E-matching is the problem of finding all matches of a pattern in an e-graph. Relational e-matching, a recent approach inspired by the databases community, has found succcess in equality saturation engines such as egglog. However, until now, this technique has not been implemented in a Satisfiability Modulo Theories (SMT) solver. The key difficulty of implementing relational e-matching in an SMT solver is \emph{backtracking}, i.e., the ability to undo previous matching decisions. We provide an initial implementation of a backtrackable, relational e-matching algorithm in Sundance, an SMT solver currently in development. We describe our approach of maintaining backtrackable indices and our e-matching algorithm based on a left-deep binary join. We evaluate our implementation on a set of synthetic benchmarks and show a median speedup of $25.0 \times$ over a top-down e-matching algorithm. However, when considering a set of benchmarks from the program verifier Verus, we see a median slowdown of $1.77 \times$. We conclude with a discussion of future work to close this gap and make relational e-matching a practical component of an SMT solver.
Mon 15 JunDisplayed time zone: Mountain Time (US & Canada) change
15:50 - 17:30 | |||
15:50 25mTalk | Relational E-matching in an SMT solver EGRAPHS Amar Shah Carnegie Mellon University, Marijn Heule Carnegie Mellon University, Bryan Parno Carnegie Mellon University, Max Willsey University of California at Berkeley | ||
16:15 25mTalk | E-Stitch: Top-Down Library Learning for E-Graphs EGRAPHS Kavi Gupta MIT, Maddy Bowers Massachusetts Institute of Technology, Armando Solar-Lezama Massachusetts Institute of Technology File Attached | ||
16:40 25mTalk | Optimizing Optimizations, Declaratively: Optimizing the Higher-Order Functions in Mathematical Optimization with egglog EGRAPHS Hiromi Ishii JIJ Pre-print File Attached | ||
17:05 25mTalk | Poseidon: Profile-Guided Numerical Rewriting at Full-Application Scale EGRAPHS Siyuan Brant Qian University of Illinois at Urbana-Champaign, Vimarsh Sathia University of Illinois Urbana Champaign, Ivan Ivanov Institute of Science Tokyo, Jan Hueckelheim Argonne National Laboratory, Paul Hovland Argonne National Laboratory, William S. Moses University of Illinois Urbana-Champaign | ||