Efficient Extraction for Effectful E-Graphs
Oliver Flatt, Anjali Pal, Yihong Zhang, Ryan Tjoa, Kirsten Graham, Alex Fischman, Chandrakana Nandi, Eli Rosenthal, Zachary Tatlock, Haobin Ni
arxiv.org/abs/2609.31887 [ππ.πΏπ»]
π¬Accepted for publication at OOPSLA 2026
ALT Egraphs have enabled recent advances in program optimization, synthesis, and verification, yet remain difficult to apply to effectful programs whose memory and I/O operations must respect execution order. Existing effect-aware extraction algorithms rely on integer linear programming (ILP) and dominate total runtime. We introduce Statewalk DP, a new extraction algorithm that enforces effect ordering efficiently without external solvers. We prove that finding any effect-safe extraction is NP-complete, but show that Statewalk DP is tractable in statewalk width, a parameter that measures the complexity of dataflow interactions among effects. In practice, statewalk width generally remains small, enabling Statewalk DP to achieve order-of-magnitude speedups over ILP extraction while producing programs comparable to LLVM across our benchmarks. We implement the algorithm in eqcc, a prototype egraph-based compiler for imperative Bril programs and demonstrate that effect-aware extraction is no lo