diff --git a/graphted.cabal b/graphted.cabal
--- a/graphted.cabal
+++ b/graphted.cabal
@@ -1,5 +1,5 @@
 name:                graphted
-version:             0.2.5.1
+version:             0.3.0.0
 synopsis:    Graph indexed monads.
 -- description: TODO
 homepage:            https://github.com/aaronfriel/graphted#readme
@@ -8,7 +8,7 @@
 author:              Aaron Friel
 maintainer:          mayreply@aaronfriel.com
 copyright:           BSD3
-category:            Control
+category:            Control, Comonads, Monads
 build-type:          Simple
 extra-source-files:  README.md
 cabal-version:       >=1.10
diff --git a/src/Control/Applicative/Graph.hs b/src/Control/Applicative/Graph.hs
--- a/src/Control/Applicative/Graph.hs
+++ b/src/Control/Applicative/Graph.hs
@@ -44,11 +44,23 @@
     type family ApplyInv f (i :: p) (j :: p) :: Constraint
     type instance ApplyInv f i j = Inv f i j
 
+    -- | The 'liftA2' operation on the graph index.
+    --
+    -- Default instance: @Lift f i j = 'Apply' f ('Apply' f ('Pure' f) i) j@ 
+    type family LiftA2 f (i :: p) (j :: p) :: p
+    type instance LiftA2 f i j = Apply f (Fmap f i) j
+
+    -- | An invariant on the indexes of 'But'.
+    --
+    -- Default instance: @ButInv m i j = 'ApplyInv' m i j@
+    type family LiftA2Inv f (i :: p) (j :: p) :: Constraint
+    type instance LiftA2Inv f i j = ApplyInv f i j
+
     -- | The then operation ('*>') on the graph index.
     --
-    -- Default instance: @'Then' f i j = 'Apply' f ('Fconst' f i) j@ 
+    -- Default instance: @'Then' f i j = 'Apply' f ('Replace' f i) j@ 
     type family Then f (i :: p) (j :: p) :: p
-    type instance Then f i j = Apply f (Fconst f i) j
+    type instance Then f i j = Apply f (Replace f i) j
 
     -- | An invariant on the indexes of 'Then'.
     --
@@ -58,9 +70,9 @@
 
     -- | The but operation ('<*') on the graph index.
     --
-    -- Default instance: @But f i j = 'Apply' f ('Apply' f ('Pure' f) i) j@ 
+    -- Default instance: @But f i j = 'LiftA2' f i j@ 
     type family But f (i :: p) (j :: p) :: p
-    type instance But f i j = Apply f (Apply f (Pure f) i) j
+    type instance But f i j = LiftA2 f i j
 
     -- | An invariant on the indexes of 'But'.
     --
@@ -71,25 +83,29 @@
     -- | Sequential application ('<*>').
     gap :: ApplyInv f i j => f i (a -> b) -> f j a -> f (Apply f i j) b
 
+    -- | Lift a binary function to actions.
+    --
+    gliftA2 :: LiftA2Inv f i j => (a -> b -> c) -> f i a -> f j b -> f (LiftA2 f i j) c 
+    default gliftA2 :: (Apply f (Fmap f i) j ~ LiftA2 f i j, ApplyInv f (Fmap f i) j)
+                    => (a -> b -> c) -> f i a -> f j b -> f (LiftA2 f i j) c
+    gliftA2 f x = gap (gmap f x)
+
     -- | Sequence actions, discarding the value of the first argument ('*>').
     --
     -- Default implementation requires the default instance of 'Then'.
     {-# INLINE gthen #-}
     gthen :: ThenInv f i j => f i a -> f j b -> f (Then f i j) b
-    default gthen :: (Apply f (Fconst f i) j ~ Then f i j, ApplyInv f (Fconst f i) j, ThenInv f (Fconst f i) j)
+    default gthen :: (Apply f (Replace f i) j ~ Then f i j, ApplyInv f (Replace f i) j, ThenInv f (Replace f i) j)
                   => f i a -> f j b -> f (Then f i j) b
-    gthen a b = (id `gconst` a) `gap` b
+    gthen a b = (id `greplace` a) `gap` b
 
     -- | Sequence actions, discarding values of the second argument ('<*').
     --
     -- Default implementation requires the default instance of 'But'.
     {-# INLINE gbut #-}
     gbut :: ButInv f i j => f i a -> f j b -> f (But f i j) a
-    default gbut :: (Apply f (Apply f (Pure f) i) j ~ But f i j, 
-                    ApplyInv f (Pure f) i, 
-                    ApplyInv f (Apply f (Pure f) i) j,
-                    ButInv f (Apply f (Pure f) i) j)
+    default gbut :: (LiftA2 f i j ~ But f i j, LiftA2Inv f i j)
                  => f i a -> f j b -> f (But f i j) a
-    gbut a b = gpure const `gap` a `gap` b
+    gbut = gliftA2 const
 
     {-# MINIMAL gap #-}
diff --git a/src/Control/MonadFail/Graph.hs b/src/Control/MonadFail/Graph.hs
--- a/src/Control/MonadFail/Graph.hs
+++ b/src/Control/MonadFail/Graph.hs
@@ -1,6 +1,6 @@
 {- |
 Module      :  Control.MonadFail.Graph
-Description :  Graph indexed monads with failure
+Description :  Graph indexed monads with failure.
 Copyright   :  (c) Aaron Friel
 License     :  BSD-3
 
