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module InvariantSpec (main, spec) where
import Data.Functor.Invariant
import Test.Hspec
import Test.Hspec.QuickCheck (prop)
import Test.QuickCheck
main :: IO ()
main = hspec spec
data Proxy a = Proxy
-----
-- These test could probably be simplified by appealing to parametricity.
spec :: Spec
spec = do
describe "Invariant" . prop "satisfies the composition law" $
composition1 (Proxy :: Proxy Integer)
(Proxy :: Proxy Bool)
(Proxy :: Proxy [Bool])
describe "Invariant2" . prop "satisfies the composition law" $
composition2 (Proxy :: Proxy Integer)
(Proxy :: Proxy Bool)
(Proxy :: Proxy Integer)
(Proxy :: Proxy Bool)
(Proxy :: Proxy (Bool,Bool))
-----
composition1
:: (Eq (f c), Show (f c), Invariant f)
=> proxy b -> proxy c -> proxy (f a)
-> Fun b c -> Fun c b
-> Fun a b -> Fun b a
-> f a
-> Property
composition1
_ _ _
(Fun _ f) (Fun _ f')
(Fun _ g) (Fun _ g')
x =
(invmap f f' . invmap g g') x
=== invmap (f . g) (g' . f') x
composition2
:: (Eq (f c1 c2), Show (f c1 c2), Invariant2 f)
=> proxy b1 -> proxy c1 -> proxy b2 -> proxy c2 -> proxy (f a1 a2)
-> Fun b1 c1 -> Fun c1 b1 -> Fun b2 c2 -> Fun c2 b2
-> Fun a1 b1 -> Fun b1 a1 -> Fun a2 b2 -> Fun b2 a2
-> f a1 a2
-> Property
composition2
_ _ _ _ _
(Fun _ f1) (Fun _ f1') (Fun _ f2) (Fun _ f2')
(Fun _ g1) (Fun _ g1') (Fun _ g2) (Fun _ g2')
x =
(invmap2 f1 f1' f2 f2' . invmap2 g1 g1' g2 g2') x
=== invmap2 (f1 . g1) (g1' . f1') (f2 . g2) (g2' . f2') x
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