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Another algorithm for bracket abstraction

Published online by Cambridge University Press:  12 March 2014

D. A. Turner*
Computer Laboratory, University of Kent, Canterbury, England


This short article presents an algorithm for bracket abstraction [1] which avoids a combinatorial explosion in the size of the resulting expression when applied repeatedly for abstraction in a series of variables. It differs from a previous solution [2] in introducing only a finite number of additional combinators and in not requiring that all the variables to be abstracted be treated together in a single operation.

Research Article
Copyright © Association for Symbolic Logic 1979

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[1]Curry, H. B. and Feys, R., Combinatory logic, vol. 1, North-Holland, Amsterdam, 1958.Google Scholar
[2]Abdali, S. K., An abstraction algorithm for combinatory logic, this Journal, vol. 41 (1976), pp. 222224.Google Scholar
[3]Schoenfinkel, M., Über die Bausteine der mathematischen Logik, Mathematische Annalen, vol. 92 (1924), pp. 305316.CrossRefGoogle Scholar
[4]Turner, D. A., SASL language manual, St. Andrews University, Fife, Scotland, 1976.Google Scholar