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 asymptoticallyall the terms are strongly normalizing and that any fixed closed term almostnever appears in a random term. Surprisingly, in combinatory logic (thetranslation of the \lambda-calculus into combinators), the result is exactlyopposite. We show that almost all terms are not strongly normalizing. This isdue to the fact that any fixed combinator almost always appears in a randomcombinator