module Exercises where

import Test.QuickCheck
import Test.QuickCheck.Checkers

--- 1
data Pair a = Pair a a deriving (Show, Eq)

instance Functor Pair where
    fmap f (Pair x y) = Pair (f x) (f y)

instance Applicative Pair where
    pure f = Pair f f
    (Pair f f') <*> (Pair x y) = Pair (f x) (f' y)

instance Arbitrary a => Arbitrary (Pair a) where
    arbitrary = do
        x <- arbitrary
        y <- arbitrary
        return $ Pair x y

instance Eq a => EqProp (Pair a) where
    (=-=) = eq

--- 2
data Two a b  = Two a b deriving (Show, Eq)

instance Functor (Two a) where
    fmap f (Two x y) = Two x (f y)

instance Monoid a => Applicative (Two a) where
    pure x = Two mempty $ x
    (Two f f') <*> (Two x y) = Two (mappend f x) (f' y)

instance (Arbitrary a, Arbitrary b) => Arbitrary (Two a b) where
    arbitrary = do
        x <- arbitrary
        y <- arbitrary
        return $ Two x y

instance (Eq a, Eq b) => EqProp (Two a b) where
    (=-=) = eq

--- 3
data Three a b c  = Three a b c deriving (Show, Eq)

instance Functor (Three a b) where
    fmap f (Three x y z) = Three x y (f z)

instance (Monoid a, Monoid b) => Applicative (Three a b) where
    pure x = Three mempty mempty x
    (Three f f' f'') <*> (Three x y z) = Three (mappend f x) (mappend f' y) (f'' z)

instance (Arbitrary a, Arbitrary b, Arbitrary c) => Arbitrary (Three a b c) where
    arbitrary = do
        x <- arbitrary
        y <- arbitrary
        z <- arbitrary
        return $ Three x y z

instance (Eq a, Eq b, Eq c) => EqProp (Three a b c) where
    (=-=) = eq

--- 4
data Three' a b = Three' a b b deriving (Show, Eq)

instance Functor (Three' a) where
    fmap f (Three' x y z) = Three' x (f y) (f z)

instance (Monoid a) => Applicative (Three' a) where
    pure x = Three' mempty x x
    (Three' f f' f'') <*> (Three' x y z) = Three' (mappend f x) (f' y) (f'' z)

instance (Arbitrary a, Arbitrary b) => Arbitrary (Three' a b) where
    arbitrary = do
        x <- arbitrary
        y <- arbitrary
        z <- arbitrary
        return $ Three' x y z

instance (Eq a, Eq b) => EqProp (Three' a b) where
    (=-=) = eq

--- 5
data Four a b c d = Four a b c d deriving (Show, Eq)

instance Functor (Four a b c) where
    fmap f (Four x y z t) = Four x y z (f t)

instance (Monoid a, Monoid b, Monoid c) => Applicative (Four a b c) where
    pure x = Four mempty mempty mempty x
    (Four f f' f'' f''') <*> (Four x y z t) = Four (mappend f x) (mappend f' y) (mappend f'' z) (f''' t)

instance (Arbitrary a, Arbitrary b, Arbitrary c, Arbitrary d) => Arbitrary (Four a b c d) where
    arbitrary = do
        x <- arbitrary
        y <- arbitrary
        z <- arbitrary
        t <- arbitrary
        return $ Four x y z t

instance (Eq a, Eq b, Eq c, Eq d) => EqProp (Four a b c d) where
    (=-=) = eq

--- 5
data Four' a b = Four' a a a b deriving (Show, Eq)

instance Functor (Four' a) where
    fmap f (Four' x y z t) = Four' x y z (f t)

instance (Monoid a) => Applicative (Four' a) where
    pure x = Four' mempty mempty mempty x
    (Four' f f' f'' f''') <*> (Four' x y z t) = Four' (mappend f x) (mappend f' y) (mappend f'' z) (f''' t)

instance (Arbitrary a, Arbitrary b) => Arbitrary (Four' a b) where
    arbitrary = do
        x <- arbitrary
        y <- arbitrary
        z <- arbitrary
        t <- arbitrary
        return $ Four' x y z t

instance (Eq a, Eq b) => EqProp (Four' a b) where
    (=-=) = eq