Complete sets of reductions modulo associativity, commutativity and identity
We describe the theory and implementation of a process which finds complete sets of reductions modulo equational theories which contain one or more associative and commutative operators with identity (ACI theories). We emphasize those features which distinguish this process from the similar one which works modulo associativity and commutativity. A primary difference is that for some rules in ACI complete sets, restrictions are required on the substitutions allowed when the rules are applied. Without these restrictions, termination cannot be guaranteed. We exhibit six examples of ACI complete sets that were generated by an implementation.
KeywordsEquational Theory Unification Algorithm Critical Pair Unification Mechanism Completion Process
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