Hostname: page-component-848d4c4894-xm8r8 Total loading time: 0 Render date: 2024-06-23T18:01:38.661Z Has data issue: false hasContentIssue false

Combinatory logic with discriminators

Published online by Cambridge University Press:  12 March 2014

John T. Kearns*
State University of New York at Buffalo


In this paper, I present a modified and extended version of combinatory logic. Schönfinkel originated the study of combinatory logic (in [2]), but its development is primarily due to H. B. Curry. In the present paper, I will make use of both the symbolism (with some modification) and the results of Curry, as found in [1].

What is novel about my version of combinatory logic is a kind of combinators which I call discriminators. These combinators discriminate between different symbols, and yield values which are determined by the symbols which are their arguments. If the normal combinators investigated by Curry are considered as functions taking (combinations of) symbols as arguments and yielding symbols as values, these combinators can rearrange and cancel their arguments or introduce new symbols.

Research Article
Copyright © Association for Symbolic Logic 1970

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


[1] Curry, Haskell B. and Feys, Robert, Combinatory logic, Vol. 1, North-Holland, Amsterdam, 1958.Google Scholar
[2] Schönfinkel, M., Über die Bausteine der mathematischen Logik, Mathematische Annalen, vol. 92 (1924), pp. 305316; English transl., From Frege to Gödel, ed. by Jean van Heijenoort. Google Scholar
[3] Turing, A. M., Computability and λ-definability, this Journal , vol. 2 (1937), pp. 153163.Google Scholar
[4] Turing, A. M., On computable numbers, with an application to the Entscheidungs problem, Proceedings of the London Mathematical Society, vol. 42 (1936), Series 2.Google Scholar