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An abstraction algorithm for combinatory logic

Published online by Cambridge University Press:  12 March 2014

S. Kamal Abdali*
Affiliation:
Rensselaer Polytechnic Institute, Troy, New York 12181

Extract

This note presents a practical algorithm for carrying out abstraction on combinatory terms. The well-known abstraction algorithms [1, pp. 188ff.] defining abstracts in terms of the combinator sets {S, K }, {B, C, K, W }, etc. operate on one variable at a time, and result in rather long abstracts when several variables are involved. These algorithms are not practical for the applications of the combinatory logic to the theory of computing which make much use of multi-variable abstraction (e.g., [2], [3]). The present algorithm performs the abstraction with respect to all specified variables in a single step, and yields abstracts in a concise form (with sizes proportional to those of given combinatory terms).

Information

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 1976

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