SUMMARY:A Tour of Temporal Logic DESCRIPTION:Speaker: Sean Watters (MSP)\nTitle: A Tour of Temporal Logic\n\nModal logic can be applied to a diverse range of use-cases by fixing different notions of model and modality. Our motivation today will be the formal verification technique of model checking\, and with this in mind\, I will focus on temporal logic. In temporal logics\, the models represent systems which change over time\, and the modalities allow us to reason about exactly how they proceed in time.\n\n I will first introduce basic relational modal logic\, and show its limitations in this domain. We will then go on a tour of LTL\, CTL\, CTL*\, and the modal 𝜇-calculus. Key destinations on the tour will include the respective expressive power and model-checking complexity of each\, particularly in comparison to the 𝜇-calculus. I will end the tour with a closer look at the model-checking problem of the 𝜇-calculus\, and its relationship to parity games.\n UID:306 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20211103T150000 DTEND;TZID=Europe/London:20211103T160000 LOCATION:Online SUMMARY:An Introduction to Finite Model Theory DESCRIPTION:Speaker: Dylan Braithwaite (MSP)\nTitle: An Introduction to Finite Model Theory\n\nModel theory in classical logic provides a number of tools useful for classifying structures described by sets of axioms. In computer science we are often interested in cases where these structures are finite\, but many results in classical model theory fail to specialise to cases where we require all models to be finite. In this talk I will give an introduction to some of the alternative techniques used for studying expressibility of finite models and discuss some interesting connections with complexity theory.\n UID:305 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20211027T150000 DTEND;TZID=Europe/London:20211027T160000 LOCATION:Online SUMMARY:Categories for persistent homology DESCRIPTION:Speaker: Riu Rodríguez Sakamoto (MSP)\nTitle: Categories for persistent homology\n\nData analysis has dealt traditionally with regression\, clustering and dimensionality reduction. Persistent homology\, a tool in Topological Data Analysis\, can be thought of as the counterpart of clustering: Instead of looking at clusters of data\, it classifies holes of data. And we mean `holes' in the most visual way: given some point cloud in a metric space\, it addresses how do we characterize regions of the space where there's no data. This talk will introduce persistence modules\, which are a central concept of the theory. We will overview their construction from data\, how we can compare between\, and stability properties.\n UID:303 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20211013T150000 DTEND;TZID=Europe/London:20211013T160000 LOCATION:Online SUMMARY:The changing shapes of cybercats DESCRIPTION:Speaker: Toby Smithe (Topos Institute and University of Oxford)\nTitle: The changing shapes of cybercats\n\nThe ménagerie of categorical models of dynamical systems is becoming a veritable zoo\, but what makes all these animals tick? In this talk\, I will introduce a new specimen: a symmetric monoidal category of continuous-time open Markov processes with general state spaces. I will explain how this category is obtained from a category of ``continuous-time coalgebras'' opindexed by polynomials\, and describe how this recipe also gives categories of nondeterministic systems in arbitrary (continuous) time. These new specimens are motivated by the cybernetic question of how to model systems that are continuously performing approximate Bayesian inference. I will therefore sketch why their better-known cousins weren't quite up to the job\, and show that our new SMC admits Bayesian inversion. Finally\, I will attempt to make contact with the MSP branch of categorical cybernetics\, asking what makes the shapes of our structures seem so similar-but-different\, and how we might begin to understand systems nested within systems.\n UID:302 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20211006T150000 DTEND;TZID=Europe/London:20211006T160000 LOCATION:Online SUMMARY:A very abridged introduction to open games DESCRIPTION:Speaker: Jules Hedges (MSP)\nTitle: A very abridged introduction to open games\n\nOpen games allow you to talk about some amount of game theory (and thus\, some amount of economics) in terms of a lot of familiar ideas from category theory and compositionality. It isn’t possible to introduce open games adequately to anyone in this amount of time\, but this talk will be the best I can manage in the circumstances. I’ll explain approximately how open games work\, and how they relate to some other interests of MSP. I’ll also do a quick demo of the open game engine\, a Haskell implementation that’s robust enough to do some Real Economics ™.\n UID:301 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210929T150000 DTEND;TZID=Europe/London:20210929T160000 LOCATION:Online SUMMARY:Dependently typed programming: do you know what you are doing? DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Dependently typed programming: do you know what you are doing?\n\nWouldn't it be nice if you could tell the computer what you mean\, so that it could help you catch not only syntax errors\, but also semantics errors? Even better\, so it could help you and guide you towards the program that you want to write? So that knowing what you are doing could become a responsibility shared between human and machine\, instead of being only your problem? Using dependent types\, and some care\, we can achieve this by encoding the precise meaning of the program in its type -- any implementation will consequently be correct *by construction*. I will give a demonstration of such dependently typed programming\, based in part on a nice recent draft functional pearl by Wouter Swierstra: "A correct-by-construction conversion to combinators" [1]. I will not assume that you know much about correct-by-construction programming\, or combinatory logic.\n\n [1] https://webspace.science.uu.nl/~swier004/publications/2021-jfp-submission -2.pdf\n UID:300 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210923T150000 DTEND;TZID=Europe/London:20210923T160000 LOCATION:Online SUMMARY:Building the behavior of graphs compositionally DESCRIPTION:Speaker: Jade Master (MSP)\nTitle: Building the behavior of graphs compositionally\n\nThe free category on a graph may be understood as an operational semantics. The objects of this free category represent states and the morphisms represent possible sequences of events which may occur. How can this operational semantics be built from smaller components? We will see how gluing graphs together is the composition of category and how the operational semantics of graphs extends to a functor on this category. Blackboxing is a process which takes a system and focuses only the relationship it induces between its inputs and outputs. In this talk we will explain how blackboxing is almost a functor\, and how the categorical framework developed so far gives insight into computation.\n UID:299 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210916T150000 DTEND;TZID=Europe/London:20210916T160000 LOCATION:Online SUMMARY:Introduction to universal coalgebra DESCRIPTION:Speaker: Ezra Schoen (MSP)\nTitle: Introduction to universal coalgebra\n\nThe aim of this presentation is to give an overview of various concepts within universal coalgebra. We will explore such topics as corecursion\, bisimulation and coalgebraic (modal) logic. No prior knowledge is required\, save for some elementary category theory.\n UID:298 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210909T150000 DTEND;TZID=Europe/London:20210909T160000 LOCATION:Online SUMMARY:All kinds of types DESCRIPTION:Speaker: Andre Videla (MSP)\nTitle: All kinds of types\n\nWhat are types? What types of types exist? Why do we do bother and what does this buy us? This introduction to type theory aims to motivate the study of type systems and demonstrate their power. No knowledge is required except for basic programming concepts\, like functions and data structures. Our journey will take us from the Set theory slums\, through the curry-howard plains\, into the type-theory ivory tower and end looking at the stars where modal logic and QTT live.\n UID:297 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210902T150000 DTEND;TZID=Europe/London:20210902T160000 LOCATION:Online SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:296 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210708T150000 DTEND;TZID=Europe/London:20210708T160000 LOCATION:Online SUMMARY:Bite me! (Rational Fixpoints of Containers) DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Bite me! (Rational Fixpoints of Containers)\n\nLeast fixpoints\, often written mu X. Blah(X)\, give us inductive types (for strictly positive Blah)\, e.g. finite lists of A given as mu X. 1 + A*X: all the lists of finite length. Greatest fixpoints\, often written nu X. Blah(X)\, give us possibly infinite type (for strictly positive Blah)\, e.g. finite lists\, but also wild infinite lists like [0,1,2,3,...] which never repeat.\n\n There is no Greek letter between mu and nu. But there is at least one interesting fixpoint between the least and the greatest: things which can loop back on themselves\, but not diverge into the wide blue yonder. That is the rational fixpoint.\n\n What are we to do with it? I don't know but I intend to find out.\n\n I shall give a deeply unsatisfactory talk on this topic which leaves more questions than answers\, for the purpose of infecting people with this problem. There will be at least one solid clue.\n UID:295 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210701T150000 DTEND;TZID=Europe/London:20210701T160000 LOCATION:Online SUMMARY:Translating Extensive Form Games to Open Games with Agency DESCRIPTION:Speaker: Matteo Capucci (MSP)\nTitle: Translating Extensive Form Games to Open Games with Agency\n\nWe show open games cover extensive form games with both perfect and imperfect information. Doing so forces us to address two current weaknesses in open games: the lack of a notion of player and their agency within open games\, and the lack of choice operators. Using the former we construct the latter\, and these choice operators subsume previous proposed operators for open games\, thereby making progress towards a core\, canonical and ergonomic calculus of game operators. Collectively these innovations increase the level of compositionality of open games\, and demonstrate their expressiveness.\n\n This is a practice talk for ACT'21.\n UID:294 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210715T150000 DTEND;TZID=Europe/London:20210715T160000 LOCATION:Online SUMMARY:Expressivity of BCI algebras DESCRIPTION:Speaker: Samuel Arsac (MSP)\nTitle: Expressivity of BCI algebras\n\nI will have a look into the expressivity of BCI-algebras\, by implementing them in Coq and by looking at them from a categorical point of view. The first step will be to implement the λ* operator as shown in [1]\, which will allow for the use of linear lambda-calculus. From this point it will be much easier to define useful terms with BCI combinators\, and I will use the encoding of booleans in linear lambda-calculus defined in [2] to create a type of duplicable and discardable booleans. In parallel\, I will talk about the categorical aspects with the notion of realisability and category of assemblies [1]\, with the aim of showing that we can obtain a linear-non-linear model.\n\n [1] Top and find sufficient convex properties on X such that F(X) satisfies the fixpoint property for continuous maps. Along the way we prove a classification theorem: every convex set can be decomposed as a family of convex subsets of vector spaces “fibred over” a semilattice (slightly improving a similar unpublished result by Tobias Fritz).\n UID:281 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210325T150000 DTEND;TZID=Europe/London:20210325T160000 LOCATION:Online SUMMARY:Type Preserving Crossover Operations for Genetic Programs DESCRIPTION:Speaker: Donovan Crichton (Australian National University)\nTitle: Type Preserving Crossover Operations for Genetic Programs\n\nThis talk serves as my formal introduction to the MSP101 Group\, and covers work from my Bachelor thesis. We will look at how dependent types can be used to enable a type-safe crossover operation to allow the generation of program examples that are guaranteed to be well typed. We'll also cover alternate approaches I could've taken\, as well as further work in the area.\n UID:280 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210318T150000 DTEND;TZID=Europe/London:20210318T160000 LOCATION:Online SUMMARY:Propositional Dynamic Logic(s) DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Propositional Dynamic Logic(s)\n\nI will provide an introduction to dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL) and will then describe a (co)algebraic framework for these logics. This framework relates program/game constructs of these logics to monad structure. The axioms of these logics express compatibility requirements between the modal operators and the monad structure.\n UID:279 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210311T150000 DTEND;TZID=Europe/London:20210311T160000 LOCATION:Online SUMMARY:Quantitative containers DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Quantitative containers\n\nQuantitative Type Theory combines linear types (where we keep track of how many times a variable is used) and dependent types (where terms can appear in types). This gives a logical system which is both expressive and precise with respect to the resource usage of programs and proofs\, with a rich model theory. I will talk about work in progress investigating data types in this setting\, in the form of "resource-aware" quantitative containers\, and their initial algebra semantics.\n\n This is joint work with Georgi Nakov.\n UID:278 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210304T150000 DTEND;TZID=Europe/London:20210304T160000 LOCATION:Online SUMMARY:Quantitative Iteration Theories DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Quantitative Iteration Theories\n\nWe develop a fixed-point extension of quantitative equational logic and give semantics in one-bounded complete quantitative algebras. Unlike previous related work about fixed-points in metric spaces\, we are working with the notion of approximate equality rather than exact equality. The result is a novel theory of fixed points which can not only provide solutions to the traditional fixed-point equations but we can also define the rate of convergence to the fixed point. We show that such a theory is the quantitative analogue of a Conway theory and also of an iteration theory\; and it reflects the metric coinduction principle. We study the Bellman equation for a Markov decision process as an illustrative example.\n\n This is a recent joint work with Gordon Plotkin and Prakash Panangaden.\n UID:277 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210225T150000 DTEND;TZID=Europe/London:20210225T160000 LOCATION:Online SUMMARY:Some Thoughts on a Datatype for Higher Genus Graphs DESCRIPTION:Speaker: Malin Altenmüller (MSP)\nTitle: Some Thoughts on a Datatype for Higher Genus Graphs\n\nCircuit diagrams are commonly modelled by graphs embedded into some oriented surface (maps). When the circuit's topology is non-trivial (e.g. for quantum circuits)\, the maps live on higher genus surfaces. I will give an introduction to the relevant graph theory and discuss some ideas on how we might be able to program with these higher genus structures. Starting from the plane case\, a multi-stack approach seems promising for approaching these more complex maps. Strategies for modelling structures with multiple stacks exist in various different contexts and any of your experiences are most welcome in the discussion!\n UID:276 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210218T160000 DTEND;TZID=Europe/London:20210218T170000 LOCATION:Online SUMMARY:Internal ∞-Categories with Families DESCRIPTION:Speaker: Nicolai Kraus (University of Nottingham)\nTitle: Internal ∞-Categories with Families\n\nIt is natural to formalise the notion of a model of type theory (especially the syntax = intended initial model) inside type theory itself. This is often done by writing the definition of a category with families (CwF) as a generalised algebraic theory. What could the success criterion from a HoTT point of view be? The typical first goal is that the initial model is an h-set or even has decidable equality. Our second goal is to make the "standard model" work\, i.e. the universe U should be a CwF in a straightforward way (cf. Mike Shulman's 2014 question whether the n-th universe in HoTT models HoTT with n-1 universes). Unfortunately\, it is hard to combine these two goals. If we include set-truncatedness explicitly in the definition of a CwF\, then the "standard model" is not a CwF. If we don't\, then the initial model is not an h-set. The root of the problem is that 1-categories are not well-behaved concepts in an untruncated setting. The natural approach are higher categories\, which corresponds to "equipping the syntax with all coherences" instead of truncating. In this talk\, I will explain one approach to this based on a type-theoretic formulation of Segal spaces\, expressed in HTS/2LTT. I will discuss what works and what is still open. The talk will be based on ) UID:275 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210211T150000 DTEND;TZID=Europe/London:20210211T160000 LOCATION:Online SUMMARY:Categorical Foundation of Gradient-Based Learning DESCRIPTION:Speaker: Bruno Gavranović (MSP)\nTitle: Categorical Foundation of Gradient-Based Learning\n\nI will give an introduction to the categorical foundation of gradient-based learning algorithms. I'll define three abstract constructions and show how they can be put together to form general neural networks. The Para construction is used to compose neural networks while keeping track of their weights. Lenses/Optics which are used to take care of the forward-backward data flow and lastly\, reverse derivative categories are used to functorially construct the backward wires from the forward ones. In addition\, we'll see that gradient descent\, Momentum\, and a number of optimizers are lenses too\, and that this framework includes learning on boolean circuits\, in addition to standard Euclidean spaces.\n UID:274 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210204T150000 DTEND;TZID=Europe/London:20210204T160000 LOCATION:Online SUMMARY:Reviewing DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Reviewing\n\nI'll talk about how I go about writing\, reading\, and responding to reviews. Reviews are an essential part of academic publishing\, but why do we do them (for free!)\, and why do we care what they say? I discuss how reviews are used by programme committees and chairs to decide what papers are selected for conferences (and journals)\, how I think you should go about doing reviews\, and why you should write reviews. I'll also talk about reading reviews written about your own work\, and how to go about the author response period effectively.\n UID:273 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210128T150000 DTEND;TZID=Europe/London:20210128T160000 LOCATION:Online SUMMARY:Combinatorics\, Topology and Game theory: a proof of Nash's theorem DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: Combinatorics\, Topology and Game theory: a proof of Nash's theorem\n\nThe aim of this talk is to state and prove Nash's theorem\, which says that every finite game with mixed strategies has a Nash equilibrium. The proof makes use of two other famous results: Sperner's lemma\, a combinatorial result about coloring the vertices of a triangulation\, and Brouwer's fixed-point theorem. Thus\, my talk will be organised into three largely independent parts: first I will sketch the proof of Sperner's lemma\; then I will use Sperner's lemma to prove Brouwer's theorem\; and finally I will use Brouwer's theorem to prove the existence of Nash equilibria.\n UID:272 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20210107T130000 DTEND;TZID=Europe/London:20210107T140000 LOCATION:Online SUMMARY:Generic metatheory of linear programming languages DESCRIPTION:Speaker: James Wood (MSP)\nTitle: Generic metatheory of linear programming languages\n\nI will give an introduction to generic metatheory in the style of Allais\, Atkey\, Chapman\, McBride\, and McKinna\, leading into new work from me and Bob. Generic metatheory is about deriving proofs and operations for a whole class of programming languages\, rather than the usual 1 language. The class we consider combines variable binding with usage-sensitivity\, and contains many variants of linear natural deduction calculi (and\, as a special case\, intuitionistic and classical calculi). We build on the framework of Allais et al. (https://arxiv.org/abs/2001.11001) and our recent use of linear algebra in linear metatheory (https://arxiv.org/abs/2005.02247).\n UID:271 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201217T130000 DTEND;TZID=Europe/London:20201217T140000 LOCATION:Online SUMMARY:Algebraic effects and effect handlers DESCRIPTION:Speaker: Sam Lindley (University of Edinburgh)\nTitle: Algebraic effects and effect handlers\n\nI'll give an introduction to algebraic effects and effect handlers as a general approach to programming and reasoning about effectful computation. I'll present the notion of a computation over an algebraic effect as a command-response tree over an effect signature quotiented by some equational theory. I'll consider how to interpret command-response trees and motivate effect handlers as the reification of such interpretations as an object language feature that provides a generic implementation strategy for algebraic effects. I'll give examples to show that it can be useful to interpret the same command-response tree using different interpretations which may not respect the same equational theory. Thus effect handlers can provide an expressive programming feature independently of any non-trivial algebraic theory.\n UID:270 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201210T130000 DTEND;TZID=Europe/London:20201210T140000 LOCATION:Online SUMMARY:Session Types DESCRIPTION:Speaker: Uma Zalakain (University of Glasgow)\nTitle: Session Types\n\nThis talk is a brief introduction to session types\, a type formalism for structured communication between concurrent programs. Instead of typing programs\, we will session type channel endpoints\, to then ensure that the programs that make use of these endpoints do so in a principled manner\, according to their session types. I will go over some of the key ideas that enable session-typed programming\, and comment on the properties that session-typed programs exhibit. As an example\, I will introduce (and comment on the oddities of) a type system that uses session types to type the pi calculus. I will close mentioning some of the extensions to session types and more advanced type systems.\n UID:269 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201203T130000 DTEND;TZID=Europe/London:20201203T140000 LOCATION:Online SUMMARY:Metrics in probabilistic context DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Metrics in probabilistic context\n\nThis talk will (probably) be a tutorial on how metrics meet probability theory and how this provides us with the context for innovative paradigms in computer science. The novel challenges that machine learning\, cyber-physical systems and statistical computational methods rise to computer science require a fundamental change of the semantics of computation. While in the past we were happy to know whether two programs/algorithms/machines behave the same or not\, today it is obvious that this is not enough for our purposes. We need\, more and more\, to be able to reason about and measure the similarity of non-identical computational behaviours. Moreover\, we need to speak about randomness in computational phenomena\, especially when we formalize learning or behaviours in unknown contexts. Last but not least\, we need to eventually replace the classic metatheory of computation with a probabilistically-based one\, where questions can be answered probabilistically within controlled confidence boundaries.\n\n I will not have the time to approach all these during the talk\, but I will try to give an overview of the mathematical instruments one needs to approach such a complex challenge.\n UID:268 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201126T130000 DTEND;TZID=Europe/London:20201126T140000 LOCATION:Online SUMMARY:Event Structures and Games DESCRIPTION:Speaker: Glynn Winskel (MSP)\nTitle: Event Structures and Games\n\nI’ll introduce event structures\, a model of computation in which behaviour is captured through partial orders of causal dependency between events. As an application I'll show their role in a theory of concurrent/distributed games and strategies\, which has been useful in the semantics of computation\, also for probabilistic and quantum programs. Though originally motivated by the limitations of traditional semantics\, through determinacy and value theorems\, and the preservation of winning/optimal strategies under composition\, a form of structural game theory is emerging. In this talk I'll concentrate on what I see as connection points with work here at Strathclyde: as a lead in\, relations with the stable domain theory of Berry and Girard\; then\, the view of strategies as profunctors\, whence how they connect to the traditional domain theory of Scott\; concluding with how distributed strategies support certain dialectica categories and lenses\, and through them open games. My hope is that these connections will be fruitful. On the one side\, distributed games can offer a rich metalanguage which extends to probabilistic and quantum computation.\n UID:267 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201119T130000 DTEND;TZID=Europe/London:20201119T140000 LOCATION:Online SUMMARY:Containers DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Containers\n\nHow do we represent and reason about data types\, in general? The theory of containers is one answer\, which is locally quite popular in the MSP group (and beyond). A container is given by a collection of shapes\, and for each shape\, a collection of positions\, where one is meant to plug in data. Containers can be used to analyse generic constructions on data types\, without resorting to a messy induction over syntax.\n\n Each container induces a functor from Set to Set\, which maps an "element type" X to the set of containers with data drawn from X. Furthermore\, there is a natural notion of morphism of containers\, with the remarkable property that it completely captures the natural transformations between the functors the containers represent: the interpretation functor from containers to the functor category from Set to Set is full and faithful. In general\, the category of containers is extremely nice\, eg containers are closed under almost all operations you can imagine (composition\, products\, coproducts\, exponentials\, initial algebras\, final coalgebras\, ...). I hope to give an introductory talk that will make the above more precise.\n UID:266 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201112T130000 DTEND;TZID=Europe/London:20201112T140000 LOCATION:Online SUMMARY:Lenses 101 DESCRIPTION:Speaker: Jules Hedges (MSP)\nTitle: Lenses 101\n\nI’ll talk about the zoo of closely-related structures (with a lot of clashing terminology) known as “lenses” and “optics”. Lenses and optics are a way of managing inherently state-heavy applications (for example videogames) in purely functional languages\, which turn out to have a lot of surprisingly deep category theory behind them. I will also talk about some of the places where lenses have recently appeared far outside their original domain\, for example in game theory\, machine learning and systems theory.\n UID:265 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201105T130000 DTEND;TZID=Europe/London:20201105T140000 LOCATION:Online SUMMARY:Probability theory with string diagrams DESCRIPTION:Speaker: Eigil Rischel (MSP)\nTitle: Probability theory with string diagrams\n\nGoing back to Lawvere\, people have tried to study probability theory in terms of monads - the idea being that for each "space" of some type\, X\, there should be a space PX of probability distributions on X\, with point-distributions and integration of distributions giving the monad structure. The Kleisli category of this monad is of particular interest: it corresponds to "stochastic maps" between spaces.