A General Semantic Construction of Dependent Refinement Type Systems, Categorically-Reference-Cited by-同舟云学术

A General Semantic Construction of Dependent Refinement Type Systems, Categorically

Published:2021 Issue: Volume: Page:406-426
ISSN:0302-9743
Container-title:Lecture Notes in Computer Science
language:
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Author:

Kura Satoshi^ORCID

Abstract

AbstractDependent refinement types are types equipped with predicates that specify preconditions and postconditions of underlying functional languages. We propose a general semantic construction of dependent refinement type systems from underlying type systems and predicate logic, that is, a construction of liftings of closed comprehension categories from given (underlying) closed comprehension categories and posetal fibrations for predicate logic. We give sufficient conditions to lift structures such as dependent products, dependent sums, computational effects, and recursion from the underlying type systems to dependent refinement type systems. We demonstrate the usage of our construction by giving semantics to a dependent refinement type system and proving soundness.

Publisher

Springer International Publishing

Link

http://link.springer.com/content/pdf/10.1007/978-3-030-71995-1_21

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