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A220471 Number of closed simply typable lambda-terms of size n with size 0 for the variables. 3
1, 2, 9, 40, 238, 1564, 11807, 98529, 904318, 9006364, 96709332, 1110858977, 13581942434, 175844515544 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Typable terms are terms that satisfy constraints which make them well formed.
The current computation requires one to generate all the plain lambda terms and to sieve out those that are typable. This is feasible for the 63782411 terms of size 10 but not for the 851368766 terms of size 11.
REFERENCES
Alonzo Church, A Formulation of the Simple Theory of Types, J. Symb. Log. 5(2): 56-68 (1940).
LINKS
Katarzyna Grygiel and Pierre Lescanne, Counting and generating lambda-terms, arXiv preprint arXiv:1210.2610, 2012
Paul Tarau, On Type-directed Generation of Lambda Terms, preprint, 2015.
Paul Tarau, "Ranking/unranking of lambda terms with compressed de Bruijn indices, CICM 2015, Lect. Not. Comp. Sci. 9140, p. 118-133
Paul Tarau, A Hiking Trip Through the Orders of Magnitude: Deriving Efficient Generators for Closed Simply-Typed Lambda Terms and Normal Forms, arXiv preprint arXiv:1608.03912, 2016
CROSSREFS
Cf. A220894.
Sequence in context: A293152 A327827 A056844 * A213095 A238372 A308475
KEYWORD
nonn,more
AUTHOR
Pierre Lescanne, Apr 10 2013
EXTENSIONS
a(11) and a(12) added from Tarau (arXiv:1507.06944, 2015). - N. J. A. Sloane, Jan 30 2016
a(13) and a(14) added from Tarau (2016). - N. J. A. Sloane, Aug 04 2017
STATUS
approved

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Last modified March 29 10:59 EDT 2024. Contains 371277 sequences. (Running on oeis4.)