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. 2021 Mar 23;12650:406–426. doi: 10.1007/978-3-030-71995-1_21

A General Semantic Construction of Dependent Refinement Type Systems, Categorically

Satoshi Kura 10,11,✉
Editors: Stefan Kiefer8, Christine Tasson9
PMCID: PMC7984113

Abstract

Dependent 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.

Contributor Information

Stefan Kiefer, Email: stekie@cs.ox.ac.uk.

Christine Tasson, Email: christine.tasson@lip6.fr.

Satoshi Kura, Email: kura@nii.ac.jp.

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