About range property for H

International audienceRecently, A. Polonsky has shown that the range property fails for H. We give here some conditions on a closed term that imply that its range has an infi nite cardinality

About range property for H

International audienceRecently, A. Polonsky has shown that the range property fails for H. We give here some conditions on a closed term that imply that its range has an infi nite cardinality

Storage operators and directed lambda-calculus

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)