A220471 Number of closed simply typable lambda-terms of size n with size 0 for the variables.

1, 2, 9, 40, 238, 1564, 11807, 98529, 904318, 9006364, 96709332, 1110858977, 13581942434, 175844515544

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

Table of n, a(n) for n=1..14.

Katarzyna Grygiel and Pierre Lescanne, Counting and generating lambda-terms, arXiv preprint arXiv:1210.2610, 2012

Paul Tarau, On a Uniform Representation for Combinators, Arithmetic, Lambda Terms and Types, preprint, 2015.

Paul Tarau, On Type-directed Generation of Lambda Terms, preprint, 2015.

Paul Tarau, On logic programming representations of lambda terms: de Bruijn indices, compression, type inference, combinatorial generation, normalization, 2015.

P. Tarau, A Logic Programming Playground for Lambda Terms, Combinators, Types and Tree-based Arithmetic Computations, arXiv preprint arXiv:1507.06944, 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

Adjacent sequences: A220468 A220469 A220470 * A220472 A220473 A220474

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