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Linear Logic
, 1992
"... this paper we will restrict attention to propositional linear logic. The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions, and greek letters for sequences of formulas. A sequent is composed of two sequences of formulas separated by a `, or turnstile symbol. One may ..."
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Cited by 24 (1 self)
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this paper we will restrict attention to propositional linear logic. The sequent calculus notation, due to Gentzen [10], uses roman letters for propositions, and greek letters for sequences of formulas. A sequent is composed of two sequences of formulas separated by a `, or turnstile symbol. One may read the sequent \Delta ` \Gamma as asserting that the multiplicative conjunction of the formulas in \Delta together imply the multiplicative disjunction of the formulas in \Gamma. A sequent calculus proof rule consists of a set of hypothesis sequents, displayed above a horizontal line, and a single conclusion sequent, displayed below the line, as below: Hypothesis1 Hypothesis2 Conclusion 4 Connections to Other Logics
Retrieving Library Functions By Unifying Types Modulo Linear Isomorphism
, 1992
"... An improved method to retrieve a library function via its Hindley/Milner type is described. Previous retrieval systems have identified types that are isomorphic in any Cartesian closed category (CCC), and have retrieved library functions of types that are either isomorphic to the query, or have ..."
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Cited by 18 (0 self)
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An improved method to retrieve a library function via its Hindley/Milner type is described. Previous retrieval systems have identified types that are isomorphic in any Cartesian closed category (CCC), and have retrieved library functions of types that are either isomorphic to the query, or have instances that are. Sometimes it is useful to instantiate the query too, which requires unification modulo isomorphism. Although unifiability modulo CCCisomorphism is undecidable, it is decidable modulo linear isomorphism, that is, isomorphism in any symmetric monoidal closed (SMC) category. We argue that the linear isomorphism should retrieve library functions almost as well as CCCisomorphism, and we report experiments with such retrieval from the Lazy ML library. When unification is used, the system retrieves too many functions, but sorting by the sizes of the unifiers tends to place the most relevant functions first. R'esum'e Ce papier pr'esente une nouvelle m'ethode pour la re...
Mutable abstract datatypes  or  how to have your state and munge it too
, 1992
"... 1 Introduction It's been said many times before: "Functional languages are great, but they can't deal with state! " to which functional programmers often reply: "But a compiler that's great, will eliminate state!" Although recent advances in compiler optimization techniques have ..."
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Cited by 15 (3 self)
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1 Introduction It's been said many times before: "Functional languages are great, but they can't deal with state! " to which functional programmers often reply: "But a compiler that's great, will eliminate state!" Although recent advances in compiler optimization techniques have eliminated many concerns over efficiency, optimizations have their own set of problems: (1) they are often expensive (in terms of compilation resources), (2) they aren't always good enough, (3) they are often hard to reason about, and (4) they are implementation dependent (and thus programs that depend on them are not portable). Perhaps more importantly, compiler optimizations aren't explicit, and in this sense are not "expressive " enough.
Functional Programming and Linear Logic
 Lecture Notes for the Summer School on Functional Programming and Constructive Logic
, 1989
"... F26.4> A ) B \Gamma ` A ) B \Gamma ` A \Gamma ` B \Gamma ` A \Gamma ` A B \Gamma ` B \Gamma ` A B \Gamma ` A B \Gamma; A ` C \Gamma; B ` C \Gamma ` C \Gamma ` ? \Gamma ` C Lecture notes for the Summer School on Functional Programming and Constructive Logic (Glasgow, September 1989). 2 1 FROM ..."
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F26.4> A ) B \Gamma ` A ) B \Gamma ` A \Gamma ` B \Gamma ` A \Gamma ` A B \Gamma ` B \Gamma ` A B \Gamma ` A B \Gamma; A ` C \Gamma; B ` C \Gamma ` C \Gamma ` ? \Gamma ` C Lecture notes for the Summer School on Functional Programming and Constructive Logic (Glasgow, September 1989). 2 1 FROM NATURAL DEDUCTION TO FUNCTIONAL PROGRAMMING Exercise 1 Check the following points: 1. In a proof of \Gamma ` A, all sequents are of the form \Gamma; \Delta ` B. 2. If \Gamma ` A is provable, so is \Gamma; \Delta ` A. 3. If \Gamma ` A
FOL: An object oriented extension to the SISAL Language (Extended Abstract)
, 1997
"... Marc Pantel, Marcel Gandriau, Patrick Sall'e IRIT/ENSEEIHT, 2, rue Charles Camichel, 31071 TOULOUSE, FRANCE, fpantel,gandri,salleg@irit.fr April 2, 1997 Abstract This paper describes an improvement of the reusability model of the SISAL language. ..."
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Marc Pantel, Marcel Gandriau, Patrick Sall'e IRIT/ENSEEIHT, 2, rue Charles Camichel, 31071 TOULOUSE, FRANCE, fpantel,gandri,salleg@irit.fr April 2, 1997 Abstract This paper describes an improvement of the reusability model of the SISAL language.
Implicative Formulae in the Vroofs as Computations ” Analogy
"... In [As871 a correspondence between the subset of Linear Logic [Gi86] involving the conjunctive tensor product only and PlacelTransition Petri Nets IRei is established. In this correspondence, formulae are regarded as distributed states and provable seqnents are computations in the net. Developing th ..."
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In [As871 a correspondence between the subset of Linear Logic [Gi86] involving the conjunctive tensor product only and PlacelTransition Petri Nets IRei is established. In this correspondence, formulae are regarded as distributed states and provable seqnents are computations in the net. Developing this i&a, MartiOliet and Meseguer [MaM89] have suggested that all the other computations of Linear Logic, which do not have an immediate correspondence with Petri Nets, should be regarded as “gedanken ” or idealized processes, providing a richer language for the specification and the study of properties of distributed computations. In this paper we apply this program to the fundamental connective of linear implication. We prove that the introduction of linear implication allows us to observe the net at a lower, more decentralized level of atomicity, where the preemption of each resource needed for the firing of a transition is represented as a separate move. We give a conservative theorem relating computations at different levels of abstraction. The categorical semantics establishes a tight correspondence among Petri nets, monoidal closed categories and tensor theories, reminiscent of the well known relation among functional languages, Cartesian closed categories and intuitionistic logic [LS86]. The identification of computations in the categorical model naturally suggests the generalisation of the notion of process [DMM89] at the lower level of atomicity. 1.
/ Towards Soft Typing in Computer Algebra
, 1998
"... This paper is a revised version of the notes for the tutorial of D. Duval at ISSAC’98. We are indebted to the participants of the working group on sketches and computer algebra for their questions and suggestions, and to C.N.R.S. for its support. This document was processed with LATEX and XYpic. ..."
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This paper is a revised version of the notes for the tutorial of D. Duval at ISSAC’98. We are indebted to the participants of the working group on sketches and computer algebra for their questions and suggestions, and to C.N.R.S. for its support. This document was processed with LATEX and XYpic.