{
  "id": 12054969,
  "title": "Refinement E-Graphs",
  "url": "https://urgent.news/2026/10/05/refinement-e-graphs",
  "topic": "tech",
  "section": "Tech",
  "published": "2026-10-05T02:23:30.000Z",
  "source": {
    "name": "Lobsters",
    "slug": "lobsters",
    "url": "https://www.philipzucker.com/refinement_egraph/"
  },
  "original_language": "en",
  "account": "Refinement e-graphs are a novel concept that expands upon the traditional e-graph by incorporating a built-in = relation, similar in privilege to the e-graph's primary =. Compiler rewrites often involve unidirectional refinements rather than bidirectional equalities, moving from an abstract program to one that can be executed on a concrete machine. This is due to the fact that source languages often have unclear evaluation order or results of operations like integer overflow or division by zero. A prototype of a refinement egraph can be found at https://github.com/philzook58/refinement-microegg. A WASM demo is available at https://www.philipzucker.com/refinement-microegg.\n\nOne interesting example is the \"Don't Care\" concept in digital circuits. This allows the optimizer to choose a result that maximizes circuit optimization. There are also refinement rewrite rules available, such as rewrite-le and rewrite-ge. These rules represent the formula forall ?a, lhs(?a) = rhs(?a) without the need to match lhs on the equality nose. The semantics of this example is Bool - Set Bool with = representing pointwise set containment.\n\nThe refinement e-graph is distinct from equating \"dontcare\" to true or false, but is distinct from equating it to either of them. Fresh constants can be used to independently equate \"dontcare\" variables. The inequality union find plays a crucial role in refinement e-graphs, as opposed to congruence closure in traditional e-graphs.\n\nIn the implementation, e-graphs have an extra degree of nondeterminism on top of the usual e-matching, where in the GE or LE mode, you may traverse an eclass - eclass = edge. This is similar to pattern matching in unification, with a few key differences like working with constraint sets and tracking variable modes. Regular extraction in e-graphs is similar to e-matching, with the \"mediation\" of the = sign between function symbol relations.",
  "summary": null,
  "key_points": [
    "Refinement e-graphs expand on traditional e-graphs with built-in = relation.",
    "Prototype and WASM demo available at GitHub and personal website.",
    "Refinement rewrite rules like rewrite-le and rewrite-ge simplify formulas."
  ],
  "editors_take": "This development allows compiler rewrites to handle unidirectional refinements, accommodating unclear evaluation orders and operations with ambiguous results, and enables optimizers to make strategic choices like in digital circuit optimization.",
  "illustration": null,
  "coverage": {
    "outlets": 1,
    "also_reported_by": []
  },
  "ai_generated": true,
  "disclaimer": "Summaries, key points and the editor’s take are written by software from other outlets’ reporting and may contain errors — always check the linked original."
}