Resource combinatory algebras

Authors:
Alberto Carraro;Thomas Ehrhard;Antonino Salibra
Affiliations:
Dipartimento di Informatica, Università Ca' Foscari Venezia, Italia and Laboratoire PPS, Université Paris-Diderot, Paris, France;Laboratoire PPS, Université Paris-Diderot, Paris, France;Dipartimento di Informatica, Università Ca' Foscari Venezia, Italia
Venue:
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Year:
2010

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Abstract

We initiate a purely algebraic study of Ehrhard and Regnier's resource λ-calculus, by introducing three equational classes of algebras: resource combinatory algebras, resource lambda-algebras and resource lambda-abstraction algebras. We establish the relations between them, laying down foundations for a model theory of resource λ-calculus. We also show that the ideal completion of a resource combinatory (resp. lambda-, lambda-abstraction) algebra induces a "classical" combinatory (resp. lambda-, lambda-abstraction) algebra, and that any model of the classical λ-calculus raising from a resource lambda-algebra determines a λ-theory which equates all terms having the same Böhm tree.