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Anytime, anywhere: modal logics for mobile ambients
 In POPL ’00: Proceedings of the 27th ACM SIGPLANSIGACT symposium on Principles of programming languages
, 2000
"... The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a m ..."
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Cited by 164 (14 self)
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The Ambient Calculus is a process calculus where processes may reside within a hierarchy of locations and modify it. The purpose of the calculus is to study mobility, which is seen as the change of spatial configurations over time. In order to describe properties of mobile computations we devise a modal logic that can talk about space as well as time, and that has the Ambient Calculus as a model. 1
Term Assignment for Intuitionistic Linear Logic
, 1992
"... In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky) and has two important properties which they lack. Th ..."
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Cited by 53 (9 self)
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In this paper we consider the problem of deriving a term assignment system for Girard's Intuitionistic Linear Logic for both the sequent calculus and natural deduction proof systems. Our system differs from previous calculi (e.g. that of Abramsky) and has two important properties which they lack. These are the substitution property (the set of valid deductions is closed under substitution) and subject reduction (reduction on terms is welltyped). We define a simple (but more general than previous proposals) categorical model for Intuitionistic Linear Logic and show how this can be used to derive the term assignment system. We also consider term reduction arising from cutelimination in the sequent calculus and normalisation in natural deduction. We explore the relationship between these, as well as with the equations which follow from our categorical model.
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 41 (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...
Petri Nets as Models of Linear Logic
 Proceedings of Colloquium on Trees in Algebra and Programming
, 1990
"... The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic. 1 Introducti ..."
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Cited by 33 (2 self)
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The chief purpose of this paper is to appraise the feasibility of Girard's linear logic as a specification language for parallel processes. To this end we propose an interpretation of linear logic in Petri nets, with respect to which we investigate the expressive power of the logic. 1 Introduction Girard's linear logic has sparked off a great deal of interest in how it might be useful in the theory of parallelism, not least because of Girard's initial claims for it [Gir87]. Linear logic has been described as a "resource conscious" logic by Mart'iOliet and Meseguer [MOM89]; in its proofs occurrences of propositions cannot be used more than once or disappear unless they are explicitly created or used up by the rules of inference. People were not long in spotting a relationship with Petri nets where there are similar ideas. Places in a Petri net hold to certain nonnegative multiplicities forming a multiset of places, traditionally called a marking; as transitions occur, multipliciti...
Completeness Results for Linear Logic on Petri Nets (Extended Abstract)
"... ) Uffe Engberg Glynn Winskel Computer Science Department Aarhus University Ny Munkegade DK8000 Aarhus C, Denmark Abstract Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic ..."
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Cited by 27 (1 self)
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) Uffe Engberg Glynn Winskel Computer Science Department Aarhus University Ny Munkegade DK8000 Aarhus C, Denmark Abstract Completeness is shown for several versions of Girard's linear logic with respect to Petri nets as the class of models. The strongest logic considered is intuitionistic linear logic, with\Omega , \Gamma , , & , \Phi and the exponential ! ("of course"), and forms of secondorder quantification. This logic is shown sound and complete with respect to atomic nets (these include nets in which every transition leads to a nonempty multiset of places). The logic is remarkably expressive, enabling descriptions of the kinds of properties one might wish to show of nets; in particular, negative properties, asserting the impossibility of an assertion, can also be expressed. email address: fengberg,gwinskelg@daimi.aau.dk, fax: ++45 86 13 57 25 0 1 Introduction In [EW90] it was shown how Petri nets can naturally be made into models of Girard's linear logic ...
Session Types as Intuitionistic Linear Propositions
"... Several type disciplines for πcalculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculu ..."
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Cited by 26 (14 self)
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Several type disciplines for πcalculi have been proposed in which linearity plays a key role, even if their precise relationship with pure linear logic is still not well understood. In this paper, we introduce a type system for the πcalculus that exactly corresponds to the standard sequent calculus proof system for dual intuitionistic linear logic. Our type system is based on a new interpretation of linear propositions as session types, and provides the first purely logical account of all (both shared and linear) features of session types. We show that our type discipline is useful from a programming perspective, and ensures session fidelity, absence of deadlocks, and a tight operational correspondence between πcalculus reductions and cut elimination steps. 1
Linearity and Laziness
 In Proc. 5th ACM Conference on Functional Programming Languages and Computer
, 1990
"... A criticism often levelled at functional languages is that they do not cope elegantly or efficiently with problems involving changes of state. In a recent paper [26], Wadler has proposed a new approach to these problems. His proposal involves the use of a type system based on the linear logic of Gir ..."
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Cited by 17 (1 self)
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A criticism often levelled at functional languages is that they do not cope elegantly or efficiently with problems involving changes of state. In a recent paper [26], Wadler has proposed a new approach to these problems. His proposal involves the use of a type system based on the linear logic of Girard [7]. This allows the programmer to specify the "natural" imperative operations without at the same time sacrificing the crucial property of referential transparency. In this paper we investigate the practicality of Wadler's approach, describing the design and implementation of a variant of Lazy ML [2]. A small example program shows how imperative operations can be used in a referentially transparent way, and at the same time it highlights some of the problems with the approach. Our implementation is based on a variant of the Gmachine [15, 1]. We give some benchmark figures to compare the performance of our machine with the original one. The results are disappointing: the cost of maintai...
The LambdaCalculus with Multiplicities
, 1993
"... We introduce a refinement of the λcalculus, where the argument of a function is a bag of resources, that is a multiset of terms, whose multiplicities indicate how many copies of them are available. We show that this "λcalculus with multiplicities" has a natural functionality theory, similar to Cop ..."
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Cited by 17 (2 self)
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We introduce a refinement of the λcalculus, where the argument of a function is a bag of resources, that is a multiset of terms, whose multiplicities indicate how many copies of them are available. We show that this "λcalculus with multiplicities" has a natural functionality theory, similar to Coppo and Dezani's intersection type discipline. In our functionality theory the conjunction is managed in a "multiplicative" manner, according to Girard's terminology. We show that this provides an adequate interpretation of the calculus, by establishing that a term is convergent if and only if it has a nontrivial functional character.
Linearizing Intuitionistic Implication
 In Proc. 6th Annual IEEE Symposium on Logic in Computer Science
, 1993
"... An embedding of the implicational propositional intuitionistic logic (iil) into the nonmodal fragment of intuitionistic linear logic (imall) is given. The embedding preserves cutfree proofs in a proof system that is a variant of iil. The embedding is efficient and provides an alternative proof of t ..."
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Cited by 16 (5 self)
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An embedding of the implicational propositional intuitionistic logic (iil) into the nonmodal fragment of intuitionistic linear logic (imall) is given. The embedding preserves cutfree proofs in a proof system that is a variant of iil. The embedding is efficient and provides an alternative proof of the pspacehardness of imall. It exploits several prooftheoretic properties of intuitionistic implication that analyze the use of resources in iil proofs. Linear logic is a refinement of classical and intuitionistic logic that provides an intrinsic and natural accounting of resources. In Girard's words [12], "linear logic is a logic behind logic." A convenient way to present linear logic is by modifying the traditional Gentzenstyle sequent calculus axiomatization of classical logic (see, e.g., [15, 22]). The modification may be briefly described in three steps. The first step is to remove two structural rules, contraction and weakening, which manipulate the use of hypotheses and conclusi...