Foundational nonuniform (Co)datatypes for higher-order logic

Jasmin Christian Blanchette; Fabian Meier; Andrei Popescu; Dmitriy Traytel

doi:10.1109/LICS.2017.8005071

Foundational nonuniform (Co)datatypes for higher-order logic

Jasmin Christian Blanchette, Fabian Meier, Andrei Popescu, Dmitriy Traytel

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

Abstract

Nonuniform (or 'nested' or 'heterogeneous') datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)induction and (co)recursion principles based on a weak variant of parametricity.

Original language	English
Title of host publication	2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)	9781509030187
DOIs	https://doi.org/10.1109/LICS.2017.8005071
Publication status	Published - 8 Aug 2017
Event	32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 - Reykjavik, Iceland Duration: 20 Jun 2017 → 23 Jun 2017

Conference

Conference	32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017
Country/Territory	Iceland
City	Reykjavik
Period	20/06/17 → 23/06/17

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10.1109/LICS.2017.8005071

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title = "Foundational nonuniform (Co)datatypes for higher-order logic",

abstract = "Nonuniform (or 'nested' or 'heterogeneous') datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)induction and (co)recursion principles based on a weak variant of parametricity.",

author = "Blanchette, {Jasmin Christian} and Fabian Meier and Andrei Popescu and Dmitriy Traytel",

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doi = "10.1109/LICS.2017.8005071",

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booktitle = "2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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note = "32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017 ; Conference date: 20-06-2017 Through 23-06-2017",

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Blanchette, JC, Meier, F, Popescu, A & Traytel, D 2017, Foundational nonuniform (Co)datatypes for higher-order logic. in 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017., 8005071, Institute of Electrical and Electronics Engineers Inc., 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017, Reykjavik, Iceland, 20/06/17. https://doi.org/10.1109/LICS.2017.8005071

Foundational nonuniform (Co)datatypes for higher-order logic. / Blanchette, Jasmin Christian; Meier, Fabian; Popescu, Andrei; Traytel, Dmitriy.

2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017. Institute of Electrical and Electronics Engineers Inc., 2017. 8005071.

Research output: Chapter in Book / Report / Conference proceeding › Conference contribution › Academic › peer-review

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N2 - Nonuniform (or 'nested' or 'heterogeneous') datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)induction and (co)recursion principles based on a weak variant of parametricity.

AB - Nonuniform (or 'nested' or 'heterogeneous') datatypes are recursively defined types in which the type arguments vary recursively. They arise in the implementation of finger trees and other efficient functional data structures. We show how to reduce a large class of nonuniform datatypes and codatatypes to uniform types in higher-order logic. We programmed this reduction in the Isabelle/HOL proof assistant, thereby enriching its specification language. Moreover, we derive (co)induction and (co)recursion principles based on a weak variant of parametricity.

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Foundational nonuniform (Co)datatypes for higher-order logic

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