Coercion completion and conservativity in coercive subtyping

Soloviev, Sergei; Zhang, Luo

doi:10.1016/s0168-0072(01)00063-x

Cited by 22 publications

(27 citation statements)

References 9 publications

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“…4 However, the coercive subtyping extension has the same syntax of terms with the original type theory (see Section 2.2 for formal details), the notion of conservative extension could not be directly applied to them and, as a consequence, in its earlier treatment [31], the notion of conservativity for coercive subtyping was not clearly spelled out and, in particular, it was not explicitly linked to the traditional studies in logic. In this paper, we give a new and adequate formulation of coercive subtyping and show that it is a conservative extension by introducing an intermediate system, the star-calculus T [C] * , in which the positions that require coercion insertions are marked by the * -symbol, and showing that T [C] * is a conservative extension of T and that T [C] * is equivalent to the coercive subtyping extension T [C].…”

Section: Introductionmentioning

confidence: 99%

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: Introductionmentioning

confidence: 99%

Coercive subtyping: Theory and implementation

Zhang¹,

Soloviev²,

Xue³

2013

Information and Computation

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“…Such a requirement applies to the extension of modern type theories with coercive subtyping and, fortunately, it meets the requirement. In fact, the coercive subtyping extension is not only consistent but conservative as long as the employed coercions are coherent 6 (the proof method in Soloviev & Luo 2002 can be used to show this). For a type theory with nice meta-theoretic properties such as Strong Normalisation (and hence logical consistency), its extension with coercive subtyping has those properties, too.…”

Section: Coercive Subtypingmentioning

confidence: 99%

Type-theoretical semantics with coercive subtyping

Zhang¹

2015

SALT

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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 advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on functional subsets. The theory of coercive subtyping adequately extends the modern type theories with a notion of subtyping and, as shown in this paper, plays a very useful role in making type theories more expressive for formal semantics. In particular, it gives a satisfactory treatment of the type-theoretic interpretation of modified common nouns and allows straightforward interpretations of interesting linguistic phenomena such as copredication, whose interpretations have been found difficult in a Montagovian setting. We shall also study some type-theoretic constructs that provide useful representational tools for formal lexical semantics, including how the so-called dot-types for representing logical polysemy may be expressed in a type theory with coercive subtyping.

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“…Incoherence would imply that the extension with coercive subtyping is not conservative in the sense that more judgements of the original type theory T can be derived. In most cases, coherence does imply conservativity (e.g., the proof method in [40] can be used to show this). When the employed coercions are coherent, one can always insert coercions correctly into a derivation in the extension to obtain a derivation in the original type theory.…”

Section: The Logical Framework and Coercive Subtypingmentioning

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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Coercion completion and conservativity in coercive subtyping

Cited by 22 publications

References 9 publications

Coercive subtyping: Theory and implementation

Coercive subtyping: Theory and implementation

Type-theoretical semantics with coercive subtyping

Manifest Fields and Module Mechanisms in Intensional Type Theory

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