A Dependent Type Theory with Names and Binding (2004)
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| Venue: | In Proceedings of the 2004 Computer Science Logic Conference, number 3210 in Lecture notes in Computer Science |
| Citations: | 15 - 1 self |
BibTeX
@INPROCEEDINGS{Schöpp04adependent,
author = {Ulrich Schöpp and Ian Stark},
title = {A Dependent Type Theory with Names and Binding},
booktitle = {In Proceedings of the 2004 Computer Science Logic Conference, number 3210 in Lecture notes in Computer Science},
year = {2004},
pages = {235--249},
publisher = {Springer-Verlag}
}
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Abstract
We consider the problem of providing formal support for working with abstract syntax involving variable binders. Gabbay and Pitts have shown in their work on Fraenkel-Mostowski (FM) set theory how to address this through first-class names: in this paper we present a dependent type theory for programming and reasoning with such names. Our development is based on a categorical axiomatisation of names, with freshness as its central notion. An associated adjunction captures constructions known from FM theory: the freshness quantifier N , name-binding, and unique choice of fresh names. The Schanuel topos --- the category underlying FM set theory --- is an instance of this axiomatisation.
