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How to safely use extensionality in Liquid Haskell

Authors:

Michael GreenbergAuthors Info & Claims

Haskell 2022: Proceedings of the 15th ACM SIGPLAN International Haskell Symposium

Pages 13 - 26

https://doi.org/10.1145/3546189.3549919

Published: 06 September 2022 Publication History

Abstract

Refinement type checkers are a powerful way to reason about functional programs. For example, one can prove properties of a slow, specification implementation and port the proofs to an optimized pure implementation that behaves the same. But to reason about higher-order programs, we must reason about equalities between functions: we need a consistent encoding of functional extensionality.

A natural but naive phrasing of the functional extensionality axiom (funExt) is inconsistent in refinement type systems with semantic subtyping and polymorphism: if we assume funExt, then we can prove false. We demonstrate the inconsistency and develop a new approach to equality in Liquid Haskell: we define a propositional equality in a library we call PEq. Using PEq avoids the inconsistency while proving useful equalities at higher types; we demonstrate its use in several case studies. We validate PEq by building a model and developing its metatheory. Additionally, we prove metaproperties of PEq inside Liquid Haskell itself using an unnamed folklore technique, which we dub 'classy induction'.

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Cited By

Hewer BHutton G(2024)Quotient Haskell: Lightweight Quotient Types for AllProceedings of the ACM on Programming Languages10.1145/36328698:POPL(785-815)Online publication date: 5-Jan-2024
https://doi.org/10.1145/3632869
Vazou N(2023)On the Practicality and Soundness of Refinement TypesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.396.1396(1-3)Online publication date: 17-Nov-2023
https://doi.org/10.4204/EPTCS.396.1
Ghalayini JKrishnaswami N(2023)Explicit Refinement TypesProceedings of the ACM on Programming Languages10.1145/36078377:ICFP(187-214)Online publication date: 31-Aug-2023
https://dl.acm.org/doi/10.1145/3607837

Index Terms

How to safely use extensionality in Liquid Haskell
1. Software and its engineering
  1. Software organization and properties
    1. Software functional properties
      1. Formal methods
        Software verification

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cover image ACM Conferences

Haskell 2022: Proceedings of the 15th ACM SIGPLAN International Haskell Symposium

September 2022

136 pages

ISBN:9781450394383

DOI:10.1145/3546189

Program Chair:
Nadia Polikarpova
University of California at San Diego, USA

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Published: 06 September 2022

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Cited By

Hewer BHutton G(2024)Quotient Haskell: Lightweight Quotient Types for AllProceedings of the ACM on Programming Languages10.1145/36328698:POPL(785-815)Online publication date: 5-Jan-2024
https://doi.org/10.1145/3632869
Vazou N(2023)On the Practicality and Soundness of Refinement TypesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.396.1396(1-3)Online publication date: 17-Nov-2023
https://doi.org/10.4204/EPTCS.396.1
Ghalayini JKrishnaswami N(2023)Explicit Refinement TypesProceedings of the ACM on Programming Languages10.1145/36078377:ICFP(187-214)Online publication date: 31-Aug-2023
https://dl.acm.org/doi/10.1145/3607837

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