test: add test for impure function correlation behavior

Need to fix the UDF test case.

Related to #8921,
trying to write down exactly what
the expected behavior is.

ibis/backends/tests/test_impure.py

@@ -0,0 +1,83 @@
+from __future__ import annotations
+
+import random
+
+import pandas.testing as tm
+import pytest
+
+import ibis
+from ibis import _
+
+
+@ibis.udf.scalar.python(side_effects=True)
+def my_random(x: float) -> float:
+    return random.random()
+
+
+mark_impures = pytest.mark.parametrize(
+    "impure",
+    [
+        pytest.param(
+            lambda _: ibis.random(),
+            id="random",
+        ),
+        pytest.param(
+            lambda _: ibis.uuid().cast(str).contains("a").cast(float),
+            id="uuid",
+        ),
+        pytest.param(
+            lambda table: my_random(table.float_col),
+            id="udf",
+        ),
+    ],
+)
+
+
+@mark_impures
+def test_impure_correlated(alltypes, impure):
+    df = (
+        alltypes.select(common=impure(alltypes))
+        .select(x=_.common, y=_.common)
+        .execute()
+    )
+    tm.assert_series_equal(df.x, df.y, check_names=False)
+
+
+@mark_impures
+def test_chained_selections(alltypes, impure):
+    # https://github.com/ibis-project/ibis/issues/8921#issue-2234327722
+    t = alltypes.mutate(num=impure(alltypes))
+    t = t.mutate(isbig=(t.num > 0.5))
+    df = t.select("num", "isbig").execute()
+    df["expected"] = df.num > 0.5
+    tm.assert_series_equal(df.isbig, df.expected, check_names=False)
+
+
+@pytest.mark.parametrize(
+    "impure",
+    [
+        pytest.param(
+            lambda _: ibis.random(),
+            id="random",
+        ),
+        pytest.param(
+            # make this a float so we can compare to .5
+            lambda _: ibis.uuid().cast(str).contains("a").cast(float),
+            id="uuid",
+        ),
+        pytest.param(
+            lambda table: my_random(table.float_col),
+            id="udf",
+            # once this is fixed, can we unify these params with the params below?
+            marks=pytest.mark.xfail(reason="executed only once"),
+        ),
+    ],
+)
+def test_impure_uncorrelated(alltypes, impure):
+    df = alltypes.select(x=impure(alltypes), y=impure(alltypes)).execute()
+    assert (df.x == df.y).mean() < 1
+    # Even if the two expressions have the exact same ID, they should still be
+    # uncorrelated
+    common = impure(alltypes)
+    df = alltypes.select(x=common, y=common).execute()
+    assert (df.x == df.y).mean() < 1