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Normal-order reduction grammars*


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.

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

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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
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Normal-order reduction grammars*

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