research-article

Universal algebra over lambda-terms and nominal terms: the connection in logic between nominal techniques and higher-order variables

Authors:

Murdoch J. Gabbay,

Dominic P. MulliganAuthors Info & Claims

LFMTP '09: Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice

Pages 64 - 73

https://doi.org/10.1145/1577824.1577835

Published: 02 August 2009 Publication History

Abstract

This paper develops the correspondence between equality reasoning with axioms using λ-terms syntax, and reasoning using nominal terms syntax. Both syntaxes involve name-abstraction: λ-terms represent functional abstraction; nominal terms represent atomsabstraction in nominal sets.

It is not evident how to relate the two syntaxes because their intended denotations are so different. We use universal algebra, the logic of equational reasoning, a logical foundation based on an equality judgement form which is spartan but which is sufficiently expressive to encode mathematics in theory and practice.

We investigate how syntax, algebraic theories, and derivability relate across λ-theories (algebra over λ-terms) and nominal algebra theories.

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Cited By

Gabbay M(2013)Nominal Terms and Nominal Logics: From Foundations to Meta-mathematicsHandbook of Philosophical Logic10.1007/978-94-007-6600-6_2(79-178)Online publication date: 9-Apr-2013
https://doi.org/10.1007/978-94-007-6600-6_2
Dowek GGabbay M(2012)Permissive-nominal logicACM Transactions on Computational Logic10.1145/2287718.228772013:3(1-36)Online publication date: 28-Aug-2012
https://dl.acm.org/doi/10.1145/2287718.2287720
Dowek GGabbay MKutsia TSchreiner WFernández M(2010)Permissive-nominal logicProceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming10.1145/1836089.1836111(165-176)Online publication date: 26-Jul-2010
https://dl.acm.org/doi/10.1145/1836089.1836111
Show More Cited By

Index Terms

Universal algebra over lambda-terms and nominal terms: the connection in logic between nominal techniques and higher-order variables
1. Theory of computation
  1. Logic
  2. Models of computation
    1. Computability

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LFMTP '09: Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages: Theory and Practice

August 2009

92 pages

ISBN:9781605585291

DOI:10.1145/1577824

Program Chairs:
James Cheney
University of Edinburgh
,
Amy Felty
University of Ottawa

Copyright © 2009 ACM.

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Published: 02 August 2009

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August 2, 2009

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Cited By

Gabbay M(2013)Nominal Terms and Nominal Logics: From Foundations to Meta-mathematicsHandbook of Philosophical Logic10.1007/978-94-007-6600-6_2(79-178)Online publication date: 9-Apr-2013
https://doi.org/10.1007/978-94-007-6600-6_2
Dowek GGabbay M(2012)Permissive-nominal logicACM Transactions on Computational Logic10.1145/2287718.228772013:3(1-36)Online publication date: 28-Aug-2012
https://dl.acm.org/doi/10.1145/2287718.2287720
Dowek GGabbay MKutsia TSchreiner WFernández M(2010)Permissive-nominal logicProceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming10.1145/1836089.1836111(165-176)Online publication date: 26-Jul-2010
https://dl.acm.org/doi/10.1145/1836089.1836111
Gabbay MMulligan D(2010)Curry-Howard for incomplete first-order logic derivations using one-and-a-half level termsInformation and Computation10.1016/j.ic.2009.09.003208:3(230-258)Online publication date: 1-Mar-2010
https://dl.acm.org/doi/10.1016/j.ic.2009.09.003

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