2 Completion and Its Applications
نویسنده
چکیده
The ability to reason with equations is important in many computer science applications, including algebraic specifications, highlevel programming languages, and automated deduction. Reasoning about equations may, for example, involve deciding if an equation "'follows" as a consequence of a given set of equations, or if an equation is "true" in a given model, or what values of the variables satisfy a given equation. Knuth's completion procedure (Knuth and Bendix, 1970). based on prior work of Evans (1951), was originally suggested as a means of taking an axiomatization of an equational theory and generating a rewrite system that can be used to decide questions of validity of identities (or the "word problem") in the given theory. In this chapter, we formalize that procedure as an inference system and describe some of its more recent applications to other aspects of equational reasoning.
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