The Sea of Nodes intermediate representation was introduced by Cliff Click in the mid 90s as an enhanced Static Single Assignment (SSA) form. It improves on the initial SSA form by relaxing the total order on instructions in basic blocks into explicit data and control dependencies. This makes programs more flexible to optimize. This graph-based representation is now used in many industrial-strength compilers, such as HotSpot or Graal. While the SSA form is now well understood from a semantic perspective-even formally verified optimizing compilers use it in their middle-end-very few semantic studies have been conducted about the Sea of Nodes. This paper presents a simple but rigorous formal semantics for a Sea of Nodes form. It comprises a denotational component to express data computation, and an operational component to express control flow. We then prove a fundamental, dominance-based semantic property on Sea of Nodes programs which determines the regions of the graph where the values of nodes are preserved. Finally, we apply our results to prove the semantic correctness of a redundant zero-check elimination optimization. All the necessary semantic properties have been mechanically verified in the Coq proof assistant.

Modern optimizing compilers rely on the Static Single Assignment (SSA) form to make optimizations fast and simpler to implement. From a semantic perspective, the SSA form is nowadays fairly well understood, as witnessed by recent advances in the field of formally verified compilers. The destruction of the SSA form, however, remains a difficult problem, even in a non-verified environment. In fact, the out-of-SSA transformation has been revisited, for correctness and performance issues, up until recently. Unsurprisingly, state-of-the-art compiler formalizations thus either completely ignore, only partially handle, or implement naively the SSA destruction. This paper reports on the implementation of such a destruction within a verified compiler. We formally define and prove the properties of the generation of Conventional SSA (CSSA) which make its destruction simple to implement and prove. Second, we implement and prove correct a coalescing destruction of CSSA,à la Boissinot et al., where variables can be coalesced according to a refined notion of interference. This formalization work extends the CompCertSSA compiler, whose correctness proof is mechanized in the Coq proof assistant. Our CSSA-based, coalescing destruction removes, on average, more than 99% of introduced copies, and leads to encouraging results concerning spilling during post-SSA register allocation.