Mechanized Dominator Tree Certification

Abstract

In modern compilers, many optimizations and analyses, in particular those based on the SSA form, rely on dominance information, so computing dominators efficiently is an important problem. The classic algorithm to compute dominators in a control flow graph is the one designed by Lengauer and Tarjan in 1979. Other efficient algorithms have been proposed since. Previous works formally verified less efficient algorithms, and formally validated parts of the Lengauer-Tarjan algorithm, but there is no complete formal verification or validation of any of the fast algorithms computing dominators so far. In 2016, Georgiadis and Tarjan described a method to tackle these. They defined a certificate with which it becomes easy to validate dominators. Following their method, we successfully implemented and proved correct a validator of dominators in the Rocq Prover, inside the CompCertSSA verified compiler. This is the first complete mechanized certification of a fast algorithm computing dominators.