Coercive Subtyping in Type Theory (1996)
| Venue: | Proc. of CSL'96, the 1996 Annual Conference of the European Association for Computer Science Logic, Utrecht. LNCS 1258 |
| Citations: | 22 - 12 self |
BibTeX
@INPROCEEDINGS{Luo96coercivesubtyping,
author = {Zhaohui Luo},
title = {Coercive Subtyping in Type Theory},
booktitle = {Proc. of CSL'96, the 1996 Annual Conference of the European Association for Computer Science Logic, Utrecht. LNCS 1258},
year = {1996},
pages = {draft.}
}
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Abstract
We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-Lof's type theory [NPS90] and the type theory UTT [Luo94]. In this approach, subtyping with specified implicit coercions is treated as a feature at the level of the logical framework; in particular, subsumption and coercion are combined in such a way that the meaning of an object being in a supertype is given by coercive definition rules for the definitional equality. It is shown that this provides a conceptually simple and uniform framework to understand subtyping and coercion relations in type theories with sophisticated type structures such as inductive types and universes. The use of coercive subtyping in formal development and in reasoning about subsets of objects is discussed in the context of computerassisted formal reasoning. 1 Introduction A type in type theory is often intuitively thought of as a set. For example, types in Martin-Lof's type theory [ML84, NPS90...
