SSA Translation Is an Abstract Interpretation

Static single assignment (SSA) form is a popular intermediate representation that helps implement useful static analyses, including global value numbering (GVN), sparse dataflow analyses, or SMT-based abstract interpretation or model checking. However, the precision of the SSA translation itself depends on static analyses, and a priori static analysis is even indispensable in the case of low-level input languages like machine code. To solve this chicken-and-egg problem, we propose to turn the SSA translation into a standard static analysis based on abstract interpretation. This allows the SSA translation to be combined with other static analyses in a single pass, taking advantage of the fact that it is more precise to combine analyses than applying passes in sequence. We illustrate the practicality of these results by writing a simple dataflow analysis that performs SSA translation, optimistic global value numbering, sparse conditional constant propagation, and loop-invariant code motion in a single small pass; and by presenting a multi-language static analyzer for both C and machine code that uses the SSA abstract domain as its main intermediate representation.