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Translating dependent type theory into higher order logic

  • Bart Jacobs
  • Tom Melham
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 664)

Abstract

This paper describes a translation of the complex calculus of dependent type theory into the relatively simpler higher order logic originally introduced by Church. In particular, it shows how type dependency as found in Martin-Löf's Intuitionistic Type Theory can be simulated in the formulation of higher order logic mechanized by the HOL theoremproving system. The outcome is a theorem prover for dependent type theory, built on top of HOL, that allows natural and flexible use of set-theoretic notions. A bit more technically, the language of the resulting theorem-prover is the internal language of a (boolean) topos (as formulated by Phoa).

Keywords

Inference Rule Type Theory Dependent Type High Order Logic Elimination Rule 
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 1993

Authors and Affiliations

  • Bart Jacobs
    • 1
  • Tom Melham
    • 2
  1. 1.Mathematical Institute RUUTA UtrechtNL
  2. 2.Computer LaboratoryUniversity of CambridgeCambridgeUK

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