\n\n It turns out that one can actually often do without the monad - the Kleisli category itself carries enough structure that one can do probability theory "internally"\, rederiving the notions of determinism\, independence of measures\, and many others. I will present this picture of probability\, and give some examples of results that can be proven in this framework.\n UID:264 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201029T130000 DTEND;TZID=Europe/London:20201029T140000 LOCATION:Online SUMMARY:Realisability DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Realisability\n\nSometimes\, we think of the category of sets and functions as a simple model of programs in a functional programming language. But sets and functions are much too expressive -- there are plenty of set theoretic functions that aren't expressible in any implementable programming language. Realisability is a way to bring functions down to earth by requiring that they are computable in some model of computation. I'll cover the construction of categories of realizable functions\, usually called the category of Assemblies\, and its interesting sub-category\, the category of Modest Sets or PERs. I'll also sketch how to interpret type theory in the category of assemblies. If there is time\, I'll also cover linear realisability.\n UID:263 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201022T130000 DTEND;TZID=Europe/London:20201022T140000 LOCATION:Online SUMMARY:Fantastic sheaves and where to find them DESCRIPTION:Speaker: Matteo Capucci (MSP)\nTitle: Fantastic sheaves and where to find them\n\nSheaves are among the oddest creatures roaming the world of mathematics. They come from the far land of algebraic geometry\, they speak a tricky language\, and they organize in unfathomably big herds ('topoi'). There's no reason to be afraid\, though: sheaves can be the tamest beasts and provide many useful services to the mathematician who's willing to learn their ways. In this talk\, I'll try to demystify sheaves by giving an elementary exposition of their basic features\, trying to convey useful intuition about their behaviour. I will also try to give a taste some of their most astounding tricks\, such as sheaf cohomology and topos-theoretic forcing.\n UID:262 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201015T130000 DTEND;TZID=Europe/London:20201015T140000 LOCATION:Online SUMMARY:Quantitative Type Theory and its application DESCRIPTION:Speaker: Andre Videla (MSP)\nTitle: Quantitative Type Theory and its application\n\nTo build upon last week's talk on Dependent types\, we will develop the intuition around Quantitative types and their usage in modern programming languages. What does it mean to program when the type system is responsible for tracking resources rather than leave this task to the programmer? What new patterns do we see? And what are the limitations we encounter and how do we fix them? This talk aims to answers those questions in an approachable and interactive way.\n UID:261 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201008T130000 DTEND;TZID=Europe/London:20201008T140000 LOCATION:Online SUMMARY:Dependent Types DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Dependent Types\n\nI'll give an introduction to the setup for dependent type theories\, in the bidirectional style\, again sketching why fundamental metatheoretic properties hold by not asking the wrong questions. In particular I'll develop the theory of dependent function types\, then add lists. Let's conspire to make append associative\, and if time permits\, map a functorial action.\n UID:260 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20201001T130000 DTEND;TZID=Europe/London:20201001T140000 LOCATION:Online SUMMARY:Introduction to Monoidal Categories DESCRIPTION:Speaker: Joe Collins (MSP)\nTitle: Introduction to Monoidal Categories\n\nA nice\, chill introduction to the basic definitions and theorems on monoidal categories. We will be defining monoidal categories and symmetric monoidal categories\, and talking about the coherence theorem and string diagrams.\n UID:259 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200924T130000 DTEND;TZID=Europe/London:20200924T140000 LOCATION:Online SUMMARY:Bidirectional STLC DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Bidirectional STLC\n\nBy way of kicking off this semester of MSP101\, I'll give an introduction to our local dialect of bidirectional type systems\, defined as mutually inductive systems of moded judgments. That is\, we not only assign a syntactic category to each place in a judgment form\, but also designate its mode as being "input"\, "subject"\, or "output". The syntactic categories of introduction and elimination forms are distinguished: the former have types as inputs\, the latter types as outputs. I'll illustrate this using the Simply Typed Lambda-Calculus\, and I'll rattle through as much metatheory thereof as I can before you bottle me off.\n UID:258 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200910T130000 DTEND;TZID=Europe/London:20200910T140000 LOCATION:https://meet.jit.si/MSP101/ SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:257 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200703T140000 DTEND;TZID=Europe/London:20200703T150000 LOCATION:Online SUMMARY:Compositional Game Theory\, compositionally DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: Compositional Game Theory\, compositionally\n\nThe recent notion of Open Games allows to study game theory in a compositional way: complex games can be obtained from smaller ones using various operators such as sequential and parallel composition. Thus\, Open Games form a symmetric monoidal category. There are many flavors of open games\, ranging from small variations on how equilibria are treated\, to more radical changes such as introducing probabilistic behavior. Proving from scratch that each variant still forms a monoidal category is tedious.\n\n I will present a compositional construction of the category of Open Games\, which consists of three main steps. In each step\, one can swap a component for a similarly-behaved one\, without disturbing the rest of the structure. Thus\, one can define many variants of Open Games with minimal effort. This compositional approach is based on the notion of Arrows\, a concept first introduced in functional programming.\n\n This is a practise talk for ACT20 next week\, and joint work with Bob\, Bruno\, Neil\, Clemens and Fred.\n UID:256 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200619T140000 DTEND;TZID=Europe/London:20200619T150000 LOCATION:Online SUMMARY:Building Resource-Dependent EDSLs in a Dependently-Typed Language DESCRIPTION:Speaker: Jan de Muijnck-Hughes (Glasgow)\nTitle: Building Resource-Dependent EDSLs in a Dependently-Typed Language\n\nWhile many people use dependent types for theorem proving some of us like to use dependent types for building\, and running\, safer programs.\n\n Idris' /Effects/ library demonstrates how to embed resource dependent algebraic effect handlers into a dependently typed host language\, providing run-time and compile-time based reasoning on type-level resources. Building upon this work\, /Resources/ is a framework for realising EDSLs with type systems that contain domain specific substructural properties. Differing from /Effects/\, /Resources/ allows a language's substructural properties to be encoded within type-level resources that are associated with language variables. Such an association allows for multiple effect instances to be reasoned about autonomically and without explicit type-level declaration. We use type-level predicates as proof that a language's substructural properties hold.\n\n Using /Resources/ we have shown how to provide correctness-by-construction guarantees that substructural properties of written programs hold when working with =Files=\, specifying Domain Specific =BiGraphs=\, and Global Session Descriptions---=Sessions=. With this talk I want to discuss the how and why of /Resources/\, and show how we can use the framework to build EDSLs with interesting type-systems.\n\n This talk is part practise talk for ECOOP 2020\, part tutorial on an important idiom for practical dependently-typed programming\, and part chance to highlight more how dependent-types are useful when programming in the real world.\n UID:254 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200612T140000 DTEND;TZID=Europe/London:20200612T150000 LOCATION:Online SUMMARY:Interpreting Dependent Type Theory in Containers DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Interpreting Dependent Type Theory in Containers\n\nIn her PhD thesis\, Tamara von Glehn showed that the Category of Containers (a.k.a. Category of Polynomials\, Category of Dependent Lenses\, Dialectica Category) supports an interpretation of dependent types. I'll present the basic constructions used\, and\, if I get to it\, show that the model refutes the principle of functional extensionality.\n UID:253 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200605T090000 DTEND;TZID=Europe/London:20200605T143000 LOCATION:Online SUMMARY:Event: Verification of Session Types Workshop (VEST) DESCRIPTION: UID:252 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200529T110000 DTEND;TZID=Europe/London:20200529T120000 LOCATION:Online SUMMARY:The 'graded types' paradigm: past\, present\, and a possible future DESCRIPTION:Speaker: Dominic Orchard (University of Kent)\nTitle: The 'graded types' paradigm: past\, present\, and a possible future\n\nIn the 1970s\, the notion of 'grading' appeared in analytic philosophy and logic as a way of making reasoning more fine-grained\, capturing 'degrees' of necessity or possibility. Somewhat independently\, grading has become a topic of interest in type theory and programming language semantics\, with graded structures again providing a means of more fine-grained reasoning. In this talk\, I will give an overview of this idea (both its past and present) and explore two uses: (1) using graded modal types for program reasoning in the context of an experimental functional language with linear and indexed types\, called Granule\; (2) specialising program semantics to give correct-by-construction arguments about program analyses and transformations. I will also give a mathematical characterisation of grading which suggests a broad paradigm\, and will briefly mention various ongoing works.\n UID:251 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200522T140000 DTEND;TZID=Europe/London:20200522T150000 LOCATION:Online SUMMARY:A quantitative model for λ-calculus DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: A quantitative model for λ-calculus\n\nResource monoids and length spaces are a semantic framework inspired from realizability\, which was introduced by Dal Lago and Hofmann in the context of implicit complexity. It has been used to define quantitative models for various programming languages (such as Elementary Affine Logic\, LFPL)\, and deduce soundness properties of the form: "Every definable function lies in a given complexity class". In this talk\, I will show how this framework can be used to measure different quantitative properties of a language than time complexity. Namely\, I will present a model of simply-typed λ-calculus such that the interpretation of a λ-term contains an upper bound on the size of its normal form.\n UID:250 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200515T140000 DTEND;TZID=Europe/London:20200515T150000 LOCATION:Online SUMMARY:A Linear Algebra Approach to Linear Metatheory DESCRIPTION:Speaker: James Wood (MSP)\nTitle: A Linear Algebra Approach to Linear Metatheory\n\nSince its introduction\, linear logic has been the cause of and solution to many problems in theoretical computer science. There are many examples in the literature of calculi which restrict usage of variables\, allowing them to capture linearity\, monotonicity\, sensitivity analysis\, privacy constraints\, and other coeffects. However\, the syntactic metatheory of these calculi is often difficult\, and rarely in a form amenable to formalisation in a proof assistant.\n\n In this talk\, I will introduce the notion of kits and environments yielding generic traversals – a method developed by Conor for proving renaming and substitution lemmas. Then\, I will discuss recent work by myself and Bob on adapting this method to semiring-graded calculi. The result is a pleasingly and surprisingly minor variation on the original\, comprising the introduction of a linear map to mediate usage annotations. This solution gives us confidence that we can tackle all of quantitative metatheory in the familiar intuitionistic style.\n UID:249 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200501T140000 DTEND;TZID=Europe/London:20200501T150000 LOCATION:Online SUMMARY:Stone duality for Markov processes (second attempt) DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Stone duality for Markov processes (second attempt)\n\nThe talk will focus on the category of Markov processes\, on Markovian logics and Aumann algebras. Markovian logics are modal logics designed to specify (approximated) properties of Markov processes and characterize their bisimilarity. Aumann algebras are the algebraic counterpart of Markovian logics\, i.e.\, they are Boolean algebras with operators that encode probabilistic information. Markovian logics are not compact and for this reason the "classic" Stone duality fails. I will present a different version of Stone duality constructed on top of Rasiowa-Sikorski lemma\, which is a result bringing topological results into Model Theory.\n\n This talk summarizes results obtained in collaboration with Dexter Kozen and Prakash Panangaden.\n UID:248 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200424T140000 DTEND;TZID=Europe/London:20200424T150000 LOCATION:Online SUMMARY:Something Else About Mary DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Something Else About Mary\n\nThis is very much work in progress\, jointly with Guillaume Allais (now of St Andrews) and Fredrik Nordvall Forsberg\, with occasional involvement from others of the usual MSP suspects.\n\n Mary is our attempt to build a virtual learning environment which offers effective support to our own classes\, building from the experience (but thankfully not the codebase) of the tools I built for teaching and assessing my first year hardware class. Last time I talked about Mary\, she was just a twinkle in my eye. Now\, she is at least a toddler.\n\n Mary is a variant on pandoc markdown which allows code fragments to be embedded in documents and document fragments to be embedded in code. This talk will focus mainly on the programming language embedded in the system which is currently called "Shonkier"\, as it is a variant on the "Shonky" language to which Frank compiles. It is untyped\, for the time being\, but that's an opportunity.\n\n The key design choice in Shonkier is that the C-style function application notation\, f(e1,..,en)\, is used for all sorts of contextualization\, and there are many such sorts. "Functions" (which already generalize to effect handlers) are but one form of context. We have also added first class environments (computed by pattern matching expressions) and guarding contexts (computed by Boolean expressions). One recent tweak which pays dividends is that effect handlers can now reply to requests with effects as well as with values. We are now free to negotiate various forms of contingency in a refreshingly direct style.\n\n In short\, we have abandoned the naive delights of being context-free in favour of being context-negotiable.\n UID:247 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200417T140000 DTEND;TZID=Europe/London:20200417T150000 LOCATION:Online at https://meet.jit.si/MSP101 SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:246 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200206T140000 DTEND;TZID=Europe/London:20200206T150000 LOCATION:LT1415 SUMMARY:Rust\, Servo and Mixed Reality Research at Mozilla DESCRIPTION:Speaker: Alan Jeffrey (Mozilla)\nTitle: Rust\, Servo and Mixed Reality Research at Mozilla\n\nMozilla is a non-profit whose mission is to expand access to\, and protect privacy on\, the Internet. Mozilla Research investigates emerging technologies\, such as programming languages and new web platforms. This talk is an overview of research efforts around the Rust programming language\, the Servo web engine\, and Mixed Reality (VR and AR) on the web.\n UID:245 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200327T140000 DTEND;TZID=Europe/London:20200327T150000 LOCATION:https://meet.jit.si/MSP101 SUMMARY:Multidimensionally-correct by construction programming DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Multidimensionally-correct by construction programming\n\nPhysical dimensions such as length\, mass and time can be used to ensure that equations are physically meaningful -- it makes no sense to add 7 metres to 12 seconds\, and in an equation such as PV = nRT\, it better be the case that both sides have the same physical dimension (in this case pressure times length^3). Even better\, dimensions can not only be used to tell scientists off when making mistakes\, but also to deduce non-trivial formulas (the famous example being that of the period of a pendulum as a function of its mass and length\, and the acceleration of gravity).\n\n From an MSP perspective\, there is a strong similarity between physical dimensions and types in programming languages\, and indeed\, this connection was explored in the 1990's by various researchers. A concrete outcome is Andrew Kennedy's implementation of units of measure in Microsoft's F# language\, which makes it possible to write F# programs that are dimensionally-correct by construction.\n\n However\, a lot of numerical software is written manipulating not single numbers\, but vectors and matrices\, using the methods of linear algebra. I will report on work in progress with Conor on extending dimensional analysis to multiple dimensions in this second sense.\n UID:243 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200403T140000 DTEND;TZID=Europe/London:20200403T150000 LOCATION:https://meet.jit.si/MSP101 SUMMARY:Completeness of Modal Logic via Stone Duality DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Completeness of Modal Logic via Stone Duality\n\nThis talk is intended to be introductory\, building on Radu's earlier intro to Stone duality. In my presentation I will show how to use duality for proving completeness of basic (propositional) modal logic. To this aim I will first recall what completeness means and then discuss two different kinds of semantics for modal logic: its algebraic semantics\, wrt which completeness of the logic is relatively straightforward\, and Kripke semantics\, which is the semantics one usually is interested in. Stone Duality allows to establish a connection between the two types of semantics such that completeness of modal logic wrt Kripke semantics follows.\n UID:242 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200306T140000 DTEND;TZID=Europe/London:20200306T150000 LOCATION:LT1310 SUMMARY:Classic puns DESCRIPTION:Speaker: James Wood (MSP)\nTitle: Classic puns\n\nThere are several principles that are taken to be characteristic of non-constructive reasoning. These include the principles of excluded middle\, double negation elimination\, and choice.\n\n On the other side\, there are several formal systems that are well known to capture only constructive reasoning. These include dependent type theory (à la Martin-Löf) and linear logic.\n\n However\, each of the systems I just listed is able to derive at least one theorem that looks an awful lot like one of the non-constructive principles I listed earlier. What's going on here?\n UID:240 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200228T140000 DTEND;TZID=Europe/London:20200228T150000 LOCATION:LT1310 SUMMARY:The Dialectica Categories DESCRIPTION:Speaker: Georgi Nakov (MSP)\nTitle: The Dialectica Categories\n\nThe Dialectica Categories were introduced in de Paiva's eponymous work as an internalized version of Gödel's functional interpretation. The interpretation translates Heyting Arithmetic (HA) into System T (intended as an axiomatization of primitive recursive functionals of finite type) and was originally developed as a tool to prove the relative consistency of HA. Translating the contraction rule poses certain problems and as a solution\, Gödel requires decidability of atomic formulae. Several variants exist that lift this restriction.\n\n In this talk\, I will present the categorical constructions from de Paiva's paper. We will investigate their structure and see how the different versions of the interpretation are accommodated in this setting. Finally\, we will conclude that in the process we have obtained a model of Intuitionistic Linear Logic.\n UID:239 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200214T140000 DTEND;TZID=Europe/London:20200214T150000 LOCATION:LT1310 SUMMARY:Towards Compositional Structures in Neural Networks DESCRIPTION:Speaker: Bruno Gavranović (MSP)\nTitle: Towards Compositional Structures in Neural Networks\n\nNeural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. However\, at the moment there is no comprehensive mathematical account of their behavior. I'm exploring the hypothesis that the language of category theory could be well suited to describe these systems in a precise manner. I will give a short tour of recent developments in this area\, mostly based around the notion of lenses.\n UID:237 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200207T140000 DTEND;TZID=Europe/London:20200207T150000 LOCATION:LT1415 SUMMARY:Stone Duality in Stochastic Context DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Stone Duality in Stochastic Context\n\nWe define Aumann algebras\, an algebraic analog of probabilistic modal logic. An Aumann algebra consists of a Boolean algebra with operators modeling probabilistic transitions. We prove that countable Aumann algebras and countably-generated continuous-space Markov processes are dual in the sense of Stone. Our results subsume existing results on completeness of probabilistic modal logics for Markov processes.\n\n This summarizes results obtained in collaboration with Dexter Kozen and Prakash Panangaden.\n UID:236 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200131T140000 DTEND;TZID=Europe/London:20200131T150000 LOCATION:LT1310 SUMMARY:Resource Constrained Programming with Full Dependent Types DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Resource Constrained Programming with Full Dependent Types\n\nI will talk about a system that combines Dependent Types and Linear Types. As an application of this system\, I will show how to transport Martin Hofmann's LFPL and Amortised Resource analysis systems for resource constrained computing to full dependent types. This results in a theory where unconstrained computations are allowed at the type level\, but only polynomial time computations at the term level. The combined system now allows one to explore the world of propositions whose proofs are not only constructive\, but also of restricted complexity.\n UID:235 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200124T140000 DTEND;TZID=Europe/London:20200124T150000 LOCATION:LT1310 SUMMARY:Simplicial Models for Multi-Agent Epistemic Logic DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: Simplicial Models for Multi-Agent Epistemic Logic\n\nEpistemic Logic is the modal logic of knowledge. It allows one to reason about a finite set of agents who can know facts about the world\, and about what the other agents know. The traditional way to interpret epistemic logic formulas is by using Kripke models: that is\, graphs whose vertices represent the possible worlds\, and whose edges indicate the agents that cannot distinguish between two worlds. I will present an alternative kind of model for epistemic logic based on chromatic simplicial complexes. Simplicial models are equivalent to Kripke models\; thus\, this connection uncovers the higher-dimensional geometric nature of knowledge. Finally\, I will show how to adapt these geometric models in order to interpret other epistemic notions\, such as belief\, distributed knowledge\, and more.\n UID:234 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200117T140000 DTEND;TZID=Europe/London:20200117T150000 LOCATION:LT1310 SUMMARY:Something About Mary DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Something About Mary\n\nQuite a few colleagues in the MSP group have experienced both the pleasure and the pain of working with my Marx system in the course of delivering our classes. (I never meant to write a virtual learning environment\, but somehow\, I sort of did.) I propose to re-engineer it from scratch and do a rather better job (suitable for wider deployment) deliberately\, and am keen to solicit assistance in this mission\, lest it be yet another engineering project distinguished by my madness and dissolution that you are\, even so\, obliged to put up with. Inevitably\, I will struggle and rapidly fail to exclude interesting computer science from the design of the system. There will be fun.\n\n Mary will be a content management system with pages written in Markdown and stored in git repositories on the department's GitLab server. However\, every such page is also a form\, supporting interactive content. Pages will therefore need to embed code for processing the data in the form\, certainly on the server\, but preferably (unlike in Marx) on the client. So Mary will embed a programming language that we might have fun designing and implementing. I propose to base this language on Frank\, an effects and handlers language that I cooked up a while back. Access to form fields can be seen as an effect: by remember the resumption for each such access\, we can model what to recompute in the client when fields change\, after the fashion of spreadsheets\, programmed in apparently direct style.\n\n Mary will also need to maintain a database to achieve cross-session persistence of student work and staff configuration data. The Marx approach to analytics over this database amounted to "grep". In the meantime\, however\, Fred and I spent quite a while thinking about how to give an account of data models and analytics at a higher level of abstraction using carefully undermarketed ideas from dependent type theory. We should consider how to adapt these ideas to manage our own data.\n\n Let's get excited and make things!\n\n (Comrades who are not Strathclyders but who are interested in effects\, types\, or just having better tools to survive this business we call higher education\, should very much feel invited to engage. I will happily export this project.)\n UID:233 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20200116T133000 DTEND;TZID=Europe/London:20200116T143000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:232 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191030T120000 DTEND;TZID=Europe/London:20191030T170000 LOCATION:University of Glasgow SUMMARY:Event: SPLS DESCRIPTION: UID:231 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191212T133000 DTEND;TZID=Europe/London:20191212T143000 LOCATION:LT1310 SUMMARY:Potato Powered Proofs DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Potato Powered Proofs\n\nStuart and I have been working on interpreters for predicative calculi which are "potato-powered" in that they work by structural recursion on inductive data which may look suspiciously like types\, but are not statically checked to be the actual types of the programs in question. This works because the calculi are presented in a bidirectional style which\, by design\, causes every redex to carry some "potatoes"\, which hopefully contain enough inductive carbohydrate to keep you going for the whole of the computation to be done.\n\n Naturally\, it would be lovely if we could prove that the interpreter's output is genuinely a reduct of its input\, and that well typed input yields normal form output (i.e.\, that an honest type gives the potatoes required to do the whole computation). How is it done? Potato-powered logical relations\, of course! I'll give a crash course on cooking programs and proofs with potatoes.\n UID:230 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191205T133000 DTEND;TZID=Europe/London:20191205T143000 LOCATION:LT1310 SUMMARY:Boolean-valued semantics DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Boolean-valued semantics\n\nThis talk is based on the paper with the same title that I have presented at LICS 2018. It is a joint work with Dana Scott\, Dexter Kozen\, Prakash Panangaden\, Robert Furber and Giorgio Bacci. We extend Dana's Boolean-valued set theory (introduced in 50's to demonstrate the independence of the continuum hypothesis) to get\, initially\, a denotational model of untyped lambda calculus\, and eventually extend it to a model of stochastic lambda calculus. The model is constructed over a space of random variables\, which inherit a natural continuous Boolean algebra structure.