Added quorum system tests + bug fix.

I was computing uniform strategies wrong. Looks like adding tests cases
was the right move!

quorums/quorum_system.py

@@ -180,8 +180,8 @@ class QuorumSystem(Generic[T]):
 
         read_quorums = self._minimize(read_quorums)
         write_quorums = self._minimize(write_quorums)
-        sigma_r = {frozenset(rq): 1 / len(rq) for rq in read_quorums}
+        sigma_r = {frozenset(q): 1 / len(read_quorums) for q in read_quorums}
-        sigma_w = {frozenset(wq): 1 / len(wq) for wq in write_quorums}
+        sigma_w = {frozenset(q): 1 / len(write_quorums) for q in write_quorums}
         return Strategy(self, sigma_r, sigma_w)
 
     def strategy(self,

tests/test_quorum_system.py

@@ -0,0 +1,132 @@
+from quorums import *
+from quorums.quorum_system import *
+import unittest
+
+class TestExpr(unittest.TestCase):
+    def test_init(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))
+
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+
+        # Specify reads.
+        qs = QuorumSystem(reads = a + b)
+        assert_equal(qs.reads, a + b)
+        assert_equal(qs.writes, a * b)
+
+        # Specify writes.
+        qs = QuorumSystem(writes = a + b)
+        assert_equal(qs.reads, a * b)
+        assert_equal(qs.writes, a + b)
+
+        # Specify neither.
+        with self.assertRaises(ValueError):
+            QuorumSystem()
+
+        # Specify both overlapping.
+        qs = QuorumSystem(reads=a+b, writes=a*b*c)
+        assert_equal(qs.reads, a+b)
+        assert_equal(qs.writes, a*b*c)
+
+        # Specify both not overlapping.
+        with self.assertRaises(ValueError):
+            QuorumSystem(reads=a+b, writes=a)
+
+    def test_uniform_strategy(self):
+        a = Node('a')
+        b = Node('b')
+        c = Node('c')
+        d = Node('d')
+
+        sigma = QuorumSystem(reads=a).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1.0,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=a+a).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1.0,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=a*a).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1.0,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=a + a*b).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1.0,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=a + a*b + a*c).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1.0,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=a + b).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1 / 2,
+            frozenset({'b'}): 1 / 2,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a', 'b'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=a + b + c).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a'}): 1 / 3,
+            frozenset({'b'}): 1 / 3,
+            frozenset({'c'}): 1 / 3,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a', 'b', 'c'}): 1.0,
+        })
+
+        sigma = QuorumSystem(reads=(a*b)+(c*d)).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a', 'b'}): 1 / 2,
+            frozenset({'c', 'd'}): 1 / 2,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a', 'c'}): 1 / 4,
+            frozenset({'a', 'd'}): 1 / 4,
+            frozenset({'b', 'c'}): 1 / 4,
+            frozenset({'b', 'd'}): 1 / 4,
+        })
+
+        sigma = QuorumSystem(reads=(a*b)+(c*d)+(a*b)+(a*b*c)).uniform_strategy()
+        self.assertEqual(sigma.sigma_r, {
+            frozenset({'a', 'b'}): 1 / 2,
+            frozenset({'c', 'd'}): 1 / 2,
+        })
+        self.assertEqual(sigma.sigma_w, {
+            frozenset({'a', 'c'}): 1 / 4,
+            frozenset({'a', 'd'}): 1 / 4,
+            frozenset({'b', 'c'}): 1 / 4,
+            frozenset({'b', 'd'}): 1 / 4,
+        })
+
+    def test_optimal_strategy(self):
+        # TODO(mwhittaker): Implement.
+        pass