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:             0.1.0.2
+version:             0.1.0.4
 synopsis:            Basic semiring class and instances
 description:         Adds a basic semiring class
 homepage:            https://github.com/oisdk/semiring-num
@@ -16,6 +16,7 @@
   hs-source-dirs:      src
   exposed-modules:     Data.Semiring
                      , Data.Semiring.Numeric
+                     , Data.Semiring.Free
                      , Test.Semiring
   build-depends:       base >= 4.9 && < 5
                      , containers >= 0.5
diff --git a/src/Data/Semiring.hs b/src/Data/Semiring.hs
--- a/src/Data/Semiring.hs
+++ b/src/Data/Semiring.hs
@@ -281,6 +281,8 @@
 instance Semiring Word16
 instance Semiring Word32
 instance Semiring Word64
+instance Semiring Float
+instance Semiring Double
 instance Semiring CUIntMax
 instance Semiring CIntMax
 instance Semiring CUIntPtr
diff --git a/src/Data/Semiring/Free.hs b/src/Data/Semiring/Free.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Semiring/Free.hs
@@ -0,0 +1,79 @@
+{-# LANGUAGE DeriveFoldable             #-}
+{-# LANGUAGE BangPatterns               #-}
+{-# LANGUAGE DeriveFunctor              #-}
+{-# LANGUAGE DeriveTraversable          #-}
+{-# LANGUAGE GeneralizedNewtypeDeriving #-}
+
+module Data.Semiring.Free
+  ( Free(..)
+  , liftFree
+  , unFree
+  ) where
+
+import           Control.Applicative (liftA2)
+
+import           Data.Coerce
+
+import           Data.Function (on)
+import           Data.List (sort)
+
+import           Data.Semiring
+import           Data.Ord (comparing)
+
+import qualified Data.Map.Strict as Map
+import           Data.Map.Strict (Map)
+
+import           Test.QuickCheck (Arbitrary(..))
+
+-- | The free semiring. Adapted from PureScript's version, available
+-- <https://pursuit.purescript.org/packages/purescript-semirings/3.0.0/docs/Data.Semiring.Free here>.
+-- Only a valid semiring if treated as a multiset, as in:
+--
+-- >>> Free [[1],[0]] == Free [[0],[1]]
+-- True
+newtype Free a = Free
+  { getFree :: [[a]]
+  } deriving (Show, Read, Functor, Foldable, Traversable, Monoid)
+
+instance Semiring (Free a) where
+  Free xs <+> Free ys = Free (xs ++ ys)
+  Free xs <.> Free ys = Free (liftA2 (++) xs ys)
+  one = Free [[]]
+  zero = Free []
+
+instance Applicative Free where
+  pure = Free . pure . pure
+  Free fs <*> Free xs = Free (liftA2 (<*>) fs xs)
+
+-- | Run a 'Free'.
+liftFree :: Semiring s => (a -> s) -> Free a -> s
+liftFree f = unFree . fmap f
+
+-- | Run a 'Free', interpreting it in the underlying semiring.
+unFree :: Semiring s => Free s -> s
+unFree = getAdd .# foldMap (Add .# getMul .# foldMap Mul) . getFree
+
+-- | Extremely slow. For testing purposes.
+instance Ord a => Eq (Free a) where
+  (==) = isAnagram `on` getFree
+
+instance Ord a => Ord (Free a) where
+  compare = comparing (sort . getFree)
+
+instance Arbitrary a => Arbitrary (Free a) where
+  arbitrary = Free <$> arbitrary
+
+infixr 9 .#
+(.#) :: Coercible b c => (b -> c) -> (a -> b) -> a -> c
+(.#) _ = coerce
+
+isAnagram :: Ord a => [a] -> [a] -> Bool
+isAnagram = go (Map.empty :: Map a Int) where
+  go !m (x:xs) (y:ys) =
+    go ( Map.alter (remZero . maybe (-1) pred) x
+       $ Map.alter (remZero . maybe 1    succ) y
+    m) xs ys
+  go !m [] [] = Map.null m
+  go _ _ _ = False
+  remZero 0 = Nothing
+  remZero n = Just n
diff --git a/test/Spec.hs b/test/Spec.hs
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -4,23 +4,27 @@
 
 import           Data.Proxy            (Proxy (..))
 import           Data.Semiring         (Add, Mul)
+import           Data.Semiring.Free
 import           Data.Semiring.Numeric
 import           Data.Set              (Set)
+import           Data.Word             (Word8)
 import           Test.DocTest
 import           Test.QuickCheck
 import           Test.Semiring
 
+
 main :: IO ()
 main = do
+  quickCheckWith (stdArgs { maxSuccess = 40, maxSize = 30} ) (semiringLaws (Proxy :: Proxy (Free Word8)))
   quickCheck (semiringLaws (Proxy :: Proxy Integer))
   quickCheck (semiringLaws (Proxy :: Proxy Bool))
   quickCheck (semiringLaws (Proxy :: Proxy (Add Integer)))
   quickCheck (semiringLaws (Proxy :: Proxy (Mul Integer)))
-  quickCheck (semiringLaws (Proxy :: Proxy (Set Ordering)))
   quickCheck (semiringLaws (Proxy :: Proxy (Integer,Integer)))
   quickCheck (semiringLaws (Proxy :: Proxy (Integer,Integer,Integer)))
   quickCheck (semiringLaws (Proxy :: Proxy (Integer,Integer,Integer,Integer)))
   quickCheck (semiringLaws (Proxy :: Proxy (Integer,Integer,Integer,Integer,Integer)))
+  quickCheck (semiringLaws (Proxy :: Proxy (Set (Add Word8)) ))
   quickCheck (semiringLaws (Proxy :: Proxy (Division Integer)))
   quickCheck (semiringLaws (Proxy :: Proxy (Bottleneck Int)))
   quickCheck (semiringLaws (Proxy :: Proxy (Łukasiewicz Integer)))
@@ -28,4 +32,5 @@
   doctest [ "-isrc"
           , "src/Data/Semiring.hs"
           , "src/Data/Semiring/Numeric.hs"
-          , "src/Test/Semiring.hs" ]
+          , "src/Test/Semiring.hs"
+          , "src/Data/Semiring/Free.hs" ]