S-Storage Operators

In 1990, J.L. Krivine introduced the notion of storage operator to simulate, for Church integers, the “call by value” in a context of a “call by name” strategy. In this present paper, we define, for every λ-term S which realizes the successor function on Church integers, the notion of S-storage operator. We prove that every storage operator is a S-storage operator. But the converse is not always true. Mathematics Subject Classification : 03B40, 68Q60 Keywords : Church integer ; Storage operator ; Call by value ; Call by name ; Head reduction ; Solvable ; Successor ; S-storage operator. 1 Definitions and notations • We denote by Λ the set of λ-terms modulo α-equivalence, and by V the set of λ-variables. • Let t, u, u1, ..., un be λ-terms, the application of t to u is denoted by (t)u. In the

• Type: Journal
• Year: 1998
• Where: MLQ
• Authors: Karim Nour
• Keywords: Church Integers, MLQ 1998, Operator, Storage Operator