Basics of Equality Saturation (egglog-python.readthedocs.io)

The tutorial demonstrates building a small optimizer for a linear-algebra-like DSL using egglog to illustrate the basics of equality saturation. It defines a Num expression type (constants, variables, addition, multiplication) with operator overloading and converters so primitives (i64, String) upcast into Num expressions. Users create an EGraph, insert expressions with let bindings, inspect them with extract, and query equivalences with check/check_fail. Rewrite rules are registered with @egraph.register using rewrite(...) .to(...), e.g., commutativity and associativity for + and *, and constant-folding rules for integer addition and multiplication. Technically important points: rules are only instantiated for terms present in the e-graph (so declaring a rule doesn’t change the graph until you run it), and egglog’s run performs batched iterations that first find all matches for all rules, then apply them and rebuild the e-graph. The tutorial shows operator overloading for primitives, built-in primitive ops, and how run produces a report of applied rewrites. As a result of these rewrites and iteration, distinct-looking expressions (e.g., 2*(x*3) and 6*x) are merged into the same E-class, demonstrating how equality saturation explores many equivalent forms simultaneously—useful for compiler optimizations, algebraic simplification, and automated program transformations in ML and systems that need provable or wide-ranging rewrite-based optimizations.