Formalizing 휋-calculus in guarded cubical Agda

Niccolò Veltri; Andrea Vezzosi

doi:10.1145/3372885.3373814

Formalizing 휋-calculus in guarded cubical Agda

Niccolò Veltri, Andrea Vezzosi

Tallinn University

Research output: Conference Article in Proceeding or Book/Report chapter › Article in proceedings › Research › peer-review

Abstract

Dependent type theories with guarded recursion have shown themselves suitable for the development of denotational semantics of programming languages. In particular Ticked Cubical Type Theory (TCTT) has been used to show that for guarded labelled transition systems (GLTS) interpretation into the denotational semantics maps bisimilar processes to equal values. In fact the two notions are proved equivalent, allowing one to reason about equality in place of bisimilarity.

We extend that result to the π-calculus, picking early congruence as the syntactic notion of equivalence between processes, showing that denotational models based on guarded recursive types can handle the dynamic creation of channels that goes beyond the scope of GLTSs.

Hence we present a fully abstract denotational model for the early π-calculus, formalized as an extended example for Guarded Cubical Agda: a novel implementation of Ticked Cubical Type Theory based on Cubical Agda.

Original language	English
Title of host publication	CPP 2020: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs ACM
Number of pages	14
Publisher	Association for Computing Machinery
Publication date	2020
Pages	270-283
ISBN (Print)	9781450370974
DOIs	https://doi.org/10.1145/3372885.3373814
Publication status	Published - 2020
Event	9th ACM SIGPLAN International Conference on Certified Programs and Proofs - Duration: 20 Jan 2020 → … https://popl20.sigplan.org/home/CPP-2020

Conference

Conference	9th ACM SIGPLAN International Conference on Certified Programs and Proofs
Period	20/01/2020 → …
Internet address	https://popl20.sigplan.org/home/CPP-2020

Keywords

Dependent type theories
Guarded recursion
Denotational semantics
π-calculus
Guarded Cubical Agda

Access to Document

10.1145/3372885.3373814

Formalizing 𝜋-calculus in guarded cubical AgdaAccepted author manuscript, 289 KB

Type theories for reactive programming
Møgelberg, R. E. (PI), Vezzosi, A. (CoI), Graulund, C. U. (CoI), Kristensen, M. B. (CoI) & Veltri, N. (CoI)
Villum Foundation
22/01/2016 → 21/01/2022
Project: Research

Cite this

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title = "Formalizing 휋-calculus in guarded cubical Agda",

abstract = "Dependent type theories with guarded recursion have shown themselves suitable for the development of denotational semantics of programming languages. In particular Ticked Cubical Type Theory (TCTT) has been used to show that for guarded labelled transition systems (GLTS) interpretation into the denotational semantics maps bisimilar processes to equal values. In fact the two notions are proved equivalent, allowing one to reason about equality in place of bisimilarity.We extend that result to the π-calculus, picking early congruence as the syntactic notion of equivalence between processes, showing that denotational models based on guarded recursive types can handle the dynamic creation of channels that goes beyond the scope of GLTSs.Hence we present a fully abstract denotational model for the early π-calculus, formalized as an extended example for Guarded Cubical Agda: a novel implementation of Ticked Cubical Type Theory based on Cubical Agda.",

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pages = "270--283",

booktitle = "CPP 2020: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs ACM",

publisher = "Association for Computing Machinery",

address = "United States",

note = "9th ACM SIGPLAN International Conference on Certified Programs and Proofs, CPP2020 ; Conference date: 20-01-2020",

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Formalizing 휋-calculus in guarded cubical Agda. / Veltri, Niccolò; Vezzosi, Andrea.
CPP 2020: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs ACM. Association for Computing Machinery, 2020. p. 270-283.

Research output: Conference Article in Proceeding or Book/Report chapter › Article in proceedings › Research › peer-review

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AU - Vezzosi, Andrea

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N2 - Dependent type theories with guarded recursion have shown themselves suitable for the development of denotational semantics of programming languages. In particular Ticked Cubical Type Theory (TCTT) has been used to show that for guarded labelled transition systems (GLTS) interpretation into the denotational semantics maps bisimilar processes to equal values. In fact the two notions are proved equivalent, allowing one to reason about equality in place of bisimilarity.We extend that result to the π-calculus, picking early congruence as the syntactic notion of equivalence between processes, showing that denotational models based on guarded recursive types can handle the dynamic creation of channels that goes beyond the scope of GLTSs.Hence we present a fully abstract denotational model for the early π-calculus, formalized as an extended example for Guarded Cubical Agda: a novel implementation of Ticked Cubical Type Theory based on Cubical Agda.

AB - Dependent type theories with guarded recursion have shown themselves suitable for the development of denotational semantics of programming languages. In particular Ticked Cubical Type Theory (TCTT) has been used to show that for guarded labelled transition systems (GLTS) interpretation into the denotational semantics maps bisimilar processes to equal values. In fact the two notions are proved equivalent, allowing one to reason about equality in place of bisimilarity.We extend that result to the π-calculus, picking early congruence as the syntactic notion of equivalence between processes, showing that denotational models based on guarded recursive types can handle the dynamic creation of channels that goes beyond the scope of GLTSs.Hence we present a fully abstract denotational model for the early π-calculus, formalized as an extended example for Guarded Cubical Agda: a novel implementation of Ticked Cubical Type Theory based on Cubical Agda.

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KW - Denotational semantics

KW - π-calculus

KW - Guarded Cubical Agda

KW - Dependent type theories

KW - Guarded recursion

KW - Denotational semantics

KW - π-calculus

KW - Guarded Cubical Agda

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DO - 10.1145/3372885.3373814

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EP - 283

BT - CPP 2020: Proceedings of the 9th ACM SIGPLAN International Conference on Certified Programs and Proofs ACM

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T2 - 9th ACM SIGPLAN International Conference on Certified Programs and Proofs

Y2 - 20 January 2020

ER -

Formalizing 휋-calculus in guarded cubical Agda

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Keywords

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Type theories for reactive programming

Cite this