This paper surveys a part of the theory ofβ-reduction inλ-calculus which might aptly be
calledperpetual reductions. The theory is concerned withperpetual reduction strategies, ie …

Outils Génériques de Modélisation et de Démonstration pour la Formalisation des
Mathématiques en Théorie des Types. Applic Page 1 HAL Id: tel-00523810 https://theses.hal.science/tel-00523810 …

Perpetual strategies in λ-calculus are analyzed from a semantical perspective. This is
achieved using suitable denotational models, computationally adequate with respect to the …

Pure type systems feature domain-specified λ-abstractions λx: AM We present a variant of
pure type systems, which we call domain-free pure type systems, with domain-free λ …

We show how to characterise compositionally a number of evaluation properties of λ-terms
using Intersection Type assignment systems. In particular, we focus on termination …

Inductive data such as finite lists and trees can elegantly be defined by constructors which
allow programmers to analyze and manipulate finite data via pattern matching. Dually …

Several proof-assistants rely on the very formal basis of Pure Type Systems (PTS). However,
some practical issues raised by the development of large proofs lead to add other features to …

In the framework of intuitionnistic logic and type theory, the concepts of «propositions» and
«types» are identified. This principle is known as the Curry-Howard isomorphism, and it is at …

Inspired by a number of different applications of rewriting logic, equational logic, and type
theory that we present and further advance in this thesis, we study a unified formalism based …

The logical and operational aspects of rewriting logic as a logical framework are tested and
illustrated in detail by representing pure type systems as object logics. More precisely, we …