\section[GHC.Base]{Module @GHC.Base@}

simple lhs test

-- to be found Monad

Other Prelude modules are much easier with fewer complex dependencies.

\begin{code}
{- | The 'Functor' class is used for types that can be mapped over.
Instances of 'Functor' should satisfy the following laws:

> fmap id  ==  id
> fmap (f . g)  ==  fmap f . fmap g

The instances of 'Functor' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
satisfy these laws.
-}

class  Functor f  where
    fmap        :: (a -> b) -> f a -> f b

    -- | Replace all locations in the input with the same value.
    -- The default definition is @'fmap' . 'const'@, but this may be
    -- overridden with a more efficient version.
    (<$)        :: a -> f b -> f a
    (<$)        =  fmap . const

{- | The 'Monad' class defines the basic operations over a /monad/,
a concept from a branch of mathematics known as /category theory/.
From the perspective of a Haskell programmer, however, it is best to
think of a monad as an /abstract datatype/ of actions.
Haskell's @do@ expressions provide a convenient syntax for writing
monadic expressions.

Minimal complete definition: '>>=' and 'return'.

Instances of 'Monad' should satisfy the following laws:

> return a >>= k  ==  k a
> m >>= return  ==  m
> m >>= (\x -> k x >>= h)  ==  (m >>= k) >>= h

Instances of both 'Monad' and 'Functor' should additionally satisfy the law:

> fmap f xs  ==  xs >>= return . f

The instances of 'Monad' for lists, 'Data.Maybe.Maybe' and 'System.IO.IO'
defined in the "Prelude" satisfy these laws.
-}

class  Monad m  where
    -- | Sequentially compose two actions, passing any value produced
    -- by the first as an argument to the second.
    (>>=)       :: forall a b. m a -> (a -> m b) -> m b
    -- | Sequentially compose two actions, discarding any value produced
    -- by the first, like sequencing operators (such as the semicolon)
    -- in imperative languages.
    (>>)        :: forall a b. m a -> m b -> m b
        -- Explicit for-alls so that we know what order to
        -- give type arguments when desugaring

    -- | Inject a value into the monadic type.
    return      :: a -> m a
    -- | Fail with a message.  This operation is not part of the
    -- mathematical definition of a monad, but is invoked on pattern-match
    -- failure in a @do@ expression.
    fail        :: String -> m a

    {-# INLINE (>>) #-}
    m >> k      = m >>= \_ -> k
    fail s      = error s

instance Functor ((->) r) where
    fmap = (.)

instance Monad ((->) r) where
    return = const
    f >>= k = \ r -> k (f r) r

instance Functor ((,) a) where
    fmap f (x,y) = (x, f y)
\end{code}