Higher-Order Rewriting: Framework, Confluence and Termination

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,...

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Bibliographic Details
Published inProcesses, Terms and Cycles: Steps on the Road to Infinity pp. 224 - 250
Main Author Jouannaud, Jean-Pierre
Format Book Chapter
LanguageEnglish
Published Berlin, Heidelberg Springer Berlin Heidelberg 2005
SeriesLecture Notes in Computer Science
Subjects
Critical Pair
Function Symbol
Normal Form
Pattern Match
Proof Assistant
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ISBN354030911X
9783540309116
ISSN0302-9743
1611-3349
DOI10.1007/11601548_14

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Summary: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].
ISBN:354030911X
9783540309116
ISSN:0302-9743
1611-3349
DOI:10.1007/11601548_14