Theories of dependent types have been proposed as a foundation of constructive
mathematics and as a framework in which to construct certified programs. In these …

String diagrams were introduced by Roger Penrose as a handy notation to manipulate
morphisms in a monoidal category. In principle, this graphical notation should encompass …

Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Lévy to
internalise substitutions into λ-calculus and to propose a mechanism for computing on …

We present a typing system with non-idempotent intersection types, typing a term syntax
covering three different calculi: the pure λ-calculus, the calculus with explicit substitutions λ …

The aim of this paper is to present the λs-calculus which is a very simple λ-calculus with
explicit substitutions and to prove its confluence on closed terms and the preservation of …

We study a simple form of standardization, here called factorization, for explicit substitutions
calculi, ie lambda-calculi where beta-reduction is decomposed in various rules. These …

This paper is the first part of a work whose purpose is to investigate duality in some related
frameworks (cartesian closed categories, lambda-calculi, intuitionistic and classical logics) …

Since the very beginning of the theory of linear logic it is known how to represent the λ λ-
calculus as linear logic proof nets. The two systems however have different granularities, in …

The lambda-calculus is a widely accepted computational model of higher-order functional
programs, yet there is not any direct and universally accepted cost model for it. As a …

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 …