Asymptotically almost all \lambda-terms are strongly normalizing
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 tra...
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Veröffentlicht in: | Logical methods in computer science 2013-02, Vol.9, Issue 1 |
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Hauptverfasser: | , , , , , |
Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 1860-5974 1860-5974 |
DOI: | 10.2168/LMCS-9(1:2)2013 |