IdentityT transformer

Haskell Excercises & Code/Chapter25 - Composing Types/transformers.hs

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+module MonadT where
+
+newtype Identity a =
+    Identity { runIdentity :: a }
+    deriving (Eq, Show)
+
+-- newtype IdentityN a = IdentityN a deriving (Eq, Show)
+
+-- Monad Transformer
+-- The identity monad transformer, what changed here is that we added one extra type argument
+newtype IdentityT f a =
+    IdentityT { runIdentityT :: f a }
+    deriving (Eq, Show)
+
+instance Functor Identity where 
+    fmap f (Identity a) = Identity (f a)
+
+instance (Functor m) => Functor (IdentityT m) where
+    fmap f (IdentityT fa) = IdentityT (fmap f fa)
+
+instance Applicative Identity where
+    pure = Identity
+    (Identity f) <*> (Identity a) = Identity (f a)
+
+instance (Applicative m) => Applicative (IdentityT m) where
+    pure x = IdentityT (pure x)
+    (IdentityT fab) <*> (IdentityT fa) = IdentityT (fab <*> fa)
+
+instance Monad Identity where
+    return = pure
+    (Identity a) >>= f = f a
+
+instance (Monad m) => Monad (IdentityT m) where
+    return = pure
+    (IdentityT ma) >>= f = IdentityT $ ma >>= runIdentityT . f
+-- breakdown the types
+--f :: a -> m b
+-- ma :: Monadic a
+-- runIdentityT :: IdentityT m a -> m a
+-- f :: a -> f a