Implementing mathematics with the Nuprl proof development system
Implementing mathematics with the Nuprl proof development system
Inheritance as implicit coercion
Information and Computation
A framework for defining logics
Journal of the ACM (JACM)
Refinement types for ML
The Coherence of Languages with Intersection Types
TACS '91 Proceedings of the International Conference on Theoretical Aspects of Computer Software
Intensionality, Extensionality, and Proof Irrelevance in Modal Type Theory
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
Proceedings of the 31st ACM SIGPLAN-SIGACT symposium on Principles of programming languages
Practical refinement-type checking
Practical refinement-type checking
Journal of Logic and Computation
Intersection-types à la Church
Information and Computation
A Bidirectional Refinement Type System for LF
Electronic Notes in Theoretical Computer Science (ENTCS)
Refinement types and computational duality
Proceedings of the 3rd workshop on Programming languages meets program verification
Representing model theory in a type-theoretical logical framework
Theoretical Computer Science
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Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. Proof irrelevance provides a mechanism for selectively hiding the identities of terms in type theories. In this paper, we show that refinement types can be interpreted as predicates using proof irrelevance in the context of the logical framework LF, establishing a uniform relationship between two previously studied concepts in type theory. The interpretation and its correctness proof are surprisingly complex, lending credence to the idea that refinement types are a fundamental construct rather than just a convenient surface syntax for certain uses of proof irrelevance.