Abstract
This paper describes methods to prove equational clauses (disjunctions of equations and inequations) in the initial algebra of an equational theory presentation. First we show that the general problem of validity can be converted into the one of satisfiability. Then we present specific procedures based on the narrowing operation, which apply when the theory is defined by a canonical set of rewrite rules. Complete refutation procedures are described and used as invalidity procedures. Finally, a narrowing procedure incorporating structural induction aspects, is proposed and the simplicity of the automated proofs is illustrated through examples.
This work was done when the author was at L.I.T.P.
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Fribourg, L. (1984). A Narrowing Procedure for Theories with Constructors. In: Shostak, R.E. (eds) 7th International Conference on Automated Deduction. CADE 1984. Lecture Notes in Computer Science, vol 170. Springer, New York, NY. https://doi.org/10.1007/978-0-387-34768-4_16
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DOI: https://doi.org/10.1007/978-0-387-34768-4_16
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