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ISBN 0 521 37181 3 iii Preface This little book comes from a short graduate course on typed λ-calculus given at the Université Paris VII in the autumn term of 1986–7. It is not intended to be encyclopedic — the Church-Rosser theorem, for instance, is not proved — and the selection of topics was really quite haphazard. Some very basic knowledge of logic is… (More)
We propose a new kind of programming language, with the following features: <list><item>a simple graph rewriting semantics, </item><item>a complete symmetry between constructors and destructors, </item><item>a type discipline for deterministic and deadlock-free (microscopic) parallelism. </item></list><italic>Interaction nets</italic> generalize Girard's… (More)
We present a subsystem of second order Linear Logic with restricted rules for expo-nentials so that proofs correspond to polynomial time algorithms, and vice-versa.
Boolean circuits are used to represent programs on finite data. Reversible Boolean circuits and quantum Boolean circuits have been introduced to modelize some physical aspects of computation. Those notions are essential in complexity theory, but we claim that a deep mathematical theory is needed to make progress in this area. For that purpose, the recent… (More)
It is shown that a very simple system of interaction com-binators, with only 3 symbols and 6 rules, is a universal model of distributed computation, in a sense that will be made precise. This paper is the continuation of the au-thor's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is… (More)
The purpose of this course is to provide an introduction to λ-calculi, specifically the simply typed lambda calculus (λ →). λ-calculi are formalisms that are useful in computer science. They are languages that express both computational and logical information. Computational information in that they can be see as functional programming languages, or more… (More)
The signiicance of the 2-dimensional calculus, which goes back to Penrose, has already been pointed out by Joyal and Street. Independently, Burroni has introduced a general notion of n-dimensional presentation and he has shown that the equational logic of terms is a special case of 2-dimensional calculus. Here, we propose a combinatorial deenition of… (More)