diff --git a/src/UniqueLogic/ST/TF/System.hs b/src/UniqueLogic/ST/TF/System.hs
--- a/src/UniqueLogic/ST/TF/System.hs
+++ b/src/UniqueLogic/ST/TF/System.hs
@@ -18,7 +18,7 @@
    constant,
    assignment2,
    assignment3,
-   Apply, arg, runApply,
+   Apply, arg, runApply, runApplyMaybe,
    -- * Solution
    solve, solveDepthFirst, solveBreadthFirst,
    query,
@@ -34,7 +34,7 @@
 import Control.Monad.Trans.Maybe (MaybeT(MaybeT), runMaybeT, mapMaybeT, )
 import Control.Monad.Trans.Identity (IdentityT, )
 import Control.Monad.ST (ST, )
-import Control.Monad (when, liftM2, ap, guard, )
+import Control.Monad (when, liftM2, ap, guard, join, )
 import Control.Applicative (Applicative, pure, (<*>), )
 import Data.Sequence (Seq, (|>), ViewL((:<)), )
 import Data.Functor.Compose (Compose(Compose))
@@ -261,7 +261,7 @@
 -}
 arg :: Variable w s a -> Apply w s a
 arg (Variable _update al av) =
-   Apply $ Compose $ MW.writer (MaybeT $ readSTRef av, [al])
+   Apply $ Compose $ MW.writer (readSTRefM av, [al])
 
 instance Functor (Apply w s) where
    fmap f (Apply a) = Apply $ fmap f a
@@ -275,6 +275,18 @@
    UMT.C w =>
    Apply w s a -> Variable w s a -> T w s ()
 runApply (Apply (Compose w)) a =
+   uncurry (runUpdate a) $ MW.runWriter w
+
+runApplyMaybe ::
+   UMT.C w =>
+   Apply w s (Maybe a) -> Variable w s a -> T w s ()
+runApplyMaybe (Apply (Compose w)) a =
    case MW.runWriter w of
-      (f, refs) ->
-         lift $ Fold.forM_ refs $ flip modifySTRef (addUpdate $ varUpdate a f)
+      (mf, refs) ->
+         runUpdate a (MaybeT $ fmap join $ runMaybeT mf) refs
+
+runUpdate ::
+   Variable w s a -> MaybeT (ST s) a ->
+   [STRef s (Updates w s)] -> T w s ()
+runUpdate a f refs =
+   lift $ Fold.forM_ refs $ flip modifySTRef (addUpdate $ varUpdate a f)
diff --git a/unique-logic-tf.cabal b/unique-logic-tf.cabal
--- a/unique-logic-tf.cabal
+++ b/unique-logic-tf.cabal
@@ -1,5 +1,5 @@
 Name:             unique-logic-tf
-Version:          0.4.0.1
+Version:          0.4.1
 License:          BSD3
 License-File:     LICENSE
 Author:           Henning Thielemann
@@ -64,7 +64,7 @@
 Build-Type:        Simple
 
 Source-Repository this
-  Tag:         0.4.0.1
+  Tag:         0.4.1
   Type:        darcs
   Location:    http://code.haskell.org/~thielema/unique-logic-tf/