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Normal Varieties of Combinators

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Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 21))

Abstract

We adopt for the most part the terminology and notation of [1]. A combinator is a term with no free variables. A set of combinators which is both recursively enumerable and closed under ß conversion is said to be Visseral ([5]). Given combinators F and G, the variety defined by Fx = Gx is the set of all combinators M such that FM = GM. Such a variety is said to be normal if both F and G are normal. In this note we shall be principally concerned with normal varieties.

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References

  1. H.P Barendregt, The Lamba Calculus, North Holland, 1984.

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  2. C. Böhlm and M. Dezani-Ciancaglini, Combinatorial problems, combinator equations and normal forms, Automated Languages and Programming, J. Loeckx, ed., Lecture Notes in Computer Science 14, Springer-Verlag, 1974, pp. 185–199.

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  3. J.W. Klop, Combinatory Reduction Systems, Math. Centrum Amsterdam, 1980.

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  4. R. Statman, On sets of solutuons to combinator equations, T.C.S. 66 (1989), 99–104.

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  5. A. Visser, Numerations, λ-calculus and arithmetic, Essays on Combinatory Logic, Lamba Calculus and Formalism, J.P Seldin and J.R Hindley, eds., Academic Press, 1980.

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© 1992 Springer-Verlag New York, Inc

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Statman, R. (1992). Normal Varieties of Combinators. In: Moschovakis, Y.N. (eds) Logic from Computer Science. Mathematical Sciences Research Institute Publications, vol 21. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2822-6_21

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  • DOI: https://doi.org/10.1007/978-1-4612-2822-6_21

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7685-2

  • Online ISBN: 978-1-4612-2822-6

  • eBook Packages: Springer Book Archive

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