diff --git a/semiring-num.cabal b/semiring-num.cabal
--- a/semiring-num.cabal
+++ b/semiring-num.cabal
@@ -1,5 +1,5 @@
 name:                semiring-num
-version:             0.4.0.0
+version:             0.5.0.0
 synopsis:            Basic semiring class and instances
 description:         Adds a basic semiring class
 homepage:            https://github.com/oisdk/semiring-num
diff --git a/src/Data/Semiring.hs b/src/Data/Semiring.hs
--- a/src/Data/Semiring.hs
+++ b/src/Data/Semiring.hs
@@ -15,6 +15,8 @@
   ( Semiring(..)
   , Add(..)
   , Mul(..)
+  , Max(..)
+  , Min(..)
   ) where
 
 
@@ -44,7 +46,6 @@
                                         CTcflag, CUid, Fd)
 
 import           Data.Monoid
-import           Data.Semigroup        (Max(..), Min(..))
 
 import           Control.Applicative   (liftA2)
 import           Data.Coerce           (coerce)
@@ -222,29 +223,74 @@
 -- Ord wrappers
 ------------------------------------------------------------------------
 
+
 -- | The "<https://ncatlab.org/nlab/show/tropical+semiring Tropical>" or
 -- min-plus semiring. It is a semiring where:
 -- @'<+>'  = 'min'@
--- @'zero' = -∞@ (represented by 'minBound')
+-- @'zero' = -∞@ (represented by 'Nothing')
 -- @'<.>'  = '<+>'@ (over the inner value)
 -- @'one'  = 'zero'@ (over the inner value)
-instance (Semiring a, Ord a, Bounded a) => Semiring (Min a) where
-  (<+>) = mappend
-  zero = mempty
-  (<.>) = (coerce :: WrapBinary Min a) (<+>)
-  one = Min zero
+newtype Min a = Min
+  { getMin :: Maybe a
+  } deriving (Eq, Ord, Read, Show, Generic, Generic1, Functor
+             ,Foldable)
 
 -- | The "<https://ncatlab.org/nlab/show/https://ncatlab.org/nlab/show/max-plus+algebra Arctic>"
 -- or max-plus semiring. It is a semiring where:
 -- @'<+>'  = 'max'@
--- @'zero' = ∞@ (represented by 'maxBound')
+-- @'zero' = ∞@ (represented by 'Nothing')
 -- @'<.>'  = '<+>'@ (over the inner value)
 -- @'one'  = 'zero'@ (over the inner value)
-instance (Semiring a, Ord a, Bounded a) => Semiring (Max a) where
+newtype Max a = Max
+  { getMax :: Maybe a
+  } deriving (Eq, Ord, Read, Show, Generic, Generic1, Functor
+             ,Foldable)
+
+instance Applicative Max where
+  pure = (coerce :: (a -> Maybe a) -> (a -> Max a)) Just
+  (<*>) = (coerce :: (Maybe (a -> b) -> Maybe a -> Maybe b)
+                  ->  Max   (a -> b) -> Max   a -> Max   b
+          ) (<*>)
+
+instance Applicative Min where
+  pure = (coerce :: (a -> Maybe a) -> (a -> Min a)) Just
+  (<*>) = (coerce :: (Maybe (a -> b) -> Maybe a -> Maybe b)
+                  ->  Min   (a -> b) -> Min   a -> Min   b
+          ) (<*>)
+
+instance Monad Max where
+  (>>=) = (coerce :: (Maybe a -> (a -> Maybe b) -> Maybe b)
+                  ->  Max   a -> (a -> Max   b) -> Max   b
+          ) (>>=)
+
+instance Monad Min where
+  (>>=) = (coerce :: (Maybe a -> (a -> Maybe b) -> Maybe b)
+                  ->  Min   a -> (a -> Min   b) -> Min   b
+          ) (>>=)
+
+instance Ord a => Monoid (Max a) where
+  mempty = Max Nothing
+  Max Nothing `mappend` x = x
+  x `mappend` Max Nothing = x
+  Max (Just x) `mappend` Max (Just y) = (Max . Just) (min x y)
+
+instance Ord a => Monoid (Min a) where
+  mempty = Min Nothing
+  Min Nothing `mappend` x = x
+  x `mappend` Min Nothing = x
+  Min (Just x) `mappend` Min (Just y) = (Min . Just) (min x y)
+
+instance (Semiring a, Ord a) => Semiring (Max a) where
   (<+>) = mappend
   zero = mempty
-  (<.>) = (coerce :: WrapBinary Max a) (<+>)
-  one = Max zero
+  (<.>) = liftA2 (<+>)
+  one = Max (Just zero)
+
+instance (Semiring a, Ord a) => Semiring (Min a) where
+  (<+>) = mappend
+  zero = mempty
+  (<.>) = liftA2 (<+>)
+  one = Min (Just zero)
 
 ------------------------------------------------------------------------
 -- (->) instance
diff --git a/test/Spec.hs b/test/Spec.hs
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -14,7 +14,6 @@
 import qualified Data.IntMap.Strict     as IntMap
 import qualified Data.Map.Strict        as Map
 import           Data.Monoid
-import           Data.Semigroup         (Max (..), Min (..))
 import           Data.Semiring
 import           Data.Semiring.Free
 import           Data.Semiring.Numeric
@@ -90,14 +89,14 @@
   smallCheck 3 (ternLawsOn Set.fromList :: TernaryLaws [[Word2]])
 
   putStrLn "Min Integer"
-  smallCheck 1000 (unLawsOn   Min :: UnaryLaws   Word2)
-  smallCheck 100  (binLawsOn  Min :: BinaryLaws  Word2)
-  smallCheck 10   (ternLawsOn Min :: TernaryLaws Word2)
+  smallCheck 1000 (unLawsOn   Min :: UnaryLaws   (Maybe Integer))
+  smallCheck 100  (binLawsOn  Min :: BinaryLaws  (Maybe Integer))
+  smallCheck 10   (ternLawsOn Min :: TernaryLaws (Maybe Integer))
 
   putStrLn "Max Integer"
-  smallCheck 1000 (unLawsOn   Max :: UnaryLaws   Word2)
-  smallCheck 100  (binLawsOn  Max :: BinaryLaws  Word2)
-  smallCheck 10   (ternLawsOn Max :: TernaryLaws Word2)
+  smallCheck 1000 (unLawsOn   Max :: UnaryLaws   (Maybe Integer))
+  smallCheck 100  (binLawsOn  Max :: BinaryLaws  (Maybe Integer))
+  smallCheck 10   (ternLawsOn Max :: TernaryLaws (Maybe Integer))
 
   putStrLn "Free Word2"
   smallCheck 4 (unLawsOn   Free :: UnaryLaws   [[Word2]])