STORAGE OPERATORS AND DIRECTED LAMBDA-CALCULUS

René David (1) , Karim Nour (1)

1 LAMA - Laboratoire de Mathématiques

Storage operators have been introduced by J.L. Krivine in [5] ; they are closed l-terms which, for a data type, allow to simulate a "call by value" while using the "call by name" strategy. In this paper, we introduce the directed l-calculus and show that it has the usual properties of the ordinary l-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 b-equivalence (theorem 5.1.1) ; - the undecidability ( and its semi-decidability ) of the problem "is a closed l-term t a storage operator for a finite set of closed normal l-terms ? " (theorems 5.2.2 and 5.2.3) ; - the existence of storage operators for every finite set of closed normal l-terms (theorem 5.4.3) ; - the computation time of the "storage operation" (theorem 5.5.2).

Domaines: Logique [math.LO]; Logique en informatique [cs.LO]

René David, Karim Nour. STORAGE OPERATORS AND DIRECTED LAMBDA-CALCULUS. The Journal of Symbolic Logic, 1995, 64 (4), p 1054-1086. ⟨hal-00385174⟩