diff --git a/tests/push/test_push_rule_evaluator.py b/tests/push/test_push_rule_evaluator.py
new file mode 100644
index 0000000000..9ae6a87d7b
--- /dev/null
+++ b/tests/push/test_push_rule_evaluator.py
@@ -0,0 +1,65 @@
+# -*- coding: utf-8 -*-
+# Copyright 2020 The Matrix.org Foundation C.I.C.
+#
+# Licensed under the Apache License, Version 2.0 (the "License");
+# you may not use this file except in compliance with the License.
+# You may obtain a copy of the License at
+#
+# http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing, software
+# distributed under the License is distributed on an "AS IS" BASIS,
+# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+# See the License for the specific language governing permissions and
+# limitations under the License.
+
+from synapse.api.room_versions import RoomVersions
+from synapse.events import FrozenEvent
+from synapse.push.push_rule_evaluator import PushRuleEvaluatorForEvent
+
+from tests import unittest
+
+
+class PushRuleEvaluatorTestCase(unittest.TestCase):
+ def setUp(self):
+ event = FrozenEvent(
+ {
+ "event_id": "$event_id",
+ "type": "m.room.history_visibility",
+ "sender": "@user:test",
+ "state_key": "",
+ "room_id": "@room:test",
+ "content": {"body": "foo bar baz"},
+ },
+ RoomVersions.V1,
+ )
+ room_member_count = 0
+ sender_power_level = 0
+ power_levels = {}
+ self.evaluator = PushRuleEvaluatorForEvent(
+ event, room_member_count, sender_power_level, power_levels
+ )
+
+ def test_display_name(self):
+ """Check for a matching display name in the body of the event."""
+ condition = {
+ "kind": "contains_display_name",
+ }
+
+ # Blank names are skipped.
+ self.assertFalse(self.evaluator.matches(condition, "@user:test", ""))
+
+ # Check a display name that doesn't match.
+ self.assertFalse(self.evaluator.matches(condition, "@user:test", "not found"))
+
+ # Check a display name which matches.
+ self.assertTrue(self.evaluator.matches(condition, "@user:test", "foo"))
+
+ # A display name that matches, but not a full word does not result in a match.
+ self.assertFalse(self.evaluator.matches(condition, "@user:test", "ba"))
+
+ # A display name should not be interpreted as a regular expression.
+ self.assertFalse(self.evaluator.matches(condition, "@user:test", "ba[rz]"))
+
+ # A display name with spaces should work fine.
+ self.assertTrue(self.evaluator.matches(condition, "@user:test", "foo bar"))
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