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Congruence Types

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Computer Science Logic (CSL 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1092))

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Abstract

We introduce a type-theoretical framework in which canonical term rewriting systems can be represented faithfully both from the logical and the computational points of view. The framework is based on congruence types, a new syntax which combines inductive, algebraic and quotient types. Congruence types improve on existing work to combine type theories with algebraic rewriting by making explicit the fact that the term-rewriting systems under consideration are initial models of an equational theory. As a result, the interaction gustavo:thesisween the type theory and the algebraic types (rewriting systems) is much more powerful than in previous work. Congruence types can be used (i) to introduce initial models of canonical term-rewriting systems (ii) to obtain a suitable computational behavior of a definable operation (iii) to provide an elegant solution to the problem of equational reasoning in type theory.

This work was partially supported by the Esprit project ‘Types: types for programs and proofs’.

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Author information

Authors and Affiliations

  1. Centrum voor Wiskunde en Informatica (CWI), Amsterdam, The Netherlands

    Gilles Barthe

  2. Faculty of Mathematics and Informatics, Technical University of Eindhoven, The Netherlands

    Herman Geuvers

  3. Faculty of Mathematics and Informatics, University of Nijmegen, The Netherlands

    Gilles Barthe & Herman Geuvers

Authors
  1. Gilles Barthe
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  2. Herman Geuvers
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Editor information

Hans Kleine Büning

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© 1996 Springer-Verlag Berlin Heidelberg

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Barthe, G., Geuvers, H. (1996). Congruence Types. In: Kleine Büning, H. (eds) Computer Science Logic. CSL 1995. Lecture Notes in Computer Science, vol 1092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61377-3_30

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  • DOI: https://doi.org/10.1007/3-540-61377-3_30

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  • Print ISBN: 978-3-540-61377-0

  • Online ISBN: 978-3-540-68507-4

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