Higher-Order rewriting: framework, confluence and termination

Authors:
Jean-Pierre Jouannaud
Affiliations:
LIX/CNRS UMR 7161 & École Polytechnique, Palaiseau
Venue:
Processes, Terms and Cycles
Year:
2005

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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].