diff --git a/Setup.hs b/Setup.hs
deleted file mode 100644
--- a/Setup.hs
+++ /dev/null
@@ -1,2 +0,0 @@
-import Distribution.Simple
-main = defaultMain
diff --git a/poly-arity.cabal b/poly-arity.cabal
--- a/poly-arity.cabal
+++ b/poly-arity.cabal
@@ -1,5 +1,5 @@
 Name:                   poly-arity
-Version:                0.0.4.1
+Version:                0.0.5
 Author:                 Athan Clark <athan.clark@gmail.com>
 Maintainer:             Athan Clark <athan.clark@gmail.com>
 License:                BSD3
@@ -8,6 +8,7 @@
 -- Description:
 Cabal-Version:          >= 1.10
 Build-Type:             Simple
+Category:               Data, Functions
 
 Library
   Default-Language:     Haskell2010
diff --git a/src/Data/Function/Poly.hs b/src/Data/Function/Poly.hs
--- a/src/Data/Function/Poly.hs
+++ b/src/Data/Function/Poly.hs
@@ -17,19 +17,33 @@
 import Data.Constraint
 import Data.HList
 
+-- | Provide a type-level list of /types/ @xs@, and a final result type @r@,
+-- construct a chain of arrows @->@ / n-ary function (which is right-associative)
+-- of each type in @xs@, ending in @r@.
 type family TypeListToArity (xs :: [*]) (r :: *) :: * where
   TypeListToArity '[] r = r -- basis
   TypeListToArity (x ': xs) r = x -> TypeListToArity xs r
 
+-- | The inverse of @TypeListToArity@.
+type family ArityToTypeList (r :: *) :: [*] where
+  ArityToTypeList (x -> r) = x ': ArityToTypeList r
+  ArityToTypeList r = '[]
+
+-- | Trim an n-ary function / chain of arrows @->@ with a type-level list of
+-- types @xs@, where each element of @xs@ __must__ unify with each element of
+-- the cons-list made with @->@.
 type family ArityMinusTypeList (r :: *) (xs :: [*]) :: * where
   ArityMinusTypeList r '[] = r -- basis
   ArityMinusTypeList (x -> r) (x ': xs) = ArityMinusTypeList r xs
 
-
+-- | Inductively constrain a function's initial arity to match a type list;
+-- as a read-only style of static arity assurance.
 type family ExpectArity (xs :: [*]) (f :: *) :: Constraint where
   ExpectArity '[] f = () -- basis
   ExpectArity (x ': xs) (x -> remainder) = ExpectArity xs remainder
 
+-- | Duplicate of <http://hackage.haskell.org/package/singletons-1.1.2.1/docs/Data-Promotion-Prelude-List.html#g:1 singletons>
+-- @Head@ function for kind-polymorphic type-level lists.
 type family Head (xs :: [k]) :: k where
   Head (x ': xs) = x
 
@@ -37,7 +51,10 @@
   Tail (x ': xs) = xs
 
 
+-- | Lift the @HList@'s internal type-level list of types to a constraint context.
 class ExpectArity xs f => ConsumeArity (xs :: [*]) (f :: *) result | xs f -> result where
+  -- | Use a /heterogeneously-typed/ list of values as input to an n-ary function,
+  -- where types must unify statically.
   appN :: f -> HList xs -> result
 
 instance ConsumeArity '[] r r where
@@ -48,6 +65,7 @@
   appN f (HCons x xs) = appN (f x) xs
 
 
+-- | Shows that an n-ary function @f@ /precisely/ ends with @r@.
 type family HasResult (f :: *) (r :: *) :: Constraint where
   HasResult r r = ()
   HasResult (x -> r') r = HasResult r' r