diff --git a/stl/__init__.py b/stl/__init__.py
index e0b5059..a3a8c45 100644
--- a/stl/__init__.py
+++ b/stl/__init__.py
@@ -1,6 +1,6 @@
 from stl.utils import terms_lens, lineq_lens, walk, and_or_lens
 from stl.utils import alw, env, andf, orf
-from stl.ast import dt_sym, t_sym
+from stl.ast import dt_sym, t_sym, TOP, BOT
 from stl.ast import LinEq, Interval, NaryOpSTL, Or, And, F, G, ModalOp, Neg, Var, AtomicPred
 from stl.parser import parse
 from stl.synth import lex_param_project
diff --git a/stl/ast.py b/stl/ast.py
index 419ff26..2a521c4 100644
--- a/stl/ast.py
+++ b/stl/ast.py
@@ -12,23 +12,48 @@ from sympy import Symbol
 dt_sym = Symbol('dt', positive=True)
 t_sym = Symbol('t', positive=True)
 
-def flatten_binary(phi):
-    t = type(phi)
-    f = lambda x: x.args if isinstance(x, t) else [x]
-    return t(tuple(fn.mapcat(f, phi.args)))
+def flatten_binary(phi, op, dropT, shortT):
+    f = lambda x: x.args if isinstance(x, op) else [x]
+    args = [arg for arg in phi.args if not isinstance(arg, type(dropT))]
+
+    if any(isinstance(arg, type(shortT)) for arg in args):
+        return shortT
+    elif not args:
+        return dropT
+    else:
+        return op(tuple(fn.mapcat(f, phi.args)))
         
 
 class AST(object):
     def __or__(self, other):
-        return flatten_binary(Or((self, other)))
+        return flatten_binary(Or((self, other)), Or, BOT, TOP)
 
     def __and__(self, other):
-        return flatten_binary(And((self, other)))
+        return flatten_binary(And((self, other)), And, TOP, BOT)
 
     def __invert__(self):
         return Neg(self)
 
 
+class _Top(AST):
+    def __repr__(self):
+        return "⊤"
+
+    def __invert__(self):
+        return Bot()
+
+
+class _Bot(AST):
+    def __repr__(self):
+        return "⊥"
+
+    def __invert__(self):
+        return Top()
+
+TOP = _Top()
+BOT = _Bot()
+
+
 class AtomicPred(namedtuple("AP", ["id", "time"]), AST):
     def __repr__(self):
         return f"{self.id}[{self.time}]"
diff --git a/stl/test_ast.py b/stl/test_ast.py
new file mode 100644
index 0000000..accbb9d
--- /dev/null
+++ b/stl/test_ast.py
@@ -0,0 +1,13 @@
+import stl
+from nose2.tools import params
+import unittest
+
+class TestSTLAST(unittest.TestCase):
+    def test_and(self):
+        phi = stl.parse("x")
+        self.assertEqual(stl.TOP, stl.TOP | phi)
+        self.assertEqual(stl.BOT, stl.BOT & phi)
+        self.assertEqual(stl.TOP, stl.TOP & stl.TOP)
+        self.assertEqual(stl.BOT, stl.BOT | stl.BOT)
+        self.assertEqual(stl.TOP, stl.TOP | stl.BOT)
+        self.assertEqual(stl.BOT, stl.TOP & stl.BOT)