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International Joint Conference on Automated Reasoning

IJCAR 2006: Automated Reasoning pp 604–618Cite as

On the Strength of Proof-Irrelevant Type Theories

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 4130))

Abstract

We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is particularly useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. Finally we show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of equality, that is, almost classical logic.

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Author information

Authors and Affiliations

  1. INRIA-Futurs and LIX, Ecole Polytechnique, France

    Benjamin Werner

Authors
  1. Benjamin Werner
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Artificial Intelligence Research Group, University of Koblenz-Landau, Universitätsstr. 1, 56070, Koblenz

    Ulrich Furbach

  2. SRI International, MS EL256,, 333 Ravenswood Avenue, 94025-3493, Menlo Park, CA, USA

    Natarajan Shankar

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© 2006 Springer-Verlag Berlin Heidelberg

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Werner, B. (2006). On the Strength of Proof-Irrelevant Type Theories. In: Furbach, U., Shankar, N. (eds) Automated Reasoning. IJCAR 2006. Lecture Notes in Computer Science(), vol 4130. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11814771_49

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  • DOI: https://doi.org/10.1007/11814771_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-37187-8

  • Online ISBN: 978-3-540-37188-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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