# Coercive Subtyping

@article{Luo1999CoerciveS, title={Coercive Subtyping}, author={Zhaohui Luo}, journal={J. Log. Comput.}, year={1999}, volume={9}, pages={105-130} }

We propose and study coercive subtyping, a formal extension with subtyping of dependent type theories such as Martin-LL of's type theory 38] and the type theory UTT 30]. In 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. This provides a conceptually simple and uniform framework to understandâ€¦Â

## 131 Citations

### Weak Transitivity in Coercive Subtyping

- BiologyTYPES
- 2002

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.

### Coercion completion and conservativity in coercive subtyping

- MathematicsAnn. Pure Appl. Log.
- 2001

### Coercive subtyping in lambda-free logical frameworks

- Computer ScienceLFMTP '09
- 2009

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.

### Theory and implementation of coercive subtyping

- Computer Science
- 2013

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.

### An Implementation of LF with Coercive Subtyping & Universes

- Computer ScienceJournal of Automated Reasoning
- 2004

It is claimed that the combination of Tarski-style universes together with coercive subtyping provides an ideal formulation of universes that is both semantically clear and practical to use.

### Constructor Subtyping

- MathematicsESOP
- 1999

This paper shows that the calculus is confluent and strongly normalizing, and admits a well-behaved theory of canonical inhabitants, provided one adopts expansive extensionality rules, including Î·-expansion, surjective pairing, and a suitable expansion rule for datatypes.

### A Calculus of Coercive Subtyping

- Computer Science
- 2009

A calculus is defined, denoted as Î»Pâ†ªâ†’, that instead of term overloading employs coercion mappings, which enables to detach the subtyping from other parts of the calculus, so that the mutual dependence between subtyped, typing and kinding can be diminished.

### Subtyping in signatures

- Biology
- 2018

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.

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