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Synthetic domain theory in type theory: Another logic of computable functions

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Theorem Proving in Higher Order Logics (TPHOLs 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1125))

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Abstract

We will present a Logic of Computable Functions based on the idea of Synthetic Domain Theory such that all functions are automatically continuous. Its implementation in the Lego proof-checker — the logic is formalized on top of the Extended Calculus of Constructions — has two main advantages. First, one gets machine checked proofs verifying that the chosen logical presentation of Synthetic Domain Theory is correct. Second, it gives rise to a LCF-like theory for verification of functional programs where continuity proofs are obsolete. Because of the powerful type theory even modular programs and specifications can be coded such that one gets a prototype setting for modular software verification and development.

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Authors and Affiliations

  1. Ludwig-Maximilians-Universität, Munich, Germany

    Bernhard Reus

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  1. Bernhard Reus
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Editor information

Gerhard Goos Juris Hartmanis Jan van Leeuwen Joakim von Wright Jim Grundy John Harrison

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© 1996 Springer-Verlag Berlin Heidelberg

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Reus, B. (1996). Synthetic domain theory in type theory: Another logic of computable functions. In: Goos, G., Hartmanis, J., van Leeuwen, J., von Wright, J., Grundy, J., Harrison, J. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1996. Lecture Notes in Computer Science, vol 1125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105416

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  • DOI: https://doi.org/10.1007/BFb0105416

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  • Print ISBN: 978-3-540-61587-3

  • Online ISBN: 978-3-540-70641-0

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