\n UID:229 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191128T133000 DTEND;TZID=Europe/London:20191128T143000 LOCATION:off-campus SUMMARY:Selective Applicative Functors (not a seminar\, due to the strike) DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Selective Applicative Functors (not a seminar\, due to the strike)\n\nAt this year's ICFP\, Mohkov\, Lukyanov\, Marlow\, and Dimino introduced "Selective Applicative Functors"\, a programming interface that is an intermediate stage between monads and applicative functors. I'll motivate what they're for\, and describe what they are\, and I'll talk about a more abstract way of thinking about them in terms of "right-skew monoidal categories".\n UID:228 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191121T133000 DTEND;TZID=Europe/London:20191121T143000 LOCATION:LT1310 SUMMARY:Expressive Logics for Coinductive Predicates DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Expressive Logics for Coinductive Predicates\n\nThe classical Hennessy-Milner theorem says that two states of an image-finite transition system are bisimilar if and only if they satisfy the same formulas of a certain modal logic. I will place this type of result in a general context\, moving from transition systems to coalgebras and from bisimilarity to coinductive predicates. Furthermore I will present a sufficient condition for a coalgebraic logic to be expressive\, i.e.\, to fully characterise a coinductive predicate on coalgebras. Our approach will be illustrated with logics characterising similarity\, divergence and a behavioural metric on automata.\n\nThis is joint work with Jurriaan Rot to be presented at CSL 2020.\n UID:227 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191114T133000 DTEND;TZID=Europe/London:20191114T143000 LOCATION:LT1310 SUMMARY:Programs and Proofs in Linear Algebra DESCRIPTION:Speaker: James Wood (MSP)\nTitle: Programs and Proofs in Linear Algebra\n\nI try to understand the ways of linear algebraists from a programming languages perspective. In particular\, I investigate the practice of specifying a linear map by giving only its action on basis elements. We can turn this practice into a nice programming language for linear maps. Furthermore\, our reasoning about these maps is significantly simplified by only considering the basis elements. Finally\, keeping track of basis elements amounts to a typing discipline\, and we can expect to get some nice properties just by observation of the types.\n\nMeanwhile\, I will try to elucidate the similarity between\, on one side\, categories of spaces and linear maps and\, on the other\, Rel\, the category of sets and relations. This forms an important part of our programming languages view.\n UID:226 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191107T133000 DTEND;TZID=Europe/London:20191107T143000 LOCATION:LT1310 SUMMARY:MSP 101: Coends and Kan extensions DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: MSP 101: Coends and Kan extensions\n\n\n UID:225 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191031T133000 DTEND;TZID=Europe/London:20191031T143000 LOCATION:LT1310 SUMMARY:Directed algebraic topology for concurrency DESCRIPTION:Speaker: Jérémy Ledent (MSP)\nTitle: Directed algebraic topology for concurrency\n\nI will give an introduction to the geometric semantics for concurrent programs that have been developed by Goubault\, Fajstrup\, Raussen et al. since the 1990's. A concurrent program can be viewed as a topological space equipped with a notion of direction\, modeling the passage of time. Thus\, in such a space\, the existence of a path from A to B does not guarantee the existence of a path from B to A. A path in a directed space corresponds to an execution of the program\; and two such executions are equivalent when the corresponding paths are homotopic\, that is\, when they can be deformed continuously into one another. This idea motivated the development of directed algebraic topology\, the analogue of algebraic topology for directed spaces.\n UID:224 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191024T133000 DTEND;TZID=Europe/London:20191024T143000 LOCATION:LT1310 SUMMARY:Hopf Monads and Formally Adding in Morphisms DESCRIPTION:Speaker: Joe Collins (MSP)\nTitle: Hopf Monads and Formally Adding in Morphisms\n\nIt should be noted that this is ongoing work. The talk that you will see is going to be very unpolished\; this is stuff that I have been working on for the past while\, and the material will not be fully formed yet. The things I say may not end up matching with reality. So with that minor caveat\, let us continue.\n\nA Hopf algebra is a monoid\, a comonoid\, and an extra endomorphism such that various commutation rules are obeyed\, and Hopf monads are a strange generalisation of Hopf algebras in the direction of monads. I have previously talked about when a Hopf algebra is a Hopf-Frobenius algebra\, and my goal now is to generalise this to the case of Hopf Monads. However\, to keep things interesting\, I am doing this in a weird way.\n\nLet T be a Hopf monad in monoidal category C. T is isomorphic to a Hopf algebra if there exists a natural transformation e: T -> 1 that respects the Hopf monad structure. There are many examples of Hopf monads which are not isomorphic to any Hopf algebras\, so this morphism does not exist in C in general. However\, what happens if I formally add in this morphism\, creating a new category C_e? In this category\, T would presumably be isomorphic to a Hopf algebra\, and this begs the question: what can T in C_e tell us about T in C? By looking at the natural functor C -> C_e\, can I use this to transfer my theorem about Hopf algebras to Hopf monads? I certainly believe so\, but let's find out together!\n UID:223 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191017T133000 DTEND;TZID=Europe/London:20191017T143000 LOCATION:LT1310 SUMMARY:Ordinals below epsilon-zero in cubical Agda DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Ordinals below epsilon-zero in cubical Agda\n\nOrdinals and ordinal notation systems play an important role in program verification\, since they can be used to prove termination of programs. We present three ordinal notation systems representing ordinals below epsilon_0 in type theory\, using recent type-theoretical innovations such as mutual inductive-inductive definitions and higher inductive types. As case studies\, we show how basic ordinal arithmetic can be developed for these systems\, and how they admit a transfinite induction principle. We prove that all three notation systems are equivalent\, so that we can transport results between them using the univalence principle. All our constructions have been implemented in cubical Agda.\n UID:222 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191010T133000 DTEND;TZID=Europe/London:20191010T143000 LOCATION:LT1310 SUMMARY:Quantitative algebras: towards a quantitative theory of effects DESCRIPTION:Speaker: Radu Mardare (MSP)\nTitle: Quantitative algebras: towards a quantitative theory of effects\n\nWe develop a quantitative analogue of equational reasoning meant to provide metric semantics for stochastic/probabilistic/quantitative systems and programming languages. Quantitative algebras are algebras over metric spaces defined by these quantitative equational theories\, and they implicitly define monads over the category of (extended) metric spaces. We have a few relevant examples of such algebras\, where the induced free algebras correspond to well-known structures\; among these are Hausdorff metrics from quantitive semilattices\, p-Wasserstein metrics (hence also the Kantorovich metric) from barycentric algebras\, the total variation metrics from a variant of barycentric algebras\, and more.\n\nThe talk is based on a series of joint works with Prakash Panangaden and Gordon Plotkin. The main results have been presented at LICS'16\, LICS'17 and LICS'18.\n UID:221 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20191003T133000 DTEND;TZID=Europe/London:20191003T143000 LOCATION:LT1310 SUMMARY:Summer trip reports DESCRIPTION:Speaker: James Wood\, Joe Collins\, Bob Atkey\, Guillaume Allais\, Fredrik Nordvall Forsberg (MSP)\nTitle: Summer trip reports\n\n\n UID:220 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190926T130000 DTEND;TZID=Europe/London:20190926T140000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:219 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190830T110000 DTEND;TZID=Europe/London:20190830T120000 LOCATION:LT1415 SUMMARY:A combinatorial representation of the operad of plane graphs DESCRIPTION:Speaker: Malin Altenmüller (MSP)\nTitle: A combinatorial representation of the operad of plane graphs\n\nI will present how we can formalise non-symmetric monoidal categories (i.e. string diagrams) in a combinatorial way. These kind of diagrams will be represented by plane graphs with a distinguished boundary vertex. For encoding plane graphs it is sufficient to store the order of neighbours for each vertex\, called a rotation system. I'll show how to define these sorts of graphs\, how to compose them and &--together with the right notion of rewriting &--how they form an operad.\n\nThis is practice for a talk I will give at STRINGS in Birmingham next week.\n UID:218 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190816T160000 DTEND;TZID=Europe/London:20190816T170000 LOCATION:LT1415 SUMMARY:Polynomial certificates for nondeterministic automata DESCRIPTION:Speaker: Rob Myers \nTitle: Polynomial certificates for nondeterministic automata\n\nGiven a deterministic finite automaton accepting /L/\, another accepting the reverse language\, and an integer /n/\, does there exist a nondeterministic acceptor with /n/ or fewer states? We've proved that this problem is in NP i.e. polynomial certificates exist. All previous algorithms constructing small nondeterministic automata for arbitrary regular languages are at best PSPACE-complete. We achieve this by explaining and substantially improving the Kameda-Weiner algorithm using coalgebraic methods. At the underlying level we use a categorical equivalence between finite join-semilattices and bipartitioned graphs.\n UID:217 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190705T160000 DTEND;TZID=Europe/London:20190705T170000 LOCATION:LT1310 SUMMARY:The Thing with Thinnings: CodeBruijn is (Free;Stuff) DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: The Thing with Thinnings: CodeBruijn is (Free;Stuff)\n\nI've been hacking away on tools to do metatheory using "codebruijn" representation of syntax. The method\, as with scoped de Bruijn representation\, is to index terms by their *scope*\, but the codebruijn method goes further\, by systematically treating the *support* of terms\, i.e.\, the particular subscope of variables which are actually *relevant*\, paired with the thinning that embeds support into scope. The key codebruijn type constructor is "pair a thing with a thinning from some support"\, and it turns any old sort of thing into something which uniformly admits further thinning just by postcomposition\, without affecting either the thing or its support.\n\nStuff-which-uniformly-admits-thinning is stuff with structure\, so there is a forgetful functor back to plain old Stuff. The Free functor which adds uniform thinning\, is its left adjoint. The codebruijn type constructor is the monad (Free;Stuff). The corresponding comonad\, (Stuff;Free)\, is rather more familiar to semanticists as the abstraction over *larger* scopes found in Kripke models.\n\nI've always been a bit shaky on adjunctions\, presheaves and what have you\, so this talk will not assume categorical confidence\, but rather seek to build intuition\, guided by a concrete example grounded in the practicalities of manipulating syntax.\n UID:216 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190627T160000 DTEND;TZID=Europe/London:20190627T170000 LOCATION:LT1310 SUMMARY:Isbell Duality\, Stone Duality\, and Physical Theories DESCRIPTION:Speaker: Kevin Dunne \nTitle: Isbell Duality\, Stone Duality\, and Physical Theories\n\n Isbell duality is an adjunction between a category of "generalised algebras" and a category of "generalised spaces"\, and is an abstraction of Stone duality. Broadly speaking\, a Stone duality is an equivalence between some category of commutative algebras\, and some category of spaces\, for example: Boolean algebras and Stone spaces\; or\, commutative C*-algebras and Hausdorff spaces.\n\nThere is a Stone duality which applies in the setting of Newtonian mechanics\, between the category of smooth manifolds and a category of commutative algebras\, and this equivalence of categories admits an extremely elegant and intuitive interpretation from the perspective of physics.\n\nI am going to discuss how to build an analogous interpretation for quantum theory using the machinery of Isbell duality\, in such a way that directly generalises Newtonian mechanics\, with the ultimate aim being to resolve some of the conceptual problems of quantum theory.\n UID:215 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190607T160000 DTEND;TZID=Europe/London:20190607T170000 LOCATION:LT1415 SUMMARY:TYPES 2019 practice talks DESCRIPTION:Speaker: Malin Altenmüller and James Wood (MSP)\nTitle: TYPES 2019 practice talks\n\nMalin and James will practice giving their talks "Containers of Applications and Applications of Containers" and "Linear metatheory via linear algebra" respectively.\n UID:214 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190529T130000 DTEND;TZID=Europe/London:20190529T140000 LOCATION:LT1415 SUMMARY:Departmental seminar: The next 700 abstract machines DESCRIPTION:Speaker: Dan Ghica (Birmingham)\nTitle: The next 700 abstract machines\n\nWe propose a new formalism for representing programming languages\, based on a universal graph-rewriting abstract machine. The calculus itself only deals with the basic structural aspects of a programming languages\, namely variables\, names (e.g. memory locations) and thunks (i.e. fragments with delayed execution). Everything else needs to be supplied as extrinsic operations\, with associated rewrite rules. This basic calculus allows us to represent all known sequential programming language features in a uniform framework\, reason abstractly about their cost\, and also reason about challenging equivalences.\n\nThis is joint work with Koko Muroya and Todd Waugh Ambridge.\n UID:213 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190503T160000 DTEND;TZID=Europe/London:20190503T170000 LOCATION:LT1310 SUMMARY:MSP 101: Fixed points of indexed containers DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: MSP 101: Fixed points of indexed containers\n\nIn an attempt to con Agda into allowing alternation of least and greatest fixed points\, I try to remember how to construct these things for indexed containers.\n UID:212 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190515T160000 DTEND;TZID=Europe/London:20190515T170000 LOCATION:LT1310 SUMMARY:Getting the unifier on your side DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Getting the unifier on your side\n\nI will explain how to write practical generic n-ary functions and combinators for n-ary relations.\n UID:211 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190510T130000 DTEND;TZID=Europe/London:20190510T140000 LOCATION:LT1415 SUMMARY:A Purely Functional Array Language and its Optimising GPU Compiler DESCRIPTION:Speaker: Troels Henriksen (University of Copenhagen)\nTitle: A Purely Functional Array Language and its Optimising GPU Compiler\n\nFuthark is a small programming language designed to be compiled to efficient parallel code. It is a statically typed\, data-parallel\, and purely functional array language\, and comes with a optimising ahead-of-time compiler that generates GPU code via OpenCL and CUDA. Futhark is not designed for graphics programming\, but instead uses the compute power of the GPU to accelerate data-parallel array computations ("GPGPU").\n\nThis talk presents the design of the Futhark language\, as well as outlines several of the key compiler optimisations that have enabled performance comparable to hand-written GPU code. Through the use of a functional source language\, we obtain strong invariants that simplify and empower the application of traditional compiler optimisation techniques. In particular\, I will discuss (i) aggressively restructuring transformations such as fusion\, (ii) loop interchange and distribution to extract flat parallel kernels from nested parallel source programs\, (iii) multi-versioned code generation that exploits as much parallelism as necessary and efficiently sequentialises the rest\, and (iv) data layout transformations to ensure coalesced memory access on GPUs.\n UID:210 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190412T160000 DTEND;TZID=Europe/London:20190412T170000 LOCATION:LT1310 SUMMARY:A Type-System of Sorts for Bigraphs DESCRIPTION:Speaker: Jan de Muijnck-Hughes (Glasgow)\nTitle: A Type-System of Sorts for Bigraphs\n\nBigraphs are a mathematical model (hypergraph) for representing the spatial and communication structures of networked entities [fn:1]. Bigraph Reactive Systems (BRS) build upon bigraphs by incorporating temporal changes to a model as specified with reaction rules. There is a wealth of theory (category) that supports reasoning about bigraphs\, and an emergent tool (BigraphER [fn:2]) for their modelling.\n\nBigraphs have an elegant algebraic structure that is general purpose and simply typed. However\, it is common to place restrictions on the shape of a bigraph by a /system of sorts/ that are applied as side-conditions. The details\, and application\, of these sorts are presented as an aside from the bigraph definition itself. This makes transformation of Bigraph models harder to enforce during manipulation as part of a BRS. We must provide runtime checks to provide relevant guarantees over model correctness.\n\nIn this talk\, I want to introduce you to the interesting world of Bigraph specification\, and my current and ongoing work on developing a dependent type-system to embed a system-of-sorts directly into the algebraic definition of bigraphs. This allows one to provide correct-by-construction guarantees that a given model is correct w.r.t. a provided system-of-sorts.\n\n[fn:1] Robin Milner. 2009. The Space and Motion of Communicating Agents. Cambridge University Press.\n[fn:2] http://dcs.gla.ac.uk/~michele/bigrapher.html\n UID:209 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190524T160000 DTEND;TZID=Europe/London:20190524T170000 LOCATION:LT1310 SUMMARY:Bigraphs with sharing and their algebra DESCRIPTION:Speaker: Michele Sevegnani (Glasgow)\nTitle: Bigraphs with sharing and their algebra\n\nBigraphical Reactive Systems (BRS) are a universal model of computation introduced by Robin Milner for the representation of interacting systems that evolve in both time and space. Bigraphs have been shown forming a category called symmetric partial monoidal category and their dynamic theory is defined in terms of rewriting and transition. A limitation of bigraphs is that the underlying model of location is a forest\, which means there is no straightforward representation of locations that can overlap or intersect. In this talk\, I will present bigraphs with sharing\, an extension of bigraphs which solves this problem by defining the model of location as a directed acyclic graph\, thus allowing a natural representation of overlapping or intersecting locations. I will give a complete presentation of the extended theory\, including a categorical semantics\, algebraic properties\, a normal form and several essential procedures for computation.\n UID:208 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190405T160000 DTEND;TZID=Europe/London:20190405T170000 LOCATION:LT1310 SUMMARY:Shonan "Programming and Reasoning with Algebraic Effects and Effect Handlers" trip report DESCRIPTION:Speaker: Bob Atkey and Conor McBride (MSP)\nTitle: Shonan "Programming and Reasoning with Algebraic Effects and Effect Handlers" trip report\n\n\n UID:207 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190401T160000 DTEND;TZID=Europe/London:20190401T170000 LOCATION:LT1310 SUMMARY:Determinacy and the red-green chase DESCRIPTION:Speaker: Johannes Marti (Universität Bremen)\nTitle: Determinacy and the red-green chase\n\nThe determinacy problem is to decide for queries v1,...,vn and q whether for every database D knowing the answers to v1,...,vn in D suffices to deduce the answer to q in D. It has been shown that this problem is undecidable if v1,...,vn and q are arbitrary conjunctive queries.\n\nIn this talk I give a gentle introduction to some of the formal tools that are used to study the determinacy problem. Especially\, I focus on the red-green chase\, which is a neat construction that links the problem of determinacy with query answering relative to ontologies. Lastly\, I might present some of our own\, very modest\, results about classes of conjunctive queries for which the determinacy problem is decidable.\n UID:206 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190320T160000 DTEND;TZID=Europe/London:20190320T170000 LOCATION:LT1310 SUMMARY:Probabilistic open games DESCRIPTION:Speaker: Alasdair Lambert (MSP)\nTitle: Probabilistic open games\n\nWe extend the Open Games framework for compositional game theory to encompass also mixed strategies\, making essential use of the discrete probability distribution monad on Set. We show how to compose the resulting probabilistic games in parallel and sequentially\, and illustrate the framework on the well-known Matching Pennies game.\n UID:205 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190315T160000 DTEND;TZID=Europe/London:20190315T170000 LOCATION:LT1310 SUMMARY:Fropf algebras DESCRIPTION:Speaker: Joe Collins (MSP)\nTitle: Fropf algebras\n\nLast time I talked\, you heard about Interacting Frobenius algebras -- this time\, get ready for "Hopf-Frobenius algebras"\, as Ross likes to call them\, or "Fropf algebras"\, as Ross doesn't like to call them. I am in the process of writing about them\, so this is going to be quite similar to the last talk except we're coming at them from a new angle\, and with new results.\n UID:204 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190308T160000 DTEND;TZID=Europe/London:20190308T170000 LOCATION:LT1415 SUMMARY:Coalgebra Learning via Duality DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Coalgebra Learning via Duality\n\nA key result in computational learning theory is Dana Angluin's L* algorithm that describes how to learn a deterministic finite automaton (DFA) using membership and equivalence queries. I will present a generalisation of this algorithm to the level of coalgebras. The approach relies on the use of logical formulas as tests\, based on a dual adjunction between states and logical theories. This allows us to learn\, e.g.\, labelled transition systems\, using modal formulas as tests.\n\nJoint work with Simone Barlocco and Jurriaan Rot.\n UID:203 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190222T160000 DTEND;TZID=Europe/London:20190222T170000 LOCATION:LT1310 SUMMARY:MSP 101: Proof-irrelevance for Dependent Type Theory DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: MSP 101: Proof-irrelevance for Dependent Type Theory\n\nProof-irrelevance can mean two similar but different things: on the one hand\, irrelevant proofs can be discarded when extracting programs to execute (run-time erasability)\, and on the other hand\, one might want to treat proofs as irrelevant during type checking (type-checking time erasability). I will give an overview of the subject\, focusing on type-checking time erasability. I suspect that at least three people in the audience knows more than me\, so my main function will be to keep things accessible. I plan to follow the recent paper "Degrees of Relatedness: A Unified Framework for Parametricity\, Irrelevance\, Ad Hoc Polymorphism\, Intersections\, Unions and Algebra in Dependent Type Theory" by Andreas Nuyts and Dominique Devriese (LICS 2018).\n UID:202 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190215T160000 DTEND;TZID=Europe/London:20190215T170000 LOCATION:LT1310 SUMMARY:Finitary indexed containers DESCRIPTION:Speaker: Malin Altenmüller (MSP)\nTitle: Finitary indexed containers\n\nI will talk about two different representatives of indexed containers which &--all together in the end &--will construct an application that manages windows on a screen.\n\nThe first instance of containers are rectangular windows. Defining these in terms of finite indexed containers (finite in the number of positions where elements can be stored) lets us interpret indices as outer boundaries. I will show some constructions on these space partitioning structures\, e.g. product operations and overlaying of windows (this will hopefully include some pretty pictures!).\n\nSecondly I will explain how we can encode applications as indexed containers (not necessarily finite\, despite the title)\, being defined in terms of commands and responses. To sum up I present the window managing application where all the above things will occur and get combined.\n\nI am working on these topics together with Conor and we are currently collocating them in a paper.\n UID:201 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190208T160000 DTEND;TZID=Europe/London:20190208T170000 LOCATION:LT1310 SUMMARY:Evaluators for bidirectional type systems DESCRIPTION:Speaker: Stuart Gale (MSP)\nTitle: Evaluators for bidirectional type systems\n\nIn this talk I'll introduce syntax and semantics of a generic bidirectionally type checked lambda calculus. I'll also show that lumps of syntax that act as a type annotation are in fact the fuel which powers structural evaluation.\n UID:200 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190201T160000 DTEND;TZID=Europe/London:20190201T170000 LOCATION:LT1310 SUMMARY:Linear logic: how hard can it be? DESCRIPTION:Speaker: James Wood (MSP)\nTitle: Linear logic: how hard can it be?\n\nIn the linear world\, we are no longer allowed to freely discard or duplicate hypotheses and conclusions. This should mean that there are fewer possible strategies for proving a given proposition\, making the task of proving things easier. However\, we find that linear logic proof search is a surprisingly powerful model of computation. In this talk\, I'll give an introduction to linear logic sequent calculus. I'll then go through a neat construction of [0] embedding quantified boolean formulae into linear logic without bangs\, and sketch the proof from the same paper that linear logic with bangs is Turing-complete. Some content from CS106 may come in handy.\n\n[0]: Lincoln\, Mitchell\, Scedrov\, Shankar\, 1992\, "Decision problems for propositional linear logic"\n UID:199 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190125T160000 DTEND;TZID=Europe/London:20190125T170000 LOCATION:LT1310 SUMMARY:MSP 101: Chu spaces DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: MSP 101: Chu spaces\n\nI'll talk about Chu Spaces\, a general construction of *-autonomous categories (a.k.a. models of classical linear logic). Chu spaces are interesting because they come with an inbuilt notion of duality\, which has been interpreted as a kind of player/opponent duality.\n UID:198 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190118T160000 DTEND;TZID=Europe/London:20190118T170000 LOCATION:LT1310 SUMMARY:Metametatheory of Bidirectional Type Systems DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Metametatheory of Bidirectional Type Systems\n\nIn previous talks\, I've written down bidirectional versions of particular type systems\, with type checking for introduction forms and type synthesis for elimination forms. But what are the metarules for writing down the rules? How do we show that following the metarules ensures good properties of the rules? I'll report some progress towards capturing the syntactic properties of "good" rules which might push us closer to the goal of metatheory by construction.\n\nNB This talk has nothing to do with bidirectional transformations.\n UID:197 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20190111T163000 DTEND;TZID=Europe/London:20190111T173000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:196 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181217T113000 DTEND;TZID=Europe/London:20181217T123000 LOCATION:Strathclyde SUMMARY:Event: SYCO 2 DESCRIPTION: UID:195 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181214T161500 DTEND;TZID=Europe/London:20181214T171500 LOCATION:LT1415 SUMMARY:Abstract differential geometry matters! DESCRIPTION:Speaker: Robin Cockett (University of Calgary )\nTitle: Abstract differential geometry matters!