Validating Dominator Trees for a Fast, Verified Dominance Test

Abstract

The problem of computing dominators in a control flow graph is central to numerous modern compiler optimizations. Many efficient algorithms have been proposed in the litterature, but mechanizing the correctness of the most sophisticated algorithms is still considered as too hard problems, and to this date, verified compilers use less optimized implementations. In contrast, production compilers, like GCC or LLVM, implement the classic, efficient Lengauer-Tarjan algorithm [12], to compute dominator trees. And subsequent optimization phases can then determine whether a CFG node dominates another node in constant time by using their respective depth-first search numbers in the dominator tree. In this work, we aim at integrating such techniques in verified compilers. We present a formally verified validator of untrusted dominator trees, on top of which we implement and prove correct a fast dominance test following these principles. We conduct our formal development in the Coq proof assistant, and integrate it in the middle-end of the CompCertSSA verified compiler. We also provide experimental results showing performance improvement over previous formalizations.

Formalizing Size-Optimal Sorting Networks: Extracting a Certified Proof Checker

“…The log files record permutations as their output on the set [n], so for example the transposition over [4] exchanging 0 and 2 would be represented as {2, 1, 0, 3}. Since we want to be skeptic about the oracle, we do not assume anything about the lists we are given; rather, we show that the property of a list of natural numbers corresponding to a permutation on [n] is decidable.…”

Mechanizing conventional SSA for a verified destruction with coalescing

“…Figure 5 presents selected rules defining the small-step operational semantics of CSSA, expressed as a labelled transition system on execution states, whose transitions are of the form σ e − → CSSA σ . For the instruction set we consider here in the paper, the observable event e labelling the transition will be the silent event 2 , and execution states σ (defined in Figure 5) are simple tuples (f, pc, rs) gathering the function f being executed, the current program point pc (a node in the code pointing the next instruction to execute), and the current local environment rs, (finitely) mapping variables 2 The full formalization of the language does handle non-silent transitions. In Figure 5, rule NopNJP is the simplest one.…”

“…After a normalization phase of RTL, we generate from there the SSA form of the code, and perform SSA-based optimizations. The generation and optimization phases are described in [1,2,12]. The work presented in this paper is represented inside the grey area.…”

A Fast Verified Liveness Analysis in SSA Form

“…3) adapting the ideas of [7] to CompCertSSA, including some advanced optimizations; -a proof of correctness of this algorithm (Sect. 4…”