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Many classical compiler optimizations can be elegantly expressed using rewrite rules of form: I =⇒ I if φ, where I, I are intermediate language instructions and φ is a property expressed in a temporal logic suitable for describing program data flow. Its reading: If the current program π contains an instruction of form I at some control point p, and if flow condition φ is satisfied at p, then replace I by I . The purpose of this paper is to show how such transformations may be proven correct.doi:10.1145/565816.503299 fatcat:n3ihj3brwrdenl5iwfa6myhg64