Asymptotically almost all \lambda-terms are strongly normalizing
Logic
2019-03-14 v5 Discrete Mathematics
Logic in Computer Science
Combinatorics
Abstract
We present quantitative analysis of various (syntactic and behavioral) properties of random \lambda-terms. Our main results are that asymptotically all the terms are strongly normalizing and that any fixed closed term almost never appears in a random term. Surprisingly, in combinatory logic (the translation of the \lambda-calculus into combinators), the result is exactly opposite. We show that almost all terms are not strongly normalizing. This is due to the fact that any fixed combinator almost always appears in a random combinator.
Cite
@article{arxiv.0903.5505,
title = {Asymptotically almost all \lambda-terms are strongly normalizing},
author = {René David and Katarzyna Grygiel and Jakub Kozic and Christophe Raffalli and Guillaume Theyssier and Marek Zaionc},
journal= {arXiv preprint arXiv:0903.5505},
year = {2019}
}