research-article

A unification algorithm for Coq featuring universe polymorphism and overloading

Authors:

Matthieu SozeauAuthors Info & Claims

ACM SIGPLAN Notices, Volume 50, Issue 9

Pages 179 - 191

https://doi.org/10.1145/2858949.2784751

Published: 29 August 2015 Publication History

Abstract

Unification is a core component of every proof assistant or programming language featuring dependent types. In many cases, it must deal with higher-order problems up to conversion. Since unification in such conditions is undecidable, unification algorithms may include several heuristics to solve common problems. However, when the stack of heuristics grows large, the result and complexity of the algorithm can become unpredictable. Our contributions are twofold: (1) We present a full description of a new unification algorithm for the Calculus of Inductive Constructions (the base logic of Coq), including universe polymorphism, canonical structures (the overloading mechanism baked into Coq's unification), and a small set of useful heuristics. (2) We implemented our algorithm, and tested it on several libraries, providing evidence that the selected set of heuristics suffices for large developments.

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Cited By

Libal TMiller D(2021)Functions-as-constructors higher-order unification: extended pattern unificationAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09774-y90:5(455-479)Online publication date: 30-Sep-2021
https://doi.org/10.1007/s10472-021-09774-y
Xie NEisenberg ROliveira B(2019)Kind inference for datatypesProceedings of the ACM on Programming Languages10.1145/33711214:POPL(1-28)Online publication date: 20-Dec-2019
https://dl.acm.org/doi/10.1145/3371121
COCKX JDEVRIESE D(2018)Proof-relevant unification: Dependent pattern matching with only the axioms of your type theoryJournal of Functional Programming10.1017/S095679681800014X28Online publication date: 10-May-2018
https://doi.org/10.1017/S095679681800014X

Index Terms

A unification algorithm for Coq featuring universe polymorphism and overloading
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Functional languages
2. Theory of computation
  1. Logic
  2. Models of computation
    1. Computability

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 50, Issue 9

ICFP '15

September 2015

436 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/2858949

Editor:
Andy Gill
University of Kansas, Lawrence, KS

Issue’s Table of Contents

ICFP 2015: Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming
August 2015
436 pages
ISBN:9781450336697
DOI:10.1145/2784731
General Chair:
Kathleen Fisher
Tufts University, USA
,
Program Chair:
John Reppy
University of Chicago, USA

Copyright © 2015 ACM.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 29 August 2015

Published in SIGPLAN Volume 50, Issue 9

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Cited By

Libal TMiller D(2021)Functions-as-constructors higher-order unification: extended pattern unificationAnnals of Mathematics and Artificial Intelligence10.1007/s10472-021-09774-y90:5(455-479)Online publication date: 30-Sep-2021
https://doi.org/10.1007/s10472-021-09774-y
Xie NEisenberg ROliveira B(2019)Kind inference for datatypesProceedings of the ACM on Programming Languages10.1145/33711214:POPL(1-28)Online publication date: 20-Dec-2019
https://dl.acm.org/doi/10.1145/3371121
COCKX JDEVRIESE D(2018)Proof-relevant unification: Dependent pattern matching with only the axioms of your type theoryJournal of Functional Programming10.1017/S095679681800014X28Online publication date: 10-May-2018
https://doi.org/10.1017/S095679681800014X

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