Call-by-Value Non-determinism in a Linear Logic Type Discipline

  • Alejandro Díaz-Caro
  • Giulio Manzonetto
  • Michele Pagani
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7734)

Abstract

We consider the call-by-value λ-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent intersection types, we endow this calculus with a type system based on the so-called Girard’s second translation of intuitionistic logic into linear logic. We prove that a term is typable if and only if it is converging, and that its typing tree carries enough information to give a bound on the length of its lazy call-by-value reduction. Moreover, when the typing tree is minimal, such a bound becomes the exact length of the reduction.

Keywords

λ-calculus linear logic non-determinism call-by-value 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Alejandro Díaz-Caro
    • 1
  • Giulio Manzonetto
    • 1
    • 2
  • Michele Pagani
    • 1
    • 2
  1. 1.Université Paris 13, Sorbonne Paris Cité, LIPNVilletaneuseFrance
  2. 2.CNRS, UMR 7030VilletaneuseFrance

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