diff --git a/Math/Sym.hs b/Math/Sym.hs
--- a/Math/Sym.hs
+++ b/Math/Sym.hs
@@ -79,7 +79,7 @@
 toVector :: StPerm -> Vector Int
 toVector = perm0
 
--- | Convert a vector to a standard permutation. The vector should a
+-- | Convert a vector to a standard permutation. The vector should be a
 -- permutation of the elements @[0..k-1]@ for some positive @k@. No
 -- checks for this are done.
 fromVector :: Vector Int -> StPerm
@@ -98,7 +98,7 @@
 infixl 6 /-/
 
 -- | The /skew sum/ of two permutations. (A definition of the
--- /direct sum/ is provided by the Monoid instance.)
+-- /direct sum/ is provided by 'mappend' of the 'Monoid' instance for 'StPerm'.)
 (/-/) :: StPerm -> StPerm -> StPerm
 u /-/ v = fromVector $ (SV.++) u' v'
     where
@@ -126,8 +126,7 @@
 
 -- | The class of permutations. Minimal complete definition: 'st' and
 -- 'act'. The default implementations of 'size' and 'idperm' can be
--- somewhat slow, so you may want to consider implementing them as
--- well.
+-- somewhat slow, so you may want to implement them as well.
 class Perm a where
 
     -- | The standardization map. If there is an underlying linear
diff --git a/Math/Sym/D8.hs b/Math/Sym/D8.hs
--- a/Math/Sym/D8.hs
+++ b/Math/Sym/D8.hs
@@ -43,44 +43,51 @@
 import qualified Math.Sym (inverse)
 import Math.Sym.Internal (revIdperm)
 
+
 -- The group elements
 -- ------------------
 
-r0, r1, r2, r3, s0, s1, s2, s3 :: Perm a => a -> a
-
 -- | Ration by 0 degrees, i.e. the identity map.
+r0 :: Perm a => a -> a
 r0 w = w
 
 -- | Ration by 90 degrees clockwise.
+r1 :: Perm a => a -> a
 r1 = s2 . s1
 
 -- | Ration by 2*90 = 180 degrees clockwise.
+r2 :: Perm a => a -> a
 r2 = r1 . r1
 
 -- | Ration by 3*90 = 270 degrees clockwise.
+r3 :: Perm a => a -> a
 r3 = r2 . r1
 
 -- | Reflection through a horizontal axis (also called 'complement').
+s0 :: Perm a => a -> a
 s0 = r1 . s2
 
 -- | Reflection through a vertical axis (also called 'reverse').
+s1 :: Perm a => a -> a
 s1 w = (fromVector . revIdperm . size) w `act` w
 
 -- | Reflection through the main diagonal (also called 'inverse').
+s2 :: Perm a => a -> a
 s2 = Math.Sym.inverse
 
 -- | Reflection through the anti-diagonal.
+s3 :: Perm a => a -> a
 s3 = s1 . r1
 
+
 -- D8, the klein four-group, and orbits
 -- ------------------------------------
 
-d8, klein4 :: Perm a => [a -> a]
-
 -- | The dihedral group of order 8 (the symmetries of a square); that is,
 -- 
 -- > d8 = [r0, r1, r2, r3, s0, s1, s2, s3]
 -- 
+d8 :: Perm a => [a -> a]
 d8 = [r0, r1, r2, r3, s0, s1, s2, s3]
 
 -- | The Klein four-group (the symmetries of a non-equilateral
@@ -88,6 +95,7 @@
 -- 
 -- > klein4 = [r0, r2, s0, s1]
 -- 
+klein4 :: Perm a => [a -> a]
 klein4 = [r0, r2, s0, s1]
 
 -- | @orbit fs x@ is the orbit of @x@ under the functions in @fs@. E.g.,
@@ -97,22 +105,26 @@
 orbit :: Ord a => Perm a => [a -> a] -> a -> [a]
 orbit fs x = map head . group $ sort [ f x | f <- fs ]
 
+
 -- Aliases
 -- -------
 
-id, rotate, complement, reverse, inverse :: Perm a => a -> a
-
 -- | @id = r0@
+id :: Perm a => a -> a
 id = r0
 
 -- | @rotate = r1@
+rotate :: Perm a => a -> a
 rotate = r1
 
 -- | @complement = s0@
+complement :: Perm a => a -> a
 complement = s0
 
 -- | @reverse = s1@
+reverse :: Perm a => a -> a
 reverse = s1
 
 -- | @inverse = s2@
+inverse :: Perm a => a -> a
 inverse = s2
diff --git a/sym.cabal b/sym.cabal
--- a/sym.cabal
+++ b/sym.cabal
@@ -1,12 +1,12 @@
 Name:                sym
-Version:             0.1
+Version:             0.1.1
 Synopsis:            Permutations, patterns, and statistics
 Description:         
   Definitions for permutations with an emphasis on permutation
   patterns and statistics.
   .
   ["Math.Sym"] Provides an efficient definition of standard
-  permutations (@StPerm@) together with a typeclass (@Perm@) whose
+  permutations, @StPerm@, together with a typeclass, @Perm@,  whose
   functionality is largely inherited from @StPerm@ using a group
   action and the standardization map.
   .
@@ -40,7 +40,7 @@
 
   Build-depends:       base >= 3 && < 5, random, vector
   
-  ghc-prof-options:    -auto-all -caf-all
+  ghc-prof-options:    -auto-all
   ghc-options:         -Wall -O2
   cc-options:          -Wall