    {-# LANGUAGE CPP #-}
    {-# LANGUAGE ScopedTypeVariables #-}

    #if HAVE_QUANTIFIED_CONSTRAINTS
    {-# LANGUAGE QuantifiedConstraints #-}
    #endif

    {-# OPTIONS_GHC -Wall #-}

    module Test.QuickCheck.Classes.Applicative
      (
    #if HAVE_UNARY_LAWS
        applicativeLaws
    #endif
      ) where

    import Control.Applicative
    import Test.QuickCheck hiding ((.&.))
    #if HAVE_UNARY_LAWS
    import Test.QuickCheck.Arbitrary (Arbitrary1(..))
    import Data.Functor.Classes (Eq1,Show1)
    #endif
    import Test.QuickCheck.Property (Property)

    import Test.QuickCheck.Classes.Internal

    #if HAVE_UNARY_LAWS

    -- | Tests the following applicative properties:
    --
    -- [/Identity/]
    --   @'pure' 'id' '<*>' v ≡ v@
    -- [/Composition/]
    --   @'pure' ('.') '<*>' u '<*>' v '<*>' w ≡ u '<*>' (v '<*>' w)@
    -- [/Homomorphism/]
    --   @'pure' f '<*>' 'pure' x ≡ 'pure' (f x)@
    -- [/Interchange/]
    --   @u '<*>' 'pure' y ≡ 'pure' ('$' y) '<*>' u@
    -- [/LiftA2 (1)/]
    --   @('<*>') ≡ 'liftA2' 'id'@
    applicativeLaws ::
    #if HAVE_QUANTIFIED_CONSTRAINTS
      (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a))
    #else
      (Applicative f, Eq1 f, Show1 f, Arbitrary1 f)
    #endif
      => proxy f -> Laws
    applicativeLaws :: forall (f :: * -> *) (proxy :: (* -> *) -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Laws
    applicativeLaws proxy f
    p = String -> [(String, Property)] -> Laws
    Laws String
    "Applicative"
      [ (String
    "Identity", proxy f -> Property
    forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeIdentity proxy f
    p)
      , (String
    "Composition", proxy f -> Property
    forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeComposition proxy f
    p)
      , (String
    "Homomorphism", proxy f -> Property
    forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a)) =>
    proxy f -> Property
    applicativeHomomorphism proxy f
    p)
      , (String
    "Interchange", proxy f -> Property
    forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeInterchange proxy f
    p)
      , (String
    "LiftA2 Part 1", proxy f -> Property
    forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeLiftA2_1 proxy f
    p)
        -- todo: liftA2 part 2, we need an equation of two variables for this
      ]

    applicativeIdentity :: forall proxy f.
    #if HAVE_QUANTIFIED_CONSTRAINTS
      (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a))
    #else
      (Applicative f, Eq1 f, Show1 f, Arbitrary1 f)
    #endif
      => proxy f -> Property
    applicativeIdentity :: forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeIdentity proxy f
    _ = (Apply f Integer -> Bool) -> Property
    forall prop. Testable prop => prop -> Property
    property ((Apply f Integer -> Bool) -> Property)
    -> (Apply f Integer -> Bool) -> Property
    forall a b. (a -> b) -> a -> b
    $ \(Apply (f Integer
    a :: f Integer)) -> f Integer -> f Integer -> Bool
    forall (f :: * -> *) a.
    (forall x. Eq x => Eq (f x), Eq a) =>
    f a -> f a -> Bool
    eq1 ((Integer -> Integer) -> f (Integer -> Integer)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Integer -> Integer
    forall a. a -> a
    id f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f Integer
    a) f Integer
    a

