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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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
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