Add basic example

Author: saulshanabrook

python/egg_smol/examples/eqsat_basic.py

@@ -0,0 +1,42 @@
+"""
+Basic equality saturation example.
+==================================
+"""
+from __future__ import annotations
+
+from egg_smol import *
+
+egraph = EGraph()
+
+
+@egraph.class_
+class Num(BaseExpr):
+    def __init__(self, value: i64Like) -> None:
+        ...
+
+    @classmethod
+    def var(cls, name: StringLike) -> Num:  # type: ignore[empty-body]
+        ...
+
+    def __add__(self, other: Num) -> Num:  # type: ignore[empty-body]
+        ...
+
+    def __mul__(self, other: Num) -> Num:  # type: ignore[empty-body]
+        ...
+
+
+# expr1 = 2 * (x + 3)
+expr1 = egraph.define("expr1", Num(2) * (Num.var("x") + Num(3)))
+# expr2 = 6 + 2 * x
+expr2 = egraph.define("expr2", Num(6) + Num(2) * Num.var("x"))
+
+a, b, c = vars_("a b c", Num)
+i, j = vars_("i j", i64)
+egraph.register(
+    rewrite(a + b).to(b + a),
+    rewrite(a * (b + c)).to((a * b) + (a * c)),
+    rewrite(Num(i) + Num(j)).to(Num(i + j)),
+    rewrite(Num(i) * Num(j)).to(Num(i * j)),
+)
+egraph.run(10)
+egraph.check(eq(expr1).to(expr2))