Transitivity in coercive subtyping

Zhang, Luo; Luo, Yong

doi:10.1016/j.ic.2004.10.008

Cited by 9 publications

(21 citation statements)

References 13 publications

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“…In other words, we consider the original formulation of coercive subtyping in [12] or that in Y. Luo's PhD thesis [20,10] where the original type theory is extended with a set C of subtyping judgements to form the coercive subtyping extension T [C]. In such a formulation, the above problem does not occur and, as we show below, the proof method of [31] can be used (and further improved) to prove that the coercive subtyping extension is indeed conservative.…”

Section: Coercive Subtyping: An Adequate Formulationmentioning

confidence: 99%

“…Structural subtyping is a natural subtyping relation for an inductive type and has been studied for arbitrary inductive types in the framework of coercive subtyping [20,19]. However, it is incompatible with subsumptive subtyping.…”

Section: Limitation Of Subsumptive Subtypingmentioning

confidence: 99%

“…As far as we know, in the literature, there are only scattered remarks to compare these two notions of subtyping (see, for example, §2.1 of [20]). In Section 4, we shall analyse them from a particular angle, discussing the idea that subsumptive subtyping is suitable for type assignment systems as employed in functional programming languages, but not suitable for type theories with canonical objects as implemented in proof assistants, and showing that coercive subtyping provides a very general framework for the latter.…”

Section: Introductionmentioning

confidence: 99%

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Coercive subtyping: Theory and implementation

Zhang¹,

Soloviev²,

Xue³

2013

Information and Computation

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International audienceCoercive subtyping is a useful and powerful framework of subtyping for type theories. The key idea of coercive subtyping is subtyping as abbreviation. In this paper, we give a new and adequate formulation of T[C], the system that extends a type theory T with coercive subtyping based on a set C of basic subtyping judgements, and show that coercive subtyping is a conservative extension and, in a more general sense, a definitional extension. We introduce an intermediate system, the star-calculus T[C]^@?, in which the positions that require coercion insertions are marked, and show that T[C]^@? is a conservative extension of T and that T[C]^@? is equivalent to T[C]. This makes clear what we mean by coercive subtyping being a conservative extension, on the one hand, and amends a technical problem that has led to a gap in the earlier conservativity proof, on the other. We also compare coercive subtyping with the 'ordinary' notion of subtyping - subsumptive subtyping, and show that the former is adequate for type theories with canonical objects while the latter is not. An improved implementation of coercive subtyping is done in the proof assistant Plastic

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Section: Coercive Subtyping: An Adequate Formulationmentioning

confidence: 99%

Section: Limitation Of Subsumptive Subtypingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Coercive subtyping: Theory and implementation

Zhang¹,

Soloviev²,

Xue³

2013

Information and Computation

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“…Coercive subtyping corresponds to the view of types as consisting of canonical objects while 'subsumptive subtyping' (the more traditional approach with the subsumption rule) to the view of type assignment [28]. Coercive subtyping can be introduced for inductive types in a natural way [28,27] subtyping is not only suitable for structural subtyping, but for non-structural subtyping.…”

Section: Remarkmentioning

confidence: 99%

“…Coercive subtyping can be introduced for inductive types in a natural way [28,27] subtyping is not only suitable for structural subtyping, but for non-structural subtyping. The use in this paper of the coercion concerning the unit type is such an example.…”

Section: Remarkmentioning

confidence: 99%

Manifest Fields and Module Mechanisms in Intensional Type Theory

Zhang

2009

Lecture Notes in Computer Science

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Abstract. Manifest fields in a type of modules are shown to be expressible in intensional type theory without strong extensional equality rules. These intensional manifest fields are made available with the help of coercive subtyping. It is shown that, for both Σ-types and dependent record types, the with-clause for expressing manifest fields can be introduced by means of the intensional manifest fields. This provides not only a higher-order module mechanism with ML-style sharing, but a powerful modelling mechanism in formalisation and verification of OO-style program modules.

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Definitional Functoriality for Dependent (Sub)Types

Laurent,

Lennon-Bertrand,

Maillard

2024

Lecture Notes in Computer Science

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Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws, equations satisfied propositionally by a large class of container-like type constructors $$F : {\text {Type}}\rightarrow {\text {Type}}$$ F : Type → Type , equipped with a $$\textrm{map}_{F} {{\,\mathrm{:}\,}}(A \rightarrow B) \rightarrow F\,A \rightarrow F\,B$$ map F : ( A → B ) → F A → F B , such as lists or trees. Promoting these equations to definitional ones strengthens the theory, enabling slicker proofs and more automation for functorial type constructors. This extension is used to modularly justify a structural form of coercive subtyping, propagating subtyping through type formers in a map-like fashion. We show that the resulting notion of coercive subtyping, thanks to the extra definitional equations, is equivalent to a natural and implicit form of subsumptive subtyping. The key result of decidability of type-checking in a dependent type system with functor laws for lists has been entirely mechanized in Coq.

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Transitivity in coercive subtyping

Cited by 9 publications

References 13 publications

Coercive subtyping: Theory and implementation

Coercive subtyping: Theory and implementation

Manifest Fields and Module Mechanisms in Intensional Type Theory

Definitional Functoriality for Dependent (Sub)Types

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