\n\nThe last few years has seen the development -- largely in Canada and Australia -- of an axiomatic approach to differential geometry based on tangent categories. Tangent categories incorporate the previous leading settings for differential geometry: finite dimensional manifolds\, synthetic differential geometry\, convenient manifolds\, etc. In addition they widen the scope significantly as they also include combinatorial species\, Goodwillie Functor calculi\, and examples from computer science. The talk will give a survey of tangent categories and some of the developments so far.\n UID:194 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181123T161500 DTEND;TZID=Europe/London:20181123T171500 LOCATION:LT1310 SUMMARY:The reachable part of a coalgebra DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: The reachable part of a coalgebra\n\nState-based transition systems are often studied relative to a specified initial state. System behavior then only depends on those states that are "reachable" from the initial state. This has both consequences for the theory (e.g. by allowing to prove non-definability results in modal logic) and practice (by making seemingly large systems more manageable) of such systems.\n\nCoalgebras provide a general model for transition systems. In this introductory talk I will discuss how to define the reachable part of a coalgebra via the notion of T-base for an endofunctor T from [1]. We will first discuss this notion and then provide a sufficient categorical condition for the existence of the T-base. We will then show how to characterise the reachable part of a coalgebra as least fixpoint of a monotone operator.\n\nThis is based on joint work with Simone Barlocco and Jurriaan Rot.\n\n========================\n[1] Alwin Blok. Interaction\, observation and denotation. Master's thesis\, ILLC Amsterdam\, 2012.\n UID:193 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181207T160000 DTEND;TZID=Europe/London:20181207T170000 LOCATION:LT1310 SUMMARY:Interacting Frobenius Algebras DESCRIPTION:Speaker: Joe Collins (MSP)\nTitle: Interacting Frobenius Algebras\n\nWhat is a Frobenius algebra? What is a Hopf algebra? And why are they such good friends? In this talk\, I will be talking about PROPs\, what an interacting Frobenius algebra is\, and some weird stuff that appears with them\, and I shall be drawing lots of pretty pictures as well.\n UID:191 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181130T161500 DTEND;TZID=Europe/London:20181130T171500 LOCATION:LT1310 SUMMARY:Dual adjunctions DESCRIPTION:Speaker: Simone Barlocco (MSP)\nTitle: Dual adjunctions\n\nCoalgebras provide an abstract framework to represent state-based transition systems. Modal logics provide a formal language to specify such systems. In our recently submitted work (joint work with Clemens Kupke and Jurriaan Rot) we devise a general algorithm to learn coalgebras. Modal formulas are used as tests to probe the behaviour of states.\n\nIn my introductory talk\, I will discuss how to set up a general framework that connects coalgebras and their modal logics via a dual adjunction. Moreover\, I will show a known result which guarantees that indistinguishable states wrt to modal formulas are behavioural equivalent\, a key fact that entails that -- whenever possible -- our algorithm learns a minimal representation of a coalgebra.\n UID:190 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181116T161500 DTEND;TZID=Europe/London:20181116T171500 LOCATION:LT1310 SUMMARY:MSP 101: Polynomial time programming languages DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: MSP 101: Polynomial time programming languages\n\nImplicit Computational Complexity is the study of programming languages or logical systems that capture complexity classes. Roughly\, every program that can be written in the language is in some complexity class. Many of the languages that have been proposed for capturing useful classes like PTIME are not much fun to program in. However\, the work of the late Martin Hofmann included work on languages like LFPL\, which only allows polynomial time computation\, but is also reasonably usable. I'll talk about LFPL\, and how the proof of polynomial time bounds works.\n UID:189 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181109T160000 DTEND;TZID=Europe/London:20181109T170000 LOCATION:LT1310 SUMMARY:The semantics of worldly type systems DESCRIPTION:Speaker: Ben Price (MSP)\nTitle: The semantics of worldly type systems\n\nI will present a type theory whose judgements are indexed by a preorder of "worlds"\, representing for example nodes in a distributed computation\, or a security level. This means a term may only typecheck at particular worlds\, and will be mobile upwards along the preorder (for instance every low security value is also a high security one). To enable talking about the world structure without compromising mobility\, the terms can talk about "shifts"\, which describe relative worlds.\n\nI then give a semantic model based on the usual presheaf model for STLC where worlds form the base category\, and shifts are endofunctors on the worlds. This semantics will show our programs are indeed oblivious to data they cannot "see". Examples will be given to demonstrate this framework in some concrete cases\, and to motivate future work.\n UID:188 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181102T160000 DTEND;TZID=Europe/London:20181102T170000 LOCATION:LT1310 SUMMARY:The Next 700 Program Transformers DESCRIPTION:Speaker: Geoff Hamilton (Dublin City University)\nTitle: The Next 700 Program Transformers\n\nIn this talk\, I will describe a hierarchy of program transformers in which the transformer at each level builds on top of the transformers at lower levels. The program transformer at the bottom of the hierarchy corresponds to positive supercompilation\, and that at the next level corresponds to distillation. I will then try to characterise the improvements that can be made at each level\, and show how the transformers can be used for program verification and theorem proving.\n UID:187 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181026T160000 DTEND;TZID=Europe/London:20181026T170000 LOCATION:LT1310 SUMMARY:Syrup: circuits with memory DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Syrup: circuits with memory\n\nBy way of giving CS106 students better tools to tackle the concept of memory in circuits\, I implemented a small programming language called (for reasons which are unlikely to become clear) Syrup. Syrup is suspiciously like a dialect of Haskell\, except that the blessed monad allows bits of state. Marking homework done in Syrup necessitates checking whether two circuits have the same /externally observable/ behaviour\, which makes it a matter of *bisimulation*. I'll talk a bit about how much fun it was implementing the decision procedure to find either a bisimulation or a countermodel (for purposes of decent feedback).\n UID:186 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181019T160000 DTEND;TZID=Europe/London:20181019T170000 LOCATION:LT1310 SUMMARY:SPLS Post-mortem DESCRIPTION:Speaker: Stuart Gale (MSP)\nTitle: SPLS Post-mortem\n\n\n UID:185 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181012T160000 DTEND;TZID=Europe/London:20181012T170000 LOCATION:LT1310 SUMMARY:Why quantum computers suck\, and what we might do about it DESCRIPTION:Speaker: Ross Duncan (Cambridge Quantum Computing)\nTitle: Why quantum computers suck\, and what we might do about it\n\nNear-term quantum computers have many limitations which make them difficult to use for stuff. I will outline some of the difficulties and handwave at some new ideas from compositional mathematics that might help us address these problems.\n UID:184 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181005T160000 DTEND;TZID=Europe/London:20181005T170000 LOCATION:LT1310 SUMMARY:ICFP trip report DESCRIPTION:Speaker: James Wood (MSP)\nTitle: ICFP trip report\n\nLast week\, I attended the ICFP conference and various associated workshops in St Louis. In this trip report\, I will talk about selected talks and the people I met there. If time allows\, I may also cover the adventures of Ioan\, one of our summer interns and current undergraduate.\n UID:183 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20181017T120000 DTEND;TZID=Europe/London:20181017T170000 LOCATION:Strathclyde SUMMARY:Event: SPLS DESCRIPTION: UID:182 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180928T160000 DTEND;TZID=Europe/London:20180928T170000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning meeting DESCRIPTION: UID:181 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180921T160000 DTEND;TZID=Europe/London:20180921T170000 LOCATION:LT1310 SUMMARY:First-order unification DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: First-order unification\n\nI'll do a 101 today\, filed under "stuff everybody should know" about first-order unification (the algorithm underlying Hindley-Milner type inference\, Prolog\, etc). But then I'll throw in the twist of considering syntax with binding. The way I cook it\, this makes essential use of the structure of the category of thinnings.\n UID:180 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180831T150000 DTEND;TZID=Europe/London:20180831T160000 LOCATION:LT1415 SUMMARY:Telescopic [Constraint] Trees\, or: Information-Aware Type Systems In Context DESCRIPTION:Speaker: Philippa Cowderoy \nTitle: Telescopic [Constraint] Trees\, or: Information-Aware Type Systems In Context\n\nThe minimalist tradition in type systems makes for easy mathematics\, but often leaves their mechanisms needlessly obscured.\n\nI build a structure for Hindley-Milner checking problems in the tradition of Type Inference in Context. This structure is derived from typing rules in the style of my first talk and mirrors data structures used for elaboration problems in dependent type systems -- offering a notation that can be used among designers and implementors of type systems and even in explaining their behaviour to users.\n UID:179 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180829T150000 DTEND;TZID=Europe/London:20180829T160000 LOCATION:LT1415 SUMMARY:Information-Aware Type Systems DESCRIPTION:Speaker: Philippa Cowderoy \nTitle: Information-Aware Type Systems\n\nThe minimalist tradition in type systems makes for easy mathematics\, but often leaves their mechanisms needlessly obscured.\n\nOne possible remedy is to track the behaviour of information in a system -- its creation\, its destruction and how it flows between constraints and source locations. I illustrate this with the Simply-Typed Lambda Calculus.\n UID:178 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180718T120000 DTEND;TZID=Europe/London:20180718T130000 LOCATION:LT1310 SUMMARY:Finite and Infinite Traces\, Inductively and Coinductively DESCRIPTION:Speaker: Jurriaan Rot (Radboud University Nijmegen)\nTitle: Finite and Infinite Traces\, Inductively and Coinductively\n\nIt is a well-known fact (used e.g. in model checking) that\, on finitely branching transition systems\, finite trace equivalence coincides with infinite trace equivalence. I will show how to prove this coinductively\, which is arguably nicer than the standard inductive proof.\n UID:177 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180613T110000 DTEND;TZID=Europe/London:20180613T120000 LOCATION:LT1310 SUMMARY:Gillette Fusion: Kits for Hutton's Razor or Type Unsafe and Scope Unsafe Programs and Their Proofs DESCRIPTION:Speaker: James Chapman (MSP)\nTitle: Gillette Fusion: Kits for Hutton's Razor or Type Unsafe and Scope Unsafe Programs and Their Proofs\n\nThe paper Type-and-Scope Safe Programs and Their Proofs abstracts the common type-and-scope safe structure from computations on lambda-terms that deliver\, e.g.\, renaming\, substitution\, evaluation\, CPS-transformation\, and printing with a name supply. By exposing this structure\, we can prove generic simulation and fusion lemmas relating operations built this way. In this talk I will present this approach but for simpler setting of Hutton's Razor. This reduces the mathematical structures involved from relative structures to the ordinary counterparts.\n UID:176 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180605T120000 DTEND;TZID=Europe/London:20180605T170000 LOCATION:Cairn Auditorium\, PG G.01\, Postgraduate Centre\, Heriot-Watt University SUMMARY:Event: SPLS DESCRIPTION: UID:175 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180529T130000 DTEND;TZID=Europe/London:20180529T140000 LOCATION:LT1310 SUMMARY:A Coinductive Proof of Policy Iteration Correctness DESCRIPTION:Speaker: Helle Hvid Hansen (TU Delft)\nTitle: A Coinductive Proof of Policy Iteration Correctness\n\nThis is the second half of Helle's talk on a (co)algebraic treatment of Markov Decision Processes. It focuses on a coinductive explanation of policy improvement using a new proof principle\, based on Banach's Fixpoint Theorem\, that we call contraction coinduction.\n UID:174 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180517T130000 DTEND;TZID=Europe/London:20180517T140000 LOCATION:LT1310 SUMMARY:HoTT for sets DESCRIPTION:Speaker: Thorsten Altenkirch (Nottingham)\nTitle: HoTT for sets\n\nBefore getting lost in the realms of higher dimensions we should see wether we can interpret set-level HoTT. We know how to deal with functional extensionality and a static universe of propositions (see Observational Type Theory) but what about a dynamic universe of propositions\, i.e. one reflecting HProps that also validates propositional extensionality. I will discuss the problems modelling this and a possible solution using globular setoids.\n\nThe dynamic prop corresponds to a subobject classifier in a topos (in particular we get unique choice) while the static universe corresponds to a quasitopos I am told.\n UID:173 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180523T160000 DTEND;TZID=Europe/London:20180523T170000 LOCATION:LT1310 SUMMARY:How Do We Model a Problem Like Mutable State? DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: How Do We Model a Problem Like Mutable State?\n\n\n UID:172 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180516T110000 DTEND;TZID=Europe/London:20180516T120000 LOCATION:LT1310 SUMMARY:Long-Term Values in Markov Decision Processes\, (Co)Algebraically DESCRIPTION:Speaker: Helle Hvid Hansen (TU Delft)\nTitle: Long-Term Values in Markov Decision Processes\, (Co)Algebraically\n\nIn this talk\, we study Markov decision processes (MDPs) with the discounted sums criterion from the perspective of coalgebra and algebra. Probabilistic systems\, similar to MDPs but without rewards\, have been extensively studied\, also coalgebraically\, from the perspective of program semantics. Here\, we focus on the role of MDPs as models in optimal planning\, where the reward structure is central. Our main contributions are: (i) a coinductive explanation of policy improvement using a new proof principle\, based on Banach's Fixpoint Theorem\, that we call contraction coinduction\, and (ii) showing that the long-term value function of a policy can be obtained via a generalized notion of corecursive algebra\, which takes boundedness into account.\n\nThis is joint work with Frank Feys (Delft) and Larry Moss (Indiana).\n UID:171 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180530T110000 DTEND;TZID=Europe/London:20180530T120000 LOCATION:LT1310 SUMMARY:Multi-Dimensional Arrays and their Types DESCRIPTION:Speaker: Artjoms Šinkarovs and Peter Hancock (Heriot-Watt)\nTitle: Multi-Dimensional Arrays and their Types\n\nThough Multi-Dimensional Arrays (MDAs) seem conceptually straightforward\, it's not easy to come up with a mathematical theory of arrays that can be used within optimising compilers. We'd like to treat arrays as functions from indices to values with some domain restrictions. It is desirable that these domain restrictions are specified in a compact form\, and are equipped with closed algebraic operations like intersection\, union\, etc. We are going to consider a few typical models like hyperrectangulars\, grids and polyhedrons.\n\nWhen typing array operations\, ideally we'd like to find a balance between tracking all the shapes of arrays and allowing for generic array operations. This proves to be tricky\, for reasons we'll explain.\n\nWe will propose\, tentatively\, an analysis of MDAs in terms of container functors. The aim is to supply concepts helpful when thinking about MDAs\, e.g. when designing notations for coding with arrays. Some intriguing gadgetry shows up.\n UID:170 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180504T110000 DTEND;TZID=Europe/London:20180504T120000 LOCATION:LT1310 SUMMARY:MSP 101: The Dialectica Interpretation DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: MSP 101: The Dialectica Interpretation\n\nA proof interpretation translates proofs of one logical system into proofs of another (example: the double-negation interpretation of classical logic into constructive logic). This often reveals some information about the original system (e.g. classical logic is equiconsistent with constructive logic). Gödel's Dialectica interpretation (named after the journal it was published in) translates Heyting arithmetic (the constructive theory of the natural numbers\, including induction) into System T (the quantifier-free theory of the simply typed lambda calculus with natural numbers) -- quantifier complexity is traded for higher type complexity. Combining this translation with (a refined) double negation translation\, one can extract System T programs from a proof of a forall-exists statement\, even if this proof is using non-constructive priciples such as Markov's Principle\, Excluded Middle\, or the Quantifier-Free Axiom of Choice. I've always found the Dialectica translation mystifying\, so I'll try to explain the intuition behind it.\n UID:169 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180419T110000 DTEND;TZID=Europe/London:20180419T120000 LOCATION:LT1310 SUMMARY:Midlands Graduate School Trip Report DESCRIPTION:Speaker: James Wood (MSP)\nTitle: Midlands Graduate School Trip Report\n\n\n UID:168 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180412T110000 DTEND;TZID=Europe/London:20180412T120000 LOCATION:LT1415 SUMMARY:Quotient Inductive-Inductive Types DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Quotient Inductive-Inductive Types\n\nHigher inductive types (HITs) in Homotopy Type Theory (HoTT) allow the definition of datatypes which have constructors for equalities over the defined type. HITs generalise quotient types and allow to define types which are not sets in the sense of HoTT (i.e. do not satisfy uniqueness of equality proofs) such as spheres\, suspensions and the torus. However\, there are also interesting uses of HITs to define sets\, such as the Cauchy reals\, the partiality monad\, and the internal\, total syntax of type theory. In each of these examples we define several types that depend on each other mutually\, i.e. they are inductive-inductive definitions. We call those HITs quotient inductive-inductive types (QIITs).\n\nAlthough there has been recent progress on the general theory of HITs\, there isn't yet a theoretical foundation of the combination of equality constructors and induction-induction\, despite having many interesting applications. In the present paper we present a first step towards a semantic definition of QIITs. In particular\, we give an initial-algebra semantics and show that this is equivalent to the section induction principle\, which justifies the intuitively expected elimination rules.\n UID:167 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180328T123000 DTEND;TZID=Europe/London:20180328T133000 LOCATION:LT1310 SUMMARY:What is a category\, actually? DESCRIPTION:Speaker: Thorsten Altenkirch (Nottingham)\nTitle: What is a category\, actually?\n\nLet us revisit the definition of a category and define it in a way which has the advantage that we can generalize it to higher dimensions. Why am I interested in higher categories (or specifically (\\infty,1)-categories)? I have a few problems in Homotopy Type Theory which I think can be solved using these beasts: the coherence problem for type theory in type theory (in the moment I cannot even define the standard model) and generalizing the Hungarian approach to Quotient Inductive Inductive Types (QIITs) to Higher Inductive Inductive Types (HIITs).\n UID:166 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180321T150000 DTEND;TZID=Europe/London:20180321T160000 LOCATION:LT1415 SUMMARY:Equivariant ZFA and the foundations of nominal techniques DESCRIPTION:Speaker: Jamie Gabbay (Heriot-Watt)\nTitle: Equivariant ZFA and the foundations of nominal techniques\n\nThe sets foundations of nominal techniques are usually taken to be Fraenkel-Mostowski set theory (which is ZFA + a finite support property). I will argue that in many situations\, a new foundation which I call Equivariant ZFA (EZFA) may be a better choice\, because you can do everything in EZFA that you can do in FM and furthermore EZFA with Choice (EZFAC) is consistent whereas FM with Choice is not.\n\n* I will define EZFA and how it interacts with Choice.\n* I will prove that EZFA is *equivalent* to ZFA.\n* I will then prove that EZFA is *not equivalent* to ZFA.\n* I will explain why I think EZFA(C) may be useful\, why my last three papers were actually written in EZFAC\, and finally I will discuss the implications this may have for mathematical foundations in general.\n\n UID:165 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180214T150000 DTEND;TZID=Europe/London:20180214T160000 LOCATION:LT1310 SUMMARY:MSP 101: Domain Theory DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: MSP 101: Domain Theory\n\nI will give an introduction to Domain Theory\, focusing on motivation. I hope to cover recursive definitions\, and solving domain equations using retraction pairs.\n UID:164 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180208T150000 DTEND;TZID=Europe/London:20180208T160000 LOCATION:LT1212 SUMMARY:Introduction to coalgebra DESCRIPTION:Speaker: Alexander Kurz (Leicester)\nTitle: Introduction to coalgebra\n\n\n UID:163 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180207T150000 DTEND;TZID=Europe/London:20180207T160000 LOCATION:LT1415 SUMMARY:Departmental seminar: From Couplings to Probabilistic Relational Program Logics DESCRIPTION:Speaker: Justin Hsu (UCL)\nTitle: From Couplings to Probabilistic Relational Program Logics\n\nMany program properties are relational\, comparing the behavior of a program (or even two different programs) on two different inputs. While researchers have developed various techniques for verifying such properties for standard\, deterministic programs\, relational properties for probabilistic programs have been more challenging. In this talk\, I will survey recent developments targeting a range of probabilistic relational properties\, with motivations from privacy\, cryptography\, machine learning. The key idea is to meld relational program logics with an idea from probability theory\, called a probabilistic coupling. The logics allow a highly compositional and surprisingly general style of analysis\, supporting clean proofs for a broad array of probabilistic relational properties.\n UID:162 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180406T110000 DTEND;TZID=Europe/London:20180406T120000 LOCATION:LT1310 SUMMARY:Setoids and Quotients DESCRIPTION:Speaker: James Chapman (MSP)\nTitle: Setoids and Quotients\n\nIn preparation for Fred's talk about "Quotient Inductive-Inductive Types" next week I will introduce quotients and setoids in type theory and some of the issues surrounding them. The use of setoids is discouraged by many doctors and can lead to a contagious and incurable condition: relation preservation. Quotients on the other hand are dangerous if not correctly handled and can lead to unsightly things appearing where they shouldn't such as inhabitants of the excluded middle.\n UID:161 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180314T150000 DTEND;TZID=Europe/London:20180314T160000 LOCATION:LT1310 SUMMARY:Quantum Computing with ZX Calculus DESCRIPTION:Speaker: Joe Collins (MSP)\nTitle: Quantum Computing with ZX Calculus\n\nQuantum mechanics is dope\, so it makes sense that making a computer using the principles of quantum mechanics would also be pretty sick. However\, the formalism that is used by physicists\, called a Hilbert space\, is not specialised for this purpose. In particular\, it is\n1) Difficult to prove properties about programs for quantum computers\n2) Difficult to see what is these programs are actually doing\n\nThankfully\, category theory is very cool! Using ZX calculus\, we can talk about quantum computing in a much clearer manner. I will be introducing some fundamental quantum mechanics and ZX calculus\, and then using ZX calculus I will talk about Shor's algorithm.\n UID:160 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180307T100000 DTEND;TZID=Europe/London:20180307T170000 LOCATION:Level 5\, School of Computing Science\, University of Glasgow SUMMARY:Event: SPLS DESCRIPTION: UID:159 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180221T150000 DTEND;TZID=Europe/London:20180221T160000 LOCATION:LT1310 SUMMARY:A Type-System for describing the Structural Topology of System-on-a-Chip Architectures DESCRIPTION:Speaker: Jan de Muijnck-Hughes (Glasgow)\nTitle: A Type-System for describing the Structural Topology of System-on-a-Chip Architectures\n\nThe protocols that describe the interactions between IP Cores on System-on-a-Chip architectures are well-documented. These protocols described not only the structural properties of the physical interfaces but also the behaviour of the emanating signals. However\, there is a disconnect between the design of SoC architectures\, their formal description\, and the verification of their implementation in known hardware description languages.\n\nWithin the Border Patrol project we are investigating how to capture and reason about the structural and behavioural properties of SoC architectures using state-of-the-art advances in programming language research. Namely\, we are investigating using dependent types and session types for the description of hardware communication.\n\nIn this talk I will discuss my work in designing a linked family of languages that captures and reasons about the topological structure of a System-on-a-Chip. These languages provide correct-by-construction guarantees over the interaction protocols themselves\; the adherence of a component that connects using said protocols\; and the validity of the specified connections. These guarantees are provided through abuse of indexed monads to reason about resource usage\; and general (ab)use of dependent types as presented in Idris.\n\nI will not cover all aspects of the languages but will concentrate my talk detailing the underlying theories that facilitate the correct-by-construction guarantees.\n UID:158 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180309T160000 DTEND;TZID=Europe/London:20180309T170000 LOCATION:LT1310 SUMMARY:MSP 101: Kan extensions DESCRIPTION:Speaker: Alasdair Lambert and Ben Price (MSP)\nTitle: MSP 101: Kan extensions\n\n\n UID:157 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180207T150000 DTEND;TZID=Europe/London:20180207T160000 LOCATION:LT1310 SUMMARY:MSP 101: The adjoint functor theorem DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: MSP 101: The adjoint functor theorem\n\nAdjoint functors arise everywhere\, but how do we find them? It is a fun exercise to prove that right adjoints preserve limits\, and\, dually\, that left adjoints preserve colimits. An adjoint functor theorem is a statement that (under certain conditions) the converse holds: a functor which preserves limits is a right adjoint. I will discuss the General Adjoint Functor Theorem\, and why Peter Johnstone considers it fundamentally useless.\n UID:155 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180131T150000 DTEND;TZID=Europe/London:20180131T160000 LOCATION:LT1310 SUMMARY:Reflections on the PhD process DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Reflections on the PhD process\n\n\n UID:154 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180124T150000 DTEND;TZID=Europe/London:20180124T160000 LOCATION:LT1310 SUMMARY:Coinduction and the Companion DESCRIPTION:Speaker: Jurriaan Rot (Radboud University Nijmegen)\nTitle: Coinduction and the Companion\n\nThe coinductive proof method can be enhanced by several techniques\, often referred to as up-to-techniques. I will talk about the basic theory of coinduction-up-to\, and a little about the more recent notion of companion. This companion is the largest valid up-to technique for a given predicate\, and gives a nice way of working with coinduction up-to.