Coercive Subtyping in Type Theory

  title={Coercive Subtyping in Type Theory},
  author={Zhaohui Luo},
  • 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

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

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

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

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

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

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



Inheritance and explicit coercion

A method is presented for providing semantic interpretations for languages which feature inheritance in the framework of statically checked, rich type disciplines, which allows the simultaneous modeling of parametric polymorphism, recursive types, and inheritance.

A logic of subtyping

A simple (and linear) calculus of sequents for subtyping as logical entailment is proposed, which allows to derive a complete and coherent approach to subtyped from a few, logically meaningful, sequents.

Subtyping dependent types

This work investigates a subtyping extension of the system /spl lambda/P, which is an abstract version of the type system of the Edinburgh Logical Framework LF, and establishes some important properties of the new system, including subject reduction.

A framework for defining logics

The Edinburgh Logical Framework provides a means to define (or present) logics through a general treatment of syntax, rules, and proofs by means of a typed λ-calculus with dependent types, whereby each judgment is identified with the type of its proofs.

A modest model of records, inheritance and bounded quantification

  • Kim B. BruceG. Longo
  • Computer Science
    [1988] Proceedings. Third Annual Information Symposium on Logic in Computer Science
  • 1988

On understanding types, data abstraction, and polymorphism

A λ-calculus-based model for type systems that allows us to explore the interaction among the concepts of type, data abstraction, and polymorphism in a simple setting, unencumbered by complexities of production programming languages is developed.

Typing algorithm in type theory with inheritance

A new typing algorithm for dependent type theory typechecks more terms by using inheritance between classes, which turns out to be powerful: it supports multiple inheritance, classes with parameters and uses new abstract classes FUNCLASS and SORTCLASS.

Program Speciication and Data Reenement in Type Theory

It is shown that a type theory with a strong logical power and nice structural mechanisms provides an adequate formalism for modular development of programs and speciications and can be developed by means of the existing proof development systems based on type theories.