    applicativeComposition :: forall proxy f.
    #if HAVE_QUANTIFIED_CONSTRAINTS
      (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a))
    #else
      (Applicative f, Eq1 f, Show1 f, Arbitrary1 f)
    #endif
      => proxy f -> Property
    applicativeComposition :: forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeComposition proxy f
    _ = (Apply f QuadraticEquation
     -> Apply f QuadraticEquation -> Apply f Integer -> Bool)
    -> Property
    forall prop. Testable prop => prop -> Property
    property ((Apply f QuadraticEquation
      -> Apply f QuadraticEquation -> Apply f Integer -> Bool)
     -> Property)
    -> (Apply f QuadraticEquation
        -> Apply f QuadraticEquation -> Apply f Integer -> Bool)
    -> Property
    forall a b. (a -> b) -> a -> b
    $ \(Apply (f QuadraticEquation
    u' :: f QuadraticEquation)) (Apply (f QuadraticEquation
    v' :: f QuadraticEquation)) (Apply (f Integer
    w :: f Integer)) ->
      let u :: f (Integer -> Integer)
    u = (QuadraticEquation -> Integer -> Integer)
    -> f QuadraticEquation -> f (Integer -> Integer)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap QuadraticEquation -> Integer -> Integer
    runQuadraticEquation f QuadraticEquation
    u'
          v :: f (Integer -> Integer)
    v = (QuadraticEquation -> Integer -> Integer)
    -> f QuadraticEquation -> f (Integer -> Integer)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap QuadraticEquation -> Integer -> Integer
    runQuadraticEquation f QuadraticEquation
    v'
       in f Integer -> f Integer -> Bool
    forall (f :: * -> *) a.
    (forall x. Eq x => Eq (f x), Eq a) =>
    f a -> f a -> Bool
    eq1 (((Integer -> Integer)
     -> (Integer -> Integer) -> Integer -> Integer)
    -> f ((Integer -> Integer)
          -> (Integer -> Integer) -> Integer -> Integer)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Integer -> Integer) -> (Integer -> Integer) -> Integer -> Integer
    forall b c a. (b -> c) -> (a -> b) -> a -> c
    (.) f ((Integer -> Integer)
       -> (Integer -> Integer) -> Integer -> Integer)
    -> f (Integer -> Integer)
    -> f ((Integer -> Integer) -> Integer -> Integer)
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f (Integer -> Integer)
    u f ((Integer -> Integer) -> Integer -> Integer)
    -> f (Integer -> Integer) -> f (Integer -> Integer)
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f (Integer -> Integer)
    v f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f Integer
    w) (f (Integer -> Integer)
    u f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> (f (Integer -> Integer)
    v f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f Integer
    w))

    applicativeHomomorphism :: forall proxy f.
    #if HAVE_QUANTIFIED_CONSTRAINTS
      (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a))
    #else
      (Applicative f, Eq1 f, Show1 f)
    #endif
      => proxy f -> Property
    applicativeHomomorphism :: forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a)) =>
    proxy f -> Property
    applicativeHomomorphism proxy f
    _ = (QuadraticEquation -> Integer -> Bool) -> Property
    forall prop. Testable prop => prop -> Property
    property ((QuadraticEquation -> Integer -> Bool) -> Property)
    -> (QuadraticEquation -> Integer -> Bool) -> Property
    forall a b. (a -> b) -> a -> b
    $ \(QuadraticEquation
    e :: QuadraticEquation) (Integer
    a :: Integer) ->
      let f :: Integer -> Integer
    f = QuadraticEquation -> Integer -> Integer
    runQuadraticEquation QuadraticEquation
    e
       in f Integer -> f Integer -> Bool
    forall (f :: * -> *) a.
    (forall x. Eq x => Eq (f x), Eq a) =>
    f a -> f a -> Bool
    eq1 ((Integer -> Integer) -> f (Integer -> Integer)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Integer -> Integer
    f f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> Integer -> f Integer
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Integer
    a) (Integer -> f Integer
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure (Integer -> Integer
    f Integer
    a) :: f Integer)