\n UID:153 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20180116T160000 DTEND;TZID=Europe/London:20180116T170000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning session DESCRIPTION: UID:152 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171208T160000 DTEND;TZID=Europe/London:20171208T170000 LOCATION:LT1310 SUMMARY:Dijkstra Monads DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Dijkstra Monads\n\nOne monad to the tune of another.\n UID:151 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171027T160000 DTEND;TZID=Europe/London:20171027T170000 LOCATION:LT1310 SUMMARY:Size-Matters in the Modal mu-Calculus DESCRIPTION:Speaker: Johannes Marti (Universität Bremen)\nTitle: Size-Matters in the Modal mu-Calculus\n\nI talk about three methods for measuring the size of formulas in the modal mu-calculus and explore how the choice between them influences the complexity of computations on formulas. Especially\, I focus on the guarded transformation\, which is a simple syntactic transformation on formulas that is commonly assumed to be polynomial but has recently been shown to require exponential time.\n\nI will complain about the mess in the literature and present two of our (Clemens\, Yde and me) own preliminary results:\n\n1) There is a polynomial guarded transformation if we measure the input formula in the number of its subformulas and measure the output formula in the size of its closure.\n\n2) If there is a polynomial guarded transformation where we measure the input formula in the size of its closure then there is a polynomial algorithm for solving parity games. Hence finding such a transformation is at least as hard as solving parity games\, which is commonly believed to be quite hard.\n\nWe employ an automata-theoretic approach that relates the different measures for the size of a formula to different constraints on the transition structure of an automaton corresponding to the formula.\n\nThis is a very technical talk but there will be many pictures!\n UID:150 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171011T120000 DTEND;TZID=Europe/London:20171011T170000 LOCATION:Informatics Forum\, Edinburgh SUMMARY:Event: SPLS DESCRIPTION: UID:149 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170922T160000 DTEND;TZID=Europe/London:20170922T170000 LOCATION:LT1310 SUMMARY:Bidirectional Martin-Löf 1971 DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Bidirectional Martin-Löf 1971\n\nPer Martin-Löf's 1971 Theory of Types is the ancestor of the type systems used today in Agda\, Coq\, Idris\, NuPRL\, and many other variations on the theme of dependent types. Its principal virtue is its simplicity: it has very few moving parts (but they move quite a lot). Its well known principal vice is its inconsistency: you can write a looping program inhabiting any type (thus 'proving' any proposition). I'll be talking about the design principles for constructing dependent type systems which are bidirectional -- clearly split into a type checking part and a type synthesis part. By following these principles\, it gets easier to establish good safety properties of these systems. In particular\, I'll sketch how to keep type safety ("well typed programs don't go wrong") separate from normalization ("all computations terminate"). Martin-Löf's 1971\, reformulated bidirectionally\, makes a good example\, because it's small and type-safe\, but not normalizing.\n UID:148 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170929T160000 DTEND;TZID=Europe/London:20170929T170000 LOCATION:LT1310 SUMMARY:Worlds DESCRIPTION:Speaker: Ben Price (MSP)\nTitle: Worlds\n\nBuilding on last week's introduction to Martin-Löf 1971\, we describe a toy type theory which not only accounts for what type terms have\, but also where they live. This extra information can be interpreted as where (physically) data lives\, at what phase (typechecking vs runtime) it exists\, when it exists\, or who has access to the data.\n\nIn return for caring about these "worlds" describing where data lives\, we get applications to distributed computing and erasure for efficient code generation\, with future work to consider productivity and security.\n UID:147 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171006T160000 DTEND;TZID=Europe/London:20171006T170000 LOCATION:LT1310 SUMMARY:Tetration DESCRIPTION:Speaker: Peter Hancock \nTitle: Tetration\n\nIn ghci\, you can write something like let two f = f . f in two two two two (+1) 0 and it will print "65536". If you write something like
let two f = f . f \; four = two . two in four ($ two) id (+1) 0 \n it will print "Occurs check: cannot construct the infinite type: a ~ a -> a".\n\nCan haskell not count to four?(*)\n\nThe topic is the compact representation of unfeasibly large numbers using a pure (Glaswegian?) universe. Some excursions into the hinterland of the topic are likely.\n\nBy the way\, tetration is the function m n |-> n ^ .. ^ n with m n's.\n\n(*) No doubt mad haskell mambo or pragma exists that will trick it into counting up to four. I will reward the most amusing/revolting demonstration with a large (reasonably priced) malt whisky.\n UID:146 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171013T160000 DTEND;TZID=Europe/London:20171013T170000 LOCATION:LT1310 SUMMARY:Coalgebraic Learning DESCRIPTION:Speaker: Simone Barlocco (MSP)\nTitle: Coalgebraic Learning\n\nAutomata learning is a well known technique to infer a finite state machine from a set of observations. One important algorithm for automata learning is the L* algorithm by Dana Angluin. In this 101 I will present a new perspective on L* using ideas from coalgebra and modal logic. After a brief recap of how L* works\, I will describe a generalisation of the L* algorithm to the coalgebraic level. I will conclude my talk with two concrete instances of the general framework: the learning of Mealy machines and of bisimulation quotients of probabilistic transition systems. Joint work with Clemens Kupke.\n UID:145 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171103T160000 DTEND;TZID=Europe/London:20171103T170000 LOCATION:LT1310 SUMMARY:Measuring the sizes of trees DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Measuring the sizes of trees\n\nI'll talk about a way of measuring the sizes of trees using weighted tree automata\, in a compositional way that works well with pattern matching. This is based on some work by Georg Moser and Martin Hofmann.\n UID:144 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171117T160000 DTEND;TZID=Europe/London:20171117T170000 LOCATION:LT1310 SUMMARY:Deep Learning DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Deep Learning\n\nI'll explain the first concepts of Deep Learning. This is an advert for a reading group on the topic which will run over the next few weeks.\n UID:143 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171110T160000 DTEND;TZID=Europe/London:20171110T170000 LOCATION:LT1310 SUMMARY:Infinite Iteration of Games DESCRIPTION:Speaker: Alasdair Lambert (MSP)\nTitle: Infinite Iteration of Games\n\nMy talk will be based on our recent paper "A Compositional Treatment of Iterated Open Games". In this paper we introduce a new operator on open games to capture the concept of subgame perfect equilibrium as well as providing final coalgebra semantics of infinite games.\n UID:141 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171201T160000 DTEND;TZID=Europe/London:20171201T170000 LOCATION:LT1310 SUMMARY:MSP 101: Hereditary substitution DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: MSP 101: Hereditary substitution\n\n\n UID:138 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20171206T130000 DTEND;TZID=Europe/London:20171206T140000 LOCATION:LT1415 SUMMARY:The Power of Parameterization in Coinductive Proof DESCRIPTION:Speaker: Chung-Kil Hur (Seoul National University)\nTitle: The Power of Parameterization in Coinductive Proof\n\nIn this talk\, I will present a simple yet powerful principle for coinductive reasoning\, which we call "parameterized coinduction". More specifically\, it is as simple as the Knaster-Tarski theorem without requiring any syntactic checking\, yet as powerful as Coq's syntactic guarded coinduction supporting incremental reasoning. As an important consequence\, parameterized coinduction can easily support complex nested induction-coinduction. \n\nWe also implemented the parameterized coinduction as the Coq library called "paco"\, which can be found at:\n\nhttp://plv.mpi-sws.org/paco\n\nThis is joint work with Georg Neis\, Derek Dreyer and Viktor Vafeiadis\, and was presented at POPL'13. \n UID:137 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170914T114000 DTEND;TZID=Europe/London:20170914T124000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning session DESCRIPTION: UID:136 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170911T140000 DTEND;TZID=Europe/London:20170911T150000 LOCATION:LT1101 (Board room) SUMMARY:Adding Cubes to Agda DESCRIPTION:Speaker: Andrea Vezzosi (Chalmers)\nTitle: Adding Cubes to Agda\n\nCubical Type Theory (CTT) provides an extension of Martin-Löf Type Theory (MLTT) where we can interpret the univalence axiom while preserving the canonicity property\, i.e. every closed term actually computes to a value. The typing and equality rules of CTT come as a fairly well-behaved extension of the ones of MLTT and the denotational model and prototype implementation help clarifying the system further.\n\nGiven the above it felt reasonable to introduce the features of CTT into a more mature proof assistant like Agda\, and this talk reports the status of this endeavour. In short:\n\n* The univalence axiom is proven as a theorem and we successfully tested its computational behavior on small examples.\n* comp computes for any parametrized data or record types\, including coinductive ones\, but it is stuck for inductive families.\n* The interaction of the path type and copatterns gives extensionality principles for coinductive records.\n* The interval I is an actual type\, we also have restriction types A[&phi&mapsto\; u] and types for partial elements Partial &phiA. Their sort makes sure comp does not apply to them.\n\nExamples are collected at https://github.com/Saizan/cubical-demo.\n UID:135 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170906T140000 DTEND;TZID=Europe/London:20170906T150000 LOCATION:LT1310 SUMMARY:Binding and Substitution in String Diagrams DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Binding and Substitution in String Diagrams\n\nIn the categorical semantics of (e.g.) the simply typed lambda calculus substitution of a variable by a term is achieved by composing morphisms. What is the equivalent notion in diagrammatic languages? What even is a "variable" in this context? I'll sketch some (pretty) rough ideas for the beginnings of a “functional language” of diagrams including substitution\, binding\, and pattern matching. It turns out to all be about operads and co-operads.\n UID:134 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170710T100000 DTEND;TZID=Europe/London:20170710T170000 LOCATION:LT1415 SUMMARY:Event: Open Games Workshop DESCRIPTION: UID:133 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170705T140000 DTEND;TZID=Europe/London:20170705T150000 LOCATION:LT1415 SUMMARY:Some enumerative\, topological\, and algebraic aspects of linear lambda calculus DESCRIPTION:Speaker: Noam Zeilberger (Birmingham)\nTitle: Some enumerative\, topological\, and algebraic aspects of linear lambda calculus\n\nEnumeration of graphs on surfaces (or "maps") is an active topic of research in combinatorics\, with links to wide-ranging domains such as algebraic geometry\, knot theory\, and mathematical physics. In the last few years\, it has also been found that map enumeration is related to the combinatorics of lambda calculus\, with various well-known families of maps in 1-to-1 correspondence with various natural families of linear lambda terms. In the talk I will begin by giving a brief survey of these enumerative connections\, then use those to motivate a closer look at the surprisingly rich topological and algebraic properties of linear lambda calculus.\n UID:132 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170615T140000 DTEND;TZID=Europe/London:20170615T150000 LOCATION:LT1310 SUMMARY:Informal introduction to knot theory and the unknotting problem DESCRIPTION:Speaker: Stuart Gale (MSP)\nTitle: Informal introduction to knot theory and the unknotting problem\n\nThis is an informal talk on the interesting properties I've found when playing with the unknotting problem (knot simplification moves that help to establish whether any given knot is a loop in complicated disguise\, or something really knotted).\n\nI'll discuss the syntax that I've used for annotating knots that leads to a(n almost) syntax based method for unknotting\, but that hints further at unknotting in a more interesting way by using an unintentional property of the syntax.\n\nI'll present some examples of the problems with representing knots and how the syntax and reduction rules help\, in my opinion\, to make unknotting more tangible.\n UID:131 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170629T140000 DTEND;TZID=Europe/London:20170629T150000 LOCATION:LT1310 SUMMARY:Syntax and semantics of Quantitative Type Theory DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Syntax and semantics of Quantitative Type Theory\n\nAt last year's WadlerFest celebration\, Conor presented a dependent type theory where variables are tagged with information about how they are used. Variable usage tagging has been developed in the non dependent setting\, starting with Girard's Linear Logic\, and culminating with recent work in contextual effects\, coeffects\, and quantitative type theories. The subtlety with dependent types lies in how to account for the difference between usage in types and terms. Conor's system handles this by treating usage in types as a "zero" usage\, so that it doesn't affect the usage in terms. This is a departure from previous "linear" type theories that maintains a strict separation between usage controlled information\, which types cannot depend on\, and unrestricted information\, which types can depend on.\n\nConor presented a syntax and typing rules for the system\, as well as an erasure property that exploits the difference between "not used" and "used"\, but doesn't do anything with the finer usage information available. I'll present a collection of models for the system that fully exploit the usage information. This will give interpretations of type theory in resource constrained computational models\, Geometry of Interaction models\, and imperative models. To maintain order\, I will gather all these notions of model under a new concept of "Quantitative Category with Families"\, a generalisation of the standard "Category with Families" class of models of dependent types.\n UID:130 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170608T140000 DTEND;TZID=Europe/London:20170608T150000 LOCATION:LT1310 SUMMARY:TYPES 2017 Trip report DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: TYPES 2017 Trip report\n\nI'll tell you about the most interesting talks\, ideas and gossip that came out of the TYPES conference in BudaPest last week.\n UID:129 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170727T140000 DTEND;TZID=Europe/London:20170727T150000 LOCATION:LT1415 SUMMARY:The Rise and Fall of Cooperative Communities DESCRIPTION:Speaker: Matteo Cavaliere (Edinburgh)\nTitle: The Rise and Fall of Cooperative Communities\n\nSocial\, biological and economic networks grow and decline with recurrent fragmentation and re-formation\, often explained in terms of external perturbations. I will present a model of dynamical networks and evolutionary game theory that explains these phenomena as consequence of imitation and endogenous conflicts between "cooperators" and "cheaters". Cooperators promote well-connected prosperous (but fragile) networks and cheaters cause the network to fragment and lose its prosperity. Once the network is fragmented it can be reconstructed by a new invasion of cooperators\, leading to recurrent cycles of formation and fragmentation observed\, for instance\, in bacterial communities and socio-economic networks. In the last part of the talk\, I will briefly introduce my current works on the role of individual decision-making in cooperative communities and the possibility of synthetic biology to address these ideas in microbial communities.\n\nReferences\n\nM. Cavaliere\, S. Sedwards\, C.E. Tarnita\, M.A. Nowak\, A. Csikasz-Nagy.\nProsperity is Associated with Instability in Dynamical Networks.\nJournal of Theoretical Biology\, 299\, 2012.\n\nPlasticity Facilitates Sustainable Growth in the Commons.\nM. Cavaliere\, J.F. Poyatos.\nJournal of the Royal Society Interface\, 10\, 2013.\n\nEco-Evolutionary Feedbacks can Rescue Cooperation in Microbial Populations.\nC. Moreno-Fenoll\, M. Cavaliere\, E. Martinez-Garcia\, J.F. Poyatos.\nScientific Reports\, 7\, 2017.\n UID:128 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170601T140000 DTEND;TZID=Europe/London:20170601T150000 LOCATION:LT1310 SUMMARY:Optimal nondeterminism: explaining the Kameda-Weiner algorithm DESCRIPTION:Speaker: Rob Myers \nTitle: Optimal nondeterminism: explaining the Kameda-Weiner algorithm\n\nThe Kameda-Weiner algorithm takes a machine (nondeterministic finite automaton) as input\, and provides an optimal machine (state-minimal nondeterministic finite automaton) as output. In this talk I will discuss work which provides a clear explanation of it\, by translating the various syntactic constructs into more meaningful order-theoretic ones\, and then composing them together to prove correctness.\n UID:127 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170525T110000 DTEND;TZID=Europe/London:20170525T120000 LOCATION:LT1310 SUMMARY:Learning via Coalgebraic Logic DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Learning via Coalgebraic Logic\n\nA key result in computational learning theory is Dana Angluin's L* algorithm that describes how to learn a regular language\, or a deterministic finite automaton (DFA)\, using membership and equivalence queries. In my talk I will present a generalisation of this algorithm using ideas from coalgebra and modal logic -- please note\, however\, that prior knowledge of these topics will not be required.\n\nIn the first part of my talk I will recall how the L* algorithm works and establish a link to the notion of a filtration from modal logic. Furthermore I will provide a brief introduction to coalgebraic modal logic. In the second part of my talk I will present a generalisation of Angluin's original algorithm from DFAs to coalgebras for an arbitrary finitary set functor T in the following sense: given a (possibly infinite) pointed T-coalgebra that we assume to be regular (i.e. having an equivalent finite representation) we can learn its finite representation by (i) asking "logical queries" (corresponding to membership queries) and (ii) making conjectures to which a teacher has to reply with a counterexample (equivalence queries). This covers (known variants of) the original L* algorithm and algorithms for learning Mealy and Moore machines. Other examples are infinite streams\, trees and bisimulation quotients of various types of transition systems.\n\nJoint work with Simone Barlocco.\n UID:126 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170518T150000 DTEND;TZID=Europe/London:20170518T160000 LOCATION:LT1310 SUMMARY:The joy of QIITs DESCRIPTION:Speaker: Thorsten Altenkirch (Nottingham)\nTitle: The joy of QIITs\n\nQuotient inductive inductive types (QIITS) are set-truncated mutually defined higher inductive types. I am going to discuss two applications of QIITs:\n\n1. define an internal syntax of Type Theory without reference to untyped preterms;\n2. define a version of the partiality monad that doesn't require countable choice.\n\nOn the one hand I think that these applications are interesting because they represent applications of HoTT which have nothing to do with homotopy theory\; on the other hand they are clearly not very higher order (in the sense of truncation levels) but can be defined in the set-truncated fragment of HoTT. Hence my question: what are interesting applications of higher types which are not directly related to synthetic homotopy theory?\n\nThis talk is based on joint work with Paolo Capriotti\, Nils Anders Danielsoon\, Gabe Dijkstra\, Ambrus Kaposi and Nicolai Kraus.\n UID:125 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170420T140000 DTEND;TZID=Europe/London:20170420T150000 LOCATION:LT1310 SUMMARY:Modular Datalog DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Modular Datalog\n\n\n UID:124 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170504T140000 DTEND;TZID=Europe/London:20170504T150000 LOCATION:LT1310 SUMMARY:MSP 101: Differential Operators DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: MSP 101: Differential Operators\n\nA traditional source of complaint from CS undergraduates (especially in the USA\, but in other places\, too) is that they are made to learn too much standard issue mathematics with little apparent relevance to computation. Differential calculus (with its usual presentational focus on physical systems) is often picked upon as the archetype. What we see in action is the fragile male ego: they are not so quick to complain about the unimportance of things they do not find difficult. All of which makes more delicious the irony that differential operators have a key role to play in understanding discrete structures\, such as automata\, datatypes\, execution stacks\, and plenty more.\n\nThe basic idea is as follows: to put your finger over any single K in the pair of words BREKEKEKEX KOAXKOAX \n you must choose either to put your finger over a single K in BREKEKEKEX and pair with KOAXKOAX intact\, or to leave BREKEKEKEX intact and cover a K in KOAXKOAX. You have just followed Leibniz's rule for differentiating a product (with respect to K)\, and computed a one-hole context for a K in a data structure.\n\nNewton\, of course\, would point out that such derivatives arise as the limit of a divided difference\, a concept worthy of study in more generality. I would point out that divided differences are often definable\, even in situtations when neither division nor difference makes much apparent sense. Notably\, Brzozowski's derivative for regular languages is a divided difference (even though it is not Leibniz's derivative).\n\nI'll work mainly with containers (which look a lot like power series) but make sure there are plenty of concrete examples. In practice\, it becomes rather useful to compute derivatives by pattern matching on types\, which is especially funny as symbolic differentiation is the first example in the literature of computing anything by pattern matching at all.\n UID:123 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170405T100000 DTEND;TZID=Europe/London:20170405T170000 LOCATION:Strathclyde\, room LT1415 SUMMARY:Event: CLAP DESCRIPTION: UID:122 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170410T090000 DTEND;TZID=Europe/London:20170410T170000 LOCATION:Strathclyde\, Room MC301 (McCance Building) SUMMARY:Event: ALCOP2017 DESCRIPTION: UID:121 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170222T150000 DTEND;TZID=Europe/London:20170222T160000 LOCATION:LT1415 SUMMARY:Departmental seminar: An introduction to Blockchains DESCRIPTION:Speaker: Andrea Bracciali (Stirling)\nTitle: An introduction to Blockchains\n\nBlockchains\, i.e. decentralised\, distributed data structures which can also carry executable code for a non-standard execution environment\, introduce new models of computation. Decentralised\, here\, means\, informally speaking\, "without central control"\, e.g. a currency without a (central) bank\, but much more. Blockchains support the recently introduced virtual currencies\, a la Bitcoin\, and a new class of decentralised applications\, including smart contracts. In this talk we will introduce the main aspects of a blockchain\, with particular reference to the Bitcoin blockchain as a paradigmatic case of such a new model of computation\, and also touching on smart contracts. No previous knowledge of bitcoin/blockchain required for this introductory talk.\n UID:120 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170215T130000 DTEND;TZID=Europe/London:20170215T140000 LOCATION:LT1415 SUMMARY:Departmental seminar: Semantics for probabilistic programming DESCRIPTION:Speaker: Chris Heunen (Edinburgh)\nTitle: Semantics for probabilistic programming\n\nStatistical models in e.g. machine learning are traditionally expressed in some sort of flow charts. Writing sophisticated models succinctly is much easier in a fully fledged programming language. The programmer can then rely on generic inference algorithms instead of having to craft one for each model. Several such higher-order functional probabilistic programming languages exist\, but their semantics\, and hence correctness\, are not clear. The problem is that the standard semantics of probability theory\, given by measurable spaces\, does not support function types. I will describe how to get around this.\n UID:119 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170206T140000 DTEND;TZID=Europe/London:20170206T150000 LOCATION:LT1415 SUMMARY:On the expressive power of user-defined effects: effect handlers\, monadic reflection\, delimited control without answer-type-modification DESCRIPTION:Speaker: Ohad Kammar (Oxford)\nTitle: On the expressive power of user-defined effects: effect handlers\, monadic reflection\, delimited control without answer-type-modification\n\nWe compare the expressive power of three programming abstractions for user-defined computational effects: Bauer and Pretnar's effect handlers\, Filinski's monadic reflection\, and delimited control. This comparison allows a precise discussion about the relative merits of each programming abstraction.\n\nWe present three calculi\, one per abstraction\, extending Levy's call-by-push-value. These comprise syntax\, operational semantics\, a natural type-and-effect system\, and\, for handlers and reflection\, a set-theoretic denotational semantics. We establish their basic meta-theoretic properties: adequacy\, soundness\, and strong normalisation. Using Felleisen's notion of a macro translation\, we show that these abstractions can macro-express each other\, and show which translations preserve typeability. We use the adequate finitary set-theoretic denotational semantics for the monadic calculus to show that effect handlers cannot be macro-expressed while preserving typeability either by monadic reflection or by delimited control. We supplement our development with a mechanised Abella formalisation.\n\nJoint work with Yannick Forster\, Sam Lindley\, and Matija Pretnar.\n UID:118 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170427T140000 DTEND;TZID=Europe/London:20170427T150000 LOCATION:LT1310 SUMMARY:What I\, Dunne\, done in my PhD DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: What I\, Dunne\, done in my PhD\n\n\n UID:117 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170330T140000 DTEND;TZID=Europe/London:20170330T150000 LOCATION:LT1310 SUMMARY:Cubical adventures in Connecticut DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Cubical adventures in Connecticut\n\nI'll report on my attempts to design a cubical type theory together with Dan Licata and Ed Morehouse during my visit to Wesleyan University\, Middletown\, Connecticut. We had something which seemed quite promising\, but that falls apart just short of the finish line\; I'll tell you about it in the hope of miraculous rescue from the audience. However\, I'll start from basics so that everyone has a chance to join in in the fun. Mentions of Donald Trump will be kept to a minimum.\n UID:116 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170323T140000 DTEND;TZID=Europe/London:20170323T150000 LOCATION:LT1310 SUMMARY:Blockchain discussion DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Blockchain discussion\n\n\n UID:115 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170316T140000 DTEND;TZID=Europe/London:20170316T150000 LOCATION:LT1310 SUMMARY:MSP 101: Operational and Denotational Semantics for PCF DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: MSP 101: Operational and Denotational Semantics for PCF\n\nPCF is the prototypical functional programming language\, with two data types (naturals and booleans)\, lambda-abstraction and recursion. PCF was introduced by Gordon Plotkin in his seminal "LCF Considered as a Programming Language" paper from 1977. Despite PCF's simplicity\, its semantics is theoretically interesting. I will introduce PCF\, its operational semantics\, the "standard" domain-theoretic denotational semantics and show that the two agree on closed programs. Finally\, I will discuss observational equivalence for PCF and show that the denotational semantics fails to be "fully abstract".