Some Algorithmic and Proof-Theoretical Aspects of Coercive Subtyping (1996)
| Venue: | In Proceedings of TYPES'96, Lecture Notes in Computer Science |
| Citations: | 6 - 0 self |
BibTeX
@INPROCEEDINGS{Jones96somealgorithmic,
author = {Alex Jones and Zhaohui Luo and sergei Soloviev},
title = {Some Algorithmic and Proof-Theoretical Aspects of Coercive Subtyping},
booktitle = {In Proceedings of TYPES'96, Lecture Notes in Computer Science},
year = {1996},
publisher = {Springer}
}
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Abstract
. Coercive subtyping offers a conceptually simple but powerful framework to understand subtyping and subset relationships in type theory. In this paper we study some of its proof-theoretic and computational properties. 1 Introduction Coercive subtyping, as first introduced in [Luo96], offers a conceptually simple but powerful framework to understand subtyping and subset relationships in type theories with sophisticated type structures such as dependent types, inductive types, and type universes. A basic idea behind coercive subtyping is that subtyping provides a powerful mechanism for notational abbreviation in type theory. If A is a subtype of B given by a specified coercion function, an object of type A can be regarded as an object of type B, that is, its image via the coercion function, and hence objects of a subtype can be used as abbreviations for objects of a supertype. With coercive subtyping, this abbreviational mechanism is formally treated at the level of the logical framewo...
