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Processes, Terms and Cycles: Steps on the Road to Infinity pp 224–250Cite as

Higher-Order Rewriting: Framework, Confluence and Termination

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3838))

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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Author information

Authors and Affiliations

  1. LIX/CNRS UMR 7161 & École Polytechnique, F-91400, Palaiseau

    Jean-Pierre Jouannaud

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  1. Jean-Pierre Jouannaud
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Editor information

Editors and Affiliations

  1. Institute of Computer Science, University of Innsbruck, Austria

    Aart Middeldorp

  2. Department of Philosophy, Utrecht University, Heidelberglaan 8, 3584 CS, Utrecht, The Netherlands

    Vincent van Oostrom

  3. Department of Theoretical Computer Science, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    Femke van Raamsdonk

  4. VU Vrije Universiteit Amsterdam,  

    Roel de Vrijer

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Jouannaud, JP. (2005). Higher-Order Rewriting: Framework, Confluence and Termination. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds) Processes, Terms and Cycles: Steps on the Road to Infinity. Lecture Notes in Computer Science, vol 3838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11601548_14

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  • DOI: https://doi.org/10.1007/11601548_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30911-6

  • Online ISBN: 978-3-540-32425-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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