research-article

Towards concurrent type theory

Authors:

Frank Pfenning,

Bernardo ToninhoAuthors Info & Claims

TLDI '12: Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation

Pages 1 - 12

https://doi.org/10.1145/2103786.2103788

Published: 28 January 2012 Publication History

Abstract

We review progress in a recent line of research that provides a concurrent computational interpretation of (intuitionistic) linear logic. Propositions are interpreted as session types, sequent proofs as processes in the pi-calculus, cut reductions as process reductions, and vice versa. The strong proof-theoretic foundation of this type system provides immediate opportunities for uniform generalization, specifically, to embed terms from a functional type theory. The resulting system satisfies the properties of type preservation, progress, and termination, as expected from a language derived via a Curry-Howard isomorphism. While very expressive, the language is strictly stratified so that dependent types for functional terms can be enforced during communication, but neither processes nor channels can appear in functional terms. We briefly speculate on how this limitation might be overcome to arrive at a fully dependent concurrent type theory.

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Cited By

Caires LToninho B(2024)The Session Abstract MachineProgramming Languages and Systems10.1007/978-3-031-57262-3_9(206-235)Online publication date: 5-Apr-2024
https://doi.org/10.1007/978-3-031-57262-3_9
Rocha PCaires L(2023)Safe Session-Based Concurrency with Shared Linear StateProgramming Languages and Systems10.1007/978-3-031-30044-8_16(421-450)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30044-8_16
Papapanagiotou PFleuriot J(2021)Object-Level Reasoning with Logics Encoded in HOL LightElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.332.2332(18-34)Online publication date: 12-Jan-2021
https://doi.org/10.4204/EPTCS.332.2
Show More Cited By

Index Terms

Towards concurrent type theory
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation
  1. Formal languages and automata theory

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cover image ACM Conferences

TLDI '12: Proceedings of the 8th ACM SIGPLAN workshop on Types in language design and implementation

January 2012

110 pages

ISBN:9781450311205

DOI:10.1145/2103786

General Chair:
Benjamin C. Pierce
Monterey, CA., USA

Copyright © 2012 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 28 January 2012

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POPL '12: The 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 28, 2012

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Overall Acceptance Rate 11 of 26 submissions, 42%

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Cited By

Caires LToninho B(2024)The Session Abstract MachineProgramming Languages and Systems10.1007/978-3-031-57262-3_9(206-235)Online publication date: 5-Apr-2024
https://doi.org/10.1007/978-3-031-57262-3_9
Rocha PCaires L(2023)Safe Session-Based Concurrency with Shared Linear StateProgramming Languages and Systems10.1007/978-3-031-30044-8_16(421-450)Online publication date: 22-Apr-2023
https://dl.acm.org/doi/10.1007/978-3-031-30044-8_16
Papapanagiotou PFleuriot J(2021)Object-Level Reasoning with Logics Encoded in HOL LightElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.332.2332(18-34)Online publication date: 12-Jan-2021
https://doi.org/10.4204/EPTCS.332.2
Toninho BCaires LPfenning F(2021)A Decade of Dependent Session TypesProceedings of the 23rd International Symposium on Principles and Practice of Declarative Programming10.1145/3479394.3479398(1-3)Online publication date: 6-Sep-2021
https://dl.acm.org/doi/10.1145/3479394.3479398
Rocha PCaires L(2021)Propositions-as-types and shared stateProceedings of the ACM on Programming Languages10.1145/34735845:ICFP(1-30)Online publication date: 19-Aug-2021
https://dl.acm.org/doi/10.1145/3473584
van den Heuvel BPérez J(2020)Session Type Systems based on Linear Logic: Classical versus IntuitionisticElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.314.1314(1-11)Online publication date: 3-Apr-2020
https://doi.org/10.4204/EPTCS.314.1
Beckmann APreining N(2018)Hyper Natural Deduction for Gödel Logic—A natural deduction system for parallel reasoningJournal of Logic and Computation10.1093/logcom/exy01928:6(1125-1187)Online publication date: 23-Jul-2018
https://doi.org/10.1093/logcom/exy019
Jia LGommerstadt HPfenning F(2016)Monitors and blame assignment for higher-order session typesACM SIGPLAN Notices10.1145/2914770.283766251:1(582-594)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2914770.2837662
Jia LGommerstadt HPfenning FBodik RMajumdar R(2016)Monitors and blame assignment for higher-order session typesProceedings of the 43rd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages10.1145/2837614.2837662(582-594)Online publication date: 11-Jan-2016
https://dl.acm.org/doi/10.1145/2837614.2837662
Toninho BYoshida N(2016)Certifying Data in Multiparty Session TypesA List of Successes That Can Change the World10.1007/978-3-319-30936-1_23(433-458)Online publication date: 25-Mar-2016
https://doi.org/10.1007/978-3-319-30936-1_23
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