Fix(Processes): Make subterm hoisting deterministic across processes

docs/changelog.md

@@ -4,6 +4,10 @@ _This project uses semantic versioning_
 
 ## UNRELEASED
 
+- Make shared-subexpression hoisting deterministic across Python processes,
+  stabilizing generated `let` bindings and serialized e-graph output
+  [#422](https://github.com/egraphs-good/egglog-python/pull/422).
+
 - Upgrade to Egglog 3 and matching `egglog-experimental` APIs
   [#414](https://github.com/egraphs-good/egglog-python/pull/414).
   - BREAKING: container rebuilding is now handled by Egglog, so `Map.rebuild()`,

python/egglog/egraph_state.py

@@ -1711,9 +1711,7 @@ def _sanitize_egg_ident(input_string: str) -> str:
 
 
 def _exprs_multiple_parents(typed_expr: TypedExprDecl) -> list[TypedExprDecl]:
-    """
-    Returns all expressions that have multiple parents (a list but semantically just an ordered set).
-    """
+    """Return multiply-parented expressions in deterministic preorder for stable synthetic let names."""
     parent_counts: dict[TypedExprDecl, int] = {}
     traversal_order: list[TypedExprDecl] = []
     traversed: set[TypedExprDecl] = set()

python/tests/test_high_level.py

@@ -3,7 +3,10 @@
 
 import importlib
 import math
+import os
 import pathlib
+import subprocess
+import sys
 from collections.abc import Callable, Iterator
 from copy import copy
 from dataclasses import dataclass
@@ -936,6 +939,47 @@ def pair(cls, left: DuplicateEdge, right: DuplicateEdge) -> DuplicateEdge: ...
     assert sum(line.endswith(" $__expr_2 $__expr_2)") for line in lines) == 1
 
 
+_DETERMINISTIC_HOISTING_SCRIPT = """
+from __future__ import annotations
+
+from egglog import EGraph, Expr, StringLike
+
+
+class B(Expr):
+    @classmethod
+    def var(cls, name: StringLike) -> B: ...
+
+    def __and__(self, other: B) -> B: ...
+
+    def __or__(self, other: B) -> B: ...
+
+
+egraph = EGraph(save_egglog_string=True)
+x, y = B.var("x"), B.var("y")
+shared = x & y
+expr = shared | y
+for _ in range(24):
+    expr = (shared & expr) | (expr & (shared | x))
+egraph.let("$e", expr)
+print(egraph.as_egglog_string, end="")
+"""
+
+
+def test_shared_subexpression_lowering_is_deterministic_across_processes() -> None:
+    transcripts = [
+        subprocess.run(
+            [sys.executable, "-c", _DETERMINISTIC_HOISTING_SCRIPT],
+            capture_output=True,
+            text=True,
+            check=True,
+            env={**os.environ, "PYTHONHASHSEED": str(seed)},
+        ).stdout
+        for seed in (1, 2, 3)
+    ]
+
+    assert transcripts[1:] == transcripts[:-1]
+
+
 def test_freeze_omits_synthetic_let_bindings() -> None:
     class FreezeLetNum(Expr):
         @classmethod