## Type Theory via Exact Categories (Extended Abstract) (1998)

Venue: | In Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science LICS '98 |

Citations: | 7 - 0 self |

### BibTeX

@INPROCEEDINGS{Birkedal98typetheory,

author = {L. Birkedal and A. Carboni and G. Rosolini and D. S. Scott},

title = {Type Theory via Exact Categories (Extended Abstract)},

booktitle = {In Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science LICS '98},

year = {1998},

pages = {188--198},

publisher = {IEEE Computer Society Press}

}

### OpenURL

### Abstract

Partial equivalence relations (and categories of these) are a standard tool in semantics of type theories and programming languages, since they often provide a cartesian closed category with extended definability. Using the theory of exact categories, we give a category-theoretic explanation of why the construction of a category of partial equivalence relations often produces a cartesian closed category. We show how several familiar examples of categories of partial equivalence relations fit into the general framework. 1 Introduction Partial equivalence relations (and categories of these) are a standard tool in semantics of programming languages, see e.g. [2, 5, 7, 9, 15, 17, 20, 22, 35] and [6, 29] for extensive surveys. They are usefully applied to give proofs of correctness and adequacy since they often provide a cartesian closed category with additional properties. Take for instance a partial equivalence relation on the set of natural numbers: a binary relation R ` N\ThetaN on th...