research-article

Programming with binders and indexed data-types

Authors:

Brigitte PientkaAuthors Info & Claims

POPL '12: Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 413 - 424

https://doi.org/10.1145/2103656.2103705

Published: 25 January 2012 Publication History

Abstract

We show how to combine a general purpose type system for an existing language with support for programming with binders and contexts by refining the type system of ML with a restricted form of dependent types where index objects are drawn from contextual LF. This allows the user to specify formal systems within the logical framework LF and index ML types with contextual LF objects. Our language design keeps the index language generic only requiring decidability of equality of the index language providing a modular design. To illustrate the elegance and effectiveness of our language, we give programs for closure conversion and normalization by evaluation.

Our three key technical contribution are: 1) We give a bi-directional type system for our core language which is centered around refinement substitutions instead of constraint solving. As a consequence, type checking is decidable and easy to trust, although constraint solving may be undecidable. 2) We give a big-step environment based operational semantics with environments which lends itself to efficient implementation. 3) We prove our language to be type safe and have mechanized our theoretical development in the proof assistant Coq using the fresh approach to binding.

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Cited By

Crichton WKrishnamurthi S(2024)A Core Calculus for Documents: Or, Lambda: The Ultimate DocumentProceedings of the ACM on Programming Languages10.1145/36328658:POPL(667-694)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632865
Schwartzentruber JPientka B(2023)Semi-Automation of Meta-Theoretic Proofs in BelugaElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.396.3396(20-35)Online publication date: 17-Nov-2023
https://doi.org/10.4204/EPTCS.396.3
Gaulin APientka B(2023)Contextual Refinement TypesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.396.2396(4-19)Online publication date: 17-Nov-2023
https://doi.org/10.4204/EPTCS.396.2
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Index Terms

Programming with binders and indexed data-types
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language features
        Data types and structures

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cover image ACM Conferences

POPL '12: Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 2012

602 pages

ISBN:9781450310833

DOI:10.1145/2103656

General Chair:
John Field
Google, USA
,
Program Chair:
Michael Hicks
University of Maryland, College Park, USA

ACM SIGPLAN Notices Volume 47, Issue 1
POPL '12
January 2012
569 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2103621
Issue’s Table of Contents

Copyright © 2012 ACM.

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Published: 25 January 2012

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POPL '12: The 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 25 - 27, 2012

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Overall Acceptance Rate 824 of 4,130 submissions, 20%

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Cited By

Crichton WKrishnamurthi S(2024)A Core Calculus for Documents: Or, Lambda: The Ultimate DocumentProceedings of the ACM on Programming Languages10.1145/36328658:POPL(667-694)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632865
Schwartzentruber JPientka B(2023)Semi-Automation of Meta-Theoretic Proofs in BelugaElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.396.3396(20-35)Online publication date: 17-Nov-2023
https://doi.org/10.4204/EPTCS.396.3
Gaulin APientka B(2023)Contextual Refinement TypesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.396.2396(4-19)Online publication date: 17-Nov-2023
https://doi.org/10.4204/EPTCS.396.2
Sano CKavanagh RPientka B(2023)Mechanizing Session-Types using a Structural View: Enforcing Linearity without LinearityProceedings of the ACM on Programming Languages10.1145/36228107:OOPSLA2(374-399)Online publication date: 16-Oct-2023
https://dl.acm.org/doi/10.1145/3622810
Errington JJang JPientka B(2021)Harpoon: Mechanizing Metatheory InteractivelyAutomated Deduction – CADE 2810.1007/978-3-030-79876-5_38(636-648)Online publication date: 5-Jul-2021
https://doi.org/10.1007/978-3-030-79876-5_38
Pientka BHermanns HZhang LKobayashi NMiller D(2020)Contextual Types, ExplainedProceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3373718.3394735(35-37)Online publication date: 8-Jul-2020
https://dl.acm.org/doi/10.1145/3373718.3394735
ABEL AALLAIS GHAMEER APIENTKA BMOMIGLIANO ASCHÄFER SSTARK K(2019)POPLMark reloaded: Mechanizing proofs by logical relationsJournal of Functional Programming10.1017/S095679681900017029Online publication date: 10-Dec-2019
https://doi.org/10.1017/S0956796819000170
CAVE APIENTKA B(2018)Mechanizing proofs with logical relations – Kripke-styleMathematical Structures in Computer Science10.1017/S096012951800015428:09(1606-1638)Online publication date: 2-Aug-2018
https://doi.org/10.1017/S0960129518000154
FELTY AMOMIGLIANO APIENTKA B(2017)Benchmarks for reasoning with syntax trees containing binders and contexts of assumptionsMathematical Structures in Computer Science10.1017/S096012951700009328:09(1507-1540)Online publication date: 5-May-2017
https://doi.org/10.1017/S0960129517000093
Georges AMurawska AOtis SPientka B(2017)LINCX: A Linear Logical Framework with First-Class ContextsProgramming Languages and Systems10.1007/978-3-662-54434-1_20(530-555)Online publication date: 19-Mar-2017
https://doi.org/10.1007/978-3-662-54434-1_20
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