diff --git a/Algebra/Lattice.hs b/Algebra/Lattice.hs
--- a/Algebra/Lattice.hs
+++ b/Algebra/Lattice.hs
@@ -9,12 +9,12 @@
     joins, meets,
     
     -- * Fixed points of chains in lattices
-    lfp, unsafeLfp,
-    gfp, unsafeGfp,
+    lfp, lfpFrom, unsafeLfp,
+    gfp, gfpFrom, unsafeGfp,
   ) where
 
 import Algebra.Enumerable
-import Algebra.PartialOrd
+import qualified Algebra.PartialOrd as PO
 
 import qualified Data.Set as S
 import qualified Data.IntSet as IS
@@ -210,23 +210,35 @@
 -- Assumes that the function is monotone and does not check if that is correct.
 {-# INLINE unsafeLfp #-}
 unsafeLfp :: (Eq a, BoundedJoinSemiLattice a) => (a -> a) -> a
-unsafeLfp = unsafeLfpFrom bottom
+unsafeLfp = PO.unsafeLfpFrom bottom
 
 -- | Implementation of Kleene fixed-point theorem <http://en.wikipedia.org/wiki/Kleene_fixed-point_theorem>.
 -- Forces the function to be monotone.
 {-# INLINE lfp #-}
 lfp :: (Eq a, BoundedJoinSemiLattice a) => (a -> a) -> a
-lfp f = unsafeLfpFrom bottom (\x -> f x `join` x)
+lfp = lfpFrom bottom
 
+-- | Implementation of Kleene fixed-point theorem <http://en.wikipedia.org/wiki/Kleene_fixed-point_theorem>.
+-- Forces the function to be monotone.
+{-# INLINE lfpFrom #-}
+lfpFrom :: (Eq a, BoundedJoinSemiLattice a) => a -> (a -> a) -> a
+lfpFrom init_x f = PO.unsafeLfpFrom init_x (\x -> f x `join` x)
 
+
 -- | Implementation of Kleene fixed-point theorem <http://en.wikipedia.org/wiki/Kleene_fixed-point_theorem>.
 -- Assumes that the function is antinone and does not check if that is correct.
 {-# INLINE unsafeGfp #-}
 unsafeGfp :: (Eq a, BoundedMeetSemiLattice a) => (a -> a) -> a
-unsafeGfp = unsafeGfpFrom top
+unsafeGfp = PO.unsafeGfpFrom top
 
 -- | Implementation of Kleene fixed-point theorem <http://en.wikipedia.org/wiki/Kleene_fixed-point_theorem>.
 -- Forces the function to be antinone.
 {-# INLINE gfp #-}
 gfp :: (Eq a, BoundedMeetSemiLattice a) => (a -> a) -> a
-gfp f = unsafeGfpFrom top (\x -> f x `meet` x)
+gfp = gfpFrom top
+
+-- | Implementation of Kleene fixed-point theorem <http://en.wikipedia.org/wiki/Kleene_fixed-point_theorem>.
+-- Forces the function to be antinone.
+{-# INLINE gfpFrom #-}
+gfpFrom :: (Eq a, BoundedMeetSemiLattice a) => a -> (a -> a) -> a
+gfpFrom init_x f = PO.unsafeGfpFrom init_x (\x -> f x `meet` x)
diff --git a/Algebra/PartialOrd.hs b/Algebra/PartialOrd.hs
--- a/Algebra/PartialOrd.hs
+++ b/Algebra/PartialOrd.hs
@@ -11,7 +11,9 @@
 import Algebra.Enumerable
 
 import qualified Data.Set as S
+import qualified Data.IntSet as IS
 import qualified Data.Map as M
+import qualified Data.IntMap as IM
 
 
 -- | A partial ordering on sets: <http://en.wikipedia.org/wiki/Partially_ordered_set>
@@ -38,8 +40,14 @@
 instance Ord a => PartialOrd (S.Set a) where
     leq = S.isSubsetOf
 
+instance PartialOrd IS.IntSet where
+    leq = IS.isSubsetOf
+
 instance (Ord k, PartialOrd v) => PartialOrd (M.Map k v) where
-    leq = M.isSubmapOf
+    m1 `leq` m2 = m1 `M.isSubmapOf` m2 && M.fold (\(x1, x2) b -> b && x1 `leq` x2) True (M.intersectionWith (,) m1 m2)
+
+instance PartialOrd v => PartialOrd (IM.IntMap v) where
+    im1 `leq` im2 = im1 `IM.isSubmapOf` im2 && IM.fold (\(x1, x2) b -> b && x1 `leq` x2) True (IM.intersectionWith (,) im1 im2)
 
 instance (Eq v, Enumerable k) => Eq (k -> v) where
     f == g = all (\k -> f k == g k) universe
diff --git a/lattices.cabal b/lattices.cabal
--- a/lattices.cabal
+++ b/lattices.cabal
@@ -1,5 +1,5 @@
 Name:               lattices
-Version:            1.1
+Version:            1.2
 Cabal-Version:      >= 1.2
 Category:           Math
 Synopsis:           Fine-grained library for constructing and manipulating lattices