\n UID:114 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170309T140000 DTEND;TZID=Europe/London:20170309T150000 LOCATION:LT1310 SUMMARY:MSP 101: Indexed Containers/Interaction Structures DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: MSP 101: Indexed Containers/Interaction Structures\n\n\n UID:113 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170302T140000 DTEND;TZID=Europe/London:20170302T150000 LOCATION:LT1310 SUMMARY:MSP 101: Separation Logic and Hoare Logic DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: MSP 101: Separation Logic and Hoare Logic\n\nHoare Logic is a logic for proving properties of programs of the form: if the initial state satisfies a precondition\, then the final state satisfies a postcondition. Hoare logic proofs are structured around the structure of the program itself\, making the system a compositional one for reasoning about pieces of programs. I'll introduce Hoare Logic for a little imperative language with WHILE loops. I'll then motivate Separation Logic\, which enriches Hoare Logic with a Frame Rule for local reasoning. \n UID:112 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170223T140000 DTEND;TZID=Europe/London:20170223T150000 LOCATION:LT1415 SUMMARY:MSP 101: Blockchain DESCRIPTION:Speaker: James Chapman (MSP)\nTitle: MSP 101: Blockchain\n\nI will try to follow on from yesterday's introduction by getting to nitty gritty of bitcoin/blockchain. I won't assume attendance of the seminar but will try not to repeat it!\n UID:111 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170216T140000 DTEND;TZID=Europe/London:20170216T150000 LOCATION:LT1310 SUMMARY:MSP 101: Automata on infinite words DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: MSP 101: Automata on infinite words\n\nIn this 101 I plan to discuss omega-automata\, i.e.\, finite automata that operate on infinite words/streams. These automata form an important tool for the specification and verification of the ongoing\, possibly infinite behaviour of a system. In my talk I will provide the standard definition(s) of omega-automata and highlight what makes omega-automata difficult from a coalgebraic perspective. Finally\, I am going to discuss the work by Ciancia & Venema that provides a first coalgebraic representation of a particular type of omega-automata\, so-called Muller automata.\n UID:110 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170209T140000 DTEND;TZID=Europe/London:20170209T150000 LOCATION:LT1310 SUMMARY:MSP 101: Automata learning DESCRIPTION:Speaker: Simone Barlocco (MSP)\nTitle: MSP 101: Automata learning\n\nAutomata learning is a well known technique to infer a finite state machine from a set of observations. One important algorithm for automata learning is the L* algorithm by Dana Angluin. In this 101\, I will explain how the L* algorithm works via an example. Afterwards\, I will discuss the ingredients of the algorithm both in the standard framework by Angluin and in a recently developed categorical/coalgebraic framework by Jacobs & Silva. Lastly\, I plan to outline the proof of the minimality of the automaton that is built by the learning algorithm.\n UID:109 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170202T140000 DTEND;TZID=Europe/London:20170202T150000 LOCATION:LT1310 SUMMARY:MSP 101: First-order logic DESCRIPTION:Speaker: Johannes Marti (MSP)\nTitle: MSP 101: First-order logic\n\nIn this 101 I outline the syntax and semantics of classical first order predicate logic. I try to also mention some of the characteristic properties of first order logic such as compactness\, the Löwenheim-Skolem theorem or locality properties in finite model theory.\n UID:108 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170126T140000 DTEND;TZID=Europe/London:20170126T150000 LOCATION:LT1310 SUMMARY:La Vie Parisienne: POPL trip report DESCRIPTION:Speaker: Conor McBride\, James Chapman\, and Bob Atkey (MSP)\nTitle: La Vie Parisienne: POPL trip report\n\n Our POPL attendees will tell us about their favourite talks\, the latest research gossip and show us their most scenic photos from POPL in Paris.\n UID:107 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170119T140000 DTEND;TZID=Europe/London:20170119T150000 LOCATION:LT1310 SUMMARY:MSP 101: Automata and games for fixpoint logics DESCRIPTION:Speaker: Johannes Marti (MSP)\nTitle: MSP 101: Automata and games for fixpoint logics\n\nI explain how we can use automata and games to understand the behaviour of modal fixpoint logics.\n UID:106 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20170112T114000 DTEND;TZID=Europe/London:20170112T124000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning session DESCRIPTION: UID:105 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161214T160000 DTEND;TZID=Europe/London:20161214T170000 LOCATION:LT1415 SUMMARY:Departmental seminar: Do be do be do DESCRIPTION:Speaker: Sam Lindley (Edinburgh)\nTitle: Do be do be do\n\nWe explore the design and implementation of Frank\, a strict functional programming language with a bidirectional effect type system designed from the ground up around a novel variant of Plotkin and Pretnar's effect handler abstraction.\n\nEffect handlers provide an abstraction for modular effectful programming: a handler acts as an interpreter for a collection of commands whose interfaces are statically tracked by the type system. However\, Frank eliminates the need for an additional effect handling construct by generalising the basic mechanism of functional abstraction itself. A function is simply the special case of a Frank /operator/ that interprets no commands.\n\nMoreover\, Frank's operators can be /multihandlers/ which simultaneously interpret commands from several sources at once\, without disturbing the direct style of functional programming with values.\n\nEffect typing in Frank employs a novel form of effect polymorphism which avoid mentioning effect variables in source code. This is achieved by propagating an /ambient ability/ inwards\, rather than accumulating unions of potential effects outwards.\n\nI'll give a tour of Frank through a selection of concrete examples.\n\n(Joint work with Conor McBride and Craig McLaughlin) \n UID:104 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161130T120000 DTEND;TZID=Europe/London:20161130T170000 LOCATION:Strathclyde SUMMARY:Event: CLAP DESCRIPTION: UID:103 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161102T140000 DTEND;TZID=Europe/London:20161102T150000 LOCATION:LT1415 SUMMARY:An introduction to many-valued logics and effect algebras DESCRIPTION:Speaker: Phil Scott (University of Ottawa)\nTitle: An introduction to many-valued logics and effect algebras\n\nThe algebras of many-valued Lukasiewicz logics (MV algebras) as well as the theory of quantum measurement (Effect algebras) have undergone considerable development in the 1980s and 1990s\; they now constitute important research fields\, with connections to several contemporary areas of mathematics\, logic\, and theoretical computer science.\n\nBoth subjects have recently attracted considerable interest among groups of researchers in categorical logic and foundations of quantum computing. I will give a leisurely introduction to MV algebras (and their associated logics)\, as well as the more general world of effect algebras. If time permits\, we will also illustrate some new results (with Mark Lawson\, Heriot-Watt) on coordinatization of some concrete MV-algebras using inverse semigroup theory.\n UID:102 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161109T120000 DTEND;TZID=Europe/London:20161109T170000 LOCATION:Room 301\, McCance building\, Strathclyde SUMMARY:Event: SPLS DESCRIPTION: UID:101 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160928T150000 DTEND;TZID=Europe/London:20160928T160000 LOCATION:LT1310 SUMMARY:Towards a Generic Treatment of Syntaxes with Binding DESCRIPTION:Speaker: Guillaume Allais (Radboud University Nijmegen)\nTitle: Towards a Generic Treatment of Syntaxes with Binding\n\nThe techniques used by the generic programming community have taught us that we can greatly benefit from exposing the common internal structure of a family of objects. One can for instance derive once and for all a wealth of iterators from an abstract characterisation of recursive datatypes as fixpoints of functors.\n\nOur previous work on type and scope preserving semantics and their properties has made us realise that numerous semantics of the lambda calculus can be presented as instances of the fundamental lemma associated to an abstract notion of 'Model'. This made it possible to avoid code duplication as well as prove these semantics' properties generically.\n\nPutting these two ideas together\, we give an abstract description of syntaxes with binding making both their recursive and scoping structure explicit. The fundamental lemma associated to these syntaxes can be instantiated to provide the user with proofs that its language is stable under renaming and substitution as well as provide a way to easily define various evaluators.\n UID:100 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160915T150000 DTEND;TZID=Europe/London:20160915T160000 LOCATION:LT1310 SUMMARY:Morphisms of open games DESCRIPTION:Speaker: Jules Hedges (Oxford)\nTitle: Morphisms of open games\n\n\n UID:99 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161214T110000 DTEND;TZID=Europe/London:20161214T120000 LOCATION:LT1310 SUMMARY:Compositional Game Theory DESCRIPTION:Speaker: Alasdair Lambert (MSP)\nTitle: Compositional Game Theory\n\nI will be discussing composition in a model of economic game theory and methods for representing the impact of choice on subsequent games. Time permitting I will also work through some games using this model.\n UID:98 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161207T110000 DTEND;TZID=Europe/London:20161207T120000 LOCATION:LT1310 SUMMARY:Nominal filters and semantics of predicate logic DESCRIPTION:Speaker: Jamie Gabbay (Heriot-Watt)\nTitle: Nominal filters and semantics of predicate logic\n\nA /filter/ P is a consistent deductively closed set of predicates. A filter is /prime/ when\n (phi or psi) in P => (phi in P or psi in P) \nIn words: if phi-or-psi is in P then phi is in P or psi is in P. Primeness gives soundness for disjunction.\n\nUsing this it is not hard to construct a semantics to propositional logic in which a predicate phi "means" the set of prime filters containing it. This is a standard "trick" for building semantics and is an extremely useful proof-method.\n\nI have developed a semantics for predicate logic and also for the lambda-calculus based on similar notions of filter\, but in a /nominal/ context -- meaning that filters are developed using Fraenkel-Mostowski (FM) set theory instead of Zermelo-Fraenkel (ZF) set theory. What matters here is that FM sets have additional name structure over ZF sets\, and this additional structure can be exploited to give semantics to the extra structure that predicates have over propositions\, and in particular the additional name structure lets us write down primeness conditions for soundness for universal quantification.\n\nThe resulting semantics is rich and interesting. In a sentence: nominal techniques help us to extend the notion of Stone representation and duality from propositional logic to full first-order logic (also with equality\, if we wish\, and also to other logics and calculi with variables and quantifiers).\n\nI will give a detailed description of the filter-style conditions involved\, and discuss some of what I think they tell us about predicates and quantification in logic and computation. More information can also be found in two papers here:\nhttp://www.gabbay.org.uk/papers.html#semooc\nhttp://www.gabbay.org .uk/papers.html#repdul\n UID:97 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161123T110000 DTEND;TZID=Europe/London:20161123T120000 LOCATION:LT1310 SUMMARY:Some model theory for the modal mu-calculus DESCRIPTION:Speaker: Yde Venema (ILLC\, Amsterdam)\nTitle: Some model theory for the modal mu-calculus\n\nWe discuss a number of semantic properties pertaining to formulas of the modal mu-calculus. For each of these properties we provide a corresponding syntactic fragment\, in the sense that a mu-calculus formula \\phi has the given property iff it is equivalent to a formula \\phi' in the corresponding fragment. Since this formula \\phi' will always be effectively obtainable from \\phi\, as a corollary\, for each of the properties under discussion\, we prove that it is decidable in elementary time whether a given mu-calculus formula has the property or not.\n\nThe properties that we study have in common that they all concern the dependency of the truth of the formula at stake\, on a single proposition letter p. In each case the semantic condition on \\phi will be that \\phi\, if true at a certain state in a certain model\, will remain true if we restrict the set of states where p holds\, to a special subset of the state space. Important examples include the properties of complete additivity and (Scott) continuity\, where the special subsets are the singletons and the finite sets\, respectively.\n\nOur proofs for these characterisation results will be automata-theoretic in nature\; we will see that the effectively defined maps on formulas are in fact induced by rather simple transformations on modal automata.\n UID:96 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161116T110000 DTEND;TZID=Europe/London:20161116T120000 LOCATION:LT1310 SUMMARY:MSP 101: Modal logic DESCRIPTION:Speaker: Johannes Marti (MSP)\nTitle: MSP 101: Modal logic\n\nModal logic provides a simple\, yet surprisingly powerful\, language for specifying properties of coalgebras. In this talk I introduce the basic modal logic that is interpreted on relational structures. My aim is to provide an idea how modal logic relates to other logics\, such as first-order and intuitionistic logic\, and to the duality between algebraic and coalgebraic structures.\n\nIf time permits\, I might also give a very informal warm-up for the modal mu-calculus which is the topic of next week's talk.\n UID:95 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161109T103000 DTEND;TZID=Europe/London:20161109T113000 LOCATION:LT1310 SUMMARY:MSP 101: Meta-theory of lambda-calculi DESCRIPTION:Speaker: Stuart Gale (MSP)\nTitle: MSP 101: Meta-theory of lambda-calculi\n\nI'll give a standard overview of Simply Typed Lambda Calculus (STLC) (syntax\, typing and computation rules) in a well-typed setting\, and then modify it to show STLC in a bidirectional setting.\n\nAfterwards I'll show Strong Confluence (Church-Rosser theorem) in the bidirectional setting.\n UID:94 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161102T110000 DTEND;TZID=Europe/London:20161102T120000 LOCATION:LT1310 SUMMARY:System F and proof-relevant parametricity DESCRIPTION:Speaker: Ben Price (MSP)\nTitle: System F and proof-relevant parametricity\n\nI shall give a brief introduction to System F.\nI will then explain how to capture our intuition about polymorphic functions behaving uniformly by relational parametricity\, and talk about ongoing work to find a notion of proof-relevant parametricity.\n UID:93 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161026T110000 DTEND;TZID=Europe/London:20161026T120000 LOCATION:LT1310 SUMMARY:MSP 101: Data types and initial-algebra semantics DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: MSP 101: Data types and initial-algebra semantics\n\nI will give a basic introduction to data types and initial-algebra semantics. The meaning of a data type is given as the initial object in a category of types with the corresponding constructors. Initiality immediately allows the modelling of a non-dependent recursion principle. I'll show how this can be upgraded to full dependent elimination\, also known as induction\, by using the uniqueness of the mediating arrow\; in fact\, induction is equivalent to recursion plus uniqueness. All possibly unfamiliar terms in this abstract will also be explained.\n UID:92 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161019T110000 DTEND;TZID=Europe/London:20161019T120000 LOCATION:LT1310 SUMMARY:MSP 101: A first introduction to coalgebra DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: MSP 101: A first introduction to coalgebra\n\nThe core subject of Computer Science is "generated behaviour" (quiz: who said this?). Coalgebra provides the categorical formalisation of generated behaviour. I am planning to provide a first\, very basic introduction to coalgebra. This will consist of two parts: i) coinduction & corecursion as means to define & reason about the (possibly) infinite behaviour of things\; ii)modal logics for coalgebras.\n UID:91 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161012T110000 DTEND;TZID=Europe/London:20161012T120000 LOCATION:LT1310 SUMMARY:MSP 101: Category Theory DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: MSP 101: Category Theory\n\n\n UID:90 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20161005T110000 DTEND;TZID=Europe/London:20161005T120000 LOCATION:LT1310 SUMMARY:MSP 101: Rewriting\, and operads DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: MSP 101: Rewriting\, and operads\n\n\n UID:89 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160928T110000 DTEND;TZID=Europe/London:20160928T120000 LOCATION:LT1310 SUMMARY:ICFP trip report DESCRIPTION:Speaker: James Chapman (MSP)\nTitle: ICFP trip report\n\n\n UID:88 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160921T110000 DTEND;TZID=Europe/London:20160921T120000 LOCATION:LT1310 SUMMARY:Eventual image functors DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Eventual image functors\n\nFor a category C we consider the endomorphism category End(C) and the subcategory of automorphisms Aut(C) -> End(C). It has been observed that for C the category of finite sets\, finite dimensional vector spaces\, or compact metric spaces this inclusion functor admits a simultaneous left and right adjoint.\n\nWe give general criteria for the existence of such adjunctions for a broad class of categories which includes FinSet\, FinVect and CompMet as special cases. This is done using the language of factorisation systems and by introducing a notion of eventual image functors which provide a general method for constructing adjunctions of this kind.\n UID:87 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160914T114000 DTEND;TZID=Europe/London:20160914T124000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning session DESCRIPTION: UID:86 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160824T160000 DTEND;TZID=Europe/London:20160824T170000 LOCATION:LT1415 SUMMARY:Information Effects for Understanding Type Systems DESCRIPTION:Speaker: Philippa Cowderoy \nTitle: Information Effects for Understanding Type Systems\n\nOr: how someone else found the maths to justify my dogma\n UID:85 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160701T140000 DTEND;TZID=Europe/London:20160701T150000 LOCATION:LT1415 SUMMARY:A New Perspective On Observables in the Category of Relations DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: A New Perspective On Observables in the Category of Relations\n\nPractice talk for Quantum Interactions.\n UID:84 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160701T140000 DTEND;TZID=Europe/London:20160701T150000 LOCATION:LT1415 SUMMARY:Interacting Frobenius Algebras are Hopf DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Interacting Frobenius Algebras are Hopf\n\nPractice talk for LICS.\n\nTheories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming\, control theory\, and quantum computing\, among others. Bonchi\, Sobocinski\, and Zanasi have shown that\, given a suitable distribution law\, a pair of Hopf algebras forms two Frobenius algebras. Coming from the perspective of quantum theory\, we take the opposite approach\, and show that interacting Frobenius algebras form Hopf algebras. We generalise \\cite{Bonchi2014a} by including non-trivial dynamics of the underlying object -- the so-called phase group -- and investigate the effects of finite dimensionality of the underlying model\, and recover the system of Bonchi et al as a subtheory in the prime power dimensional case. We show that the presence of a non-trivial phase group means that the theory cannot be formalised as a distributive law.\n UID:83 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160606T090000 DTEND;TZID=Europe/London:20160606T170000 LOCATION:McCance building\, Strathclyde SUMMARY:Event: Quantum Physics and Logic 2016 DESCRIPTION: UID:82 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160601T120000 DTEND;TZID=Europe/London:20160601T130000 LOCATION:LT1310 SUMMARY:Interacting Frobenius algebras DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Interacting Frobenius algebras\n\nPractice talk for QPL.\n\nTheories featuring the interaction between a Frobenius algebra and a Hopf algebra have recently appeared in several areas in computer science: concurrent programming\, control theory\, and quantum computing\, among others. Bonchi\, Sobocinski\, and Zanasi (2014) have shown that\, given a suitable distributive law\, a pair of Hopf algebras forms two Frobenius algebras. Here we take the opposite approach\, and show that interacting Frobenius algebras form Hopf algebras. We generalise (BSZ 2014) by including non-trivial dynamics of the underlying object -- the so-called phase group -- and investigate the effects of finite dimensionality of the underlying model. We recover the system of Bonchi et al as a subtheory in the prime power dimensional case\, but the more general theory does not arise from a distributive law.\n UID:81 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160504T110000 DTEND;TZID=Europe/London:20160504T120000 LOCATION:LT1310 SUMMARY:Factorisation Systems and Algebra DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Factorisation Systems and Algebra\n\nI'll show how to generalise some results from algebra (think groups\, rings\, R-modules etc.) to a categorical setting using factorisation systems and an appropriate notion of finiteness on the objects of a category.\n UID:80 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160427T110000 DTEND;TZID=Europe/London:20160427T120000 LOCATION:LT1310 SUMMARY:Typing with Leftovers DESCRIPTION:Speaker: Guillaume Allais (Radboud University Nijmegen)\nTitle: Typing with Leftovers\n\n\n UID:79 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160419T160000 DTEND;TZID=Europe/London:20160419T170000 LOCATION:LT1415 SUMMARY:Departmental seminar: Formal languages\, coinductively formalized DESCRIPTION:Speaker: Andreas Abel (Chalmers and Gothenburg University)\nTitle: Formal languages\, coinductively formalized\n\nFormal languages and automata are taught to every computer science student. However\, the student will most likely not see the beautiful coalgebraic foundations.\n\nIn this talk\, I recapitulate how infinite trees can represent formal languages (sets of strings). I explain Agda's coinduction mechanism based on copatterns and demonstrate that it allows an elegant representation of the usual language constructions like union\, concatenation\, and Kleene star\, with the help of Brzozowski derivatives. We will also investigate how to reason about equality of languages using bisimulation and coinductive proofs.\n UID:78 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160414T103000 DTEND;TZID=Europe/London:20160414T170000 LOCATION: School of Informatics\, Edinburgh SUMMARY:Event: Categories\, Logic\, and Physics\, Scotland DESCRIPTION: UID:77 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160331T103000 DTEND;TZID=Europe/London:20160331T113000 LOCATION:LT1415 SUMMARY:Presentations by candidates for the 'Coalgebraic Foundations of Semi-Structured Data' RA position DESCRIPTION:Speaker: \nTitle: Presentations by candidates for the 'Coalgebraic Foundations of Semi-Structured Data' RA position\n\n\n UID:76 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160323T160000 DTEND;TZID=Europe/London:20160323T170000 LOCATION:LT1415 SUMMARY:Departmental seminar: A static analyser for concurrent Java DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: A static analyser for concurrent Java\n\nThreadSafe is a static analysis tool for finding bugs in concurrent Java code that has been used by companies across the world to analyse and find bugs in large mission industrial applications. I will talk about how ThreadSafe works\, and our experiences in applying static analysis technology to the "real world".\n\nThreadSafe is available from http://www.contemplateltd.com/\n UID:75 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160525T153000 DTEND;TZID=Europe/London:20160525T163000 LOCATION:LT908 SUMMARY:Departmental seminar: A Compositional Approach to Game Theory DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: A Compositional Approach to Game Theory\n\nI will sketch an alternative approach to economic game theory based upon the computer science idea of compositionality: concretely we i) give a number of operators for building up complex and irregular games from smaller and simpler games\; and ii) show how the Nash equilibrium of these complex games can be defined recursively from their simpler components. We apply compositional reasoning to sophisticated games where agents must reason about how their actions affect future games and how those future games effect the utility they receive. This forces us into a second innovation -- we augment the usual lexicon of games with a dual notion to utility because\, in order for games to accept utility\, this utility must be generated by other games. Our third innovation is to represent our games as string diagrams so as to give a clear visual interface to manipulate them. Our fourth\, and final\, innovation is a categorical formalisation of these intuitive diagrams which ensures our reasoning about them is fully rigorous.\n\nThe talk will be general so as appeal to as wide an audience as possible. In particular\, no knowledge of category theory will be assumed!\n UID:74 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160317T110000 DTEND;TZID=Europe/London:20160317T120000 LOCATION:LT1310 SUMMARY:On the rule algebraic reformulation of graph rewriting DESCRIPTION:Speaker: Nicolas Behr (Edinburgh)\nTitle: On the rule algebraic reformulation of graph rewriting\n\nMotivated by the desire to understand the combinatorics of graph rewriting systems\, it proved necessary to invent a formulation of graph rewriting itself that is not based on category theoretic structures as in the traditional framework\, but on the concept of diagrammatic combinatorial Hopf algebras and reductions thereof. In this talk\, I will present how the classical example of the Heisenberg-Weyl algebra of creation and annihilation of indistinguishable particles\, which can alternatively be interpreted as the algebra of discrete graph rewriting\, gave the initial clues for this novel framework. In hindsight\, to pass from the special case of discrete graph rewriting to the case of general graph rewriting required every aspect of the framework of diagrammatic combinatorial Hopf algebras as a guideline for the construction\, yet none of the traditional category theoretic ideas\, whence one might indeed consider this reformulation as an independent formulation of graph rewriting.\n\nThe new framework results in a number of surprising results even directly from the formulation itself: besides the two main variants of graph rewriting known in the literature (DPO and SPO rewriting)\, there exist two more natural variants in the new framework. For all four variants\, graph rewriting rules are encoded in so-called rule diagrams\, with their composition captured in the form of diagrammatic compositions followed by one of four variants of reduction operations. Besides the general structure theory of the resulting algebras aka the rule algebras\, one of the most important results to date of this framework in view of applications is the possibility to formulate stochastic graph rewriting systems in terms of the canonical representations of the rule algebras. Notably\, this is closely analogous to the formulation of chemical reaction systems in terms of the canonical representation of the Heisenberg-Weyl algebra aka the bosonic Fock space. The presentation will not assume any prior knowledge of the audience on the particular mathematics required for this construction\, and will be given on the whiteboard. The work presented is the result of a collaboration with Vincent Danos and Ilias Garnier (ENS Paris/LFCS University of Edinburgh)\, and (in an earlier phase) with Tobias Heindel (University of Copenhagen).