Internal Type Theory (1996)
| Venue: | Lecture Notes in Computer Science |
| Citations: | 33 - 7 self |
BibTeX
@INPROCEEDINGS{Dybjer96internaltype,
author = {Peter Dybjer},
title = {Internal Type Theory},
booktitle = {Lecture Notes in Computer Science},
year = {1996},
pages = {120--134},
publisher = {Springer}
}
Years of Citing Articles
Bookmark
 |
 |
 |
 |
 |
 |
OpenURL
Abstract
. We introduce categories with families as a new notion of model for a basic framework of dependent types. This notion is close to ordinary syntax and yet has a clean categorical description. We also present categories with families as a generalized algebraic theory. Then we define categories with families formally in Martin-Lof's intensional intuitionistic type theory. Finally, we discuss the coherence problem for these internal categories with families. 1 Introduction In a previous paper [8] I introduced a general notion of simultaneous inductiverecursive definition in intuitionistic type theory. This notion subsumes various reflection principles and seems to pave the way for a natural development of what could be called "internal type theory", that is, the construction of models of (fragments of) type theory in type theory, and more generally, the formalization of the metatheory of type theory in type theory. The present paper is a first investigation of such an internal type theor...
