research-article

Which simple types have a unique inhabitant?

Authors:

Gabriel Scherer,

Didier RémyAuthors Info & Claims

ICFP 2015: Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming

Pages 243 - 255

https://doi.org/10.1145/2784731.2784757

Published: 29 August 2015 Publication History

Abstract

We study the question of whether a given type has a unique inhabitant modulo program equivalence. In the setting of simply-typed lambda-calculus with sums, equipped with the strong --equivalence, we show that uniqueness is decidable. We present a saturating focused logic that introduces irreducible cuts on positive types ``as soon as possible''. Backward search in this logic gives an effective algorithm that returns either zero, one or two distinct inhabitants for any given type. Preliminary application studies show that such a feature can be useful in strongly-typed programs, inferring the code of highly-polymorphic library functions, or ``glue code'' inside more complex terms.

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Cited By

Veltri NWan C(2024)Semi-Substructural Logics with AdditivesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.402.8402(63-80)Online publication date: 23-Apr-2024
https://doi.org/10.4204/EPTCS.402.8
Liang CMiller D(2024)Focusing Gentzen’s LK Proof SystemPeter Schroeder-Heister on Proof-Theoretic Semantics10.1007/978-3-031-50981-0_9(275-313)Online publication date: 13-Feb-2024
https://doi.org/10.1007/978-3-031-50981-0_9
Veltri N(2023)Maximally Multi-focused Proofs for Skew Non-Commutative MILLLogic, Language, Information, and Computation10.1007/978-3-031-39784-4_24(377-393)Online publication date: 11-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-39784-4_24
Show More Cited By

Index Terms

Which simple types have a unique inhabitant?
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs

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cover image ACM Conferences

ICFP 2015: Proceedings of the 20th ACM SIGPLAN International Conference on Functional Programming

August 2015

436 pages

ISBN:9781450336697

DOI:10.1145/2784731

General Chair:
Kathleen Fisher
Tufts University, USA
,
Program Chair:
John Reppy
University of Chicago, USA

ACM SIGPLAN Notices Volume 50, Issue 9
ICFP '15
September 2015
436 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2858949
Editor:
Andy Gill
University of Kansas, Lawrence, KS
Issue’s Table of Contents

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Published: 29 August 2015

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ICFP'15: 20th ACM SIGPLAN International Conference on Functional Programming

August 31 - September 2, 2015

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Cited By

Veltri NWan C(2024)Semi-Substructural Logics with AdditivesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.402.8402(63-80)Online publication date: 23-Apr-2024
https://doi.org/10.4204/EPTCS.402.8
Liang CMiller D(2024)Focusing Gentzen’s LK Proof SystemPeter Schroeder-Heister on Proof-Theoretic Semantics10.1007/978-3-031-50981-0_9(275-313)Online publication date: 13-Feb-2024
https://doi.org/10.1007/978-3-031-50981-0_9
Veltri N(2023)Maximally Multi-focused Proofs for Skew Non-Commutative MILLLogic, Language, Information, and Computation10.1007/978-3-031-39784-4_24(377-393)Online publication date: 11-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-39784-4_24
Uustalu TVeltri NWan C(2022)Proof Theory of Skew Non-Commutative MILLElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.358.9358(118-135)Online publication date: 14-Apr-2022
https://doi.org/10.4204/EPTCS.358.9
Rioux NZdancewic S(2020)Computation focusingProceedings of the ACM on Programming Languages10.1145/34089774:ICFP(1-27)Online publication date: 3-Aug-2020
https://dl.acm.org/doi/10.1145/3408977
Miltner AMaina SFisher KPierce BWalker DZdancewic S(2019)Synthesizing symmetric lensesProceedings of the ACM on Programming Languages10.1145/33416993:ICFP(1-28)Online publication date: 26-Jul-2019
https://dl.acm.org/doi/10.1145/3341699
Maina SMiltner AFisher KPierce BWalker DZdancewic S(2018)Synthesizing quotient lensesProceedings of the ACM on Programming Languages10.1145/32367752:ICFP(1-29)Online publication date: 30-Jul-2018
https://dl.acm.org/doi/10.1145/3236775
DOWNEN PARIOLA Z(2018)A tutorial on computational classical logic and the sequent calculusJournal of Functional Programming10.1017/S095679681800002328Online publication date: 1-Feb-2018
https://doi.org/10.1017/S0956796818000023
Wang XDillig ISingh R(2017)Program synthesis using abstraction refinementProceedings of the ACM on Programming Languages10.1145/31581512:POPL(1-30)Online publication date: 27-Dec-2017
https://dl.acm.org/doi/10.1145/3158151
Miltner AFisher KPierce BWalker DZdancewic S(2017)Synthesizing bijective lensesProceedings of the ACM on Programming Languages10.1145/31580892:POPL(1-30)Online publication date: 27-Dec-2017
https://dl.acm.org/doi/10.1145/3158089
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