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

  • Alejandro Díaz-Caro
  • Giulio Manzonetto
  • Michele Pagani
Conference paper

DOI: 10.1007/978-3-642-35722-0_12

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7734)
Cite this paper as:
Díaz-Caro A., Manzonetto G., Pagani M. (2013) Call-by-Value Non-determinism in a Linear Logic Type Discipline. In: Artemov S., Nerode A. (eds) Logical Foundations of Computer Science. LFCS 2013. Lecture Notes in Computer Science, vol 7734. Springer, Berlin, Heidelberg

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations