Abstract
We present a term rewriting procedure based on congruence closure that can be used with arbitrary equational theories. This procedure is motivated by the pragmatic need to handle equational theories where confluence can not be achieved. The procedure uses context free grammars to represent equivalence classes of terms. The procedure rewrites grammars rather than terms and uses congruence closure to maintain certain congruence properties of the grammar. Grammars provide concise representations of large term sets. Infinite term sets can be represented with finite grammars and exponentially large term sets can be represented with linear sized grammars. Although the procedure is primarily intended for use in nonconfluent theories, it also provides a new kind of confluence that can be used to give canonical rewriting systems for theories that are difficult to handle in other ways.
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© 1992 Springer-Verlag Berlin Heidelberg
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McAllester, D. (1992). Grammar rewriting. In: Kapur, D. (eds) Automated Deduction—CADE-11. CADE 1992. Lecture Notes in Computer Science, vol 607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-55602-8_160
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DOI: https://doi.org/10.1007/3-540-55602-8_160
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