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Categorical completeness results for the simply-typed lambda-calculus

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Typed Lambda Calculi and Applications (TLCA 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 902))

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Abstract

We investigate, in a categorical setting, some completeness properties of beta-eta conversion between closed terms of the simplytyped lambda calculus. A cartesian-closed category is said to be complete if, for any two unconvertible terms, there is some interpretation of the calculus in the category that distinguishes them. It is said to have a complete interpretation if there is some interpretation that equates only interconvertible terms. We give simple necessary and sufficient conditions on the category for each of the two forms of completeness to hold. The classic completeness results of, e.g., Friedman and Plotkin are immediate consequences. As another application, we derive a syntactic theorem of Statman characterizing beta-eta conversion as a maximum consistent congruence relation satisfying a property known as typical ambiguity.

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Authors and Affiliations

  1. LFCS, Department of Computer Science, University of Edinburgh, JCMB, The King's Buildings, EH9 3JZ, Edinburgh

    Alex K. Simpson

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  1. Alex K. Simpson
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Mariangiola Dezani-Ciancaglini Gordon Plotkin

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© 1995 Springer-Verlag Berlin Heidelberg

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Simpson, A.K. (1995). Categorical completeness results for the simply-typed lambda-calculus. In: Dezani-Ciancaglini, M., Plotkin, G. (eds) Typed Lambda Calculi and Applications. TLCA 1995. Lecture Notes in Computer Science, vol 902. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0014068

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  • DOI: https://doi.org/10.1007/BFb0014068

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-59048-4

  • Online ISBN: 978-3-540-49178-1

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