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2011 Proceedings of the Eighth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)

Lambda terms of bounded unary height

Abstract

We aim at the asymptotic enumeration of lambda-terms of a given size where the order of nesting of abstractions is bounded whereas the size is tending to infinity. This is done by means of a generating function approach and singularity analysis. The generating functions appear to be composed of nested square roots which exhibit unexpected phenomena. We derive the asymptotic number of such lambda-terms and it turns out that the order depends on the bound of the height. Furthermore, we present some observations when generating such lambda randomly and explain why powerful tools for random generation, such as Boltzmann samplers, face serious difficulties in generating lambda-terms.

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cover image Proceedings
2011 Proceedings of the Eighth Workshop on Analytic Algorithmics and Combinatorics (ANALCO)
Pages: 23 - 32
Editors: Philippe Flajolet, INRIA Rocquencourt, Le Chesnay, France and Daniel Panario, Carleton University, Ottawa, Ontario, Cananda
ISBN (Online): 978-1-61197-301-3

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Published online: 18 December 2013

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*
Supported by ANR projects BOOLE NT09-432755 and Magnum, Austrian Science Foundation FWF, NFN-Project S9604, ÖAD, grant F03/2010, and PHC Amadeus 23091UD.

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