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LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
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LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
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RTA'05 Proceedings of the 16th international conference on Term Rewriting and Applications
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ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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This paper introduces a semantics for rewriting that is independent of the data being rewritten and which, nevertheless, models key concepts such as substitution which are central to rewriting algorithms. We demonstrate the naturalness of this construction by showing how it mirrors the usual treatment of algebraic theories as coequalizers of monads. We also demonstrate its naturalness by showing how it captures several canonical forms of rewriting.