Rewriting logic is both a logical framework where many logics can be naturally represented, and a semantic framework where many computational systems and programming languages, including concurrent ones, can be both specified and executed. Maude is a declarative specification and programming language based on rewriting logic. For reasoning about the logics and systems represented in the rewriting logic framework symbolic methods are of great importance. This paper discusses various symbolic methods that address crucial reasoning needs in rewriting logic, how they are supported by Maude and other symbolic engines, and various applications that these methods and engines make possible. Because of the generality of rewriting logic, these methods are widely applicable: they can be used in many areas and can provide useful reasoning components for other reasoning engines.
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