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Formal parametric polymorphism

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Pierre-Louis CurienAuthors Info & Claims

POPL '93: Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 157 - 170

https://doi.org/10.1145/158511.158622

Published: 01 March 1993 Publication History

Abstract

A polymorphic function is parametric if its behavior does not depend on the type at which it is instantiated. Starting with Reynolds' work, the study of parametricity is typically semantic. In this paper, we develop a syntactic approach to parametricity, and a formal system that embodies this approach: system ℜ. Girard's system F deals with terms and types; ℜ is an extension of F that deals also with relations between types.

In ℜ, it is possible to derive theorems about functions from their types, or "theorems for free", as Wadler calls them. An easy"theorem for free" asserts that the type ∀(X)X → Bool contains only constant functions; this is not provable in F. There are many harder and more substantial examples. Various metatheorems can also be obtained, such as a syntactic version of Reynolds' abstraction theorem.

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Cited By

Çiçek EQu WBarthe GGaboardi MGarg DMcKinley KFisher K(2019)Bidirectional type checking for relational propertiesProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314603(533-547)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314603
AGUIRRE ABARTHE GGABOARDI MGARG DSTRUB P(2019)A relational logic for higher-order programsJournal of Functional Programming10.1017/S095679681900014529Online publication date: 21-Oct-2019
https://doi.org/10.1017/S0956796819000145
Drumond MDaglis AMirzadeh NUstiugov DPicorel JFalsafi BGrot BPnevmatikatos D(2018)Algorithm/Architecture Co-Design for Near-Memory ProcessingACM SIGOPS Operating Systems Review10.1145/3273982.327399252:1(109-122)Online publication date: 28-Aug-2018
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Index Terms

Formal parametric polymorphism
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Semantics
      2. Syntax
    2. General programming languages
      1. Language features
        Procedures, functions and subroutines
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs
      1. Functional constructs
      2. Type structures
    2. Program semantics

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cover image ACM Conferences

POPL '93: Proceedings of the 20th ACM SIGPLAN-SIGACT symposium on Principles of programming languages

March 1993

510 pages

ISBN:0897915607

DOI:10.1145/158511

Chairmen:
Mary Van Deusen
IBM Watson Research Center
,
Bernard Lang
INRIA Rocquencourt

Copyright © 1993 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 March 1993

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POPL '93 Paper Acceptance Rate 39 of 199 submissions, 20%;

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

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Cited By

Çiçek EQu WBarthe GGaboardi MGarg DMcKinley KFisher K(2019)Bidirectional type checking for relational propertiesProceedings of the 40th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3314221.3314603(533-547)Online publication date: 8-Jun-2019
https://dl.acm.org/doi/10.1145/3314221.3314603
AGUIRRE ABARTHE GGABOARDI MGARG DSTRUB P(2019)A relational logic for higher-order programsJournal of Functional Programming10.1017/S095679681900014529Online publication date: 21-Oct-2019
https://doi.org/10.1017/S0956796819000145
Drumond MDaglis AMirzadeh NUstiugov DPicorel JFalsafi BGrot BPnevmatikatos D(2018)Algorithm/Architecture Co-Design for Near-Memory ProcessingACM SIGOPS Operating Systems Review10.1145/3273982.327399252:1(109-122)Online publication date: 28-Aug-2018
https://dl.acm.org/doi/10.1145/3273982.3273992
Wangwiwattana CDing XLarson E(2018)PupilNet, Measuring Task Evoked Pupillary Response using Commodity RGB Tablet CamerasProceedings of the ACM on Interactive, Mobile, Wearable and Ubiquitous Technologies10.1145/31611641:4(1-26)Online publication date: 8-Jan-2018
https://dl.acm.org/doi/10.1145/3161164
Aguirre ABarthe GGaboardi MGarg DStrub P(2017)A relational logic for higher-order programsProceedings of the ACM on Programming Languages10.1145/31102651:ICFP(1-29)Online publication date: 29-Aug-2017
https://dl.acm.org/doi/10.1145/3110265
Singh ADziurzanski PMendis HIndrusiak L(2017)A Survey and Comparative Study of Hard and Soft Real-Time Dynamic Resource Allocation Strategies for Multi-/Many-Core SystemsACM Computing Surveys10.1145/305726750:2(1-40)Online publication date: 11-Apr-2017
https://dl.acm.org/doi/10.1145/3057267
Bernardy JMoulin G(2012)A Computational Interpretation of ParametricityProceedings of the 2012 27th Annual IEEE/ACM Symposium on Logic in Computer Science10.1109/LICS.2012.25(135-144)Online publication date: 25-Jun-2012
https://dl.acm.org/doi/10.1109/LICS.2012.25
Bernardy JJansson PPaterson R(2012)Proofs for freeJournal of Functional Programming10.1017/S095679681200005622:2(107-152)Online publication date: 1-Mar-2012
https://dl.acm.org/doi/10.1017/S0956796812000056
Krishnaswami NBenton N(2012)Adding equations to system f typesProceedings of the 21st European conference on Programming Languages and Systems10.1007/978-3-642-28869-2_21(417-435)Online publication date: 24-Mar-2012
https://dl.acm.org/doi/10.1007/978-3-642-28869-2_21
Bernardy JLasson M(2011)Realizability and parametricity in pure type systemsProceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software10.5555/1987171.1987181(108-122)Online publication date: 26-Mar-2011
https://dl.acm.org/doi/10.5555/1987171.1987181
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