Results 1  10
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24
Barbed Bisimulation
, 1992
"... Machine [8]. In this technique, axioms for a structural congruence relation are introduced prior to the reduction system, in order to to break a rigid, geometrical vision of concurrency; then reduction rules can easily be presented in which redexes are indeed subterms again. It can then be shown 1 ..."
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Cited by 233 (20 self)
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Machine [8]. In this technique, axioms for a structural congruence relation are introduced prior to the reduction system, in order to to break a rigid, geometrical vision of concurrency; then reduction rules can easily be presented in which redexes are indeed subterms again. It can then be shown 1 that modulo structural congruence the reduction relation exactly represents the silent action of the transition semantics. It is left as an open problem in [11] how to recover from such a formulation the familiar congruences which are based upon a labelled transition system. It turns out that this is not a trivial problem. We tackle it in this paper for the simple case of CCS and strong observational equivalence (). Because the reduction relation coincides with the silent action \Gamma! of the labelled transition system (as mentioned above), we can remain within the latter framework. But we wish to retain the spirit of the reduction semantics as far as possible, in the sense that we wish t...
Games and Full Abstraction for the Lazy lambdacalculus
 In Proceedings, Tenth Annual IEEE Symposium on Logic in Computer Science
, 1995
"... ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typ ..."
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Cited by 139 (9 self)
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ion for the Lazy calculus Samson Abramsky Guy McCusker Department of Computing Imperial College of Science, Technology and Medicine 180 Queen's Gate London SW7 2BZ United Kingdom Abstract We define a category of games G, and its extensional quotient E . A model of the lazy calculus, a typefree functional language based on evaluation to weak head normal form, is given in G, yielding an extensional model in E . This model is shown to be fully abstract with respect to applicative simulation. This is, so far as we know, the first purely semantic construction of a fully abstract model for a reflexivelytyped sequential language. 1 Introduction Full Abstraction is a key concept in programming language semantics [9, 12, 23, 26]. The ingredients are as follows. We are given a language L, with an `observational preorder'  on terms in L such that P  Q means that every observable property of P is also satisfied by Q; and a denotational model MJ\DeltaK. The model M is then said to be f...
Confluence properties of Weak and Strong Calculi of Explicit Substitutions
 JOURNAL OF THE ACM
, 1996
"... Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence prope ..."
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Cited by 130 (7 self)
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Categorical combinators [12, 21, 43] and more recently oecalculus [1, 23], have been introduced to provide an explicit treatment of substitutions in the calculus. We reintroduce here the ingredients of these calculi in a selfcontained and stepwise way, with a special emphasis on confluence properties. The main new results of the paper w.r.t. [12, 21, 1, 23] are the following: 1. We present a confluent weak calculus of substitutions, where no variable clashes can be feared. 2. We solve a conjecture raised in [1]: oecalculus is not confluent (it is confluent on ground terms only). This unfortunate result is "repaired" by presenting a confluent version of oecalculus, named the Envcalculus in [23], called here the confluent oecalculus.
Distributed Processes and Location Failures
 Theoretical Computer Science
, 1997
"... . Site failure is an essential aspect of distributed systems; nonetheless its effect on programming language semantics remains poorly understood. To model such systems, we define a process calculus in which processes are run at distributed locations. The language provides operators to kill locations ..."
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Cited by 59 (7 self)
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. Site failure is an essential aspect of distributed systems; nonetheless its effect on programming language semantics remains poorly understood. To model such systems, we define a process calculus in which processes are run at distributed locations. The language provides operators to kill locations, to test the status (dead or alive) of locations, and to spawn processes at remote locations. Using a variation of bisimulation, we provide alternative characterizations of strong and weak barbed congruence for this language, based on an operational semantics that uses configurations to record the status of locations. We then derive a second, symbolic characterization in which configurations are replaced by logical formulae. In the strong case the formulae come from a standard propositional logic, while in the weak case a temporal logic with past time modalities is required. The symbolic characterization establishes that, in principle, barbed congruence for such languages can be checked ef...
