Intersection Types for the Resource Control Lambda Calculi

Pierre Lescanne; Silvia Ghilezan; Jelena Ivetic; Silvia Likavec

Intersection Types for the Resource Control Lambda Calculi

Pierre Lescanne ¹ Silvia Ghilezan ² Jelena Ivetic ² Silvia Likavec ³

1 LIP - Laboratoire de l'Informatique du Parallélisme

2 Faculty of engineering, University of Novi Sad

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, /\® and /\®-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 /\® by adapting the reducibility method. Then we prove that typability implies strong normalisation in /\®-Gtz by using a combination of well-orders and a suitable embedding of /\®-Gtz-terms into /\®-terms which preserves types and enables the simulation of all its reductions by the operational semantics of the /\®-calculus. Finally, we prove that strong normalisation implies typability in both systems using head subject expansion.

Mots-clés : lambda calculus sequent calculus resource control intersection types strong normalisation

Document type :

Conference papers

Domain :

Mathematics [math] / Logic [math.LO]

Computer Science [cs] / Logic in Computer Science [cs.LO]

Complete list of metadatas

https://hal-ens-lyon.archives-ouvertes.fr/ensl-00654755
Contributor : Pierre Lescanne <>
Submitted on : Thursday, December 22, 2011 - 8:28:12 PM
Last modification on : Tuesday, April 24, 2018 - 1:52:22 PM

Intersection Types for the Resource Control Lambda Calculi

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Intersection Types for the Resource Control Lambda Calculi

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