Asymptotic Properties of Combinatory Logic

We present a quantitative analysis of random combinatory logic terms. Our main goal is to investigate likelihood of semantic properties of random combinators. We show that asymptotically almost all weakly normalizing terms are not strongly normalizing. Moreover, we present a proof that asymptotically almost all strongly normalizing terms are not in normal form. We also prove that asymptotically almost all normal forms in combinatory logic are not typeable.

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