Intersection Types for the Resource Control Lambda Calculi

  • Silvia Ghilezan
  • Jelena Ivetić
  • Pierre Lescanne
  • Silvia Likavec
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6916)

Abstract

We propose intersection type assignment systems for two resource control term calculi: the lambda calculus and the sequent lambda calculus with explicit operators for weakening and contraction. These resource control calculi, λ ® and \(\lambda_\circledR^{Gtz}\), respectively, capture the computational content of intuitionistic natural deduction and intuitionistic sequent logic with explicit structural rules. Our main contribution is the characterisation of strong normalisation of reductions in both calculi. We first prove that typability implies strong normalisation in λ ® by adapting the reducibility method. Then we prove that typability implies strong normalisation in \(\lambda_\circledR^{Gtz}\) by using a combination of well-orders and a suitable embedding of \(\lambda_\circledR^{Gtz}\)-terms into λ ®-terms which preserves types and enables the simulation of all its reductions by the operational semantics of the λ ®-calculus. Finally, we prove that strong normalisation implies typability in both systems using head subject expansion.

Keywords

Intersection Type Reduction Rule Resource Control Substructural Logic Strong Normalisation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Silvia Ghilezan
    • 1
  • Jelena Ivetić
    • 1
  • Pierre Lescanne
    • 2
  • Silvia Likavec
    • 3
  1. 1.Faculty of Technical SciencesUniversity of Novi SadSerbia
  2. 2.École Normal Supérieure de LyonUniversity of LyonFrance
  3. 3.Dipartimento di InformaticaUniversità di TorinoItaly

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