Abstract
A connection between lambda calculus and the algebra of near semi-rings is discussed. Among the results is the following completeness theorem.
A first-order equation in the language of binary associative distributive algebras is true in all such algebras if and only if the interpretations of the first order terms as lambda terms beta-eta convert to one another. A similar result holds for equations containing free variables.
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References
Barendregt, H.P.: The Lambda Calculus. North Holland (1984)
Birget, J.C.: Monoid generalizations of the Richard Thompson groups. Journal of Pure and Applied Algebra 213, 264–278 (2009)
Church, A.: The Calculi of Lambda Conversion. PUP (1941)
Coppo, M., Dezani, M.: A new type assignment for lambda terms. Archiv fur Math. Logik 19 (1978)
Curry, H.B.: Combinatory Logic, vol. 1. North Holland (1958)
Freyd, P., Heller, A.: Splitting homotopy idempotents II. Journal of Pure and Applied Algebra 89, 93–195 (1993)
Hoogewijs, J.: Semi-nearring embeddings. Med. Konink. Vlaamse Acad. Wetensch. Lett. Schone Kunst. Belgie Kl. Wetensch 32(2), 3–11 (1970)
Pottinger, G.: A type assignment for strongly normalizable lambda terms. Curry Festschrift (1980)
Statman, R.: Freyd’s hierarchy of combinator monoids. In: LICS (1991)
Thompson, R.: Embeddings into finitely generated groups which preserve the word problem. In: Adian, Boone, Higman (eds.) The Word Problem. Studies in Logic and the Foundation of Mathematics, vol. 95, pp. 401–441. North Holland (1980)
Van Hoorn, W., Van Rootselaar, B.: Fundamental notions in the theory of semi-near rings. Comp. Math. 18, 65–78 (1967)
Artin, M.: Algebra. Prentice Hall (2011)
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Statman, R. (2014). Near Semi-rings and Lambda Calculus. In: Dowek, G. (eds) Rewriting and Typed Lambda Calculi. RTA TLCA 2014 2014. Lecture Notes in Computer Science, vol 8560. Springer, Cham. https://doi.org/10.1007/978-3-319-08918-8_28
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DOI: https://doi.org/10.1007/978-3-319-08918-8_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08917-1
Online ISBN: 978-3-319-08918-8
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