Efficiently computing static single assignment form and the control dependence graph
ACM Transactions on Programming Languages and Systems (TOPLAS)
Modern complier implementation in C: basic techniques
Modern complier implementation in C: basic techniques
Global Data Flow Analysis and Iterative Algorithms
Journal of the ACM (JACM)
A fast algorithm for finding dominators in a flowgraph
ACM Transactions on Programming Languages and Systems (TOPLAS)
A unified approach to global program optimization
POPL '73 Proceedings of the 1st annual ACM SIGACT-SIGPLAN symposium on Principles of programming languages
On loops, dominators, and dominance frontiers
ACM Transactions on Programming Languages and Systems (TOPLAS)
Interactive Theorem Proving and Program Development
Interactive Theorem Proving and Program Development
Dominator tree verification and vertex-disjoint paths
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
A Formally Verified Compiler Back-end
Journal of Automated Reasoning
Formalizing the LLVM intermediate representation for verified program transformations
POPL '12 Proceedings of the 39th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A formally verified SSA-Based middle-end: Static single assignment meets compcert
ESOP'12 Proceedings of the 21st European conference on Programming Languages and Systems
Formal verification of SSA-based optimizations for LLVM
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
Finding dominators via disjoint set union
Journal of Discrete Algorithms
Formal Verification of an SSA-Based Middle-End for CompCert
ACM Transactions on Programming Languages and Systems (TOPLAS)
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One prerequisite to the formal verification of modern compilers is to formalize computing dominators, which enable SSA forms, advanced optimizations, and analysis. This paper provides an abstract specification of dominance analysis that is sufficient for formalizing modern compilers; it describes a certified implementation and instance of the specification that is simple to design and reason about, and also reasonably efficient. The paper also presents applications of dominance analysis: an SSA-form type checker, verifying SSA-based optimizations, and constructing dominator trees. This development is a part of the Vellvm project. All proofs and implementation have been carried out in Coq.