Abstract
We study the sequence of numbers corresponding to \(\lambda \)-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 \(\lambda \)-terms containing an arbitrary fixed subterm, showing that strongly normalizing terms are of density 0 among all \(\lambda \)-terms.
This work was partially supported by the grant 2013/11/B/ST6/00975 founded by the Polish National Science Center.
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Bendkowski, M., Grygiel, K., Lescanne, P., Zaionc, M. (2016). A Natural Counting of Lambda Terms. In: Freivalds, R., Engels, G., Catania, B. (eds) SOFSEM 2016: Theory and Practice of Computer Science. SOFSEM 2016. Lecture Notes in Computer Science(), vol 9587. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-49192-8_15
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