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Recovering purity with comonads and capabilities

Authors:

Vikraman Choudhury,

Neel KrishnaswamiAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 4, Issue ICFP

Article No.: 111, Pages 1 - 28

https://doi.org/10.1145/3408993

Published: 03 August 2020 Publication History

Abstract

In this paper, we take a pervasively effectful (in the style of ML) typed lambda calculus, and show how to extend it to permit capturing pure expressions with types. Our key observation is that, just as the pure simply-typed lambda calculus can be extended to support effects with a monadic type discipline, an impure typed lambda calculus can be extended to support purity with a comonadic type discipline.

We establish the correctness of our type system via a simple denotational model, which we call the capability space model. Our model formalises the intuition common to systems programmers that the ability to perform effects should be controlled via access to a permission or capability, and that a program is capability-safe if it performs no effects that it does not have a runtime capability for. We then identify the axiomatic categorical structure that the capability space model validates, and use these axioms to give a categorical semantics for our comonadic type system. We then give an equational theory (substitution and the call-by-value β and η laws) for the imperative lambda calculus, and show its soundness relative to this semantics.

Finally, we give a translation of the pure simply-typed lambda calculus into our comonadic imperative calculus, and show that any two terms which are βη-equal in the STLC are equal in the equational theory of the comonadic calculus, establishing that pure programs can be mapped in an equation-preserving way into our imperative calculus.

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Cited By

Boruch-Gruszecki AOdersky MLee ELhoták OBrachthäuser J(2023)Capturing TypesACM Transactions on Programming Languages and Systems10.1145/361800345:4(1-52)Online publication date: 20-Nov-2023
https://dl.acm.org/doi/10.1145/3618003
Brachthäuser JSchuster PLee EBoruch-Gruszecki A(2022)Effects, capabilities, and boxes: from scope-based reasoning to type-based reasoning and backProceedings of the ACM on Programming Languages10.1145/35273206:OOPSLA1(1-30)Online publication date: 29-Apr-2022
https://dl.acm.org/doi/10.1145/3527320
BAHR P(2022)Modal FRP for all: Functional reactive programming without space leaks in HaskellJournal of Functional Programming10.1017/S095679682200013232Online publication date: 26-Dec-2022
https://doi.org/10.1017/S0956796822000132
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Index Terms

Recovering purity with comonads and capabilities
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
      2. Syntax
    2. General programming languages
      1. Language types
        Functional languages
2. Theory of computation
  1. Logic
  2. Semantics and reasoning
    1. Program semantics
      1. Categorical semantics
      2. Denotational semantics

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 4, Issue ICFP

August 2020

1070 pages

EISSN:2475-1421

DOI:10.1145/3415018

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Copyright © 2020 Owner/Author.

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

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Association for Computing Machinery

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Publication History

Published: 03 August 2020

Published in PACMPL Volume 4, Issue ICFP

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Cited By

Boruch-Gruszecki AOdersky MLee ELhoták OBrachthäuser J(2023)Capturing TypesACM Transactions on Programming Languages and Systems10.1145/361800345:4(1-52)Online publication date: 20-Nov-2023
https://dl.acm.org/doi/10.1145/3618003
Brachthäuser JSchuster PLee EBoruch-Gruszecki A(2022)Effects, capabilities, and boxes: from scope-based reasoning to type-based reasoning and backProceedings of the ACM on Programming Languages10.1145/35273206:OOPSLA1(1-30)Online publication date: 29-Apr-2022
https://dl.acm.org/doi/10.1145/3527320
BAHR P(2022)Modal FRP for all: Functional reactive programming without space leaks in HaskellJournal of Functional Programming10.1017/S095679682200013232Online publication date: 26-Dec-2022
https://doi.org/10.1017/S0956796822000132
Marshall DVollmer MOrchard D(2022)Linearity and Uniqueness: An Entente CordialeProgramming Languages and Systems10.1007/978-3-030-99336-8_13(346-375)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99336-8_13
Odersky MBoruch-Gruszecki ABrachthäuser JLee ELhoták ORichard-Foy JDoeraene S(2021)Safer exceptions for ScalaProceedings of the 12th ACM SIGPLAN International Symposium on Scala10.1145/3486610.3486893(1-11)Online publication date: 17-Oct-2021
https://dl.acm.org/doi/10.1145/3486610.3486893

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