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module TraversableScratch where
import qualified Data.Foldable as F
import Test.QuickCheck
newtype Identity a = Identity a
deriving (Eq, Ord, Show)
instance Functor Identity where
fmap f (Identity x) = Identity (f x)
instance Foldable Identity where
foldMap f (Identity x) = f x
instance Traversable Identity where
traverse f (Identity x) = Identity <$> f x
--------------------------------------------------------------------------------
data Optional a
= Nada
| Some a
deriving (Eq, Show)
instance Functor Optional where
fmap f Nada = Nada
fmap f (Some x) = Some (f x)
instance Foldable Optional where
foldMap f Nada = mempty
foldMap f (Some x) = f x
instance Traversable Optional where
traverse f Nada = pure Nada
traverse f (Some x) = Some <$> f x
--------------------------------------------------------------------------------
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
foldMap f Nil = mempty
foldMap f (Cons x xs) = mappend (f x) (foldMap f xs)
instance Traversable List where
sequenceA Nil = pure Nil
sequenceA (Cons x xs) = Cons <$> x <*> sequenceA xs
--------------------------------------------------------------------------------
data Three a b c = Three a b c
deriving (Eq, Show)
instance Functor (Three a b) where
fmap f (Three x y z) = Three x y (f z)
instance Foldable (Three a b) where
foldMap f (Three _ _ z) = f z
instance Traversable (Three a b) where
sequenceA (Three x y z) = (\z' -> Three x y z') <$> z
--------------------------------------------------------------------------------
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
foldMap f (Pair x y) = f y
instance Traversable (Pair a) where
sequenceA (Pair x y) = (\y' -> Pair x y') <$> y
--------------------------------------------------------------------------------
data Big a b = Big a b b
deriving (Eq, Show)
instance Functor (Big a) where
fmap f (Big x y z) = Big x (f y) (f z)
instance Foldable (Big a) where
foldMap f (Big x y z) = f y <> f z
instance Traversable (Big a) where
sequenceA (Big x y z) = (\y' z' -> Big x y' z') <$> y <*> z
--------------------------------------------------------------------------------
data Bigger a b = Bigger a b b b
deriving (Eq, Show)
instance Functor (Bigger a) where
fmap f (Bigger w x y z) = Bigger w (f x) (f y) (f z)
instance Foldable (Bigger a) where
foldMap f (Bigger w x y z) = f x <> f y <> f z
instance Traversable (Bigger a) where
sequenceA (Bigger w x y z) = (\x' y' z' -> Bigger w x' y' z') <$> x <*> y <*> z
--------------------------------------------------------------------------------
data Tree a
= Empty
| Leaf a
| Node (Tree a) a (Tree a)
deriving (Eq, Show)
instance Functor Tree where
fmap f Empty = Empty
fmap f (Leaf x) = Leaf (f x)
fmap f (Node lhs x rhs) = Node (fmap f lhs) (f x) (fmap f rhs)
instance Foldable Tree where
foldMap f Empty = mempty
foldMap f (Leaf x) = f x
foldMap f (Node lhs x rhs) = (foldMap f lhs) <> (f x) <> (foldMap f rhs)
instance Traversable Tree where
sequenceA Empty = pure Empty
sequenceA (Leaf x) = Leaf <$> x
sequenceA (Node lhs x rhs) = Node <$> sequenceA lhs <*> x <*> sequenceA rhs
|
