René David ; Katarzyna Grygiel ; Jakub Kozic ; Christophe Raffalli ; Guillaume Theyssier et al. - Asymptotically almost all \lambda-terms are strongly normalizing

lmcs:848 - Logical Methods in Computer Science, February 15, 2013, Volume 9, Issue 1 - https://doi.org/10.2168/LMCS-9(1:2)2013
Asymptotically almost all \lambda-terms are strongly normalizing

Authors: René David ; Katarzyna Grygiel ; Jakub Kozic ; Christophe Raffalli ; Guillaume Theyssier ; Marek Zaionc

    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.


    Volume: Volume 9, Issue 1
    Published on: February 15, 2013
    Accepted on: June 25, 2015
    Submitted on: September 27, 2010
    Keywords: Mathematics - Logic,Computer Science - Discrete Mathematics,Computer Science - Logic in Computer Science,Mathematics - Combinatorics,G.2.1

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    Source : ScholeXplorer HasVersion DOI 10.48550/arxiv.0903.5505
    • 10.48550/arxiv.0903.5505
    Asymptotically almost all ��-terms are strongly normalizing
    David, Ren�� ; Grygiel, Katarzyna ; Kozic, Jakub ; Raffalli, Christophe ; Theyssier, Guillaume ; Zaionc, Marek ;

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