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Programming via rewriting is a part of the declarative programming which is illustrated by the languages: OBJ, Maude, CafeOBJ, CASL and so on. Programming via rewriting is very close to the equational logic. In the equational logic a set Γ of axioms is given. Axioms are Horn clauses, called also conditional equations. We are looking for all universal quantified equalities which are consequences...
Using the machinery of proof orders originally introduced by Bachmair and Dershowitz in the context of canonical equational proofs, we give an abstract, strategy-independent presentation of Groebner basis procedures and prove the correctness of two classical criteria for recognising superfluous S-polynomials, Buchberger's criteria 1 and 2, w.r.t. arbitrary fair and correct basis construction strategies...
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