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The Essence of Generalized Algebraic Data Types

Authors:

Filip Sieczkowski,

Sergei Stepanenko,

Jonathan Sterling,

Lars BirkedalAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 8, Issue POPL

Article No.: 24, Pages 695 - 723

https://doi.org/10.1145/3632866

Published: 05 January 2024 Publication History

Abstract

This paper considers direct encodings of generalized algebraic data types (GADTs) in a minimal suitable lambda-calculus. To this end, we develop an extension of System F_ω with recursive types and internalized type equalities with injective constant type constructors. We show how GADTs and associated pattern-matching constructs can be directly expressed in the calculus, thus showing that it may be treated as a highly idealized modern functional programming language. We prove that the internalized type equalities in conjunction with injectivity rules increase the expressive power of the calculus by establishing a non-macro-expressibility result in F_ω, and prove the system type-sound via a syntactic argument. Finally, we build two relational models of our calculus: a simple, unary model that illustrates a novel, two-stage interpretation technique, necessary to account for the equational constraints; and a more sophisticated, binary model that relaxes the construction to allow, for the first time, formal reasoning about data-abstraction in a calculus equipped with GADTs.

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Cited By

Pereira FRaposo CNaik MPereira FTitzer B(2024)The Essence of the Flyweight Design PatternProceedings of the Workshop Dedicated to Jens Palsberg on the Occasion of His 60th Birthday10.1145/3694848.3694855(30-38)Online publication date: 22-Oct-2024
https://dl.acm.org/doi/10.1145/3694848.3694855
Clement BRémy DRadanne G(2024)Fulfilling OCaml Modules with TransparencyProceedings of the ACM on Programming Languages10.1145/36498188:OOPSLA1(194-222)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649818

Index Terms

The Essence of Generalized Algebraic Data Types
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Data types and structures
2. Theory of computation
  1. Logic
    1. Type theory
  2. Semantics and reasoning
    1. Program reasoning

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 8, Issue POPL

January 2024

2820 pages

EISSN:2475-1421

DOI:10.1145/3554315

Editor:
Michael Hicks
Amazon, USA

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Copyright © 2024 Owner/Author.

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

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 05 January 2024

Published in PACMPL Volume 8, Issue POPL

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Cited By

Pereira FRaposo CNaik MPereira FTitzer B(2024)The Essence of the Flyweight Design PatternProceedings of the Workshop Dedicated to Jens Palsberg on the Occasion of His 60th Birthday10.1145/3694848.3694855(30-38)Online publication date: 22-Oct-2024
https://dl.acm.org/doi/10.1145/3694848.3694855
Clement BRémy DRadanne G(2024)Fulfilling OCaml Modules with TransparencyProceedings of the ACM on Programming Languages10.1145/36498188:OOPSLA1(194-222)Online publication date: 29-Apr-2024
https://dl.acm.org/doi/10.1145/3649818

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