The Lazy Lambda Calculus in a Concurrency Scenario (Extended Abstract)
 Information and Computation
, 1994
"... ) Davide Sangiorgi LFCS  Department of Computer Science Edinburgh University Edinburgh  EH9 3JZ  UK Abstract The use of lambda calculus in richer settings, possibly involving parallelism, is examined in terms of its effect on the equivalence between lambda terms. We concentrate here on Abra ..."
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Cited by 58 (8 self)
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) Davide Sangiorgi LFCS  Department of Computer Science Edinburgh University Edinburgh  EH9 3JZ  UK Abstract The use of lambda calculus in richer settings, possibly involving parallelism, is examined in terms of its effect on the equivalence between lambda terms. We concentrate here on Abramsky's lazy lambda calculus and we follow two directions. First, the lambda calculus is studied within a process calculus by examining the equivalence $ induced by Milner's encoding into the calculus. We give exact operational and denotational characterizations for $. Secondly, we examine Abramsky's applicative bisimulation when the lambda calculus is augmented with (wellformed) operators, i.e. symbols equipped with reduction rules describing their behaviour. Then, maximal discrimination is obtained when all operators are considered; we show that this discrimination coincides with the one given by $ and that the adoption of certain nondeterministic operators is sufficient and necessary...
Filter Models for ConjunctiveDisjunctive λcalculi
, 1996
"... The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction i ..."
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Cited by 11 (6 self)
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The distinction between the conjunctive nature of nondeterminism as opposed to the disjunctive character of parallelism constitutes the motivation and the starting point of the present work. λcalculus is extended with both a nondeterministic choice and a parallel operator; a notion of reduction is introduced, extending fireduction of the classical calculus. We study type assignment systems for this calculus, together with a denotational semantics which is initially defined constructing a set semimodel via simple types. We enrich the type system with intersection and union types, dually reflecting the disjunctive and conjunctive behaviour of the operators, and we build a filter model. The theory of this model is compared both with a Morrisstyle operational semantics and with a semantics based on a notion of capabilities.
An investigation into Functions as Processes
 In Proc. Ninth International Conference on the Mathematical Foundations of Programming Semantics (MFPS'93
, 1993
"... . In [Mil90] Milner examines the encoding of the calculus into the ßcalculus [MPW92]. The former is the universally accepted basis for computations with functions, the latter aims at being its counterpart for computations with processes. The primary goal of this paper is to continue the study of M ..."
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Cited by 11 (1 self)
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. In [Mil90] Milner examines the encoding of the calculus into the ßcalculus [MPW92]. The former is the universally accepted basis for computations with functions, the latter aims at being its counterpart for computations with processes. The primary goal of this paper is to continue the study of Milner's encodings. We focus mainly on the lazy calculus [Abr87]. We show that its encoding gives rise to a model, in which a weak form of extensionality holds. However the model is not fully abstract: To obtain full abstraction, we examine both the restrictive approach, in which the semantic domain of processes is cut down, and the expansive approach, in which calculus is enriched with constants to obtain a direct characterisation of the equivalence on terms induced, via the encoding, by the behavioural equivalence adopted on the processes. Our results are derived exploiting an intermediate representation of Milner's encodings into the HigherOrder ßcalculus, an !order extension of ...
Characterizing Convergent Terms in Object Calculi via Intersection Types
"... We give a simple characterization of convergent terms in Abadi and Cardelli untyped Object Calculus (&calculus) via intersection types. We consider a calculus with records and its intersection type assignment system. We prove that convergent terms are characterized by their types. The cha ..."
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Cited by 11 (4 self)
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We give a simple characterization of convergent terms in Abadi and Cardelli untyped Object Calculus (&calculus) via intersection types. We consider a calculus with records and its intersection type assignment system. We prove that convergent terms are characterized by their types. The characterization is then inherited by the object calculus via selfapplication interpretation.
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 8 (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...