2025-03-10: Zanzi Mihejevs (GlAiVe Research)

Fri, 7 Mar 2025 13:53:46 +0000

Zanzi Mihejevs (GlAiVe Research)

A canonical bidirectional typing discipline through polarised System L

Abstract

What 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.

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.

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.

2025-03-10 15:00:00 UTC
LT412 and Online