Grammar Rewriting
Abstract
The author presents 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 prove equations in equational theories where confluence cannot 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. For example, under grammar rewriting there is a finite canonical rewrite system for idempotent semigroups, a theory which has been shown not to have any finite canonical system under traditional notions of rewriting.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1991
- Accession Number
- ADA259675
Entities
People
- David Mcallester
Organizations
- Massachusetts Institute of Technology