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Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed types

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Neelakantan R. KrishnaswamiAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 3, Issue POPL

Article No.: 9, Pages 1 - 28

https://doi.org/10.1145/3290322

Published: 02 January 2019 Publication History

Abstract

Bidirectional typechecking, in which terms either synthesize a type or are checked against a known type, has become popular for its applicability to a variety of type systems, its error reporting, and its ease of implementation. Following principles from proof theory, bidirectional typing can be applied to many type constructs. The principles underlying a bidirectional approach to indexed types (generalized algebraic datatypes) are less clear. Building on proof-theoretic treatments of equality, we give a declarative specification of typing based on focalization. This approach permits declarative rules for coverage of pattern matching, as well as support for first-class existential types using a focalized subtyping judgment. We use refinement types to avoid explicitly passing equality proofs in our term syntax, making our calculus similar to languages such as Haskell and OCaml. We also extend the declarative specification with an explicit rules for deducing when a type is principal, permitting us to give a complete declarative specification for a rich type system with significant type inference. We also give a set of algorithmic typing rules, and prove that it is sound and complete with respect to the declarative system. The proof requires a number of technical innovations, including proving soundness and completeness in a mutually recursive fashion.

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Cited By

Parreaux LBoruch-Gruszecki AFan AChau C(2024)When Subtyping Constraints Liberate: A Novel Type Inference Approach for First-Class PolymorphismProceedings of the ACM on Programming Languages10.1145/36328908:POPL(1418-1450)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632890
Sieczkowski FStepanenko SSterling JBirkedal L(2024)The Essence of Generalized Algebraic Data TypesProceedings of the ACM on Programming Languages10.1145/36328668:POPL(695-723)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632866
Cui CJiang SOliveira B(2023)Greedy Implicit Bounded QuantificationProceedings of the ACM on Programming Languages10.1145/36228717:OOPSLA2(2083-2111)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622871
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Index Terms

Sound and complete bidirectional typechecking for higher-rank polymorphism with existentials and indexed 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

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 3, Issue POPL

January 2019

2275 pages

EISSN:2475-1421

DOI:10.1145/3302515

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Copyright © 2019 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: 02 January 2019

Published in PACMPL Volume 3, Issue POPL

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Cited By

Parreaux LBoruch-Gruszecki AFan AChau C(2024)When Subtyping Constraints Liberate: A Novel Type Inference Approach for First-Class PolymorphismProceedings of the ACM on Programming Languages10.1145/36328908:POPL(1418-1450)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632890
Sieczkowski FStepanenko SSterling JBirkedal L(2024)The Essence of Generalized Algebraic Data TypesProceedings of the ACM on Programming Languages10.1145/36328668:POPL(695-723)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632866
Cui CJiang SOliveira B(2023)Greedy Implicit Bounded QuantificationProceedings of the ACM on Programming Languages10.1145/36228717:OOPSLA2(2083-2111)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622871
Economou DKrishnaswami NDunfield J(2023)Focusing on Refinement TypingACM Transactions on Programming Languages and Systems10.1145/361040845:4(1-62)Online publication date: 20-Dec-2023
https://dl.acm.org/doi/10.1145/3610408
Tanabe YLubis LAotani TMasuhara H(2023)Compilation Semantics for a Programming Language with VersionsProgramming Languages and Systems10.1007/978-981-99-8311-7_1(3-23)Online publication date: 26-Nov-2023
https://dl.acm.org/doi/10.1007/978-981-99-8311-7_1
Castagna GLaurent MNguyễn KLutze M(2022)On type-cases, union elimination, and occurrence typingProceedings of the ACM on Programming Languages10.1145/34986746:POPL(1-31)Online publication date: 12-Jan-2022
https://dl.acm.org/doi/10.1145/3498674
Lakhani ZDas ADeYoung HMordido APfenning F(2022)Polarized SubtypingProgramming Languages and Systems10.1007/978-3-030-99336-8_16(431-461)Online publication date: 29-Mar-2022
https://doi.org/10.1007/978-3-030-99336-8_16
Eisenberg RDuboc GWeirich SLee D(2021)An existential crisis resolved: type inference for first-class existential typesProceedings of the ACM on Programming Languages10.1145/34735695:ICFP(1-29)Online publication date: 19-Aug-2021
https://dl.acm.org/doi/10.1145/3473569
Dunfield JKrishnaswami N(2021)Bidirectional TypingACM Computing Surveys10.1145/345095254:5(1-38)Online publication date: 25-May-2021
https://dl.acm.org/doi/10.1145/3450952
Lo SLu QWang CPaik HZhu L(2021)A Systematic Literature Review on Federated Machine LearningACM Computing Surveys10.1145/345028854:5(1-39)Online publication date: 25-May-2021
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