Abstract
In this paper we propose a system, based onλβδ-calculus, where the restriction of Church'sδ to normal forms is dropped, while the monotony properties are weakened. The main feature of such a system is that the Church-Rosser property is maintained and all provable equalities between closed terms are semidecidable within it.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barendregt, H. et al.: Degrees reductions and representability in theλ-calculus. Preprint Utrecht University, 1976.
Barendregt, H.: Normed uniformly reflexive structures. Proceedings of the Symposium onλ-calculus and computer science theory. Berlin, Heidelberg, New York: Springer 1975.
Church, A.: The calculi ofλ-conversion. Princeton: Princeton University Press 1941.
Hindley, R., Mitschke, G.: Some remarks about the connections between combinatory logic and axiomatic recursion theory. Arch. math. Logik18, 99–103 (1977).
Hyland, J.M.E.: A syntactic characterization of the equality in some models for the lambda calculus. J. of London Math. Soc. 361–370 (1976).
Kearns, J.T.: Combinatory Logic with discriminators, J. of Symb. Logic34, 561–575 (1969).
Klop, J.: A counterexample of the CR property ofλ-calculus + DMM → M, Draft, December 1977.
Mitschke, G.: Discriminators in combinatory logic andλ-calculus, Preprint n. 336, Darmstadt University, February 1977.
Rosen, B.K.: Tree-manipulating systems and Church-Rosser Theorems, JACM20, 160–187 (1973).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Longo, G., Zilli, M.V. Aλδ-calculus with an algorithmicδ . Arch math Logik 20, 41–52 (1980). https://doi.org/10.1007/BF02011137
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02011137