research-article

Foundational extensible corecursion: a proof assistant perspective

Authors:

Jasmin Christian Blanchette,

Andrei Popescu,

Dmitriy TraytelAuthors Info & Claims

ICFP 2015: Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming

Pages 192 - 204

https://doi.org/10.1145/2784731.2784732

Published: 29 August 2015 Publication History

Abstract

This paper presents a formalized framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under "friendly" operations, including constructors. Friendly corecursive functions can be registered as such, thereby increasing the corecursor's expressiveness. The metatheory is formalized in the Isabelle proof assistant and forms the core of a prototype tool. The corecursor is derived from first principles, without requiring new axioms or extensions of the logic.

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Index Terms

Foundational extensible corecursion: a proof assistant perspective
1. Theory of computation

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cover image ACM Conferences

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

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
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Published: 29 August 2015

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Cited By

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https://doi.org/10.1007/978-3-031-77019-7_3
Kună?Ar OPopescu A(2019)A Consistent Foundation for Isabelle/HOLJournal of Automated Reasoning10.1007/s10817-018-9454-862:4(531-555)Online publication date: 1-Apr-2019
https://dl.acm.org/doi/10.1007/s10817-018-9454-8
Schlichtkrull A(2018)Formalization of the Resolution Calculus for First-Order LogicJournal of Automated Reasoning10.1007/s10817-017-9447-z61:1-4(455-484)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1007/s10817-017-9447-z
Blanchette JMeier FPopescu ATraytel DAceto LIngólfsdóttir A(2017)Foundational nonuniform (co)datatypes for higher-order logicProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330006(1-12)Online publication date: 20-Jun-2017
https://dl.acm.org/doi/10.5555/3329995.3330006
Madhavan RKulal SKuncak V(2017)Contract-based resource verification for higher-order functions with memoizationACM SIGPLAN Notices10.1145/3093333.300987452:1(330-343)Online publication date: 1-Jan-2017
https://dl.acm.org/doi/10.1145/3093333.3009874
Madhavan RKulal SKuncak VCastagna GGordon A(2017)Contract-based resource verification for higher-order functions with memoizationProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009874(330-343)Online publication date: 1-Jan-2017
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Biendarra JBlanchette JBouzy ADesharnais MFleury MHölzl JKunčar OLochbihler AMeier FPanny LPopescu ASternagel CThiemann RTraytel D(2017)Foundational (Co)datatypes and (Co)recursion for Higher-Order LogicFrontiers of Combining Systems10.1007/978-3-319-66167-4_1(3-21)Online publication date: 29-Aug-2017
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