Language definitions as rewrite theories

K is a formal framework for defining operational semantics of programming languages. The K-Maude compiler translates K language definitions to Maude rewrite theories. The compiler enables program execution by using the Maude rewrite engine with the compiled definitions, and program analysis by using various Maude analysis tools. Ksupports symbolic execution in Maude by means of an automatic transformation of language definitions. The transformed definition is called the symbolic extension   of the original definition. In this paper we investigate the theoretical relationship between Klanguage definitions and their Maude translations, between symbolic extensions of Kdefinitions and their Maude translations, and how the relationship between K definitions and their symbolic extensions is reflected on their respective representations in Maude. In particular, the results show how analysis performed with Maude tools can be formally lifted up to the original language definitions.