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We study ground confluence and inductive validity in equational specifications that are interpreted in a constructor based way. By defining semantics of the specification in an appropriate way, we are able to transfer the proof-byconsistency concepts from unstructured specifications to constructor based specifications, where the unstructured specifications with their usual semantics are included as a special case. We further show that the proof-by-consistency concepts not only apply to inductive theorem proving, but can as well be employed to prove ground confluence of rewrite systems. So we present a refutationally complete prover for ground confluence and inductive validity that applies to unstructured as well as constructor based equational specifications.

Proving ground confluence and inductive validity in constructor based equational specifications