diff --git a/src/Data/Semiring/Tropical.hs b/src/Data/Semiring/Tropical.hs
--- a/src/Data/Semiring/Tropical.hs
+++ b/src/Data/Semiring/Tropical.hs
@@ -7,13 +7,46 @@
 Stability    : experimental
 Portability  : Linux
 
-This file just contains the minimal definition of "tropical," meaning
-any tropical object has to be an ordered semiring.
+This is a module for Tropical numbers. If you don't know what those are, read
+<http://en.wikipedia.org/wiki/Tropical_geometry this Wikipedia entry>.
 
+Tropical numbers form a 'Semiring'. Semirings are like
+<https://en.wikipedia.org/wiki/Ring_(mathematics) normal rings>, but
+you can't subtract.
+
+The Tropical semiring, or 𝕋, is {ℝ ∪ {∞}, ⊕, ⊙}. Those are, in Haskell
+terms, 'Real', 'Infinity', '(.+.)', and '(.*.)', respectively.
+
+Tropical addition and multiplication are
+
+a ⊕ b = min {a, b}, ∀ a, b ∈ 𝕋
+
+a ⊙ b = a + b, ∀ a, b ∈ 𝕋
+
 -}
 
-module Data.Semiring.Tropical where
+module Data.Semiring.Tropical
+  (
+  -- * Tropical things
+  -- 
+  -- 
+    Tropical(..)
 
+  -- ** Tropical operations
+  , (.+.)
+  , (.*.)
+  , (./.)
+  , (.^.)
+
+  -- ** Helper Things
+  , Operator
+  , TropicalOperator
+  , zero
+  , one
+  )
+
+where
+
 import Data.Semiring
 
 -- |Tropical numbers are like real numbers, except zero is the same
@@ -22,8 +55,25 @@
                           | Infinity                    -- ^Infinity
   deriving (Eq, Ord, Show)
 
+-- |Helper type for binary operators  
 type Operator a = a -> a -> a
+-- |An operator over something tropical
+type TropicalOperator a = Operator (Tropical a) 
 
+-- | Some notes - 
+-- 
+-- Tropical addition is the same as taking the minimum. Because
+-- 
+-- min {a, ∞} = a, ∀ a ∈ ℝ
+-- 
+-- 'Infinity' is the additive identity, or 'zero', in Semiring terms. 
+-- 
+-- Tropical multiplication is the sum. Because 
+-- 
+-- a + 0 = 0, ∀ a ∈ ℝ
+-- 
+-- @Tropical 0@ is the multiplicative identity, or 'one' in Semiring
+-- terms.
 instance Real a => Semiring (Tropical a) where
   -- |Tropical addition is the same as taking the minimum
   a .+. b = min a b
@@ -39,15 +89,15 @@
 
 -- |Tropical division. Remember, if Infinity is tropical zero, then
 -- you can't divide by it!
-(./.) :: Real a => Operator (Tropical a)
+(./.) :: Real a => TropicalOperator a
 _ ./. Infinity          = undefined
 Infinity ./. _          = Infinity
 a ./. b                 = Tropical $ (realValue a) - (realValue b)
 
--- -- |Tropical exponentiation - same as classical multiplication. A
--- -- mildly interesting correlary is that tropical exponentiation is
--- -- commutative. That is, y .^. x = x .^. y, for x and y tropical.
-(.^.) :: Real a => Operator (Tropical a)
+-- |Tropical exponentiation - same as classical multiplication. A
+-- mildly interesting correlary is that tropical exponentiation is
+-- commutative. That is, y .^. x = x .^. y, for x and y tropical.
+(.^.) :: Real a => TropicalOperator a
 a .^. b
   | Infinity==a || Infinity==b  = Infinity
   | otherwise                   = Tropical $ (realValue a) * (realValue b)
diff --git a/tropical.cabal b/tropical.cabal
--- a/tropical.cabal
+++ b/tropical.cabal
@@ -2,7 +2,7 @@
 -- documentation, see http://haskell.org/cabal/users-guide/
 
 name:                 tropical
-version:              0.0.0.1
+version:              0.0.0.2
 synopsis:             A library for tropical mathematics.
 description:
   Tropical numbers are the same as real numbers, except the operations are