** CANCELED **, Dec. 12, 2019

Programme

10:30 – 12:00
Damiano Mazza (CNRS, Univ. Paris 13)

Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most notably machine learning, where it is the key for efficiently training (deep) neural networks. Recent years have witnessed the quick growth of a research field called differentiable programming, the aim of which is to express computational graphs more synthetically and modularly by resorting to actual programming languages endowed with control flow operators and higher-order combinators, such as map and fold. In this paper, we extend the backpropagation algorithm to a paradigmatic example of such a programming language: we define a compositional program transformation from the simply-typed lambda-calculus to itself augmented with a notion of linear negation, and prove that this computes the gradient of the source program with the same efficiency as first-order backpropagation. The transformation is completely effect-free and thus provides a purely logical understanding of the dynamics of backpropagation.

14:00 – 15:00
Cristina Matache (Oxford University (UK))

I will talk about definitions of program equivalence, for a language with algebraic effects in the style of Plotkin and Power. Program equivalence is a long-standing problem in computer science, made more difficult by the presence of higher-order functions and algebraic effects. In this talk I will present a logic whose formulas represent properties of effectful programs. The satisfaction relation of the logic induces a notion of program equivalence. Notably, the induced equivalence coincides with contextual equivalence (which equates programs with the same observable behaviour) and also with an applicative bisimilarity.

This is based on joint work with Sam Staton which appeared at FOSSACS 2019, see https://link.springer.com/content/pdf/10.1007%2F978-3-030-17127-8_22 .pdf

15:30 – 16:30
Amina Doumane (CNRS, ENS de Lyon)

We provide a finite set of axioms for identity-free Kleene lattices, which we prove sound and complete for the equational theory of their relational models. Our proof builds on the completeteness theorem for Kleene algebra, and on a novel automata construction that makes it possible to extract axiomatic proofs using a Kleene-like algorithm.

We provide a finite set of axioms for identity-free Kleene lattices, which we prove sound and complete for the equational theory of their relational models. Our proof builds on the completeteness theorem for Kleene algebra, and on a novel automata construction that makes it possible to extract axiomatic proofs using a Kleene-like algorithm.