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arXiv · 2101.09655

Relational Type Theory (All Proofs)

Aaron Stump·Benjamin Delaware·Christopher Jenkins
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Abstract

This paper introduces Relational Type Theory (RelTT), a new approach to type theory with extensionality principles, based on a relational semantics for types. The type constructs of the theory are those of System F plus relational composition, converse, and promotion of application of a term to a relation. A concise realizability semantics is presented for these types. The paper shows how a number of constructions of traditional interest in type theory are possible in RelTT, including eta-laws for basic types, inductive types with their induction principles, and positive-recursive types. A crucial role is played by a lemma called Identity Inclusion, which refines the Identity Extension property familiar from the semantics of parametric polymorphism. The paper concludes with a type system for RelTT, paving the way for implementation.

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Aaron Stump, Benjamin Delaware, Christopher Jenkins. 2021-01-24. Relational Type Theory (All Proofs). https://arxiv.org/abs/2101.09655

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