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A NATURAL COUNTING OF LAMBDA TERMS

Abstract : We study the sequences of numbers corresponding to lambda terms of given sizes, where the size is this of lambda terms with de Bruijn indices in a very natural model where all the operators have size 1. For plain lambda terms, the sequence corresponds to two families of binary trees for which we exhibit bijections. We study also the distribution of normal forms, head normal forms and strongly normalizing terms. In particular we show that strongly normalizing terms are of density 0 among plain terms.
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https://hal-ens-lyon.archives-ouvertes.fr/ensl-01159746
Contributor : Pierre Lescanne <>
Submitted on : Thursday, July 2, 2015 - 9:38:28 AM
Last modification on : Friday, April 20, 2018 - 3:44:25 PM
Long-term archiving on: : Tuesday, April 25, 2017 - 10:09:51 PM

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  • HAL Id : ensl-01159746, version 2
  • ARXIV : 1506.02367

Citation

Maciej Bendkowski, Katarzyna Grygiel, Pierre Lescanne, Marek Zaionc. A NATURAL COUNTING OF LAMBDA TERMS. 2015. ⟨ensl-01159746v2⟩

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