×

Point-fixe sur un ensemble restreint. (Fixed points on a restricted set). (French) Zbl 0642.03009

Summary: The article presents a constructive proof of the existence of normalizing fixed-point operators restricted to \(\lambda\)-term subclasses. Domains where fixed-point operators can be defined cover usual areas of functional programming applications.

MSC:

03B40 Combinatory logic and lambda calculus
68N01 General topics in the theory of software

References:

[1] 1. H. P. BARENDREGT, The Lambda Calculus, Its Syntax and Semantics. Studies in Logic and Foundations of Mathematics, vol. 103, North-Holland Publishing Compagny. Zbl0467.03010 MR774952 · Zbl 0467.03010
[2] 2. P. BELLOT, Propriétés logico-combinatoires desSystèmes de programmation sans variables, Thèse de 3e cycle, Paris-VI, L.I.T.P., 84-30, 1984.
[3] 3. A. BERARDUCCI, Programmazione Funzionale e Rappresentabilità inalcuni Sistemi di Logica Combinatoria, Tesi di laurea in Matematica, Roma, 1983.
[4] 4. C. BOEHM, Modèle arithmétique de la Logique Combinatoire, Lambda-Calcul et sémantique formelle des langages de programmation, L.I.T.P.-E.N.S.T.A., 1979, p. 97, 108
[5] 5. A. CHURCH, The Calculi of Lambda conversion, Annals of Math. Studies, 6, Princeton University Press, 1941. MR5274 JFM67.0041.01 · JFM 67.0041.01
[6] 6. H. B. CURRY, Combinatory Logic, vol. I, North Holland, Amsterdam, 1958. Zbl0081.24104 MR94298 · Zbl 0081.24104
[7] 7. C.T. LIEU, Étude d’une Extension Combinatoire des Entiers naturels. Application à la Programmation fonctionnelle. Thèse de 3e cycle, Paris-VI, L.I.T.P., 84-27, 1984.
[8] 8. M. MEZGHICHE, Intertraduction entre le Lambea-Calcul et la Logique Combinatoire, Thèse de 3e cycle, Paris-VII, L.I.T.P., 83-25, 1983.
[9] 9. A. M. TURING, The p-functions in \lambda -K-conversion, J. Symbolic Logic, vol. 2, 1937, p. 164. JFM63.0825.01 · JFM 63.0825.01
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.