research-article

Nominal system T

Author:

Andrew M. PittsAuthors Info & Claims

POPL '10: Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

Pages 159 - 170

https://doi.org/10.1145/1706299.1706321

Published: 17 January 2010 Publication History

Abstract

This paper introduces a new recursion principle for inductive data modulo α-equivalence of bound names. It makes use of Odersky-style local names when recursing over bound names. It is formulated in an extension of Gödel's System T with names that can be tested for equality, explicitly swapped in expressions and restricted to a lexical scope. The new recursion principle is motivated by the nominal sets notion of "α-structural recursion", whose use of names and associated freshness side-conditions in recursive definitions formalizes common practice with binders. The new Nominal System T presented here provides a calculus of total functions that is shown to adequately represent α-structural recursion while avoiding the need to verify freshness side-conditions in definitions and computations. Adequacy is proved via a normalization-by-evaluation argument that makes use of a new semantics of local names in Gabbay-Pitts nominal sets.

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Cited By

Fairweather EFernández M(2018)Typed Nominal RewritingACM Transactions on Computational Logic10.1145/316155819:1(1-46)Online publication date: 8-Feb-2018
https://dl.acm.org/doi/10.1145/3161558
RAHLI VBICKFORD M(2017)Validating Brouwer's continuity principle for numbers using named exceptionsMathematical Structures in Computer Science10.1017/S096012951700017228:06(942-990)Online publication date: 2-Nov-2017
https://doi.org/10.1017/S0960129517000172
Rahli VBickford MAvigad JChlipala A(2016)A nominal exploration of intuitionismProceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs10.1145/2854065.2854077(130-141)Online publication date: 18-Jan-2016
https://dl.acm.org/doi/10.1145/2854065.2854077
Show More Cited By

Index Terms

Nominal system T
1. Mathematics of computing
  1. Continuous mathematics
    1. Calculus
      1. Lambda calculus
  2. Mathematical analysis
    1. Calculus
      1. Lambda calculus
2. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
      1. Syntax
    2. General programming languages
      1. Language features
        Recursion

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cover image ACM Conferences

POPL '10: Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

January 2010

520 pages

ISBN:9781605584799

DOI:10.1145/1706299

General Chair:
Manuel Hermenegildo
IMDEA-Software and T.U. of Madrid, Spain
,
Program Chair:
Jens Palsberg
UCLA, University of California, Los Angeles

ACM SIGPLAN Notices Volume 45, Issue 1
POPL '10
January 2010
500 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1707801
Issue’s Table of Contents

Copyright © 2010 ACM.

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Published: 17 January 2010

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POPL '10: The 37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 17 - 23, 2010

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Cited By

Fairweather EFernández M(2018)Typed Nominal RewritingACM Transactions on Computational Logic10.1145/316155819:1(1-46)Online publication date: 8-Feb-2018
https://dl.acm.org/doi/10.1145/3161558
RAHLI VBICKFORD M(2017)Validating Brouwer's continuity principle for numbers using named exceptionsMathematical Structures in Computer Science10.1017/S096012951700017228:06(942-990)Online publication date: 2-Nov-2017
https://doi.org/10.1017/S0960129517000172
Rahli VBickford MAvigad JChlipala A(2016)A nominal exploration of intuitionismProceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs10.1145/2854065.2854077(130-141)Online publication date: 18-Jan-2016
https://dl.acm.org/doi/10.1145/2854065.2854077
Pouillard NPottier F(2012)A unified treatment of syntax with bindersJournal of Functional Programming10.1017/S095679681200025122:4-5(614-704)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1017/S0956796812000251
Cheney JNorrish MVestergaard R(2012)Formalizing AdequacyJournal of Automated Reasoning10.1007/s10817-011-9221-649:2(209-239)Online publication date: 1-Aug-2012
https://dl.acm.org/doi/10.1007/s10817-011-9221-6
Gabbay MLitak TPetrişan D(2011)Stone duality for nominal Boolean algebras with ИProceedings of the 4th international conference on Algebra and coalgebra in computer science10.5555/2040096.2040112(192-207)Online publication date: 30-Aug-2011
https://dl.acm.org/doi/10.5555/2040096.2040112
Fairweather EFernández MGabbay M(2011)Principal types for nominal theoriesProceedings of the 18th international conference on Fundamentals of computation theory10.5555/2034214.2034228(160-172)Online publication date: 22-Aug-2011
https://dl.acm.org/doi/10.5555/2034214.2034228
Gabbay MCiancia V(2011)Freshness and name-restriction in sets of traces with namesProceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software10.5555/1987171.1987202(365-380)Online publication date: 26-Mar-2011
https://dl.acm.org/doi/10.5555/1987171.1987202
Westbrook EFrisby NBrauner P(2011)Hobbits for HaskellACM SIGPLAN Notices10.1145/2096148.203468146:12(35-46)Online publication date: 22-Sep-2011
https://dl.acm.org/doi/10.1145/2096148.2034681
Westbrook EFrisby NBrauner PClaessen K(2011)Hobbits for HaskellProceedings of the 4th ACM symposium on Haskell10.1145/2034675.2034681(35-46)Online publication date: 22-Sep-2011
https://dl.acm.org/doi/10.1145/2034675.2034681
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