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Storage operators and directed lambda-calculus

Published online by Cambridge University Press:  12 March 2014

René David  and
Karim Nour
René David
Affiliation:
LAMA—Equipe de Logique, Université de Savoie, Campus Scientifique, 73376 Le Bourget du Lac Cédex, France, E-mail: david@univ-savoie.fr
Karim Nour
Affiliation:
LAMA—Equipe de Logique, Université de Savoie, Campus Scientifique, 73376 Le Bourget du Lac Cédex, France, E-mail: nour@univ-savoie.fr
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Abstract

Storage operators have been introduced by J. L. Krivine in [5] they are closed λ-terms which, for a data type, allow one to simulate a “call by value” while using the “call by name” strategy. In this paper, we introduce the directed λ-calculus and show that it has the usual properties of the ordinary λ-calculus. With this calculus we get an equivalent—and simple—definition of the storage operators that allows to show some of their properties:

• the stability of the set of storage operators under the β-equivalence (Theorem 5.1.1);

• the undecidability (and semidecidability) of the problem “is a closed λ-term t a storage operator for a finite set of closed normal λ-terms?” (Theorems 5.2.2 and 5.2.3);

• the existence of storage operators for every finite set of closed normal λ-terms (Theorem 5.4.3);

• the computation time of the “storage operation” (Theorem 5.5.2).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 60 , Issue 4 , December 1995 , pp. 1054 - 1086
Copyright
Copyright © Association for Symbolic Logic 1995

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References

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