2021-07-15: Samuel Arsac (MSP)

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

Samuel Arsac (MSP)

Expressivity of BCI algebras

Abstract

I 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.

[1] https://www.kurims.kyoto-u.ac.jp/~naophiko/paper/realizability.pdf
[2] https://www.cs.brandeis.edu/~mairson/Papers/jfp02.pdf

2021-07-15 15:00:00 UTC
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