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:             0.1.0.4
+version:             0.1.0.5
 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
@@ -126,6 +126,20 @@
   zero = Set.empty
   one = Set.singleton mempty
 
+-- | A polynomial in /x/ can be defined as a list of its coefficients,
+-- where the /i/th element is the coefficient of /x^i/. This is the
+-- semiring for such a list. Adapted from <https://pdfs.semanticscholar.org/702d/348c32133997e992db362a19697d5607ab32.pdf here>.
+instance Semiring a => Semiring [a] where
+  one = [one]
+  zero = []
+  [] <+> ys = ys
+  xs <+> [] = xs
+  (x:xs) <+> (y:ys) = (x <+> y) : (xs <+> ys)
+  [] <.> _ = []
+  _ <.> [] = []
+  (x:xs) <.> (y:ys) =
+    (x <.> y) : (map (x <.>) ys <+> map (<.> y) xs <+> (xs <.> ys))
+
 ------------------------------------------------------------------------
 -- Addition and multiplication newtypes
 ------------------------------------------------------------------------
diff --git a/test/Spec.hs b/test/Spec.hs
--- a/test/Spec.hs
+++ b/test/Spec.hs
@@ -12,10 +12,13 @@
 import           Test.QuickCheck
 import           Test.Semiring
 
+smallCheck :: Testable prop => prop -> IO ()
+smallCheck = quickCheckWith (stdArgs { maxSuccess = 40, maxSize = 30})
 
 main :: IO ()
 main = do
-  quickCheckWith (stdArgs { maxSuccess = 40, maxSize = 30} ) (semiringLaws (Proxy :: Proxy (Free Word8)))
+  smallCheck (semiringLaws (Proxy :: Proxy (Free Word8)))
+  quickCheck (semiringLaws (Proxy :: Proxy [Integer]))
   quickCheck (semiringLaws (Proxy :: Proxy Integer))
   quickCheck (semiringLaws (Proxy :: Proxy Bool))
   quickCheck (semiringLaws (Proxy :: Proxy (Add Integer)))