\n UID:73 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160303T110000 DTEND;TZID=Europe/London:20160303T120000 LOCATION:LT1310 SUMMARY:Comprehensive Parametric Polymorphism DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Comprehensive Parametric Polymorphism\n\nIn this talk\, we explore the fundamental category-theoretic structure needed to model relational parametricity (i.e.\, the fact that polymorphic programs preserve all relations) for the polymorphic lambda calculus (a.k.a. System F). Taken separately\, the notions of categorical model of impredicative polymorphism and relational parametricity are well-known (lambda2-fibrations and reflexive graph categories\, respectively). Perhaps surprisingly\, simply combining these two structures results in a notion that only enjoys the expected properties in case the underlying category is well-pointed. This rules out many categories of interest (e.g. functor categories) in the semantics of programming languages.\n\nTo circumvent this restriction\, we modify the definition of fibrational model of impredicative polymorphism by adding one further ingredient to the structure: comprehension in the sense of Lawvere. Our main result is that such comprehensive models\, once further endowed with reflexive-graph-category structure\, enjoy the expected consequences of parametricity. This is proved using a type-theoretic presentation of the category-theoretic structure\, within which the desired consequences of parametricity are derived. Working in this type theory requires new techniques\, since equality relations are not available\, so that standard arguments that exploit equality need to be reworked.\n\nThis is joint work with Neil Ghani and Alex Simpson\, and a dry run for a talk in Cambridge the week after.\n UID:72 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160126T150000 DTEND;TZID=Europe/London:20160126T160000 LOCATION:LT1310 SUMMARY:Rewriting modulo symmetric monoidal structure DESCRIPTION:Speaker: Aleks Kissinger (Nijmegen)\nTitle: Rewriting modulo symmetric monoidal structure\n\nString diagrams give a powerful graphical syntax for morphisms in symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.\n\nAn important role in many such approaches is played by equational theories of diagrams\, which can be oriented and used as rewrite systems. In this talk\, I'll lay the foundations for this form of rewriting by interpreting diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs\, subject to a soundness condition called convexity\, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.\n\nIf there's time\, I'll also discuss some of the results we have in developing the rewrite theory of hypergraphs for SMCs\, namely termination proofs via graph metrics and strongly convex critical pair analysis.\n UID:71 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160126T103000 DTEND;TZID=Europe/London:20160126T113000 LOCATION:LT1310 SUMMARY:Enriched Lawvere Theories DESCRIPTION:Speaker: John Power (Bath)\nTitle: Enriched Lawvere Theories\n\nIn this talk\, we consider extending Lawvere theories to allow enrichment in a base category such as CMonoid\, Poset or Cat. In doing so\, we see that we need to alter the formulation in a fundamental way\, using the notion of cotensor\, a kind of limit that is hidden in the usual accounts of ordinary category theory but is fundamental to enriched category theory. If time permits\, we will briefly consider the specific issues that arise when one has two-dimensional structure in the enriching category\, as exemplified by Poset and Cat.\n UID:70 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160125T103000 DTEND;TZID=Europe/London:20160125T113000 LOCATION:LT1310 SUMMARY:Lawvere Theories DESCRIPTION:Speaker: John Power (Bath)\nTitle: Lawvere Theories\n\nIn 1963\, Bill Lawvere characterised universal algebra in category theoretic terms. His formulation being category theoretic was not its central contribution: more fundamental was its presentation independence. Three years later\, monads were proposed as another category theoretic formulation of universal algebra. Overall\, the former are technically better but the relationship is particularly fruitful and the latter are more prominent\, cf Betamax vs VHS. So we study Lawvere theories carefully in the setting of universal algebra and in relation to monads.\n UID:69 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160225T110000 DTEND;TZID=Europe/London:20160225T120000 LOCATION:LT1310 SUMMARY:Excuse My Extrusion DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Excuse My Extrusion\n\nI have recently begun to learn about the Cubical Type Theory of Coquand et al.\, as an effective computational basis for Voevodsky's Univalent Foundations\, inspired by a model of type theory in cubical sets. It is in some ways compelling in its simplicity\, but in other ways intimidating in its complexity. In order to get to grips with it\, I have begun to develop my own much less subtle variation on the theme. If I am lucky\, I shall get away with it. If I am unlucky\, I shall have learned more about why Cubical Type Theory has to be as subtle as it is.\n\nMy design separates Coquand's all-powerful "compose" operator into smaller pieces\, dedicated to more specific tasks\, such as transitivity of paths. Each type path Q : S = T\, induces a notion of value path s {Q} t\, where either s : S\, or s is •\, "blob"\, and similarly\, t : T or t = •. A "blob" at one end indicates that the value at that end of the path is not mandated by the type. This liberalisation in the formation of "equality" types allows us to specify the key computational use of paths between types\, extrusion:\n\nif Q : S = T and s : S\, then s ⌢• Q : s {Q} •\n\nThat is\, whenever we have a value s at one end of a type path Q : S = T\, we can extrude that value across the type path\, getting a value path which is s at the S end\, but whose value at the T end is not specified in advance of explaining how to compute it. Extrusion gives us a notion of coercion-by-equality which is coherent by construction. It is defined by recursion on the structure of type paths. Univalence can be added to the system by allowing the formation of types interpolating two equivalent types\, with extrusion demanding the existence of the corresponding interpolant values\, computed on demand by means of the equivalence.\n\nSo far\, there are disconcerting grounds for optimism\, but the whole of the picture has not yet emerged: I may just have pushed the essential complexity into one corner\, or the whole thing may be holed below the waterline. But if it does turn out to be nonsense\, it will be nonsense for an interesting reason.\n UID:68 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160218T140000 DTEND;TZID=Europe/London:20160218T150000 LOCATION:LT1310 SUMMARY:Coalgebraic Dynamic Logics DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Coalgebraic Dynamic Logics\n\nI will present work in progress on a (co)algebraic framework that allows to uniformly study dynamic modal logics such as Propositional Dynamic Logic (PDL) and Game Logic (GL). Underlying our framework is the basic observation that the program/game constructs of PDL/GL arise from monad structure\, and that the axioms of these logics correspond to compatibility requirements between the modalities and this monad structure. So far we have a general soundness and completeness result for PDL-like logics wrt T-coalgebras for a monad T. I will discuss our completeness theorem\, its limitations and plans for extending our results. [For the latter we might require the help of koalas\, wallabies and wombats.]\n UID:67 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160211T110000 DTEND;TZID=Europe/London:20160211T120000 LOCATION:LT1310 SUMMARY:Introduction to (infinity\, 1)-categories DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Introduction to (infinity\, 1)-categories\n\nInfinity-categories simultaneously generalise topological spaces and categories. Intuitively\, a (weak) infinity-category should have objects\, morphisms\, 2-morphisms\, 3-morphisms\, ... and identity morphisms and composition which is suitably unital and associative up to a higher (invertible) morphism (the number 1 in (infinity\, 1)-category means that k-morphisms for k > 1 are invertible) . The trouble begins when one naively tries to make these coherence conditions precise\; already 4-categories famously requires 51 pages to define explicitly (http://math.ucr.edu/home/baez/trimble/tetracategories.html). Instead\, one typically turns to certain "models" of infinity-categories that encode all this data implicitly\, usually as some kind of simplicial object with additional properties. I will introduce two such models: quasicategories and complete Segal spaces. If time allows\, I will also discuss hopes and dreams about internalising these notions in Type Theory\, which should give a satisfactory treatment of category theory in Type Theory without assuming Uniqueness of Identity Proofs.\n UID:66 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160204T110000 DTEND;TZID=Europe/London:20160204T120000 LOCATION:LT1310 SUMMARY:Two Constructions on Games DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: Two Constructions on Games\n\nI've been working with Jules Hedges on a compositional model of game theory. After briefly reminding you of the model\, I'll discuss where we are at -- namely the definition of morphisms between games\, and the treatment of choice and iteration of games. I'm hoping you will be able to shed some light on this murky area. There is a draft paper if anyone is interested.\n UID:65 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160128T110000 DTEND;TZID=Europe/London:20160128T120000 LOCATION:LT1310 SUMMARY:Introduction to sheaves DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Introduction to sheaves\n\n\n UID:64 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160121T110000 DTEND;TZID=Europe/London:20160121T120000 LOCATION:LT1310 SUMMARY:Overview: A Type Theory for Probabilistic and Bayesian Reasoning DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Overview: A Type Theory for Probabilistic and Bayesian Reasoning\n\nThe probabilistic calculus introduced in the eponymous paper by Robin Adams and Bart Jacobs is inspired by quantum theory by considering that conditional probabilities can be seen as side-effect-free measurements. A type-theoretic treatment of this semantic observation leads\, once equipped with suitable computation rules\, to the ability to do exact conditional inference.\n\nI will present the type theory and the accompanying computation rules proposed in the paper and discuss some of the interesting open questions I will be working on in the near future. \n UID:63 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20160113T134000 DTEND;TZID=Europe/London:20160113T144000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning session DESCRIPTION: UID:62 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151202T110000 DTEND;TZID=Europe/London:20151202T120000 LOCATION:LT1310 SUMMARY:Introduction to coherence spaces\, and how to use them for dependent session types DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: Introduction to coherence spaces\, and how to use them for dependent session types\n\nCoherence spaces are a simplification of Scott domains\, introduced by Girard to give a semantics to the polymorphic lambda-calculus. While investigating the structure of coherence spaces\, Girard noticed that the denotation of the function type in coherence spaces can be decomposed into two independent constructions: a linear ("use-once") function space\, and a many-uses-into-one-use modality. And so Linear Logic was discovered.\n\nCoherence spaces are interesting because they model computation at a low level in terms of interchange of atomic 'tokens' of information. This makes them a useful tool for understanding several different computational phenomena.\n\nIn this talk\, I'll show how coherence spaces naturally model session types\, via Wadler's interpretation of Classical Linear Logic as a session-typed pi-calculus\, and how that interpretation extends to an interpretation of a dependently typed version of session types.\n UID:61 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151118T110000 DTEND;TZID=Europe/London:20151118T120000 LOCATION:LT1310 SUMMARY:The categorical structure of von Neumann algebras DESCRIPTION:Speaker: Bram Westerbaan (Nijmegen)\nTitle: The categorical structure of von Neumann algebras\n\nI would like to speak about the categorical structure of the category of von Neumann algebras\, with as morphisms normal\, completely positive\, unital linear maps. For some years my colleagues and I have worked on identifying basic structures in this category\, and while surprisingly many things do not exist or do not work in this category (it's not a topos or even an extensive category\, there's no epi-mono factorisation system\, there is no dagger\, colimits -- if they exist at all -- are horrendous...)\, we did find some structure (the products behave reasonable in some sense\, there is a 'quotient'\, and 'comprehension'\, and we have a universal property for the minimal Stinespring dilation\, and a universal property for M_2--the qubit). There is no deep category theory involved by any standards\, and I promise I will spare you the functional analysis\, so it should be a light talk.\n UID:60 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151111T110000 DTEND;TZID=Europe/London:20151111T120000 LOCATION:LT1310 SUMMARY:The Power of Coalitions DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: The Power of Coalitions\n\nDue to popular demand I am going to give a brief introduction to Marc Pauly's Coalition Logic\, a propositional modal logic that allows to reason about the power of coalitions in strategic games. I will provide motivation and basic definitions. Furthermore I am planning to discuss how the logic can be naturally viewed as a coalgebraic logic and what we gain from the coalgebraic perspective. Finally -- if (preparation) time permits -- I am going to say how the logic can be applied to the area of mechanism design.\n UID:59 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151022T150000 DTEND;TZID=Europe/London:20151022T160000 LOCATION:LT1415 SUMMARY:Semantics for Social Systems where Theory about the System Changes the System DESCRIPTION:Speaker: Viktor Winschel (ETH Zurich)\nTitle: Semantics for Social Systems where Theory about the System Changes the System\n\nIn societies the notion of a law is not given by nature. Instead social dynamics are driven by the theories the citizens have about the dynamics of the social system. Obviously self-referential mathematical structures\, developed in computer science\, are candidates to be applied in social sciences for this foundational issue. We will see a prototypical game theoretical problem where several computer scientific tools can help to discuss these structures. It is a long standing problem in economics and of human kind and their scarce recourses: "should we go to a bar that is always so overcrowded"?\n UID:58 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151006T150000 DTEND;TZID=Europe/London:20151006T160000 LOCATION:LT1415 SUMMARY:Proof-theoretic semantics for dynamic logics DESCRIPTION:Speaker: Alessandra Palmigiano (TU Delft)\nTitle: Proof-theoretic semantics for dynamic logics\n\nResearch in the proof theory of dynamic logics has recently gained momentum. However\, features which are essential to these logics prevent standard proof-theoretic methodologies to apply straightforwardly. In this talk\, I will discuss the main properties proof systems should enjoy in order to serve as suitable environments for an inferential theory of meaning (proof-theoretic semantics). Then\, I'll identify the main challenges to the inferential semantics research agenda posed by the very features of dynamic logics which make them so appealing and useful to applications. Finally\, I'll illustrate a methodology generating multi-type display calculi\, which has been successful on interesting case studies (dynamic epistemic logic\, propositional dynamic logic\, monotone modal logic).\n\nReferences\n\n1. S. Frittella\, G. Greco\, A. Kurz\, A. Palmigiano\, V. Sikimić\, A Proof-Theoretic Semantic Analysis of Dynamic Epistemic Logic\, Journal of Logic and Computation\, Special issue on Substructural logic and information dynamics (2014)\, DOI:10.1093/logcom/exu063.\n\n2. S. Frittella\, G. Greco\, A. Kurz\, A. Palmigiano\, V. Sikimić\, Multi-type Display Calculus for Dynamic Epistemic Logic\, Journal of Logic and Computation\, Special issue on Substructural logic and information dynamics (2014)\, DOI:10.1093/logcom/exu068.\n\n3. S. Frittella\, G. Greco\, A. Kurz\, A. Palmigiano\, Multi-type Display Calculus for Propositional Dynamic Logic\, Special issue on Substructural logic and information dynamics (2014)\, DOI:10.1093/logcom/exu064.\n\n4. S. Frittella\, G. Greco\, A. Kurz\, A. Palmigiano\, V. Sikimić\, Multi-type Sequent Calculi\, Proc. Trends in Logic XIII\, A. Indrzejczak\, J. Kaczmarek\, M. Zawidski eds\, p 81-93\, 2014.\n\n5. G. Greco\, A. Kurz\, A. Palmigiano\, Dynamic Epistemic Logic Displayed\, Proc. Fourth International Workshop on Logic\, Rationality and Interaction (LORI 2013) Eds: Huaxin Huang\, Davide Grossi\, Olivier Roy eds\, 2013.\n UID:57 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150925T160000 DTEND;TZID=Europe/London:20150925T170000 LOCATION:LT1415 SUMMARY:Coinduction\, Equilibrium and Rationality of Escalation DESCRIPTION:Speaker: Pierre Lescanne (ENS Lyon)\nTitle: Coinduction\, Equilibrium and Rationality of Escalation\n\nEscalation is the behavior of players who play forever in the same game. Such a situation is a typical field for application of coinduction which is the tool conceived for reasoning in infinite mathematical structures. In particular\, we use coinduction to study formally the game called /dollar auction/\, which is considered as the paradigm of escalation. Unlike what is admitted since 1971\, we show that\, provided one assumes that the other agent will always stop\, bidding is rational\, because it results in a subgame perfect equilibrium. We show that this is not the only rational strategy profile (the only subgame perfect equilibrium). Indeed if an agent stops and will stop at every step\, whereas the other agent keeps bidding\, we claim that he is rational as well because this corresponds to another subgame perfect equilibrium. In the infinite dollar auction game the behavior in which both agents stop at each step is not a Nash equilibrium\, hence is not a subgame perfect equilibrium\, hence is not rational. Fortunately\, the notion of rationality based on coinduction fits with common sense and experience. Finally the possibility of a rational escalation in an arbitrary game can be expressed as a predicate on games and the rationality of escalation in the dollar auction game can be proved as a theorem which we have verified in the proof assistant COQ. In this talk we will recall the principles of infinite extensive games and use them to introduce coinduction and equilibria (Nash equilibrium\, subgame perfect equilibrium). We will show how one can prove that the two strategy profiles presented above are equilibria and how this leads to a "rational" escalation in the dollar auction. We will show that escalation may even happen in much simpler game named 0,1-game.\n UID:56 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151028T110000 DTEND;TZID=Europe/London:20151028T120000 LOCATION:LT1310 SUMMARY:Interacting Frobenius Algebras Are Hopf DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Interacting Frobenius Algebras Are Hopf\n\nCommutative Frobenius algebras play an important role in both Topological Quantum Field Theory and Categorical Quantum Mechanics\; in the first case they correspond to 2D TQFTs\, while in the second they are non-degenerate observables. I will consider the case of "special" Frobenius algebras\, and their associated group of phases. This gives rise to a free construction from the category of abelian groups to the PROP generated by this Frobenius algebra. Of course a theory with only one observable is not very interesting. I will consider how two such PROPs should be combined\, and show that if the two algebras (i) jointly form a bialgebra and (ii) their units are "mutually real"\; then they jointly form a Hopf algebra. This gives a "free" model of a pair of strongly complementary observables. I will also consider which unitary maps must exist in such models.\n\nSlides are here (http://personal.strath.ac.uk/ross.duncan/talks/2015/vienna.pdf) if you want a preview.\n UID:55 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151021T123000 DTEND;TZID=Europe/London:20151021T170000 LOCATION:Edinburgh SUMMARY:Event: SPLS DESCRIPTION: UID:54 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151014T110000 DTEND;TZID=Europe/London:20151014T120000 LOCATION:LT1310 SUMMARY:Type and Scope Preserving Semantics DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Type and Scope Preserving Semantics\n\nWe introduce a notion of type and scope preserving semantics generalising Goguen and McKinna's "Candidates for Substitution" approach to defining one traversal generic enough to be instantiated to renaming first and then substitution. Its careful distinction of environment and model values as well as its variation on a structure typical of a Kripke semantics make it capable of expressing renaming and substitution but also various forms of Normalisation by Evaluation as well as\, perhaps more surprisingly\, monadic computations such as a printing function.\n\nWe then demonstrate that expressing these algorithms in a common framework yields immediate benefits: we can deploy some logical relations generically over these instances and obtain for instance the fusion lemmas for renaming\, substitution and normalisation by evaluation as simple corollaries of the appropriate fundamental lemma. All of this work has been formalised in Agda.\n UID:53 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20151007T120000 DTEND;TZID=Europe/London:20151007T170000 LOCATION:Dundee SUMMARY:Event: STP DESCRIPTION: UID:52 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150930T110000 DTEND;TZID=Europe/London:20150930T120000 LOCATION:LT1310 SUMMARY:ICFP trip report DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: ICFP trip report\n\n\n UID:51 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150923T113000 DTEND;TZID=Europe/London:20150923T123000 LOCATION:LT1310 SUMMARY:Event: MSP101 Planning session DESCRIPTION: UID:50 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150916T110000 DTEND;TZID=Europe/London:20150916T120000 LOCATION:LT1310 SUMMARY:Contextuality\, path logic and a modal logic for Social Choice Theory DESCRIPTION:Speaker: Giovanni Ciná (Amsterdam)\nTitle: Contextuality\, path logic and a modal logic for Social Choice Theory\n\nSocial Choice functions are procedures used to aggregate the preferences of individuals into a collective decision. We outline two recent abstract approaches to SCFs: a recent sheaf treatment of Arrow's Theorem by Abramsky and a modal logic studied by Ulle Endriss and myself. We show how to relate the categorical modelling of Social Choice problems to said work in Modal Logic. This insight prompts a number of research questions\, from the relevance of sheaf-like condition to the modelling of properties of SCFs on varying electorates.\n UID:49 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150902T110000 DTEND;TZID=Europe/London:20150902T120000 LOCATION:LT1310 SUMMARY:Concurrent games DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Concurrent games\n\n\n UID:48 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150813T150000 DTEND;TZID=Europe/London:20150813T160000 LOCATION:LT1415 SUMMARY:The Polymorphic Blame Calculus and Parametricity DESCRIPTION:Speaker: Jeremy Siek (Indiana University)\nTitle: The Polymorphic Blame Calculus and Parametricity\n\nThe Polymorphic Blame Calculus (PBC) of Ahmed et al. (2011) combines polymorphism\, as in System F\, with type dynamic and runtime casts\, as in the Blame Calculus. The PBC is carefully designed to ensure relational parametricity\, that is\, to ensure that type abstractions do not reveal their abstracted types. The operational semantics of PBC uses runtime sealing and syntactic barriers to enforce parametricity. However\, it is an open question as to whether these mechanisms actually guarantee parametricity for the PBC. Furthermore\, there is some question regarding what parametricity means in the context of the PBC\, as we have examples that are morally parametric but not technically so. This talk will review the design of the PBC with respect to ensuring parametricity and hopefully start a discussion regarding what parametricity should mean for the PBC.\n UID:47 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150826T110000 DTEND;TZID=Europe/London:20150826T120000 LOCATION:LT1310 SUMMARY:Comonadic Cellular Automata II DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Comonadic Cellular Automata II\n\nThis is a sequel to my last 101 where I spoke about describing cellular automata as algebras of a comonad on Set. I'll describe how we can make sense of "generalised cellular automata" (probabilistic/non-deterministic/quantum\, for example) as comonads on other categories via distributive laws of monads and comonads.\n UID:46 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150723T110000 DTEND;TZID=Europe/London:20150723T120000 LOCATION:LT1310 SUMMARY:Free interacting observables DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Free interacting observables\n\n\n UID:45 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150526T160000 DTEND;TZID=Europe/London:20150526T170000 LOCATION:LT1415 SUMMARY:Final coalgebras from corecursive algebras DESCRIPTION:Speaker: Paul Levy (Birmingham)\nTitle: Final coalgebras from corecursive algebras\n\nWe give a technique to construct a final coalgebra out of modal logic. An element of the final coalgebra is a set of modal formulas. The technique works for both the finite and the countable powerset functors. Starting with a corecursive algebra\, we coinductively obtain a suitable subalgebra. We see - first with an example\, and then in the general setting of modal logic on a dual adjunction - that modal theories form a corecursive algebra\, so that this construction may be applied.\n\nWe generalize the framework to categories other than Set\, and look at examples in Poset and in the opposite category of Set.\n UID:44 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150513T110000 DTEND;TZID=Europe/London:20150513T120000 LOCATION:LT1310 SUMMARY:Two-dimensional proof-relevant parametricity DESCRIPTION:Speaker: Federico Orsanigo (MSP)\nTitle: Two-dimensional proof-relevant parametricity\n\nRelational parametricity is a fundamental concept within theoretical computer science and the foundations of programming languages\, introduced by John Reynolds. His fundamental insight was that types can be interpreted not just as functors on the category of sets\, but also as equality preserving functors on the category of relations. This gives rise to a model where polymorphic functions are uniform in a suitable sense\; this can be used to establish e.g. representation independence\, equivalences between programs\, or deriving useful theorems about programs from their type alone.\n\n The relations Reynolds considered were proof-irrelevant\, which from a type theoretic perspective is a little limited. As a result\, one might like to extend his work to deal with proof-relevant\, i.e. set-valued relations. However naive attempts to do this fail: the fundamental property of equality preservation cannot be established. Our insight is that just as one uses parametricity to restrict definable elements of a type\, one can use parametricity of proofs to ensure equality preservation. The idea of parametricity for proofs can be formalised using the idea of 2-dimensional logical relations. Interestingly\, these 2-dimensional relations have clear higher dimensional analogues where (n+1)-relations are fibered over a n-cube of n-relations. Thus the story of proof relevant logical relations quickly expands into one of higher dimensional structures similar to the cubical sets which arises in Homotopy Type Theory. Of course\, there are also connections to Bernardy and Moulin's work on internal parametricity.