Strong functional pearl: Harper’s regular-expression matcher in Cedille

Stump, Aaron; Jenkins, Christa; Spahn, S; McDonald, Colin

doi:10.1145/3409004

Cited by 2 publications

(1 citation statement)

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“…RelTT may be compared with previous work of Stump et al on Cedille [25], [26], [27]. Both systems aim at a minimalistic extension of a small pure type system as a foundation for type theory.…”

Section: Related Workmentioning

confidence: 99%

Relational Type Theory (All Proofs)

Stump,

Delaware,

Jenkins

2021

Preprint

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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 η-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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Section: Related Workmentioning

confidence: 99%

Relational Type Theory (All Proofs)

Stump,

Delaware,

Jenkins

2021

Preprint

Self Cite

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A Type-Based Approach to Divide-and-Conquer Recursion in Coq

Abreu

Delaware

Hubers

et al. 2023

Proc. ACM Program. Lang.

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This paper proposes a new approach to writing and verifying divide-and-conquer programs in Coq. Extending the rich line of previous work on algebraic approaches to recursion schemes, we present an algebraic approach to divide-and-conquer recursion: recursions are represented as a form of algebra, and from outer recursions, one may initiate inner recursions that can construct data upon which the outer recursions may legally recurse. Termination is enforced entirely by the typing discipline of our recursion schemes. Despite this, our approach requires little from the underlying type system, and can be implemented in System F ω plus a limited form of positive-recursive types. Our implementation of the method in Coq does not rely on structural recursion or on dependent types. The method is demonstrated on several examples, including mergesort, quicksort, Harper’s regular-expression matcher, and others. An indexed version is also derived, implementing a form of divide-and-conquer induction that can be used to reason about functions defined via our method.

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Strong functional pearl: Harper’s regular-expression matcher in Cedille

Cited by 2 publications

References 34 publications

Relational Type Theory (All Proofs)

Relational Type Theory (All Proofs)

A Type-Based Approach to Divide-and-Conquer Recursion in Coq

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