A natural counting of lambda terms
Logic in Computer Science
2016-05-18 v3 Discrete Mathematics
Programming Languages
Combinatorics
Logic
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.
Keywords
Cite
@article{arxiv.1506.02367,
title = {A natural counting of lambda terms},
author = {Maciej Bendkowski and Katarzyna Grygiel and Pierre Lescanne and Marek Zaionc},
journal= {arXiv preprint arXiv:1506.02367},
year = {2016}
}