\n UID:43 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150508T150000 DTEND;TZID=Europe/London:20150508T160000 LOCATION:LT1415 SUMMARY:Departmental seminar: The probability of the Alabama paradox DESCRIPTION:Speaker: Svante Linusson (KTH\, Stockholm)\nTitle: The probability of the Alabama paradox\n\nThere exists various possible methods to distribute seats proportionally between states (or parties) in a parliament. Hamilton's method (also known as the method of largest reminder) was abandoned in the USA because of some drawbacks\, in particular the possibility of the Alabama paradox\, but it is still in use in many other countries.\n\nIn recent work (joint with Svante Janson) we give\, under certain assumptions\, a closed formula for the probability that the Alabama paradox occurs given the vector p_1,...,p_m of relative sizes of the states.\n\nFrom the theorem we deduce a number of consequences. For example it is shown that the expected number of states that will suffer from the Alabama paradox is asymptotically bounded above by 1/e. For random (uniformly distributed) relative sizes p_1,...,p_m the expected number of states to suffer from the Alabama paradox converges to slightly more than a third of this\, or approximately 0.335/e=0.123\, as m -> infinity.\n\n I will assume no prior knowledge of electoral mathematics\, but begin by giving a brief background to various methods suggested and used for the distribution of seats proportionally in a parliament (it's all in the rounding).\n UID:42 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150506T110000 DTEND;TZID=Europe/London:20150506T120000 LOCATION:LT1310 SUMMARY:Game theory in string diagrams DESCRIPTION:Speaker: Jules Hedges (Queen Mary University of London)\nTitle: Game theory in string diagrams\n\nWe define a category whose morphisms are 'games relative to a continuation'\, designed to allow games to be built recursively from simple components. The resulting category has interesting structure similar to (but weaker than) compact closed\, and comes with an associated string diagram language.\n UID:41 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150429T110000 DTEND;TZID=Europe/London:20150429T120000 LOCATION:LT1310 SUMMARY:An Introduction to Differential Privacy DESCRIPTION:Speaker: Bob Atkey (MSP)\nTitle: An Introduction to Differential Privacy\n\nLet's say you have a database of people's private information. For SCIENCE\, or some other reason\, you want to let third parties query your data to learn aggregate information about the people described in the database. However\, you have a duty to the people whose information your database contains not to reveal any of their individual personal information. How do you determine which queries you will let third parties execute\, and those you will not?\n\n"Differential Privacy" defines a semantic condition on probabilistic queries that identifies queries that are safe to execute\, up to some "privacy budget".\n\nI'll present the definition of differential privacy\, talk a bit about why it is better than some 'naive' alternatives (e.g.\, anonymisation)\, and also describe how the definition can be seen as an instance of relational parametricity.\n\nA good place to read about the definition of differential privacy is the book "The Algorithmic Foundations of Differential Privacy" by Cynthia Dwork and Aaron Roth.\n UID:40 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150320T150000 DTEND;TZID=Europe/London:20150320T160000 LOCATION:LT1415 SUMMARY:Departmental seminar: Approximating transition systems DESCRIPTION:Speaker: Chris Heunen (Oxford)\nTitle: Approximating transition systems\n\nClassical computation\, invertible computation\, probabilistic computation\, and quantum computation\, form increasingly more sophisticated labelled transition systems. How can we approximate a transition system by less sophisticated ones? Considering all ways to get probabilistic information out of a quantum system leads to domain-theoretic ideas\, that also apply in the accompanying Boolean logic. I will survey to what extent these domains characterise the system\, leading with examples from quantum theory\, in a way that is accessible to a broad audience of computer scientists\, mathematicians\, and logicians.\n UID:39 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150429T150000 DTEND;TZID=Europe/London:20150429T160000 LOCATION:LT1415 SUMMARY:Departmental seminar: Cyclic homology from mixed distributive laws DESCRIPTION:Speaker: Uli Kraehmer (University of Glasgow)\nTitle: Cyclic homology from mixed distributive laws\n\nIn pure mathematics\, cyclic homology is an invariant of associative algebras that is motivated by algebra\, topology and even mathematicial physics. However\, when studied from an abstract point of view it turns out to be an invariant of a pair of a monad and a comonad that are related by a mixed distributive law\, and I speculate that this could lead to some potential applications in computer science.\n\n(based on joint work with Niels Kowalzig and Paul Slevin)\n UID:38 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150422T140000 DTEND;TZID=Europe/London:20150422T150000 LOCATION:LT1310 SUMMARY:Patterns to avoid: (dependent) stringly-typed programming DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Patterns to avoid: (dependent) stringly-typed programming\n\nType : Set\nType = String -> Bool\n UID:37 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150311T110000 DTEND;TZID=Europe/London:20150311T120000 LOCATION:LT1310 SUMMARY:Collapsing DESCRIPTION:Speaker: Peter Hancock \nTitle: Collapsing\n\nThe topic comes from theory of infinitary proofs\, and cut-elimination. In essence it is about nicely-behaved maps from higher "infinities" to lower ones\, as the infinitary proofs are er\, infinite\, and can be thought of as glorified transfinite iterators. What might nice behaviour mean?\n\nYou can think of it as how to fit an uncountable amount of beer into a bladder whose capacity is merely countable. (Or maybe even finite.)\n\nThe most ubiquitous form of infinity is the regular cardinal\, iepassing from a container F to F + (mu F -> _)\, where mu is the W-type operation. I'll "explain" regular collapsing as being all about diagonalisation.\n\n\n UID:36 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150304T140000 DTEND;TZID=Europe/London:20150304T150000 LOCATION:LT1415 SUMMARY:Event: A HoTT-Date with Thorsten Altenkirch DESCRIPTION: UID:35 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150218T120000 DTEND;TZID=Europe/London:20150218T170000 LOCATION:Royal College Building\, room RC512 SUMMARY:Event: SPLS @ Strathclyde DESCRIPTION: UID:34 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150211T110000 DTEND;TZID=Europe/London:20150211T120000 LOCATION:LT1415 SUMMARY:Totality versus Turing Completeness? DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Totality versus Turing Completeness?\n\nI gave an SPLS talk (http://www.dcs.gla.ac.uk/research/spls/Mar12/)\, which was mostly propaganda\, about why people should stop claiming that totality loses Turing completeness. There was some technical stuff\, too\, about representing a recursive definition as a construction in the free monad whose effect is calling out to an oracle for recursive calls: that tells you what it is to be recursive without prejudicing how to run it. I'm trying to write this up double-quick as a paper for the miraculously rubbery MPC deadline\, with more explicit attention to the monad morphisms involved. So I'd be grateful if you would slap down the shtick and make me more morphic. The punchline is that the Bove-Capretta domain predicate construction is a (relative) monad morphism from the free monad with a recursion oracle to the (relative) monad of Dybjer-Setzer Induction-Recursion codes. But it's worth looking at other monad morphisms (especially to the Delay monad) along the way.\n UID:33 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150128T163000 DTEND;TZID=Europe/London:20150128T173000 LOCATION:LT1415 SUMMARY:Runners for your computations DESCRIPTION:Speaker: Tarmo Uustalu (Institute of Cybernetics\, Tallinn)\nTitle: Runners for your computations\n\nWhat structure is required of a set so that computations in a given notion of computation can be run statefully this with set as the state space? Some answers: To be able to serve stateful computations\, a set must carry the structure of a lens\; for running interactive I/O computations statefully\, a "responder-listener" structure is necessary etc. I will observe that\, in general\, to be a runner of computations for an algebraic theory (defined as a set equipped with a monad morphism between the corresponding monad and the state monad for this set) is the same as to be a comodel of this theory\, ie a coalgebra of the corresponding comonad. I will work out a number of instances. I will also compare runners to handlers.\n UID:32 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20150122T110000 DTEND;TZID=Europe/London:20150122T120000 LOCATION:LT1310 SUMMARY:Termination\, later DESCRIPTION:Speaker: James Chapman (Institute of Cybernetics\, Tallinn)\nTitle: Termination\, later\n\nIt would be a great shame if dependently-typed programming (DTP) restricted us to only writing very clever programs that were a priori structurally recursive and hence obviously terminating. Put another way\, it is a lot to ask of the programmer to provide the program and its termination proof in one go\, programmers should also be supported in working step-by-step. I will show a technique that lowers the barrier of entry\, from showing termination to only showing productivity up front\, and then later providing the opportunity to show termination (convergence). I will show an example of a normaliser for STLC represented in Agda as a potentially non-terminating but nonetheless productive corecursive function targeting the coinductive delay monad.\n\n(Joint work with Andreas Abel)\n UID:31 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141217T110000 DTEND;TZID=Europe/London:20141217T120000 LOCATION:LT1310 SUMMARY:Worlds\, Types and Quantification DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Worlds\, Types and Quantification\n\nI've managed to prove a theorem that I've been chasing for a while. The trouble\, of course\, was *stating* it. I'll revisit the motivation for extending type systems with an analysis of not just *what* things are but *where*\, *when*\, *whose*\, etc. The idea is that typed constructions occur in one of a preordered set of worlds\, with scoping restricted so that information flows only "upwards" from one world to another. Worlds might correspond to "at run time" and "during typechecking"\, or to computation in distinct cores\, or in different stages\, etc. What does the dependent function space mean in this setting? For a long time\, I thought that each world had its own universal quantifier\, for abstracting over stuff from that world. Failure to question this presumption is what led to failure to state a theorem I could prove. By separating quantifiers from worlds\, I have fixed the problem. I'll show how to prove the key fact: if I can build something in one world and then move it to another\, then it will also be a valid construction once it has arrived at its destination.\n UID:30 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141210T110000 DTEND;TZID=Europe/London:20141210T120000 LOCATION:LT1310 SUMMARY:ZX and PROPs DESCRIPTION:Speaker: Aleks Kissinger (Oxford)\nTitle: ZX and PROPs\n\n\n UID:29 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141203T140000 DTEND;TZID=Europe/London:20141203T150000 LOCATION:LT1310 SUMMARY:Event: HoTT reading group @ Strathclyde DESCRIPTION:We will read the paper A Model of Type Theory in Cubical Sets (http://drops.dagstuhl.de/opus/volltexte/2014/4628/pdf/7.pdf) by Marc Bezem (http://www.ii.uib.no/~bezem/)\, Thierry Coquand (http://www.cse.chalmers.se/~coquand/) and Simon Huber (http://www.cse.chalmers.se/~simonhu/). Thierry's Variation on cubical sets (http://www.cse.chalmers.se/~coquand/comp.pdf) might also be useful. *Administrative details*: meet for lunch at 12am for those who want to\, reading group starts at 2pm. UID:28 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141119T120000 DTEND;TZID=Europe/London:20141119T130000 LOCATION:LT1310 SUMMARY:Arrow's Theorem and Escalation DESCRIPTION:Speaker: Neil Ghani and Clemens Kupke (MSP)\nTitle: Arrow's Theorem and Escalation\n\nNeil and Clemens will report back from the Lorentz Center Workshop on Logics for Social Behaviour (http://www.cs.le.ac.uk/people/akurz/lsb.html).\n UID:27 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141126T110000 DTEND;TZID=Europe/London:20141126T120000 LOCATION:LT1310 SUMMARY:Diagrammatic languages for monoidal categories DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Diagrammatic languages for monoidal categories\n\nMonoidal categories are essentially 2-dimensional things\, so why on earth would we represent them using a linear string of symbols? I'll talk about how to use string diagrams for monoidal categories\, graph rewriting for reasoning within them\, and how the syntax can be extended to handle certain kinds of infinitary expressions with the infamous !-box. If there's time I'll finish with some half-baked (eh... basically still looking for the on switch of the oven...) ideas of how to generalise them.\n UID:26 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141106T090000 DTEND;TZID=Europe/London:20141106T100000 LOCATION:LT1310 SUMMARY:Comonadic Cellular Automata DESCRIPTION:Speaker: Kevin Dunne (MSP)\nTitle: Comonadic Cellular Automata\n\nKevin will be giving an informal talk about some of the stuff he has been learning about. He'll give the definition of a cellular automaton and then talk about how this definition can be phrased in terms of a comonad.\n UID:25 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141105T110000 DTEND;TZID=Europe/London:20141105T120000 LOCATION:Boardroom (LT1101d) SUMMARY:Logical Relations for Monads by Categorical TT-Lifting DESCRIPTION:Speaker: Shin-ya Katsumata (Kyoto University)\nTitle: Logical Relations for Monads by Categorical TT-Lifting\n\nLogical relations are widely used to study various properties of typed lambda calculi. By extending them to the lambda calculus with monadic types\, we can gain understanding of the properties on functional programming languages with computational effects. Among various constructions of logical relations for monads\, I will talk about a categorical TT-lifting\, which is a semantic analogue of Lindley and Stark's leapfrog method.\n\nAfter reviewing some fundamental properties of the categorical TT-lifting\, we apply it to the problem of relating two monadic semantics of a call-by-value functional programming language with computational effects. This kind of problem has been considered in various forms: for example\, the relationship between monadic style and continuation passing style representations of call-by-value programs was studied around '90s. We give a set of sufficient conditions to solve the problem of relating two monadic semantics affirmatively. These conditions are applicable to a wide range of such problems.\n UID:24 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141027T140000 DTEND;TZID=Europe/London:20141027T150000 LOCATION:Boardroom (LT1101d) SUMMARY:Constructing analysis-directed semantics DESCRIPTION:Speaker: Dominic Orchard (Imperial College London)\nTitle: Constructing analysis-directed semantics\n\nAll kinds of semantics are syntax directed: the semantics follows from the syntax. Some varieties of semantics are syntax and type directed. In this talk\, I'll discuss syntax\, type\, *and* analysis directed semantics (analysis-directed semantics for short!)\, for analyses other than types. An analysis-directed semantics maps from terms coupled with derivations of a static program analysis into some semantic domain. For example\, the simply-typed lambda calculus with an effect system maps to the category generated by a strong parametric effect monad (due to Katsumata) and a bounded-linear logic-like analysis (described as a coeffect systems) maps to a category generated by various structures related to monoidal comonads. I'll describe a general technique for building analysis-directed semantics where semantic objects and analysis objects have the same structure and are coupled by lax homomorphisms between them. This aids proving semantic properties: the proof tree of an equality for two program analyses implies the rules needed to prove equality of the programs' denotations.\n UID:23 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141112T110000 DTEND;TZID=Europe/London:20141112T120000 LOCATION:LT1310 SUMMARY:Lambda-abstraction and other diabolical contrivances DESCRIPTION:Speaker: Peter Hancock \nTitle: Lambda-abstraction and other diabolical contrivances\n\nThe topic is the unholy trinity of eta\, zeta\, and xi. I'll indicate how Curry managed to give a finite combinatorial axiomatisation of this nastiness\, by anticipating (almost-but-not-*quite*) McBride et al's applicative functors.\n UID:22 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141029T120000 DTEND;TZID=Europe/London:20141029T170000 LOCATION:Dundee SUMMARY:Event: SICSA CSE Meeting on Effects and Coeffects Systems and their use for resource control DESCRIPTION: UID:21 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141022T110000 DTEND;TZID=Europe/London:20141022T120000 LOCATION:LT1310 SUMMARY:Higher dimensional parametricity and its cubical structure DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: Higher dimensional parametricity and its cubical structure\n\nNeil will talk about partial progress made during the summer on higher dimensional parametricity and the cubical structures that seem to arise. \nDetails will be kept to a minimum and\, of course\, concepts stressed.\n UID:20 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141015T120000 DTEND;TZID=Europe/London:20141015T170000 LOCATION:Heriot Watt SUMMARY:Event: SPLS DESCRIPTION: UID:19 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141008T110000 DTEND;TZID=Europe/London:20141008T120000 LOCATION:LT1310 SUMMARY:"Real-world data" and dependent types DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: "Real-world data" and dependent types\n\nConor has offered to talk to us about what he has been thinking about recently. He says this includes models\, views\, and dependent types.\n UID:18 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20141001T110000 DTEND;TZID=Europe/London:20141001T120000 LOCATION:LT1310 SUMMARY:Initial algebras via strong dinaturality\, internally DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Initial algebras via strong dinaturality\, internally\n\n Or: My summer with Steve\nOr: How Christine and Frank were right\, after all\nOr: Inductive types for the price of function extensionality and impredicative Set\n\n Christine Paulin-Mohring and Frank Pfenning suggested to use impredicative encodings of inductive types in the Calculus of Constructions\, but this was later abandoned\, since it is "well-known" that induction principles\, i.e. dependent elimination\, can not be derived for this encoding. It now seems like it is possible to give a variation of this encoding for which the induction principle is derivable after all. The trick is to use identity types to cut down the transformations of type (Pi X : Set) . (F(X) -> X) -> X to the ones that are internally strongly dinatural\, making use of a formula for a "generalised Yoneda Lemma" by Uustalu and Vene.\n UID:17 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140815T150000 DTEND;TZID=Europe/London:20140815T160000 LOCATION:LT1310 SUMMARY:Internal parametricity DESCRIPTION:Speaker: Fredrik Nordvall Forsberg (MSP)\nTitle: Internal parametricity\n\n\n UID:16 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140528T110000 DTEND;TZID=Europe/London:20140528T120000 LOCATION:LT1310 SUMMARY:Graphical algebraic foundations for monad stacks DESCRIPTION:Speaker: Ohad Kammar (Cambridge)\nTitle: Graphical algebraic foundations for monad stacks\n\nOhad gave an informal overview of his current draft\, with the following abstract:\n\nHaskell incorporates computational effects modularly using sequences of monad transformers\, termed monad stacks. The current practice is to find the appropriate stack for a given task using intractable brute force and heuristics. By restricting attention to algebraic stack combinations\, we provide a linear-time algorithm for generating all the appropriate monad stacks\, or decide no such stacks exist. Our approach is based on Hyland\, Plotkin\, and Power's algebraic analysis of monad transformers\, who propose a graph-theoretical solution to this problem. We extend their analysis with a straightforward connection to the modular decomposition of a graph and to cographs\, a.k.a. series-parallel graphs.\n\nWe present an accessible and self-contained account of this monad-stack generation problem\, and\, more generally\, of the decomposition of a combined algebraic theory into sums and tensors\, and its algorithmic solution. We provide a web-tool implementing this algorithm intended for semantic investigations of effect combinations and for monad stack generation.\n UID:15 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140521T110000 DTEND;TZID=Europe/London:20140521T120000 LOCATION:LT1310 SUMMARY:Coalgebraic Foundations of Databases DESCRIPTION:Speaker: Clemens Kupke (MSP)\nTitle: Coalgebraic Foundations of Databases\n\n This 101 is intended to be a brainstorming session on possible links between the theory of coalgebras and the theory of databases. I will outline some ideas in this direction and I am looking forward to your feedback.\n UID:14 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140514T110000 DTEND;TZID=Europe/London:20140514T120000 LOCATION:LT1310 SUMMARY:Resource aware contexts and proof search for IMLL DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Resource aware contexts and proof search for IMLL\n\nIn Intuitionistic Multiplicative Linear Logic\, the right introduction rule for tensors implies picking a 2-partition of the set of assumptions and use each component to inhabit the corresponding tensor's subformulas. This makes a naive proof search algorithm intractable. Building a notion of resource availability in the context and massaging the calculus into a more general one handling both resource consumption and a notion of "leftovers" of a subproof allows for a well-structured well-typed by construction proof search mechanism.\n\n Here is an Agda file (http://gallais.org/code/LinearProofSearch/poc.LinearProofSearch.html) implementing the proof search algorithm.\n UID:13 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140407T110000 DTEND;TZID=Europe/London:20140407T120000 LOCATION:LT1310 SUMMARY:Nominal sets DESCRIPTION:Speaker: Jamie Gabbay (Heriot-Watt)\nTitle: Nominal sets\n\n\n UID:12 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140402T110000 DTEND;TZID=Europe/London:20140402T120000 LOCATION:LT1310 SUMMARY:Towards cubical type theory DESCRIPTION:Speaker: Thorsten Altenkirch (Nottingham)\nTitle: Towards cubical type theory\n\n\n UID:11 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140319T110000 DTEND;TZID=Europe/London:20140319T120000 LOCATION:LT1310 SUMMARY:The selection monad transformer DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: The selection monad transformer\n\nGuillaume presented parts of Hedges' paper Monad transformers for backtracking search (http://www.eecs.qmul.ac.uk/~julesh/papers/monad_transformers.pdf) (accepted to MSFP 2014 (http://www.cs.bham.ac.uk/~pbl/msfp2014/)). The paper extends Escardo and Oliva's work on the selection and continuation monads to the corresponding monad transformers\, with applications to backtracking search and game theory.\n UID:10 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140305T150000 DTEND;TZID=Europe/London:20140305T160000 LOCATION:LT1310 SUMMARY:Lagrange inversion DESCRIPTION:Speaker: Stuart Hannah (Strathclyde Combinatorics)\nTitle: Lagrange inversion\n\nStuart spoke about Lagrange inversion\, a species-theoretic attempt to discuss the existence of solutions to equations defining species.\n UID:9 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140228T140000 DTEND;TZID=Europe/London:20140228T150000 LOCATION:LT1310 SUMMARY:Species DESCRIPTION:Speaker: Neil Ghani (MSP)\nTitle: Species\n\nNeil spoke about how adding structured quotients to containers gives rise to a larger class of data types.\n UID:8 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140219T110000 DTEND;TZID=Europe/London:20140219T120000 LOCATION:LT1310 SUMMARY:Synthetic Differential Geometry DESCRIPTION:Speaker: Tim Revell (MSP)\nTitle: Synthetic Differential Geometry\n\nTim gave a brief introduction to Synthetic Differential Geometry. This is an attempt to treat smooth spaces categorically so we can extend the categorical methods used in the discrete world of computer science to the continuous work of physics. \n UID:7 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140212T110000 DTEND;TZID=Europe/London:20140212T120000 LOCATION:LT1310 SUMMARY:Worlds DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: Worlds\n\nConor talked about worlds (aka phases\, aka times\, ...): why one might bother\, and how we might go about equipping type theory with a generic notion of permitted information flow.\n UID:6 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140205T110000 DTEND;TZID=Europe/London:20140205T120000 LOCATION:LT1310 SUMMARY:Operads DESCRIPTION:Speaker: Miles Gould (Edinburgh)\nTitle: Operads\n\nMiles has kindly agreed to come through and tell us about Operads\, thus revisiting the topic of his PhD and the city in which he did it. \n UID:5 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140122T110000 DTEND;TZID=Europe/London:20140122T120000 LOCATION:LT1310 SUMMARY:Overview of (extensions of) inductive-recursive definitions DESCRIPTION:Speaker: Lorenzo Malatesta (MSP)\nTitle: Overview of (extensions of) inductive-recursive definitions\n\n\n UID:4 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20140108T110000 DTEND;TZID=Europe/London:20140108T120000 LOCATION:LT1310 SUMMARY:On the recently found inconsistency of the univalence axiom in current Agda and Coq DESCRIPTION:Speaker: Conor McBride (MSP)\nTitle: On the recently found inconsistency of the univalence axiom in current Agda and Coq\n\n\n UID:3 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20131218T110000 DTEND;TZID=Europe/London:20131218T120000 LOCATION:LT1310 SUMMARY:Quantum Mechanics DESCRIPTION:Speaker: Ross Duncan (MSP)\nTitle: Quantum Mechanics\n\n\n UID:2 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20131120T110000 DTEND;TZID=Europe/London:20131120T120000 LOCATION:LT1310 SUMMARY:Classical Type Theories DESCRIPTION:Speaker: Robin Adams (MSP visitor)\nTitle: Classical Type Theories\n\nIn 1987\, Felleisen showed how to add control operators (for things like exceptions and unconditional jumps) to the untyped lambda-calculus. In 1990\, Griffin idly wondered what would happen if one did the same in a typed lambda calculus. The answer came out: the inhabited types become the theorems of classical logic.\n\n I will present the lambda mu-calculus\, one of the cleanest attempts to add control operators to a type theory. We'll cover the good news: the inhabited types are the tautologies of minimal classical logic\, and Godel's Double Negation translation from classical to intuitionistic logic turns into the CPS translation.\n\nAnd the bad news: control operators don't play well with other types. Add natural numbers (or some other inductive type)\, and you get inconsistency. Add Sigma-types\, and you get degeneracy (any two objects of the same type are definitionally equal). It gets worse: add plus-types\, and you break Subject Reduction.\n UID:1 END:VEVENT BEGIN:VEVENT DTSTAMP;TZID=Europe/London:20260414T153808 DTSTART;TZID=Europe/London:20131113T110000 DTEND;TZID=Europe/London:20131113T120000 LOCATION:LT1310 SUMMARY:Continuation Passing Style DESCRIPTION:Speaker: Guillaume Allais (MSP)\nTitle: Continuation Passing Style\n\nI chose to go through (parts of) Hatcliff and Danvy's paper "A Generic Account of Continuation-Passing Styles" (http://dl.acm.org/citation.cfm?id=178053) (POPL 94) which gives a nice factorization of various CPS transforms in terms of: \n * embeddings from STLC to Moggi's computational meta-language (either call-by-value\, call-by-name\, or whatever you can come up with)\n * followed by a generic CPS transform transporting terms from ML back to STLC\n Here is an Agda file (http://gallais.org/code/GenericCPS/definitions.html) containing what we had the time to see.\n UID:0 END:VEVENT END:VCALENDAR