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Handling delimited continuations with dependent types

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Kenichi AsaiAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 2, Issue ICFP

Article No.: 69, Pages 1 - 31

https://doi.org/10.1145/3236764

Published: 30 July 2018 Publication History

Abstract

Dependent types are a powerful tool for maintaining program invariants. To take advantage of this aspect in real-world programming, efforts have been put into enriching dependently typed languages with missing constructs, most notably, effects. This paper presents a language that has two practically interesting ingredients: dependent inductive types, and the delimited control constructs shift and reset. When integrating delimited control into a dependently typed language, however, two challenges arise. First, the dynamic nature of control operators, which is the source of their expressiveness, can break fundamental language properties such as logical consistency and subject reduction. Second, CPS translations, which we often use to define the semantics of control operators, do not scale straightforwardly to dependently typed languages. We solve the former issue by restricting dependency of types, and the latter using answer-type polymorphism of pure terms. The main contribution of this paper is to give a sound type system of our language, as well as a type-preserving CPS translation. We also discuss various extensions, which would make our language more like a full-spectrum proof assistant but pose non-trivial issues.

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Cited By

Kawamata FUnno HSekiyama TTerauchi T(2024)Answer Refinement Modification: Refinement Type System for Algebraic Effects and HandlersProceedings of the ACM on Programming Languages10.1145/36332808:POPL(115-147)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3633280
Sekiyama TUnno H(2023)Temporal Verification with Answer-Effect Modification: Dependent Temporal Type-and-Effect System with Delimited ContinuationsProceedings of the ACM on Programming Languages10.1145/35712647:POPL(2079-2110)Online publication date: 9-Jan-2023
https://dl.acm.org/doi/10.1145/3571264
Sekiyama TTsukada TIgarashi A(2020)Signature restriction for polymorphic algebraic effectsProceedings of the ACM on Programming Languages10.1145/34089994:ICFP(1-30)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3408999

Index Terms

Handling delimited continuations with dependent types
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Control structures
        Polymorphism
      2. Language types
        Functional languages
2. Theory of computation
  1. Logic
    1. Type theory
  2. Semantics and reasoning
    1. Program constructs
      1. Control primitives

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 2, Issue ICFP

September 2018

1133 pages

EISSN:2475-1421

DOI:10.1145/3243631

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Copyright © 2018 Owner/Author.

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 30 July 2018

Published in PACMPL Volume 2, Issue ICFP

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Cited By

Kawamata FUnno HSekiyama TTerauchi T(2024)Answer Refinement Modification: Refinement Type System for Algebraic Effects and HandlersProceedings of the ACM on Programming Languages10.1145/36332808:POPL(115-147)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3633280
Sekiyama TUnno H(2023)Temporal Verification with Answer-Effect Modification: Dependent Temporal Type-and-Effect System with Delimited ContinuationsProceedings of the ACM on Programming Languages10.1145/35712647:POPL(2079-2110)Online publication date: 9-Jan-2023
https://dl.acm.org/doi/10.1145/3571264
Sekiyama TTsukada TIgarashi A(2020)Signature restriction for polymorphic algebraic effectsProceedings of the ACM on Programming Languages10.1145/34089994:ICFP(1-30)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3408999

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