Intersection types for the resource control lambda calculi

  • Authors:

  • Silvia Ghilezan;Jelena Ivetić;Pierre Lescanne;Silvia Likavec

  • Affiliations:

  • University of Novi Sad, Faculty of Technical Sciences, Serbia;University of Novi Sad, Faculty of Technical Sciences, Serbia;University of Lyon, École Normal Supérieure de Lyon, France;Dipartimento di Informatica, Università di Torino, Italy

  • Venue:
  • ICTAC'11 Proceedings of the 8th international conference on Theoretical aspects of computing
  • Year:
  • 2011

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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 λ®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 λ®Gtz by using a combination of well-orders and a suitable embedding of λ®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.