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Translating Dependent Type Theory into Higher Order Logic (1993)
| Venue: | IN PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON TYPED LAMBDA CALCULI AND APPLICATIONS, VOLUME 664 OF LECTURE NOTES IN COMPUTER SCIENCE |
| Citations: | 13 - 2 self |
BibTeX
@INPROCEEDINGS{Jacobs93translatingdependent,
author = {Bart Jacobs and Tom Melham},
title = {Translating Dependent Type Theory into Higher Order Logic},
booktitle = {IN PROCEEDINGS OF THE SECOND INTERNATIONAL CONFERENCE ON TYPED LAMBDA CALCULI AND APPLICATIONS, VOLUME 664 OF LECTURE NOTES IN COMPUTER SCIENCE},
year = {1993},
pages = {209--229},
publisher = {Springer}
}
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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 theorem-proving 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).
