module Lib where

import Data.Monoid
import Data.Traversable
import Test.QuickCheck
import Test.QuickCheck.Checkers

--
-- Identity
--
newtype Identity a = Identity a
    deriving (Eq, Ord, Show)

instance Functor Identity where
    fmap f (Identity x) = Identity $ f x

instance Applicative Identity where
    pure = Identity
    (Identity f) <*> x = fmap f x

instance Foldable Identity where
    foldr f acc (Identity x) = f x acc

instance Arbitrary a => Arbitrary (Identity a) where
    arbitrary = fmap Identity $ arbitrary

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

instance Traversable Identity where
    traverse f (Identity x) = Identity <$> f x

--
-- Constant
--
newtype Constant a b = Constant { getConstant :: a }
    deriving (Eq, Ord, Show)

instance Functor (Constant a) where
    fmap _ (Constant x) = Constant x

instance Monoid a => Applicative (Constant a) where
    pure _ = Constant mempty
    (Constant x) <*> (Constant y) = Constant $ mappend x y

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

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

instance Foldable (Constant a) where
    foldMap _ (Constant _) = mempty

instance Traversable (Constant a) where
    traverse f (Constant x) = pure $ Constant x

--
-- Maybe
--
data Optional a = Nada | Yep a deriving (Show, Eq, Ord)

instance Monoid a => Monoid (Optional a) where
    mempty = Nada
    mappend Nada _ = Nada
    mappend _ Nada = Nada
    mappend (Yep x) (Yep y) = Yep $ mappend x y

instance Applicative Optional where
    pure = Yep
    (Yep f) <*> (Yep x) = Yep $ f x
    Nada <*> (Yep x) = Nada
    _ <*> Nada = Nada

instance Functor Optional where
    fmap _ Nada = Nada
    fmap f (Yep x) = Yep $ f x

instance Foldable Optional where
    foldr f acc Nada = acc
    foldr f acc (Yep x) = f x acc

instance Traversable Optional where
    traverse f Nada = pure Nada
    traverse f (Yep x) = Yep <$> f x

instance (CoArbitrary a, Arbitrary a) => Arbitrary (Optional a) where
    arbitrary = do
        x <- arbitrary
        frequency [ (1, return Nada)
                  , (2, return $ Yep x)
                  ]

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

--
-- List
--
data List a = Nil | Cons a (List a) deriving (Eq, Show)

instance Functor List where
    fmap _ Nil = Nil
    fmap f (Cons x xs) = Cons (f x) (fmap f xs)

instance Foldable List where
    foldr _ acc Nil = acc
    foldr f acc (Cons x xs) = f x (foldr f acc xs)

instance Traversable List where
    sequenceA Nil = pure Nil
    sequenceA (Cons x xs) = Cons <$> x <*> (sequenceA xs)

instance Arbitrary a => Arbitrary (List a) where
    arbitrary = sized go
        where go 0 = pure Nil
              go n = do
                  xs <- go (n - 1)
                  x <- arbitrary
                  return $ Cons x xs

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

--
-- Three
--
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 Foldable (Three a b) where
    foldr f acc (Three x y z) = (f z acc)

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

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

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

instance Foldable (Pair a) where
    foldr f acc (Pair x y) = (f y acc)

instance Traversable (Pair a) where
    traverse f (Pair x y) = fmap (Pair x) (f y)

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

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

--
-- Big
--
data Big a b = Big a b b deriving (Eq, Show)

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

instance Foldable (Big a) where
    foldr f acc (Big _ y z) = (f y (f z acc)) 

instance Traversable (Big a) where
    traverse f (Big x y z) = (Big x) <$> (f y) <*> (f z)

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

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

--
-- Bigger
--
data Bigger a b = Bigger a b b b deriving (Eq, Show)

instance Functor (Bigger a) where
    fmap f (Bigger x y z t) = Bigger x (f y) (f z) (f t)

instance Foldable (Bigger a) where
    foldr f acc (Bigger _ y z t) = f y $ f z $ f t acc

instance Traversable (Bigger a) where
    traverse f (Bigger x y z t) = (Bigger x) <$> (f y) <*> (f z) <*> (f t)

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

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