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Infinite objects in type theory

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Types for Proofs and Programs (TYPES 1993)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 806))

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Abstract

We show that infinite objects can be constructively understood without the consideration of partial elements, or greatest fixed-points, through the explicit consideration of proof objects. We present then a proof system based on these explanations. According to this analysis, the proof expressions should have the same structure as the program expressions of a pure functional lazy language: variable, constructor, application, abstraction, case expressions, and local let expressions.

This research has been done within the ESPRIT Basic Research Action “Types for Proofs and Programs”. It has been paid by NUTEK, Chalmers and the University of Göteborg.

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Author information

Authors and Affiliations

  1. Programming Methodology Group. Department of Computer Sciences, Chalmers University of Technology and University of Göteborg, S-412 96, Göteborg, Sweden

    Thierry Coquand

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  1. Thierry Coquand
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Editor information

Henk Barendregt Tobias Nipkow

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© 1994 Springer-Verlag Berlin Heidelberg

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Coquand, T. (1994). Infinite objects in type theory. In: Barendregt, H., Nipkow, T. (eds) Types for Proofs and Programs. TYPES 1993. Lecture Notes in Computer Science, vol 806. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58085-9_72

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  • DOI: https://doi.org/10.1007/3-540-58085-9_72

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58085-0

  • Online ISBN: 978-3-540-48440-0

  • eBook Packages: Springer Book Archive

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