Instruction set commutivity

We present a state property called congruence and show how it can be used to demonstrate commutivity of instructions in a modern load-store architecture. Our analysis is particularly important in pipelined microprocessors where instructions are frequently reordered to avoid costly delays in execution caused by hazards. Our work has significant implications to safety and security critical applications since reordering can easily change the meaning and an instruction sequence and current techniques are largely ad hoc. Our work is done in a mechanical theorem prover and results in a set of trustworthy rules for instruction reordering. The mechanization makes it practical to analyze the entire instruction set.