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Computation and reasoning: a type theory for computer science
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Typing algorithm in type theory with inheritance
Proceedings of the 24th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
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An Implementation of LF with Coercive Subtyping & Universes
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Coercive Subtyping in Type Theory
CSL '96 Selected Papers from the10th International Workshop on Computer Science Logic
POPL '84 Proceedings of the 11th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
A Type Driven Theory of Predication with Complex Types
Fundamenta Informaticae - Logic for Pragmatics
Manifest Fields and Module Mechanisms in Intensional Type Theory
Types for Proofs and Programs
Transitivity in coercive subtyping
Information and Computation
Contextual analysis of word meanings in type-theoretical semantics
LACL'11 Proceedings of the 6th international conference on Logical aspects of computational linguistics
Dot-types and their implementation
LACL'12 Proceedings of the 7th international conference on Logical Aspects of Computational Linguistics
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Coercive 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.