2023-04-28: Vikraman Choudhury (University of Glasgow)

Tue, 14 Oct 2025 16:51:42 +0000

Vikraman Choudhury (University of Glasgow)

Continuations and co-exponentials

Abstract

Growing 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.

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.

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.

2023-04-28 15:00:00 UTC
LT711 and Online