diff --git a/VERSION b/VERSION
--- a/VERSION
+++ b/VERSION
@@ -1,12 +1,22 @@
+0.9.0 (2014-XX-XX):
+    - Control.Unification.Types: changed the fundeps on BindingMonad
+      and RankedBindingMonad so that things compile under GHC 7.8.2
+    - Data.Functor.Fixedpoint: eta-expanded RULES to avoid GHC >=
+      7.8 warnings about them potentially not firing due to (.)
+      being inlined first.
 0.8.1 (2014-05-27):
-    - Control.Unification.Types: added Functor, Foldable, and Traversable instances for UnificationFailure. (h/t Graham Rogers)
+    - Control.Unification.Types: added Functor, Foldable, and
+      Traversable instances for UnificationFailure. (h/t Graham Rogers)
 0.8.0 (2012-07-11):
     - Control.Unification.Types: Changed the type of Unifiable.zipMatch
 0.7.0 (2012-03-19):
     - Renamed MutTerm to UTerm (and MutVar to UVar)
     - Replaced the Variable.eqVar method by plain old Eq.(==)
-    - Control.Unification: added getFreeVarsAll, applyBindingsAll, freshenAll
-    - Swapped type argument order for MutTerm, so that it can be a functor etc. Also changed BindingMonad, UnificationFailure, Rank, and RankedBindingMonad for consistency.
+    - Control.Unification: added getFreeVarsAll, applyBindingsAll,
+      freshenAll
+    - Swapped type argument order for MutTerm, so that it can be a
+      functor etc. Also changed BindingMonad, UnificationFailure,
+      Rank, and RankedBindingMonad for consistency.
 0.6.0 (2012-02-17):
     - Removed the phantom type argument for Variables.
 0.5.0 (2011-07-12):
diff --git a/src/Control/Unification/Types.hs b/src/Control/Unification/Types.hs
--- a/src/Control/Unification/Types.hs
+++ b/src/Control/Unification/Types.hs
@@ -5,7 +5,7 @@
 
 {-# OPTIONS_GHC -Wall -fwarn-tabs #-}
 ----------------------------------------------------------------
---                                                  ~ 2014.05.27
+--                                                  ~ 2014.05.28
 -- |
 -- Module      :  Control.Unification.Types
 -- Copyright   :  Copyright (c) 2007--2014 wren gayle romano
@@ -196,6 +196,9 @@
             . showString msg
             )
 
+-- TODO: transformers-0.4.1.0 deprecated this, use
+-- Control.Monad.Trans.Except instead. (transformers-0.3.0.0 is
+-- fine)
 instance Error (UnificationFailure t v) where
     noMsg  = UnknownError ""
     strMsg = UnknownError
@@ -263,7 +266,7 @@
 -- we make the same assumptions everywhere we use @BindingMonad@.
 
 class (Unifiable t, Variable v, Applicative m, Monad m) =>
-    BindingMonad t v m | m -> t v
+    BindingMonad t v m | m t -> v, v m -> t
     where
     
     -- | Given a variable pointing to @UTerm t v@, return the
@@ -321,7 +324,9 @@
 -- compression is asymptotically optimal, the constant factors may
 -- make it worthwhile to stick with the unweighted path compression
 -- supported by 'BindingMonad'.
-class (BindingMonad t v m) => RankedBindingMonad t v m | m -> t v where
+class (BindingMonad t v m) =>
+    RankedBindingMonad t v m | m t -> v, v m -> t
+    where
     
     -- | Given a variable pointing to @UTerm t v@, return its
     -- rank and the term it's bound to.
diff --git a/src/Data/Functor/Fixedpoint.hs b/src/Data/Functor/Fixedpoint.hs
--- a/src/Data/Functor/Fixedpoint.hs
+++ b/src/Data/Functor/Fixedpoint.hs
@@ -16,9 +16,13 @@
 -- http://www.mail-archive.com/glasgow-haskell-users@haskell.org/msg14313.html
 {-# OPTIONS_GHC -O2 -fenable-rewrite-rules #-}
 
+-- NOTE #1: on GHC >= 7.8 we need to eta expand rules to avoid a
+-- warning about the fact that the rule may never fire because (.)
+-- might inline first...
+
 {-# OPTIONS_GHC -Wall -fwarn-tabs #-}
 ----------------------------------------------------------------
---                                                    2013.05.11
+--                                                    2014.05.28
 -- |
 -- Module      :  Data.Functor.Fixedpoint
 -- Copyright   :  Copyright (c) 2007--2014 wren gayle romano
@@ -114,9 +118,10 @@
 "hmap id"
         hmap id = id
 
