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Interaction Combinators
 Information and Computation
, 1995
"... This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction ..."
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Cited by 43 (3 self)
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This paper is the continuation of the author 's work on interaction nets, inspired by Girard's proof nets for linear logic, but no preliminary knowledge of these topics is required for its reading. Introduction
Once Upon a Polymorphic Type
, 1998
"... We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and app ..."
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Cited by 42 (6 self)
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We present a sound typebased `usage analysis' for a realistic lazy functional language. Accurate information on the usage of program subexpressions in a lazy functional language permits a compiler to perform a number of useful optimisations. However, existing analyses are either adhoc and approximate, or defined over restricted languages. Our work extends the Once Upon A Type system of Turner, Mossin, and Wadler (FPCA'95). Firstly, we add type polymorphism, an essential feature of typed functional programming languages. Secondly, we include general Haskellstyle userdefined algebraic data types. Thirdly, we explain and solve the `poisoning problem', which causes the earlier analysis to yield poor results. Interesting design choices turn up in each of these areas. Our analysis is sound with respect to a Launchburystyle operational semantics, and it is straightforward to implement. Good results have been obtained from a prototype implementation, and we are currently integrating the system into the Glasgow Haskell Compiler.
Partial Proof Trees as Building Blocks for a Categorial Grammar
 Linguistics and Philosophy
, 1997
"... We describe a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system. The PPTs are obtained by unfolding the arguments of the type that would be associated with a lexical item in a simple categorial grammar. The PPTs are the basic types in the system and a ..."
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Cited by 39 (10 self)
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We describe a categorial system (PPTS) based on partial proof trees (PPTs) as the building blocks of the system. The PPTs are obtained by unfolding the arguments of the type that would be associated with a lexical item in a simple categorial grammar. The PPTs are the basic types in the system and a derivation proceeds by combining PPTs together. We describe the construction of the finite set of basic PPTs and the operations for combining them. PPTS can be viewed as a categorial system incorporating some of the key insights of lexicalized tree adjoining grammar, namely the notion of an extended domain of locality and the consequent factoring of recursion from the domain of dependencies. PPTS therefore inherits the linguistic and computational properties of that system, and so can be viewed as a `middle ground' between a categorial grammar and a phrase structure grammar. We also discuss the relationship between PPTS, natural deduction, and linear logic proofnets, and argue that natural ...
Pomset Logic: A NonCommutative Extension of Classical Linear Logic
, 1997
"... We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherenc ..."
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Cited by 39 (10 self)
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We extend the multiplicative fragment of linear logic with a noncommutative connective (called before), which, roughly speaking, corresponds to sequential composition. This lead us to a calculus where the conclusion of a proof is a Partially Ordered MultiSET of formulae. We firstly examine coherence semantics, where we introduce the before connective, and ordered products of formulae. Secondly we extend the syntax of multiplicative proof nets to these new operations. We then prove strong normalisation, and confluence. Coming back to the denotational semantics that we started with, we establish in an unusual way the soundness of this calculus with respect to the semantics. The converse, i.e. a kind of completeness result, is simply stated: we refer to a report for its lengthy proof. We conclude by mentioning more results, including a sequent calculus which is interpreted by both the semantics and the proof net syntax, although we are not sure that it takes all proof nets into account...
Frühwirth: A LinearLogic Semantics For Constraint Handling Rules
 Proceedings of CP 2005
, 2005
"... Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of t ..."
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Abstract. We motivate and develop a linear logic declarative semantics for CHR ∨ , an extension of the CHR programming language that integrates concurrent committed choice with backtrack search and a predefined underlying constraint handler. We show that our semantics maps each of these aspects of the language to a distinct aspect of linear logic. We show how we can use this semantics to reason about derivations in CHR ∨ and we present strong theorems concerning its soundness and completeness. 1
The Finite Model Property For Various Fragments Of Linear Logic
, 1997
"... B stand for formulas. The connectives of propositional linear logic are: ffl the multiplicatives A & B, A\Omega B, ?, 1; ffl the additives A&B, A \Phi B, ?, 0; ffl the exponentials ?A, !A. Linear negation A ? is only given for positive atoms. It is extended to all formulas by A ?? = ..."
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Cited by 28 (0 self)
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B stand for formulas. The connectives of propositional linear logic are: ffl the multiplicatives A & B, A\Omega B, ?, 1; ffl the additives A&B, A \Phi B, ?, 0; ffl the exponentials ?A, !A. Linear negation A ? is only given for positive atoms. It is extended to all formulas by A ?? = A and by (A & B) ? = A ?\Omega B ? ; ? ? = 1; (A &B) ? = A ? \Phi B ?
Noncommutative logic II: sequent calculus and phase semantics
, 1998
"... INTRODUCTION Noncommutative logic is a unication of :  commutative linear logic (Girard 1987) and  cyclic linear logic (Girard 1989; Yetter 1990), a classical conservative extension of the Lambek calculus (Lambek 1958). In a previous paper with Abrusci (Abrusci and Ruet 1999) we presented the mu ..."
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INTRODUCTION Noncommutative logic is a unication of :  commutative linear logic (Girard 1987) and  cyclic linear logic (Girard 1989; Yetter 1990), a classical conservative extension of the Lambek calculus (Lambek 1958). In a previous paper with Abrusci (Abrusci and Ruet 1999) we presented the multiplicative fragment of noncommutative logic, with proof nets and a sequent calculus based on the structure of order varieties, and a sequentialization theorem. Here we consider full propositional noncommutative logic. Noncommutative logic. Let us rst review the basic ideas. Consider the purely noncommutative fragment of linear logic, obtained by removing the exchange rule entirely : ` ; ; ; , ` ; ; ; y This work has been partly carried out at LIENSCNRS, Ecole Normale Superieure (Paris), at McGill University
Separation logic contracts for a Javalike language with fork/join
, 2008
"... We adapt a variant of permissionaccounting separation logic to a concurrent Javalike language with fork/join. To support both concurrent reads and information hiding, we combine fractional permissions with abstract predicates. As an example, we present a separation logic contract for iterators t ..."
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We adapt a variant of permissionaccounting separation logic to a concurrent Javalike language with fork/join. To support both concurrent reads and information hiding, we combine fractional permissions with abstract predicates. As an example, we present a separation logic contract for iterators that prevents data races and concurrent modifications. Our program logic is presented in an algorithmic style: we avoid structural rules for Hoare triples and formalize logical reasoning about typed heaps by natural deduction rules and a set of sound axioms. We show that verified programs satisfy the following properties: data race freedom, absence of nulldereferences and partial correctness.
Between logic and quantic: a tract
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2003
"... We present a quantum interpretation of the perfect part of linear logic, by means of quantum coherent spaces. In particular this yields a novel interpretation of the reduction of the wave packet as the expression of ηconversion, a.k.a, extensionality. ..."
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We present a quantum interpretation of the perfect part of linear logic, by means of quantum coherent spaces. In particular this yields a novel interpretation of the reduction of the wave packet as the expression of ηconversion, a.k.a, extensionality.