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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.
Must Preorder in NonDeterministic Untyped λcalculus
 IN CAAP '92, VOLUME 581 OF LNCS
, 1992
"... This paper studies the interplay between functional application and nondeterministic choice in the context of untyped λcalculus. We introduce an operational semantics which is based on the idea of must preorder, coming from the theory of process algebras. To characterize this relation, we build a ..."
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Cited by 11 (1 self)
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This paper studies the interplay between functional application and nondeterministic choice in the context of untyped λcalculus. We introduce an operational semantics which is based on the idea of must preorder, coming from the theory of process algebras. To characterize this relation, we build a model using the classical inverse limit construction, and we prove it fully abstract using a generalization of Böhm trees.
NonDeterministic Extensions of Untyped λcalculus
 INFO. AND COMP
, 1995
"... The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in ..."
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Cited by 6 (0 self)
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The main concern of this paper is the study of the interplay between functionality and non determinism. Indeed the first question we ask is whether the analysis of parallelism in terms of sequentiality and non determinism, which is usual in the algebraic treatment of concurrency, remains correct in presence of functional application and abstraction. We identify non determinism in the setting of λcalculus with the absence of the ChurchRosser property plus the inconsistency of the equational theory obtained by the symmetric closure of the reduction relation. We argue in favour of a distinction between non determinism and parallelism, due to the conjunctive nature of the former in contrast to the disjunctive character of the latter. This is the basis of our analysis of the operational and denotational semantics of non deterministiccalculus, which is the classical calculus plus a choice operator, and of our election of bounded indeterminacy as the semantical counterpart of conjunctive non determinism. This leads to operational semantics based on...
The Discriminating Power of Multiplicities in the λCalculus
, 1996
"... The λcalculus with multiplicities is a refinement of the lazy λcalculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over ..."
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Cited by 2 (0 self)
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The λcalculus with multiplicities is a refinement of the lazy λcalculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual λterms. We prove in particular that the observational equivalence induced by contexts with multiplicities coincides with the equality of LévyLongo trees associated with λterms. This is a consequence of the characterization we give of the corresponding observational precongruence, as an intensional preorder involving etaexpansion, namely Ong's lazy PlotkinScottEngeler preorder.
The Discriminating Power of Multiplicities in the LambdaCalculus
, 1996
"... The calculus with multiplicities is a refinement of the lazy calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over th ..."
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Cited by 1 (0 self)
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The calculus with multiplicities is a refinement of the lazy calculus where the argument in an application comes with a multiplicity, which is an upper bound to the number of its uses. This introduces potential deadlocks in the evaluation. We study the discriminating power of this calculus over the usual terms. We prove in particular that the observational equivalence induced by contexts with multiplicities coincides with the equality of L'evyLongo trees associated with terms. This is a consequence of the characterization we give of the corresponding observational precongruence, as an intensional preorder involving jexpansion, namely Ong's lazy PlotkinScottEngeler preorder. 1 Introduction The calculus with multiplicities was introduced in [5] for the purpose of studying the relationship between the calculus and Milner's ßcalculus [13]. It is a "resource conscious" refinement of the calculus, based on the following observation: in an application MN the argument N is infini...
lambdaCalculus, Multiplicities and the piCalculus
, 1995
"... : In this paper we study the semantics of the calculus induced by Milner's encoding into the ßcalculus. We show that the resulting may testing preorder on terms coincides with the inclusion of L'evyLongo trees. To establish this result, we use a refinement of the calculus where the argument of ..."
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: In this paper we study the semantics of the calculus induced by Milner's encoding into the ßcalculus. We show that the resulting may testing preorder on terms coincides with the inclusion of L'evyLongo trees. To establish this result, we use a refinement of the calculus where the argument of a function may be of limited availability. In our  calculus with multiplicities, evaluation is deterministic, but it may deadlock, due to the lack of resources. We show that this feature is enough to make the calculus as discriminating as the ßcalculus. Keywords: functional and concurrent languages, semantics, lambdacalculus (R'esum'e : tsvp) Partially supported by the ESPRIT Basic Research Project 6454  CONFER. Present address: Universit`a di Bologna, Dipartimento di Matematica, Piazza di Porta San Donato 5, 40127 Bologna, Italy. Unite de recherche INRIA SophiaAntipolis 2004 route des Lucioles, BP 93, 06902 SOPHIAANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77  Telec...