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A Functional Theory of Local Names
, 1994
"... ## is an extension of the #calculus with a binding construct for local names. The extension has properties analogous to classical #calculus and preserves all observational equivalences of #. It is useful as a basis for modeling widespectrum languages that build on a functional core. 1 Introducti ..."
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## is an extension of the #calculus with a binding construct for local names. The extension has properties analogous to classical #calculus and preserves all observational equivalences of #. It is useful as a basis for modeling widespectrum languages that build on a functional core. 1 Introduction Recentyears have given us a good deal of theoretical research on the interaction of imperative programming #exempli#ed byvariable assignment# and functional programming #exempli#ed by higher order functions# #3,6,19,21, 24#. The common method of all these works is to propose a #calculus extended with imperative features and to carry out an exploration of the operational semantics of the new calculus. Based on our own experience in devising such an extended # calculus #13#, the presentwork singles out the name, whose only observational property is its identity, as an essential componentofany such extension. We present a simple extension of the pure #calculus with names; we showby ex...
LabelSelective LambdaCalculus Syntax and Confluence
, 1995
"... . We introduce an extension of calculus, called labelselective  calculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in ..."
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. We introduce an extension of calculus, called labelselective  calculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in order to preserve currying. This extension of calculus is conservative in the sense that when the set of labels is the singleton f1g, it coincides with calculus. The main result of this paper is that the labelselective calculus is confluent. In other words, argument selection and reduction commute. Keywords. Calculus, record calculus, concurrency, communication. 1 Synopsis Many modern programming languages allow specifying arguments of functions and procedures by symbolic keywords as well as using the traditional and natural numeric positions [16, 12, 4]. Symbolic keywords are usually handled as syntactic sugar and "compiled away" as numeric positions. This is made easy if the langua...
Lambda and pi calculi, CAM and SECD machines
, 2001
"... We analyse machines that implement the callbyvalue reduction strategy of the λcalculus: two environment machines—CAM and SECD—and two encodings into the πcalculus—due to Milner and Vasconcelos. To establish the relation between the various machines, we setup a notion of reduction machine and two ..."
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We analyse machines that implement the callbyvalue reduction strategy of the λcalculus: two environment machines—CAM and SECD—and two encodings into the πcalculus—due to Milner and Vasconcelos. To establish the relation between the various machines, we setup a notion of reduction machine and two notions of correspondences: operational—in which a reduction step in the source machine is mimicked by a sequence of steps in the target machine—and convergent—where only reduction to normal form is simulated. We show that there are operational correspondences from the λcalculus into CAM, and from CAM and from SECD into the πcalculus. Plotkin completes the picture by showing that there is a convergent correspondence from the λcalculus into SECD. 1
LabelSelective ...Calculus
"... We introduce an extension of calculus, called labelselective calculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in ord ..."
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We introduce an extension of calculus, called labelselective calculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in order to preserve currying. This extension of calculus is conservative in the sense that when the set of labels is the singleton f1g, it coincides with calculus. The main result of this paper is the proof that the labelselective calculus is confluent. In other words, argument selection and reduction commute. R esum e Nous presentons une extension du calcul, appelee calcul labelselectif, dans laquelle les arguments des fonctions sont selectionnes par des etiquettes. L'ensemble des etiquettes comprend des positions numeriques aussi bien que des motclefs symboliques. Alors que ces derniers jouissent d'une commutativite libre, les premiers obeissent a une precedence relative pour preserver...
The callbyvalue lambdacalculus, the SECD machine, and the picalculus
, 2000
"... We present an encoding of the callbyvalue lambdacalculus into the picalculus, alternative to the wellknown Milner's encodings. We show that our encoding is barbed congruent (under typed contexts) to Milner's "light" encoding, and that it takes two pisteps to mimic a betareduction for normaliz ..."
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We present an encoding of the callbyvalue lambdacalculus into the picalculus, alternative to the wellknown Milner's encodings. We show that our encoding is barbed congruent (under typed contexts) to Milner's "light" encoding, and that it takes two pisteps to mimic a betareduction for normalizing terms. We describe a translation of Plotkin's SECD machine into the picalculus, and show that there is an operational correspondence between a SECD machine and its encoding. Equipped with a notion of statebased machine and two kinds of correspondences between them, we compare the encodings of the callbyvalue lambdacalculus and the SECD machine into the picalculus. Contents 1 Introduction 2 2 The correspondences 4 2.1 Machines and correspondences . . . . . . . . . . . . . . . . . . . 4 2.2 Some properties of convergences . . . . . . . . . . . . . . . . . . 5 2.3 Summary of the correspondences . . . . . . . . . . . . . . . . . . 6 3 The callbyvalue #calculus 8 4 The SECD machin...
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"... to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of the Paris Research Laboratory of Digital Equipment Centre Technique Euro ..."
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to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of the Paris Research Laboratory of Digital Equipment Centre Technique Europe, in RueilMalmaison, France; an acknowledgement of the authors and individual contributors to the work; and all applicable portions of the copyright notice. Copying, reproducing, or republishing for any other purpose shall require a license with payment of fee to the Paris Research Laboratory. All rights reserved. We introduce an extension ofcalculus, called labelselectivecalculus, in which arguments of functions are selected by labels. The set of labels includes numeric positions as well as symbolic keywords. While the latter enjoy free commutation, the former must comply with relative precedence in order to preserve currying. This extension ofcalculus is conservative in the sense that when the set of labels is the singleton f1g, it coincides withcalculus. The main result of this paper is the proof that the labelselectivecalculus is confluent. In other words, argument selection and reduction commute. Résumé