【BAYES COFFEE HOUSE TECH TALK SERIES】The Duality of Abstraction
Vikraman Choudury will give a talk, in person and online, for the Coffee House Tech Talk Series. Details of the talk are below.
Title: The Duality of Abstraction
Speaker: Vikraman Choudury
When: 11am Tue 17 Oct 2023
Where: Bayes Coffee House, 4/F Bayes Centre
Meeting ID: 99020138
There are well-known dualities of computation in the form of dual calculi, stemming from the duality of values and continuations. In this talk, I will present and develop the following perspective: just as higher-order functions give you exponentials, higher-order continuations give you co-exponentials – a fact well-known to semanticists in various forms.
From this perspective, I will show how values and abstraction can be dualised to co-values and co-abstraction, producing a λƛ (lambda-lambda-bar) calculus, which exhibits both. I will develop the syntax and semantics of this language, and give a computational interpretation in terms of speculative execution and backtracking. Using this language, I will show how to recover control operators, the computational interpretation of classical logic, various applications of continuations, and a complete axiomatisation of control effects.
Vikraman is a Research Associate at the University of Glasgow, UK, and soon to be a Marie Skłodowska-Curie Fellow at the University of Bologna, Italy. Previously, Vikraman was a Research Fellow at the University of Cambridge, UK, and even before that, a PhD student and Paul Purdom Fellow at Indiana University, USA. Vikraman’s research interests are in the mathematical foundations of computation and the semantics of reversible, linear, functional, concurrent, effectful programming languages, using category theory.