Issue 8743: Improve interoperability between sets and the collections.Set abstract base class.
diff --git a/Lib/test/test_collections.py b/Lib/test/test_collections.py
index ee28a6c..6407b6f 100644
--- a/Lib/test/test_collections.py
+++ b/Lib/test/test_collections.py
@@ -720,14 +720,166 @@
 
         cs = MyComparableSet()
         ncs = MyNonComparableSet()
+        self.assertFalse(ncs < cs)
+        self.assertTrue(ncs <= cs)
+        self.assertFalse(ncs > cs)
+        self.assertTrue(ncs >= cs)
+
+    def assertSameSet(self, s1, s2):
+        # coerce both to a real set then check equality
+        self.assertSetEqual(set(s1), set(s2))
+
+    def test_Set_interoperability_with_real_sets(self):
+        # Issue: 8743
+        class ListSet(Set):
+            def __init__(self, elements=()):
+                self.data = []
+                for elem in elements:
+                    if elem not in self.data:
+                        self.data.append(elem)
+            def __contains__(self, elem):
+                return elem in self.data
+            def __iter__(self):
+                return iter(self.data)
+            def __len__(self):
+                return len(self.data)
+            def __repr__(self):
+                return 'Set({!r})'.format(self.data)
+
+        r1 = set('abc')
+        r2 = set('bcd')
+        r3 = set('abcde')
+        f1 = ListSet('abc')
+        f2 = ListSet('bcd')
+        f3 = ListSet('abcde')
+        l1 = list('abccba')
+        l2 = list('bcddcb')
+        l3 = list('abcdeedcba')
+
+        target = r1 & r2
+        self.assertSameSet(f1 & f2, target)
+        self.assertSameSet(f1 & r2, target)
+        self.assertSameSet(r2 & f1, target)
+        self.assertSameSet(f1 & l2, target)
+
+        target = r1 | r2
+        self.assertSameSet(f1 | f2, target)
+        self.assertSameSet(f1 | r2, target)
+        self.assertSameSet(r2 | f1, target)
+        self.assertSameSet(f1 | l2, target)
+
+        fwd_target = r1 - r2
+        rev_target = r2 - r1
+        self.assertSameSet(f1 - f2, fwd_target)
+        self.assertSameSet(f2 - f1, rev_target)
+        self.assertSameSet(f1 - r2, fwd_target)
+        self.assertSameSet(f2 - r1, rev_target)
+        self.assertSameSet(r1 - f2, fwd_target)
+        self.assertSameSet(r2 - f1, rev_target)
+        self.assertSameSet(f1 - l2, fwd_target)
+        self.assertSameSet(f2 - l1, rev_target)
+
+        target = r1 ^ r2
+        self.assertSameSet(f1 ^ f2, target)
+        self.assertSameSet(f1 ^ r2, target)
+        self.assertSameSet(r2 ^ f1, target)
+        self.assertSameSet(f1 ^ l2, target)
+
+        # Don't change the following to use assertLess or other
+        # "more specific" unittest assertions.  The current
+        # assertTrue/assertFalse style makes the pattern of test
+        # case combinations clear and allows us to know for sure
+        # the exact operator being invoked.
+
+        # proper subset
+        self.assertTrue(f1 < f3)
+        self.assertFalse(f1 < f1)
+        self.assertFalse(f1 < f2)
+        self.assertTrue(r1 < f3)
+        self.assertFalse(r1 < f1)
+        self.assertFalse(r1 < f2)
+        self.assertTrue(r1 < r3)
+        self.assertFalse(r1 < r1)
+        self.assertFalse(r1 < r2)
         with self.assertRaises(TypeError):
-            ncs < cs
+            f1 < l3
         with self.assertRaises(TypeError):
-            ncs <= cs
+            f1 < l1
         with self.assertRaises(TypeError):
-            cs > ncs
+            f1 < l2
+
+        # any subset
+        self.assertTrue(f1 <= f3)
+        self.assertTrue(f1 <= f1)
+        self.assertFalse(f1 <= f2)
+        self.assertTrue(r1 <= f3)
+        self.assertTrue(r1 <= f1)
+        self.assertFalse(r1 <= f2)
+        self.assertTrue(r1 <= r3)
+        self.assertTrue(r1 <= r1)
+        self.assertFalse(r1 <= r2)
         with self.assertRaises(TypeError):
-            cs >= ncs
+            f1 <= l3
+        with self.assertRaises(TypeError):
+            f1 <= l1
+        with self.assertRaises(TypeError):
+            f1 <= l2
+
+        # proper superset
+        self.assertTrue(f3 > f1)
+        self.assertFalse(f1 > f1)
+        self.assertFalse(f2 > f1)
+        self.assertTrue(r3 > r1)
+        self.assertFalse(f1 > r1)
+        self.assertFalse(f2 > r1)
+        self.assertTrue(r3 > r1)
+        self.assertFalse(r1 > r1)
+        self.assertFalse(r2 > r1)
+        with self.assertRaises(TypeError):
+            f1 > l3
+        with self.assertRaises(TypeError):
+            f1 > l1
+        with self.assertRaises(TypeError):
+            f1 > l2
+
+        # any superset
+        self.assertTrue(f3 >= f1)
+        self.assertTrue(f1 >= f1)
+        self.assertFalse(f2 >= f1)
+        self.assertTrue(r3 >= r1)
+        self.assertTrue(f1 >= r1)
+        self.assertFalse(f2 >= r1)
+        self.assertTrue(r3 >= r1)
+        self.assertTrue(r1 >= r1)
+        self.assertFalse(r2 >= r1)
+        with self.assertRaises(TypeError):
+            f1 >= l3
+        with self.assertRaises(TypeError):
+            f1 >=l1
+        with self.assertRaises(TypeError):
+            f1 >= l2
+
+        # equality
+        self.assertTrue(f1 == f1)
+        self.assertTrue(r1 == f1)
+        self.assertTrue(f1 == r1)
+        self.assertFalse(f1 == f3)
+        self.assertFalse(r1 == f3)
+        self.assertFalse(f1 == r3)
+        self.assertFalse(f1 == l3)
+        self.assertFalse(f1 == l1)
+        self.assertFalse(f1 == l2)
+
+        # inequality
+        self.assertFalse(f1 != f1)
+        self.assertFalse(r1 != f1)
+        self.assertFalse(f1 != r1)
+        self.assertTrue(f1 != f3)
+        self.assertTrue(r1 != f3)
+        self.assertTrue(f1 != r3)
+        self.assertTrue(f1 != l3)
+        self.assertTrue(f1 != l1)
+        self.assertTrue(f1 != l2)
 
     def test_Mapping(self):
         for sample in [dict]: