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A rewrite logic semantic definitional framework for programming languages is introduced, called K, together with partially automated translations of K language definitions into rewriting logic and into C. The framework is exemplified by defining SILF, a simple imperative language with functions. The translation of K definitions into rewriting logic enables the use of the various analysis tools developed for rewrite logic specifications, while the translation into C allows for very efficient interpreters. A suite of tests show the performance of interpreters compiled from K definitions.