Backpropagation is a classic automatic differentiation algorithm computing the gradient of
functions specified by a certain class of simple, first-order programs, called computational …

Whether the number of β-steps in the λ-calculus can be taken as a reasonable time cost
model (that is, polynomially related to the one of Turing machines) is a delicate problem …

Evaluating higher-order functional programs through abstract machines inspired by the
geometry of the interaction is known to induce space efficiencies, the price being time …

A cornerstone of the theory of λ-calculus is that intersection types characterise termination
properties. They are a flexible tool that can be adapted to various notions of termination, and …

This paper revisits the Interaction Abstract Machine (IAM), a machine based on Girard's
Geometry of Interaction, introduced by Mackie and Danos & Regnier. It is an unusual …

Extending the λ-calculus with a construct for sharing, such as let expressions, enables a
special representation of terms: iterated applications are decomposed by introducing …

We present an efficient implementation of the full-reducing call-by-value strategy for the pure
λ-calculus in the form of an abstract machine. The presented machine has been …

We present an abstract machine for a strong call-by-need strategy in the lambda calculus.
The machine has been derived automatically from a higher-order evaluator that uses the …

This paper studies useful sharing, which is a sophisticated optimization for lambda-calculi, in
the context of call-by-need evaluation in presence of open terms. Useful sharing turns out to …

The encoding of proof systems and type theories in logical frameworks is key to allow the
translation of proofs from one system to the other. The λΠ-calculus modulo rewriting is a …