+-- cf., NOTE #1
 "hmap-compose"
-    forall (eps :: forall a. g a -> h a) (eta :: forall a. f a -> g a).
-        hmap eps . hmap eta = hmap (eps . eta)
+    forall (eps :: forall a. g a -> h a) (eta :: forall a. f a -> g a) x.
+        hmap eps (hmap eta x) = hmap (eps . eta) x
     #-}
 
 
@@ -128,8 +133,12 @@
 hmapM eps = anaM (eps . unFix)
 
 {-# RULES
-"hmapM return"                                  hmapM return = return
--- "hmapM-compose" forall eps eta. hmap eps <=< hmap eta = hmapM (eps <=< eta)
+"hmapM return"
+    hmapM return = return
+
+-- "hmapM-compose"
+--     forall eps eta.
+--         hmap eps <=< hmap eta = hmapM (eps <=< eta)
     #-}
 
 
@@ -141,20 +150,29 @@
 ymap f = Fix . fmap f . unFix
 
 {-# RULES
-"ymap id"                          ymap id = id
-"ymap-compose" forall f g. ymap f . ymap g = ymap (f . g)
+"ymap id"
+        ymap id = id
+
+-- cf., NOTE #1
+"ymap-compose"
+    forall f g x.
+        ymap f (ymap g x) = ymap (f . g) x
     #-}
 
 
 -- | A monadic variant of 'ymap'.
 ymapM :: (Traversable f, Monad m)
       => (Fix f -> m (Fix f)) -> Fix f -> m (Fix f)
-{-# INLINE ymapM #-}
+{-# INLINE [0] ymapM #-}
 ymapM f = liftM Fix . mapM f . unFix
 
 {-# RULES
-"ymapM id"                          ymapM return = return
--- "ymapM-compose" forall f g. ymapM f <=< ymapM g = ymapM (f <=< g)
+"ymapM id"
+        ymapM return = return
+
+-- "ymapM-compose"
+--     forall f g.
+--         ymapM f <=< ymapM g = ymapM (f <=< g)
     #-}
 
 
@@ -190,10 +208,10 @@
 "cata-refl"
         cata Fix = id
 
--- TODO: do we still need eta-expanded variants of rules?
+-- cf., NOTE #1
 "cata-compose"
-    forall (eps :: forall a. f a -> g a) phi.
-        cata phi . cata (Fix . eps) = cata (phi . eps)
+    forall (eps :: forall a. f a -> g a) phi x.
+        cata phi (cata (Fix . eps) x) = cata (phi . eps) x
     #-}
 
 -- We can't really use this one because of the implication constraint
@@ -210,7 +228,7 @@
 --
 -- N.B., this orders the side effects from the bottom up.
 cataM :: (Traversable f, Monad m) => (f a -> m a) -> (Fix f -> m a)
-{-# INLINE cataM #-}
+{-# INLINE [0] cataM #-}
 cataM phiM = self
     where
     self = phiM <=< (mapM self . unFix)
@@ -258,9 +276,10 @@
         ana unFix = id
 
 -- BUG: I think I dualized this right...
+-- cf., NOTE #1
 "ana-compose"
-    forall (eps :: forall a. f a -> g a) psi.
-        ana (eps . unFix) . ana psi = ana (eps . psi)
+    forall (eps :: forall a. f a -> g a) psi x.
+        ana (eps . unFix) (ana psi x) = ana (eps . psi) x
     #-}
 
 -- We can't really use this because of the implication constraint
diff --git a/unification-fd.cabal b/unification-fd.cabal
--- a/unification-fd.cabal
+++ b/unification-fd.cabal
@@ -1,5 +1,5 @@
 ----------------------------------------------------------------
--- wren gayle romano <wren@community.haskell.org>    ~ 2014.05.27
+-- wren gayle romano <wren@community.haskell.org>   ~ 2014.05.28
 ----------------------------------------------------------------
 
 -- By and large Cabal >=1.2 is fine; but >= 1.6 gives tested-with:
@@ -8,7 +8,7 @@
 Build-Type:     Simple
 
 Name:           unification-fd
-Version:        0.8.1
+Version:        0.9.0
 Stability:      experimental
 Homepage:       http://code.haskell.org/~wren/
 Author:         wren gayle romano
@@ -21,9 +21,9 @@
 Synopsis:       Simple generic unification algorithms.
 Description:    Simple generic unification algorithms.
 
--- BUG: does not work with GHC 7.8.0. Need to fix that
+-- No longer compiles with GHC-6.12.1 since Data.Monoid does not export (<>) in Control.Unification.Types. The backwards compatibility is not considered worth adding CPP noise...
 Tested-With:
-    GHC == 6.12.1, GHC == 7.6.1
+    GHC == 7.6.1, GHC == 7.6.3, GHC == 7.8.2
 Extra-source-files:
     AUTHORS, README, VERSION
 Source-Repository head