Added expr tests + bug fix.

I wasn't computing the resilience of a choose quorum system correctly.
I'm happy I decided to add some unit tests!

quorums/expr.py

@@ -242,7 +242,8 @@ class Choose(Expr[T]):
         return sum(e._num_leaves() for e in self.es)
 
     def _dup_free_min_failures(self) -> int:
-        return sum(sorted(e._dup_free_min_failures() for e in self.es)[:self.k])
+        subfailures = [e._dup_free_min_failures() for e in self.es]
+        return sum(sorted(subfailures)[:len(subfailures) - self.k + 1])
 
 
 def choose(k: int, es: List[Expr[T]]) -> Expr[T]:

tests/test_expr.py

@@ -0,0 +1,214 @@
+from quorums import *
+from quorums.expr import *
+from typing import Any, FrozenSet
+import unittest
+
+class TestExpr(unittest.TestCase):
+    def test_quorums(self):
+        def assert_equal(e: Expr[str], xs: List[Set[str]]) -> None:
+            self.assertEqual(frozenset(frozenset(q) for q in e.quorums()),
+                             frozenset(frozenset(x) for x in xs))
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+        e = Node('e')
+        f = Node('f')
+
+        assert_equal(a+b+c, [{'a'}, {'b'}, {'c'}])
+        assert_equal(a*b*c, [{'a', 'b', 'c'}])
+        assert_equal(a + b*c, [{'a'}, {'b', 'c'}])
+        assert_equal(a*a*a, [{'a'}])
+        assert_equal(a+a+a, [{'a'}])
+        assert_equal(a*(a+b), [{'a'}, {'a', 'b'}])
+        assert_equal(choose(1, [a, b, c]), [{'a'}, {'b'}, {'c'}])
+        assert_equal(choose(2, [a, b, c]), [{'a', 'b'}, {'a', 'c'}, {'b', 'c'}])
+        assert_equal(choose(3, [a, b, c]), [{'a', 'b', 'c'}])
+        assert_equal((a+b) * (c+d), [
+            {'a', 'c'}, {'a', 'd'}, {'b', 'c'}, {'b', 'd'}
+        ])
+        assert_equal((a+b) * (a+c), [
+            {'a'}, {'a', 'c'}, {'a', 'b'}, {'b', 'c'}
+        ])
+        assert_equal(
+            choose(2, [
+                choose(2, [a, b, c]),
+                choose(2, [d, e, f]),
+                choose(2, [a, c, e]),
+            ]), [
+                {'a','b','d','e'}, {'a','b','d','f'}, {'a','b','e','f'},
+                {'a','c','d','e'}, {'a','c','d','f'}, {'a','c','e','f'},
+                {'b','c','d','e'}, {'b','c','d','f'}, {'b','c','e','f'},
+                {'a','b','a','c'}, {'a','b','a','e'}, {'a','b','c','e'},
+                {'a','c','a','c'}, {'a','c','a','e'}, {'a','c','c','e'},
+                {'b','c','a','c'}, {'b','c','a','e'}, {'b','c','c','e'},
+                {'d','e','a','c'}, {'d','e','a','e'}, {'d','e','c','e'},
+                {'d','f','a','c'}, {'d','f','a','e'}, {'d','f','c','e'},
+                {'e','f','a','c'}, {'e','f','a','e'}, {'e','f','c','e'},
+        ])
+
+    def test_is_quorum(self):
+        def assert_quorum(e: Expr[str], q: Set[str]) -> None:
+            self.assertTrue(e.is_quorum(q))
+
+        def assert_not_quorum(e: Expr[str], q: Set[str]) -> None:
+            self.assertFalse(e.is_quorum(q))
+
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+        e = Node('e')
+        f = Node('f')
+
+        expr = a + b + c
+        assert_quorum(expr, {'a'})
+        assert_quorum(expr, {'b'})
+        assert_quorum(expr, {'c'})
+        assert_quorum(expr, {'a', 'b'})
+        assert_quorum(expr, {'a', 'c'})
+        assert_quorum(expr, {'b', 'c'})
+        assert_quorum(expr, {'a', 'b', 'c'})
+        assert_quorum(expr, {'a', 'x'})
+        assert_not_quorum(expr, set())
+        assert_not_quorum(expr, {'x'})
+
+        expr = a * b * c
+        assert_quorum(expr, {'a', 'b', 'c'})
+        assert_quorum(expr, {'a', 'b', 'c', 'x'})
+        assert_not_quorum(expr, set())
+        assert_not_quorum(expr, {'a'})
+        assert_not_quorum(expr, {'b'})
+        assert_not_quorum(expr, {'c'})
+        assert_not_quorum(expr, {'a', 'b'})
+        assert_not_quorum(expr, {'a', 'c'})
+        assert_not_quorum(expr, {'b', 'c'})
+        assert_not_quorum(expr, {'x'})
+        assert_not_quorum(expr, {'a', 'x'})
+
+        expr = choose(2, [a, b, c])
+        assert_quorum(expr, {'a', 'b'})
+        assert_quorum(expr, {'a', 'c'})
+        assert_quorum(expr, {'b', 'c'})
+        assert_quorum(expr, {'a', 'b', 'c'})
+        assert_quorum(expr, {'a', 'b', 'c', 'x'})
+        assert_not_quorum(expr, {'a'})
+        assert_not_quorum(expr, {'b'})
+        assert_not_quorum(expr, {'c'})
+        assert_not_quorum(expr, {'x'})
+
