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A complete axiom system for isomorphism of types in closed categories

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Book cover Logic Programming and Automated Reasoning (LPAR 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 698))

Abstract

It is shown, that ordinary isomorphisms (associativity and commutativity of tensor, isomorphisms for tensor unit and currying) provide a complete axiom system for the isomorphism of types in Symmetric Monoidal Closed categories. This gives also a decision algorithm. The problem originally arises from computer science, as the isomorphism of types in SMC categories corresponds to the isomorphism of types in linear lambda calculus, and could be used for search in databases.

supported by CLICS grant (on leave from S.Petersburg Institute for Informatics, Russian Academy of Sciences)

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Authors and Affiliations

  1. Computer Science Department, Aarhus University, Ny Munkegade, B.540, DK 8000, Aarhus C, Denmark

    S. Soloviev

Authors
  1. S. Soloviev
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Editor information

Andrei Voronkov

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© 1993 Springer-Verlag Berlin Heidelberg

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Soloviev, S. (1993). A complete axiom system for isomorphism of types in closed categories. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1993. Lecture Notes in Computer Science, vol 698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56944-8_71

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  • DOI: https://doi.org/10.1007/3-540-56944-8_71

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56944-2

  • Online ISBN: 978-3-540-47830-0

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