diff --git a/free-category.cabal b/free-category.cabal
index f334502..5c4a11c 100644
--- a/free-category.cabal
+++ b/free-category.cabal
@@ -45,6 +45,32 @@ library
     -fwarn-deprecations
   default-language: Haskell2010
 
+test-suite test-cats
+  type:
+      exitcode-stdio-1.0
+  hs-source-dirs:
+      test
+  main-is:
+      Main.hs
+  other-modules:
+      Test.Queue
+  default-language: Haskell2010
+  build-depends:
+      base
+    , QuickCheck
+    , tasty-quickcheck
+    , tasty
+    , free-algebras
+
+    , free-category
+  ghc-options:
+    -Wall
+    -fwarn-incomplete-record-updates
+    -fwarn-incomplete-uni-patterns
+    -fno-ignore-asserts
+    -fwarn-deprecations
+  default-language: Haskell2010
+
 benchmark bench-cats
   hs-source-dirs:
       bench
diff --git a/test/Main.hs b/test/Main.hs
new file mode 100644
index 0000000..d76b3c7
--- /dev/null
+++ b/test/Main.hs
@@ -0,0 +1,15 @@
+module Main (main) where
+
+import           Test.Tasty
+
+import qualified Test.Queue
+
+main :: IO ()
+main = defaultMain tests
+
+tests :: TestTree
+tests =
+  testGroup "free-categories"
+    -- data structures
+  [ Test.Queue.tests
+  ]
diff --git a/test/Test/Queue.hs b/test/Test/Queue.hs
new file mode 100644
index 0000000..6b3e4d5
--- /dev/null
+++ b/test/Test/Queue.hs
@@ -0,0 +1,111 @@
+{-# LANGUAGE DataKinds           #-}
+{-# LANGUAGE FlexibleInstances   #-}
+{-# LANGUAGE GADTs               #-}
+{-# LANGUAGE KindSignatures      #-}
+{-# LANGUAGE PolyKinds           #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications    #-}
+
+module Test.Queue (tests) where
+
+import           Prelude hiding ((.), id)
+import           Text.Show.Functions ()
+
+import           Control.Category.Free.Internal
+
+import           Test.QuickCheck
+import           Test.Tasty (TestTree, testGroup)
+import           Test.Tasty.QuickCheck (testProperty)
+
+tests :: TestTree
+tests =
+  testGroup "Queue"
+  [ testProperty "cons"   prop_cons
+  , testProperty "uncons" prop_uncons
+  , testProperty "snoc"   prop_snoc
+  , testProperty "foldr"  (prop_foldr @Int)
+  , testProperty "foldr"  (prop_foldl @Int)
+  ]
+
+data K = K
+
+data Tr (a :: K) (b :: K) where
+    A :: Int -> Tr 'K 'K
+
+instance Eq (Tr 'K 'K) where
+    A i == A j = i == j
+
+instance Show (Tr a b) where
+    show (A i) = "A " ++ show i
+
+instance Arbitrary (Tr 'K 'K) where
+    arbitrary = A <$> arbitrary
+
+toList :: Queue Tr 'K 'K -> [Tr 'K 'K]
+toList q = case q of
+    ConsQ a@A{} as -> a : toList as
+    _              -> []
+
+
+fromList :: [Tr 'K 'K] -> Queue Tr 'K 'K
+fromList []              = NilQ
+fromList (a : as) = ConsQ a (fromList as)
+
+instance Arbitrary (Queue Tr 'K 'K) where
+    arbitrary = fromList <$> arbitrary
+    shrink q  = map fromList $ shrinkList (const []) (toList q)
+
+
+prop_uncons :: Queue Tr 'K 'K -> Bool
+prop_uncons q = case (q, toList q) of
+    (ConsQ a@A{} _, a' : _) -> a == a'
+    (NilQ, []) -> True
+    _          -> False
+
+
+prop_cons :: Tr 'K 'K -> Queue Tr 'K 'K -> Bool
+prop_cons a@A{} q = case cons a q of
+    ConsQ a'@A{} _ -> a' == a'
+    _              -> False
+
+
+prop_snoc :: Tr 'K 'K -> Queue Tr 'K 'K -> Bool
+prop_snoc a@A{} q = last (toList (q `snoc` a)) == a
+
+
+data TrA a (x :: K) (y :: K) where
+    TrA :: a -> TrA a 'K 'K
+
+instance Show a => Show (TrA a 'K 'K) where
+    show (TrA a) = "TrA " ++ show a
+
+instance Eq a => Eq (TrA a k k) where
+    TrA a == TrA b = a == b
+
+instance Arbitrary a => Arbitrary (TrA a 'K 'K) where
+    arbitrary = TrA <$> arbitrary
+    shrink (TrA a) = map TrA (shrink a)
+
+
+prop_foldr :: forall a.
+              Eq a
+           => (Int -> a -> a)
+           -> TrA a 'K 'K
+           -> Queue Tr 'K 'K
+           -> Bool
+prop_foldr f a q = foldrQ g a q == foldr g a (toList q)
+  where
+    g :: Tr y z-> TrA a x y -> TrA a x z
+    g (A i) (TrA j) = TrA (f i j)
+
+
+prop_foldl :: forall a.
+              Eq a
+           => (a -> Int -> a)
+           -> TrA a 'K 'K
+           -> Queue Tr 'K 'K
+           -> Bool
+prop_foldl f a q = foldlQ g a q == foldl g a (toList q)
+  where
+    g :: TrA a y z-> Tr x y -> TrA a x z
+    g (TrA j) (A i) = TrA (f j i)