+        expr = (a+b) * (c+d)
+        assert_quorum(expr, {'a', 'c'})
+        assert_quorum(expr, {'a', 'c'})
+        assert_quorum(expr, {'a', 'd'})
+        assert_quorum(expr, {'b', 'd'})
+        assert_quorum(expr, {'a', 'b', 'd'})
+        assert_quorum(expr, {'b', 'c', 'd'})
+        assert_quorum(expr, {'a', 'b', 'd'})
+        assert_quorum(expr, {'a', 'c', 'd'})
+        assert_quorum(expr, {'a', 'b', 'd'})
+        assert_quorum(expr, {'b', 'c', 'd'})
+        assert_quorum(expr, {'a', 'b', 'd'})
+        assert_quorum(expr, {'b', 'c', 'd'})
+        assert_quorum(expr, {'a', 'b', 'c', 'd'})
+        assert_not_quorum(expr, {'a'})
+        assert_not_quorum(expr, {'b'})
+        assert_not_quorum(expr, {'c'})
+        assert_not_quorum(expr, {'d'})
+        assert_not_quorum(expr, {'a', 'b'})
+        assert_not_quorum(expr, {'c', 'd'})
+        assert_not_quorum(expr, {'a', 'b', 'x'})
+
+    def test_resilience(self):
+        def assert_resilience(e: Expr[str], n: int):
+            self.assertEqual(e.resilience(), n)
+
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+        e = Node('e')
+        f = Node('f')
+
+        assert_resilience(a, 0)
+        assert_resilience(a + b, 1)
+        assert_resilience(a + b + c, 2)
+        assert_resilience(a + b + c + d, 3)
+        assert_resilience(a, 0)
+        assert_resilience(a * b, 0)
+        assert_resilience(a * b * c, 0)
+        assert_resilience(a * b * c * d, 0)
+        assert_resilience((a + b) * (c + d), 1)
+        assert_resilience((a + b + c) * (d + e + f), 2)
+        assert_resilience((a + b + c) * (a + e + f), 2)
+        assert_resilience((a + a + c) * (d + e + f), 1)
+        assert_resilience((a + a + a) * (d + e + f), 0)
+        assert_resilience(a*b + b*c + a*d + a*d*e, 1)
+        assert_resilience(choose(2, [a, b, c]), 1)
+        assert_resilience(choose(2, [a, b, c, d, e]), 3)
+        assert_resilience(choose(3, [a, b, c, d, e]), 2)
+        assert_resilience(choose(4, [a, b, c, d, e]), 1)
+        assert_resilience(choose(2, [a+b+c, d+e, f]), 2)
+        assert_resilience(choose(2, [a*b, a*c, d]), 0)
+        assert_resilience(choose(2, [a+b, a+c, a+d]), 2)
+
+    def test_dual(self):
+        def quorums(e: Expr['str']) -> FrozenSet[FrozenSet[str]]:
+            return frozenset(frozenset(q) for q in e.quorums())
+
+        def assert_equal(x: Expr['str'], y: Expr['str']) -> None:
+            self.assertEqual(quorums(x), quorums(y))
+
+        def assert_dual(x: Expr['str'], y: Expr['str']) -> None:
+            assert_equal(x.dual(), y)
+
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+        e = Node('e')
+
+        assert_dual(a, a)
+        assert_dual(a + b, a * b)
+        assert_dual(a + a, a * a)
+        assert_dual((a + b) * (c + d), (a * b) + (c * d))
+        assert_dual((a + b) * (a + d), (a * b) + (a * d))
+        assert_dual((a + b) * (a + a), (a * b) + (a * a))
+        assert_dual((a + a) * (a + a), (a * a) + (a * a))
+        assert_dual((a + (a * b)) + ((c * d) + a),
+                    (a * (a + b)) * ((c + d) * a))
+        assert_dual(choose(2, [a, b, c]), choose(2, [a, b, c]))
+        assert_dual(choose(2, [a+b, c+d, e]), choose(2, [a*b, c*d, e]))
+        assert_dual(choose(3, [a, b, c, d, e]), choose(3, [a, b, c, d, e]))
+        assert_dual(choose(2, [a, b, c, d, e]), choose(4, [a, b, c, d, e]))
+        assert_dual(choose(4, [a, b, c, d, e]), choose(2, [a, b, c, d, e]))
+
+    def test_dup_free(self):
+        def assert_dup_free(e: Expr['str']) -> None:
+            self.assertTrue(e.dup_free())
+
+        def assert_not_dup_free(e: Expr['str']) -> None:
+            self.assertFalse(e.dup_free())
+
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+        e = Node('e')
+        f = Node('f')
+
+        assert_dup_free(a)
+        assert_dup_free(a + b)
+        assert_dup_free(a * b)
+        assert_dup_free(a * b + c)
+        assert_dup_free(choose(2, [a, b, c]))
+        assert_dup_free(choose(2, [a*b, c, d+e+f]))
+        assert_dup_free(choose(3, [a, b, c, d, e]))
+        assert_dup_free((a + b) * (c + (d * e)))
+
+        assert_not_dup_free(a + a)
+        assert_not_dup_free(a * a)
+        assert_not_dup_free(a * (b + a))
+        assert_not_dup_free(choose(2, [a, b, a]))
+        assert_not_dup_free(choose(3, [a, b, c, d, a]))
+        assert_not_dup_free((a + b) * (c + (d * a)))