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This document contains a formal description of the Rhodium language. Section 1 presents the Rhodium syntax. Section 2 presents our composing framework, which is used to formalize Rhodium analyses. Section 3 presents forward analyses and transformations, whereas section 4 presents backward analyses and transformations. Sections 5 and 6 present the frameworks for flow-insensitive and interprocedural analyses, respectively. Finally, appendix A is a transcript of all of our Rhodium code. 1 Chapter