Verified construction of static single assignment form

Abstract

Modern compilers use intermediate representations in static single assignment (SSA) form, which simplifies many optimizations. However, the high implementation complexity of efficient SSA construction algorithms poses a challenge to verified compilers. In this paper, we consider a variant of the recent SSA construction algorithm by Braun et al. that combines simplicity and efficiency, and is therefore a promising candidate to tackle this challenge. We prove the correctness of the algorithm using the theorem prover Isabelle/HOL. Furthermore, we prove that the algorithm constructs pruned SSA form and, in case of a reducible control flow graph, minimal SSA form. To the best of our knowledge, these are the first formal proofs regarding the quality of an SSA construction algorithm. Finally, we replace the SSA construction of the CompCertSSA project with code extracted by Isabelle's code generator to demonstrate the applicability to real world programs.