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Combining Type Theory and Untyped Set Theory

  • Chad E. Brown
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4130)

Abstract

We describe a dependent type theory with proof irrelevance. Within this framework, we give a representation of a form of Mac Lane set theory and discuss automated support for constructing proofs within this set theory. One of the novel aspects of the representation is that one is allowed to use any class (in the set theory) as a type (in the type theory). Such class types allow a natural way of representing partial functions (e.g., the first and second operators on the class of Kuratowski ordered pairs). We also discuss how automated search can be used to construct proofs. In particular, the first-order prover Vampire can be called to solve a challenge problem (the injective Cantor Theorem) which is notoriously difficult for higher-order automated provers.

Keywords

Type Theory Class Type Simple Type Automate Reasoning Logical Framework 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Chad E. Brown
    • 1
  1. 1.Universität des SaarlandesSaarbrückenGermany

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