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The πCalculus in Direct Style
, 1997
"... We introduce a calculus which is a direct extension of both the and the π calculi. We give a simple type system for it, that encompasses both Curry's type inference for the calculus, and Milner's sorting for the πcalculus as particular cases of typing. We observe that the various contin ..."
Abstract

Cited by 70 (2 self)
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We introduce a calculus which is a direct extension of both the and the π calculi. We give a simple type system for it, that encompasses both Curry's type inference for the calculus, and Milner's sorting for the πcalculus as particular cases of typing. We observe that the various continuation passing style transformations for terms, written in our calculus, actually correspond to encodings already given by Milner and others for evaluation strategies of terms into the πcalculus. Furthermore, the associated sortings correspond to wellknown double negation translations on types. Finally we provide an adequate cps transform from our calculus to the πcalculus. This shows that the latter may be regarded as an "assembly language", while our calculus seems to provide a better programming notation for higherorder concurrency.
On the Semantics of the CallbyName CPS Transform
"... Sangiorgi has shown that the semantics induced by Milner's encoding of the callbyname calculus in the ßcalculus is the equality of L#vyLongo trees. Later it was realized that Milner's encodings are actually variations on wellknown continuation passing style transforms. Then a questi ..."
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Cited by 4 (0 self)
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Sangiorgi has shown that the semantics induced by Milner's encoding of the callbyname calculus in the ßcalculus is the equality of L#vyLongo trees. Later it was realized that Milner's encodings are actually variations on wellknown continuation passing style transforms. Then a question is: is the discriminating ability due to ßcalculus features, or is it already ooeered by the cps transform? We show that the latter is true: the semantics induced by the callbyname cps transform on terms is L#vyLongo trees equality. Keywords continuationpassingstyle transforms, calculus, L#vyLongo trees, B#hmout technique. 1. Introduction The Calculus In this note we study the semantics induced by Plotkin's callbyname cps transform [13], which has for both source and target languages the calculus. To start with, we øx some notations regarding this calculus (we sometimes deviate from the notations of Barendregt's book [1]), which we assume the reader is familiar with. We denote by ...