    applicativeInterchange :: forall proxy f.
    #if HAVE_QUANTIFIED_CONSTRAINTS
      (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a))
    #else
      (Applicative f, Eq1 f, Show1 f, Arbitrary1 f)
    #endif
      => proxy f -> Property
    applicativeInterchange :: forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeInterchange proxy f
    _ = (Apply f QuadraticEquation -> Integer -> Bool) -> Property
    forall prop. Testable prop => prop -> Property
    property ((Apply f QuadraticEquation -> Integer -> Bool) -> Property)
    -> (Apply f QuadraticEquation -> Integer -> Bool) -> Property
    forall a b. (a -> b) -> a -> b
    $ \(Apply (f QuadraticEquation
    u' :: f QuadraticEquation)) (Integer
    y :: Integer) ->
      let u :: f (Integer -> Integer)
    u = (QuadraticEquation -> Integer -> Integer)
    -> f QuadraticEquation -> f (Integer -> Integer)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap QuadraticEquation -> Integer -> Integer
    runQuadraticEquation f QuadraticEquation
    u'
       in f Integer -> f Integer -> Bool
    forall (f :: * -> *) a.
    (forall x. Eq x => Eq (f x), Eq a) =>
    f a -> f a -> Bool
    eq1 (f (Integer -> Integer)
    u f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> Integer -> f Integer
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure Integer
    y) (((Integer -> Integer) -> Integer)
    -> f ((Integer -> Integer) -> Integer)
    forall a. a -> f a
    forall (f :: * -> *) a. Applicative f => a -> f a
    pure ((Integer -> Integer) -> Integer -> Integer
    forall a b. (a -> b) -> a -> b
    $ Integer
    y) f ((Integer -> Integer) -> Integer)
    -> f (Integer -> Integer) -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f (Integer -> Integer)
    u)

    applicativeLiftA2_1 :: forall proxy f.
    #if HAVE_QUANTIFIED_CONSTRAINTS
      (Applicative f, forall a. Eq a => Eq (f a), forall a. Show a => Show (f a), forall a. Arbitrary a => Arbitrary (f a))
    #else
      (Applicative f, Eq1 f, Show1 f, Arbitrary1 f)
    #endif
      => proxy f -> Property
    applicativeLiftA2_1 :: forall (proxy :: (* -> *) -> *) (f :: * -> *).
    (Applicative f, forall a. Eq a => Eq (f a),
     forall a. Show a => Show (f a),
     forall a. Arbitrary a => Arbitrary (f a)) =>
    proxy f -> Property
    applicativeLiftA2_1 proxy f
    _ = (Apply f QuadraticEquation -> Apply f Integer -> Bool) -> Property
    forall prop. Testable prop => prop -> Property
    property ((Apply f QuadraticEquation -> Apply f Integer -> Bool)
     -> Property)
    -> (Apply f QuadraticEquation -> Apply f Integer -> Bool)
    -> Property
    forall a b. (a -> b) -> a -> b
    $ \(Apply (f QuadraticEquation
    f' :: f QuadraticEquation)) (Apply (f Integer
    x :: f Integer)) ->
      let f :: f (Integer -> Integer)
    f = (QuadraticEquation -> Integer -> Integer)
    -> f QuadraticEquation -> f (Integer -> Integer)
    forall a b. (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
    fmap QuadraticEquation -> Integer -> Integer
    runQuadraticEquation f QuadraticEquation
    f'
       in f Integer -> f Integer -> Bool
    forall (f :: * -> *) a.
    (forall x. Eq x => Eq (f x), Eq a) =>
    f a -> f a -> Bool
    eq1 (((Integer -> Integer) -> Integer -> Integer)
    -> f (Integer -> Integer) -> f Integer -> f Integer
    forall a b c. (a -> b -> c) -> f a -> f b -> f c
    forall (f :: * -> *) a b c.
    Applicative f =>
    (a -> b -> c) -> f a -> f b -> f c
    liftA2 (Integer -> Integer) -> Integer -> Integer
    forall a. a -> a
    id f (Integer -> Integer)
    f f Integer
    x) (f (Integer -> Integer)
    f f (Integer -> Integer) -> f Integer -> f Integer
    forall a b. f (a -> b) -> f a -> f b
    forall (f :: * -> *) a b. Applicative f => f (a -> b) -> f a -> f b
    <*> f Integer
    x)

    #endif