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Normal-order reduction grammars*

Part of: JFP Research Articles

Published online by Cambridge University Press:  17 January 2017

MACIEJ BENDKOWSKI
MACIEJ BENDKOWSKI*
Affiliation:
Theoretical Computer Science Department, Faculty of Mathematics and Computer Science, Jagiellonian University, ul. Prof. Łojasiewicza 6, 30-348 Kraków, Poland (e-mail: maciej.bendkowski@tcs.uj.edu.pl)
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Abstract

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We present an algorithm which, for given n, generates an unambiguous regular tree grammar defining the set of combinatory logic terms, over the set {S, K} of primitive combinators, requiring exactly n normal-order reduction steps to normalize. As a consequence of Curry and Feys's standardization theorem, our reduction grammars form a complete syntactic characterization of normalizing combinatory logic terms. Using them, we provide a recursive method of constructing ordinary generating functions counting the number of SK-combinators reducing in n normal-order reduction steps. Finally, we investigate the size of generated grammars giving a primitive recursive upper bound.

Type
Articles
Information
Journal of Functional Programming , Volume 27 , 2017 , e6
Copyright
Copyright © Cambridge University Press 2017 

Footnotes

*

This work was partially supported within the Polish National Science Center grant 2013/11/B/ST6/00975.

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