Haskell Derivation Basics

Basics.hs

module Basics where

{-
1. What is Semigroup? Define the type class.

2. What is Monoid? Define the type class.

3. What is Functor? Define the type class.

4. What is Applicative? Define the type class.

5. What is Monad? Define the type class.

6. Define fmap in terms of bind.

7. Define bind in terms of fmap and join.

-}

BasicsAnswers.hs

module BasicsAnswers where

{- 1. Semigroup is a type class that defines a single function: 
  mappend (<>) 
-}

class Semigroup where
  (<>) :: a -> a -> a


{- 2. Monoid is a type class whose parent is Semigroup, but adds an additional function: 
  mempty 
-}

class Semigroup a => Monoid a where
  mempty :: a


{- 3. Functor is a type class without a parent, and defines two functions:
  fmap (<$>) 
  <$ 
-}

class Functor (f :: * -> *) where
  fmap :: (a -> b) -> f a -> fb
  <$ :: a -> f b -> f a


{- 4. Applicative is a type class whose parent is Functor, but adds an additional four functions: 
   applicative (<*>)
   pure
   *>
   <*
-}

class Functor f => Applicative (f :: * -> *) where
  pure :: a -> f a
  (<*>) :: f (a -> b) -> f a -> f b
  (*>) :: f a -> f b -> f b
  (<*) :: f a -> f b -> f a


{- 5. Monad is a type class whose parent is Applicative, but adds an additional four functions:
   return
   bind (>>=)
   sequence (>>)
   fail
-}

class Applicative m => Monad (m :: * -> *) where
  return :: a -> m a
  (>>=) :: (a -> m b) -> m a -> m b
  (>>) :: m a -> m b -> m b
  fail :: String -> m a

{- 6. Define fmap in terms of bind: -}

fmap' (a -> b) -> f a -> f b
fmap' f a = a >>= return . f

{- 7. Define bind in terms of fmap and join -}

(>>=) :: (a -> m b) -> m a -> m b
(>>=) f m = join $ f <$> m