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Working with Mathematical Structures in Type Theory

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Types for Proofs and Programs (TYPES 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4941))

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Abstract

We address the problem of representing mathematical structures in a proof assistant which: 1) is based on a type theory with dependent types, telescopes and a computational version of Leibniz equality; 2) implements coercive subtyping, accepting multiple coherent paths between type families; 3) implements a restricted form of higher order unification and type reconstruction. We show how to exploit the previous quite common features to reduce the “syntactic” gap between pen&paper and formalised algebra. However, to reach our goal we need to propose unification and type reconstruction heuristics that are slightly different from the ones usually implemented. We have implemented them in Matita.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Bologna, Mura Anteo Zamboni, 7, 40127, Bologna, Italy

    Claudio Sacerdoti Coen & Enrico Tassi

Authors
  1. Claudio Sacerdoti Coen
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  2. Enrico Tassi
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Marino Miculan Ivan Scagnetto Furio Honsell

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Sacerdoti Coen, C., Tassi, E. (2008). Working with Mathematical Structures in Type Theory. In: Miculan, M., Scagnetto, I., Honsell, F. (eds) Types for Proofs and Programs. TYPES 2007. Lecture Notes in Computer Science, vol 4941. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68103-8_11

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  • DOI: https://doi.org/10.1007/978-3-540-68103-8_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-68084-0

  • Online ISBN: 978-3-540-68103-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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