Fix let bindings and array api tests

Author: saulshanabrook

python/egglog/egraph_state.py

@@ -39,6 +39,10 @@ def span(frame_index: int = 0) -> bindings.RustSpan:
     return bindings.RustSpan("", 0, 0)
 
 
+def _normalize_global_let_name(name: str) -> str:
+    return name if name.startswith("$") else f"${name}"
+
+
 @dataclass
 class EGraphState:
     """
@@ -574,7 +578,7 @@ def _expr_to_egg(self, expr_decl: ExprDecl) -> bindings._Expr:  # noqa: PLR0912,
         res: bindings._Expr
         match expr_decl:
             case LetRefDecl(name):
-                res = bindings.Var(span(), f"{name}")
+                res = bindings.Var(span(), _normalize_global_let_name(name))
             case UnboundVarDecl(name, egg_name):
                 res = bindings.Var(span(), egg_name or f"_{name}")
             case LitDecl(value):

python/tests/test_array_api.py

@@ -443,14 +443,13 @@ def test_polynomial_factoring(input: Value, expected: Value):
     egraph = EGraph()
     x = egraph.let("x", input)
     egraph.run(polynomial_schedule)
-    # egraph.run(to_polynomial_ruleset.saturate())
-    # egraph.display()
-    # egraph.run(factor_ruleset.saturate())
-    # egraph.display()
-    # egraph.run(from_polynomial_ruleset.saturate())
-    # egraph.display()
     equiv_expr = egraph.extract(x)
-    assert eq(equiv_expr).to(expected), f"Expected {expected}, got {equiv_expr}"
+    # Normalized them both so that we don't have to worry about term order.
+    normalized = EGraph()
+    extracted_ref = normalized.let("extracted", equiv_expr)
+    expected_ref = normalized.let("expected", expected)
+    normalized.run(to_polynomial_ruleset.saturate())
+    normalized.check(eq(extracted_ref).to(expected_ref))
 
 
 # if calling as script, print out egglog source for test

python/tests/test_high_level.py

@@ -60,6 +60,17 @@ def __mul__(self, other: Math) -> Math: ...
     egraph.check(eq(expr1).to(expr2))
 
 
+def test_let_auto_prefixes_global_names(capfd: pytest.CaptureFixture[str]):
+    egraph = EGraph(save_egglog_string=True)
+
+    x = egraph.let("x", i64(1))
+    egraph.check(eq(x).to(i64(1)))
+
+    captured = capfd.readouterr()
+    assert "should start with `$`" not in captured.err
+    assert "(let $x " in egraph.as_egglog_string
+
+
 def test_fib():
     egraph = EGraph()