diff --git a/mtl/sugar.py b/mtl/sugar.py
new file mode 100644
index 0000000..54db20d
--- /dev/null
+++ b/mtl/sugar.py
@@ -0,0 +1,29 @@
+from mtl import ast
+
+
+def alw(phi, *, lo=0, hi=float('inf')):
+    return ast.G(ast.Interval(lo, hi), phi)
+
+
+def env(phi, *, lo=0, hi=float('inf')):
+    return ~alw(~phi, lo=lo, hi=hi)
+
+
+def implies(x, y):
+    return ~x | y
+
+
+def xor(x, y):
+    return (x | y) & ~(x & y)
+
+
+def iff(x, y):
+    return (x & y) | (~x & ~y)
+
+
+def until(phi, psi):
+    return ast.WeakUntil(phi, psi) & env(psi)
+
+
+def timed_until(phi, psi, lo, hi):
+    return env(psi, lo=lo, hi=hi) & alw(until(phi, psi), lo=0, hi=lo)
diff --git a/mtl/test_boolean_eval.py b/mtl/test_boolean_eval.py
index 7c5ed64..fb4cbad 100644
--- a/mtl/test_boolean_eval.py
+++ b/mtl/test_boolean_eval.py
@@ -55,5 +55,5 @@ def test_temporal_identity4(phi):
 
 @given(MetricTemporalLogicStrategy)
 def test_temporal_identity5(phi):
-    assert mtl.until(mtl.TOP, phi)(x, 0, quantitative=False) \
-        == mtl.env(phi)(x, 0, quantitative=False)
+    assert mtl.TOP.until(phi)(x, 0, quantitative=False) \
+        == phi.eventually()(x, 0, quantitative=False)
diff --git a/mtl/utils.py b/mtl/utils.py
index e2591b2..25e5da0 100644
--- a/mtl/utils.py
+++ b/mtl/utils.py
@@ -5,8 +5,8 @@ from math import isfinite
 from discrete_signals import signal
 import numpy as np
 
-import mtl.ast
-from mtl.ast import (And, G, Interval, Neg, Next, WeakUntil,
+from mtl import ast
+from mtl.ast import (And, G, Neg, Next, WeakUntil,
                      AtomicPred, _Bot)
 
 oo = float('inf')