# Translating dependent type theory into higher order logic

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## 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
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## References

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© Springer-Verlag Berlin Heidelberg 1993