The π-Calculus in Direct Style

  • Authors:
  • Gérard Boudol

  • Affiliations:
  • INRIA Sophia-Antipolis, BP 93, Sophia Antipolis Cedex, FRANCE. gerard.boudol@sophia.inria.fr

  • Venue:
  • Higher-Order and Symbolic Computation
  • Year:
  • 1998

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Abstract

We introduce a calculus which is a direct extension of both theλ and the π calculi. We give a simple type system for it,that encompasses both Curry‘s type inference for theλ-calculus, and Milner‘s sorting for the π-calculus asparticular cases of typing. We observe that the various continuationpassing style transformations for λ-terms, written in ourcalculus, actually correspond to encodings already given by Milner andothers for evaluation strategies of λ-terms into theπ-calculus. Furthermore, the associated sortings correspond towell-known double negation translations on types. Finally we providean adequate CPS transform from our calculus to theπ-calculus. This shows that the latter may be regarded as an“assembly language”, while our calculus seems to provide a betterprogramming notation for higher-order concurrency. We conclude bydiscussing some alternative design decisions.