Some properties of random lambda terms
Résumé
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 due to the fact that any fixed combinator almost always appears in a random combinator.
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