chapter

Higher-Order rewriting: framework, confluence and termination

Author:

Jean-Pierre JouannaudAuthors Info & Claims

Processes, Terms and Cycles: steps on the Road to Infinity

January 2005

Pages 224 - 250

Published: 01 January 2005 Publication History

Abstract

Equations are ubiquitous in mathematics and in computer science as well. This first sentence of a survey on first-order rewriting borrowed again and again characterizes best the fundamental reason why rewriting, as a technology for processing equations, is so important in our discipline [10]. Here, we consider higher-order rewriting, that is, rewriting higher-order functional expressions at higher-types. Higher-order rewriting is a useful generalization of first-order rewriting: by rewriting higher-order functional expressions, one can process abstract syntax as done for example in program verification with the prover Isabelle [27]; by rewriting expressions at higher-types, one can implement complex recursion schemas in proof assistants like Coq [12].

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Cited By

Fairweather EFernández M(2018)Typed Nominal RewritingACM Transactions on Computational Logic (TOCL)10.1145/316155819:1(1-46)Online publication date: 8-Feb-2018
https://dl.acm.org/doi/10.1145/3161558
Jouannaud JRubio A(2015)Normal Higher-Order TerminationACM Transactions on Computational Logic10.1145/269991316:2(1-38)Online publication date: 9-Mar-2015
https://dl.acm.org/doi/10.1145/2699913
Brauner PHoutmann CKirchner C(2007)Superdeduction at workRewriting Computation and Proof10.5555/2391276.2391285(132-166)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.5555/2391276.2391285
Show More Cited By

Higher-Order rewriting: framework, confluence and termination
1. Mathematics of computing
  1. Mathematical analysis
    1. Calculus
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
  2. Models of computation

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Published In

cover image Guide books

Processes, Terms and Cycles: steps on the Road to Infinity

January 2005

638 pages

ISBN:354030911X

Editors:
Aart Middeldorp
Institute of Computer Science, University of Innsbruck, Austria
,
Vincent Oostrom
Department of Philosophy, Utrecht University, Heidelberglaan 8, Utrecht, The Netherlands
,
Femke Raamsdonk
Department of Theoretical Computer Science, Vrije Universiteit, De Boelelaan 1081a, Amsterdam, The Netherlands
,
Roel Vrijer
Department of Theoretical Computer Science, VU Vrije Universiteit Amsterdam, De Boelelaan 1081a, Amsterdam

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 01 January 2005

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Cited By

Fairweather EFernández M(2018)Typed Nominal RewritingACM Transactions on Computational Logic (TOCL)10.1145/316155819:1(1-46)Online publication date: 8-Feb-2018
https://dl.acm.org/doi/10.1145/3161558
Jouannaud JRubio A(2015)Normal Higher-Order TerminationACM Transactions on Computational Logic10.1145/269991316:2(1-38)Online publication date: 9-Mar-2015
https://dl.acm.org/doi/10.1145/2699913
Brauner PHoutmann CKirchner C(2007)Superdeduction at workRewriting Computation and Proof10.5555/2391276.2391285(132-166)Online publication date: 1-Jan-2007
https://dl.acm.org/doi/10.5555/2391276.2391285
Jouannaud JRubio A(2007)Polymorphic higher-order recursive path orderingsJournal of the ACM (JACM)10.1145/1206035.120603754:1(1-48)Online publication date: 1-Mar-2007
https://dl.acm.org/doi/10.1145/1206035.1206037
Jouannaud JRubio A(2006)Higher-order orderings for normal rewritingProceedings of the 17th international conference on Term Rewriting and Applications10.1007/11805618_29(387-399)Online publication date: 12-Aug-2006
https://dl.acm.org/doi/10.1007/11805618_29

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