research-article

Integrating Linear and Dependent Types

Authors:

Neelakantan R. Krishnaswami,

Nick BentonAuthors Info & Claims

POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 17 - 30

https://doi.org/10.1145/2676726.2676969

Published: 14 January 2015 Publication History

Abstract

In this paper, we show how to integrate linear types with type dependency, by extending the linear/non-linear calculus of Benton to support type dependency. Next, we give an application of this calculus by giving a proof-theoretic account of imperative programming, which requires extending the calculus with computationally irrelevant quantification, proof irrelevance, and a monad of computations. We show the soundness of our theory by giving a realizability model in the style of Nuprl, which permits us to validate not only the beta-laws for each type, but also the eta-laws. These extensions permit us to decompose Hoare triples into a collection of simpler type-theoretic connectives, yielding a rich equational theory for dependently-typed higher-order imperative programs. Furthermore, both the type theory and its model are relatively simple, even when all of the extensions are considered.

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Atkey R(2024)Polynomial Time and Dependent TypesProceedings of the ACM on Programming Languages10.1145/36329188:POPL(2288-2317)Online publication date: 5-Jan-2024
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Patterson DWagner AAhmed ACong YDagand P(2023)Semantic Encapsulation using Linking TypesProceedings of the 8th ACM SIGPLAN International Workshop on Type-Driven Development10.1145/3609027.3609405(14-28)Online publication date: 30-Aug-2023
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Index Terms

Integrating Linear and Dependent Types
1. Theory of computation
  1. Semantics and reasoning
    1. Program semantics

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cover image ACM Conferences

POPL '15: Proceedings of the 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 2015

716 pages

ISBN:9781450333009

DOI:10.1145/2676726

General Chair:
Sriram Rajamani
Microsoft Research, India
,
Program Chair:
David Walker
Princeton University, USA

ACM SIGPLAN Notices Volume 50, Issue 1
POPL '15
January 2015
682 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2775051
Editor:
Andy Gill
University of Kansas, Lawrence, KS
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Published: 14 January 2015

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Cited By

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https://dl.acm.org/doi/10.1145/3632918
Patterson DWagner AAhmed ACong YDagand P(2023)Semantic Encapsulation using Linking TypesProceedings of the 8th ACM SIGPLAN International Workshop on Type-Driven Development10.1145/3609027.3609405(14-28)Online publication date: 30-Aug-2023
https://dl.acm.org/doi/10.1145/3609027.3609405
Mordido ASpaderna JThiemann PVasconcelos V(2023)Parameterized Algebraic ProtocolsProceedings of the ACM on Programming Languages10.1145/35912777:PLDI(1389-1413)Online publication date: 6-Jun-2023
https://dl.acm.org/doi/10.1145/3591277
New MLicata D(2023)A Formal Logic for Formal Category TheoryFoundations of Software Science and Computation Structures10.1007/978-3-031-30829-1_6(113-134)Online publication date: 21-Apr-2023
https://doi.org/10.1007/978-3-031-30829-1_6
Dagnino FPasquali F(2022)Logical Foundations of Quantitative EqualityProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533337(1-13)Online publication date: 2-Aug-2022
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Patterson DMushtak NWagner AAhmed AJhala RDillig I(2022)Semantic soundness for language interoperabilityProceedings of the 43rd ACM SIGPLAN International Conference on Programming Language Design and Implementation10.1145/3519939.3523703(609-624)Online publication date: 9-Jun-2022
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Choudhury PEades III HEisenberg RWeirich S(2021)A graded dependent type system with a usage-aware semanticsProceedings of the ACM on Programming Languages10.1145/34343315:POPL(1-32)Online publication date: 4-Jan-2021
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Fu PKishida KSelinger PHermanns HZhang LKobayashi NMiller D(2020)Linear Dependent Type Theory for Quantum Programming LanguagesProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394765(440-453)Online publication date: 8-Jul-2020
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Chen CChoudhury VCarette JSabry A(2020)Fractional TypesReversible Computation10.1007/978-3-030-52482-1_10(169-186)Online publication date: 9-Jul-2020
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Goertzel B(2020)What Kind of Programming Language Best Suits Integrative AGI?Artificial General Intelligence10.1007/978-3-030-52152-3_15(142-152)Online publication date: 16-Sep-2020
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