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Linear Logic Without Boxes
, 1992
"... Girard's original definition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets w ..."
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Cited by 54 (0 self)
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Girard's original definition of proof nets for linear logic involves boxes. The box is the unit for erasing and duplicating fragments of proof nets. It imposes synchronization, limits sharing, and impedes a completely local view of computation. Here we describe an implementation of proof nets without boxes. Proof nets are translated into graphs of the sort used in optimal calculus implementations; computation is performed by simple graph rewriting. This graph implementation helps in understanding optimal reductions in the calculus and in the various programming languages inspired by linear logic. 1 Beyond the calculus The calculus is not entirely explicit about the operations of erasing and duplicating arguments. These operations are important both in the theory of the  calculus and in its implementations, yet they are typically treated somewhat informally, implicitly. The proof nets of linear logic [1] provide a refinement of the calculus where these operations become explici...
Asynchronous Communication Model Based on Linear Logic
 Formal Aspects of Computing
, 1995
"... We propose a new framework called ACL for concurrent computation based on linear logic. ACL is a kind of linear logic programming framework, where its operational semantics is described in terms of proof construction in linear logic. We also give a modeltheoretic semantics as a natural extension of ..."
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Cited by 51 (6 self)
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We propose a new framework called ACL for concurrent computation based on linear logic. ACL is a kind of linear logic programming framework, where its operational semantics is described in terms of proof construction in linear logic. We also give a modeltheoretic semantics as a natural extension of phase semantics, a model of linear logic. Our framework well captures concurrent computation based on asynchronous communication. It will, therefore, provide us with a new insight into other models of concurrent computation from a logical point of view. We also expect ACL to become a formal framework for verification, reasoning, and transformation of concurrent programs by the use of techniques for traditional logic programming. ACL's attractive features for concurrent programming paradigms are also discussed. 1 Introduction For future massively parallel processing environments, concurrent programming languages based on asynchronous communication would become more and more important. Due ...
Communication as Fair Distribution of Knowledge
 In Proc. of OOPSLA'91
, 1991
"... We introduce an abstract form of interobject communication for objectoriented concurrent programming based on the proof theory of Linear Logic, a logic introduced to provide a theoretical basis for the study of concurrency. Such a form of communication, which we call forumbased communication, ca ..."
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Cited by 47 (13 self)
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We introduce an abstract form of interobject communication for objectoriented concurrent programming based on the proof theory of Linear Logic, a logic introduced to provide a theoretical basis for the study of concurrency. Such a form of communication, which we call forumbased communication, can be seen as a refinement of blackboardbased communication in terms of a more local notion of resource consumption. Forumbased communication is introduced as part of a new computational model for the objectoriented concurrent programming language LO, presented at last year OOPSLA/ECOOP (1990), which exploits the prooftheory of Linear Logic also to achieve a powerful form of knowledgesharing.
Proof Nets for Intuitionistic Linear Logic
 Essential Nets, Research Report
"... Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cutelimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof o ..."
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Cited by 44 (1 self)
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Abstract. We present a class of proof nets that are specially designed for Intuitionistic Linear Logic, for which we give a correctness criterion, as well as a cutelimination procedure. The proof of sequentialization uses a special kind of oriented paths. In this paper we present a class of proof objects for intuitionistic linear logic with the connectives ⊗, ⊸, � and! 1; in particular we can interpret the simply typed lambda calculus, with or without product types. We call these proof nets essential nets. We will formulate a correctness criterion for them: there is an intrinsic property that characterizes the essential nets that do come from proofs in the sequent calculus; it turns out that every such (correct) essential net represents a large number of sequent proofs that differ by inessential details. Thus essential nets, as should be the case for proof nets in general, have the power of eliminating a lot of the bureaucracy in the sequent calculus. We will give a cutelimination procedure for essential nets which is based on that correctness criterion. That procedure is not one that can be said to be
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
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
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Cited by 42 (3 self)
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This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
Interaction Systems I: The theory of optimal reductions
 Mathematical Structures in Computer Science
, 1994
"... We introduce a new class of higher order rewriting systems, called Interaction Systems (IS's). IS's come from Lafont's (Intuitionistic) Interaction Nets [Lafont 1990] by dropping the linearity constraint. In particular, we borrow from Interaction Nets the syntactical bipartitions o ..."
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Cited by 40 (7 self)
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We introduce a new class of higher order rewriting systems, called Interaction Systems (IS's). IS's come from Lafont's (Intuitionistic) Interaction Nets [Lafont 1990] by dropping the linearity constraint. In particular, we borrow from Interaction Nets the syntactical bipartitions of operators into constructors and destructors and the principle of binary interaction. As a consequence, IS's are a subclass of Klop's Combinatory Reduction Systems [Klop 1980] where the CurryHoward analogy still "makes sense". Destructors and constructors respectively corresponds to left and right logical introduction rules, interaction is cut and reduction is cutelimination. Interaction Systems have been primarily motivated by the necessity of extending the practice of optimal evaluators for calculus [Lamping 1990, Gonthier et al. 1992a] to other computational constructs as conditionals and recursion. In this paper we focus on the theoretical aspects of optimal reductions. In particular, we ge...
Cyclic Lambda Calculi
, 1997
"... . We precisely characterize a class of cyclic lambdagraphs, and then give a sound and complete axiomatization of the terms that represent a given graph. The equational axiom system is an extension of lambda calculus with the letrec construct. In contrast to current theories, which impose restrictio ..."
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Cited by 39 (5 self)
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. We precisely characterize a class of cyclic lambdagraphs, and then give a sound and complete axiomatization of the terms that represent a given graph. The equational axiom system is an extension of lambda calculus with the letrec construct. In contrast to current theories, which impose restrictions on where the rewriting can take place, our theory is very liberal, e.g., it allows rewriting under lambdaabstractions and on cycles. As shown previously, the reduction theory is nonconfluent. We thus introduce an approximate notion of confluence. Using this notion we define the infinite normal form or L'evyLongo tree of a cyclic term. We show that the infinite normal form defines a congruence on the set of terms. We relate our cyclic lambda calculus to the traditional lambda calculus and to the infinitary lambda calculus. Since most implementations of nonstrict functional languages rely on sharing to avoid repeating computations, we develop a variant of our calculus that enforces the ...
Dactl: An Experimental Graph Rewriting Language
 Proc. 4th International Workshop on Graph Grammars
, 1991
"... This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examp ..."
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Cited by 36 (7 self)
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This paper gives some examples of how computation in a number of languages may be described as graph rewriting, giving the Dactl notation for the examples shown. It goes on to present the Dactl model more formally before giving a formal definition of the syntax and semantics of the language. 2 Examples of Computation by Graph Rewriting
Operational congruences for reactive systems
, 2001
"... This document consists of a slightly revised and corrected version of a dissertation ..."
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Cited by 35 (4 self)
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This document consists of a slightly revised and corrected version of a dissertation