Minimal Static Single Assignment Form

This formalization is an extension to [3]. In their work, the authors have shown that Braun et al.’s static single assignment (SSA) construction algorithm [1] produces minimal SSA form for input programs with a reducible control flow graph (CFG). However Braun et al. also proposed an extension to their algorithm that they claim produces minimal SSA form even for irreducible CFGs. In this formalization we support that claim by giving a mechanized proof. As the extension of Braun et al.’s algorithm aims for removing socalled redundant strongly connected components (sccs) of φ functions, we show that this suffices to guarantee minimality according to Cytron et al. [2].