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

Multi types–aka non-idempotent intersection types–have been used. to obtain quantitative
bounds on higher-order programs, as pioneered by de Carvalho. Notably, they bound at the …

This paper introduces the exponential substitution calculus (ESC), a new presentation of cut
elimination for IMELL, based on proof terms and building on the idea that exponentials can …

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 …

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 λ-calculus is a handy formalism to specify the evaluation of higher-order programs. It is
not very handy, however, when one interprets the specification as an execution mechanism …

The Spirit of Node Replication. Page 358 The Spirit of Node Replication Delia Kesner1 , 2, Loıc
Peyrot 1, and Daniel Ventura3 ⋆ 1 Université de Paris, CNRS, IRIF, Paris, France { kesner …

We present the stellar resolution, a" flexible" tile system based on Robinson's first-order
resolution. After establishing formal definitions and basic properties of the stellar resolution …

The (untyped) lambda-calculus is almost 90 years old. And yet-we argue here-its study is far
from being over. The paper is a bird's eye view of the questions the author worked on in the …