Coercive Subtyping in Type Theory

@inproceedings{Luo1996CoerciveSI,
  title={Coercive Subtyping in Type Theory},
  author={Zhaohui Luo},
  booktitle={CSL},
  year={1996}
}
  • Zhaohui Luo
  • Published in CSL 21 September 1996
  • Computer Science
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… 

Coercive Subtyping

TLDR
This approach, subtyping with speciied implicit coercions is treated as a feature at the level of the logical framework; in particular, the meaning of an object being in a supertype is given by coercive deenition rules for the deenitional equality.

Coercive subtyping: Theory and implementation

Theory and implementation of coercive subtyping

TLDR
This thesis points out the problem in the old formulation of coercive subtyping in [Luo99], gives a new and adequate formulation T [C], the system that extends a type theory T with coercive subTYping based on a set C of basic subtyped judgements, and shows that coerciveSubtyping is a conservative extension and, in a more general sense, a definitional extension.

Transitivity in coercive subtyping

Weak Transitivity in Coercive Subtyping

TLDR
The notion of Weak Transitivity is proposed and studied, suitable subtyping rules for certain parameterised inductive types are considered and its coherence is proved and the admissibility of substitution and weak transitivity in the coercive subtyped framework is proved.

On Subtyping in Type Theories with Canonical Objects

TLDR
This paper introduces a type system with signatures where coercive subtyping relations can be specified, and argues that this provides a suitable subtyped mechanism for type theories with canonical objects.

Coercive subtyping in lambda-free logical frameworks

TLDR
It is shown how TF< may be embedded in the logical framework LF, and hence how results about LF may be deduced from results about TF<, and the metatheory of the resulting framework is developed.

Subtyping in signatures

TLDR
A new way of adding coercive subtyping to type theory, specifically by annotating certain functions in assumptions, is introduced, arguing that this is more handy to represent practical cases.

Type-theoretical semantics with coercive subtyping

In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as functional subsets of entities as in Montague grammar. This brings about important
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