@@ -8,7 +8,42 @@
 Stability   :  unstable
 Portability :  portable
 
+This is only used in Do Notation with refutable patterns. e.g.:
+
+@
+    do  Just a <- m
+        k a
+@
+
+Is desugared as:
+
+@
+    let f (Just a) = k a
+        f _        = fail "Pattern match failure in do expression..."    
+    in m >>= k
+@
+
+With @-XApplicativeDo@, there are two outstanding issues:
+
+__First__, This will not compile (https://ghc.haskell.org/trac/ghc/ticket/13648) as
+the body statements @m1@ and @m2@ are desugared incorrectly:
+
+@
+    f m1 m2 k = do
+        m1
+        m2
+        k
+@
+
+To resolve, replace @m1@ with @_ <- m1@.
+
+__Second__, @'fail'@ must be in scope (https://ghc.haskell.org/trac/ghc/ticket/13649)
+when wildcard patterns are used. The module "Prelude.Graphted" takes care of
+this, and custom preludes must as well. A @'GMonadFail'@ constraint will not
+be added unless a refutable pattern is used.
+
 -}
+
 
 {-# LANGUAGE DefaultSignatures     #-}
 {-# LANGUAGE FlexibleContexts      #-}
diff --git a/src/Data/Functor/Graph.hs b/src/Data/Functor/Graph.hs
--- a/src/Data/Functor/Graph.hs
+++ b/src/Data/Functor/Graph.hs
@@ -27,19 +27,19 @@
     type family Fmap f (i :: p) :: p
     type instance Fmap f i = i
 
-    -- | The fconst operation ('<$') on the graph index.
+    -- | The Replace operation ('<$') on the graph index.
     --
-    -- Default instance: @Fconst f i = 'Fmap' f i@ 
-    type family Fconst f (i :: p) :: p
-    type instance Fconst f i = Fmap f i
+    -- Default instance: @Replace f i = 'Fmap' f i@ 
+    type family Replace f (i :: p) :: p
+    type instance Replace f i = Fmap f i
 
     -- | Map a function over over the functor ('fmap').
     gmap :: (a -> b) -> f i a -> f (Fmap f i) b
 
     -- | Replace all values with a constant ('<$').
     --
-    -- Default implementation requires the default instance of 'Fconst'.
-    {-# INLINABLE gconst #-}
-    gconst :: a -> f i b -> f (Fconst f i) a
-    default gconst :: (Fconst f i ~ Fmap f i) => a -> f i b -> f (Fconst f i) a
-    gconst = gmap . const
+    -- Default implementation requires the default instance of 'Replace'.
+    {-# INLINABLE greplace #-}
+    greplace :: a -> f i b -> f (Replace f i) a
+    default greplace :: (Replace f i ~ Fmap f i) => a -> f i b -> f (Replace f i) a
+    greplace = gmap . const
diff --git a/src/Data/GWrapped.hs b/src/Data/GWrapped.hs
--- a/src/Data/GWrapped.hs
+++ b/src/Data/GWrapped.hs
@@ -49,10 +49,10 @@
 
 instance Functor f => GFunctor (GWrapped f) where
     gmap f = GWrapped . fmap f . unG
-    gconst f = GWrapped . ((<$) f) . unG
+    greplace f = GWrapped . ((<$) f) . unG
 
 instance Applicative f => GApplicative (GWrapped f) where
-    type But (GWrapped m) i j = i
+    type But (GWrapped f) i j = i
     gap   (GWrapped m) (GWrapped k) = GWrapped $ m <*> k
     gthen (GWrapped m) (GWrapped k) = GWrapped $ m  *> k
     gbut  (GWrapped m) (GWrapped k) = GWrapped $ m <* k
diff --git a/src/Data/GWrappedIx.hs b/src/Data/GWrappedIx.hs
--- a/src/Data/GWrappedIx.hs
+++ b/src/Data/GWrappedIx.hs
@@ -27,9 +27,6 @@
 import Control.Monad.Indexed
 import Data.Functor.Indexed
 
-import Control.Applicative (Alternative (..))
-import Control.Monad       (MonadPlus (..))
-
 import GHC.Exts (Any)
 
 -- | Wrap a two-parameter-indexed type constructor:
@@ -72,10 +69,10 @@
 
 instance IxFunctor f => GFunctor (WrappedIx f) where
     gmap f = WrappedIx . imap f . unIx
-    gconst a = WrappedIx . imap (const a) . unIx
+    greplace a = WrappedIx . imap (const a) . unIx
 
 instance IxApplicative f => GApplicative (WrappedIx f) where
-    type But   (WrappedIx m) l r = '( FstIx l, SndIx r )
+    type But (WrappedIx f) l r = '( FstIx l, SndIx r )
     gap   (WrappedIx m) (WrappedIx k) = WrappedIx $ m <<*>> k
     gthen (WrappedIx m) (WrappedIx k) = WrappedIx $ m *>> k
     gbut (WrappedIx m) (WrappedIx k) = WrappedIx $ m <<* k
diff --git a/src/Prelude/Graphted.hs b/src/Prelude/Graphted.hs
--- a/src/Prelude/Graphted.hs
+++ b/src/Prelude/Graphted.hs
@@ -59,8 +59,8 @@
 fmap :: GFunctor f => (a -> b) -> f i a -> f (Fmap f i) b
 fmap = gmap
 
-(<$) :: GFunctor f => b -> f i a -> f (Fconst f i) b
-(<$) = gconst
+(<$) :: GFunctor f => b -> f i a -> f (Replace f i) b
+(<$) = greplace
 
 (<$>) :: GFunctor f => (a -> b) -> f i a -> f (Fmap f i) b
 (<$>) = fmap