Abstract
We study the sequence of numbers corresponding to λ-terms of given size in the model based on de Bruijn indices. It turns out that the sequence enumerates also two families of binary trees, i.e. black-white and zigzag-free ones.We provide a constructive proof of this fact by exhibiting appropriate bijections. Moreover, we investigate the asymptotic density of λ-terms containing an arbitrary fixed subterm, showing that strongly normalizing terms are of density 0 among all λ-terms.
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Bendkowski, M., Grygiel, K., Lescanne, P., & Zaionc, M. (2015). A natural counting of lambda terms. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9587, pp. 183–194). Springer Verlag. https://doi.org/10.1007/978-3-662-49192-8_15
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