-----------------------------------------------------------------------------
-- |
-- Module      :  Control.Monad
-- Copyright   :  (c) The University of Glasgow 2001
-- License     :  BSD-style (see the file libraries/base/LICENSE)
-- 
-- Maintainer  :  libraries@haskell.org
-- Stability   :  provisional
-- Portability :  portable
--
-- The 'Functor', 'Monad' and 'MonadPlus' classes,
-- with some useful operations on monads.

module Control.Monad
    (
    -- * Functor and monad classes

      Functor(fmap)
    , Monad((>>=), (>>), return, fail)

    , MonadPlus (   -- class context: Monad
          mzero     -- :: (MonadPlus m) => m a
        , mplus     -- :: (MonadPlus m) => m a -> m a -> m a
        )
    -- * Functions

    -- ** Naming conventions
    -- $naming

    -- ** Basic functions from the "Prelude"

    , mapM          -- :: (Monad m) => (a -> m b) -> [a] -> m [b]
    , mapM_         -- :: (Monad m) => (a -> m b) -> [a] -> m ()
    , sequence      -- :: (Monad m) => [m a] -> m [a]
    , sequence_     -- :: (Monad m) => [m a] -> m ()
    , (=<<)         -- :: (Monad m) => (a -> m b) -> m a -> m b

    -- ** Generalisations of list functions

    , join          -- :: (Monad m) => m (m a) -> m a
    , msum          -- :: (MonadPlus m) => [m a] -> m a
    , filterM       -- :: (Monad m) => (a -> m Bool) -> [a] -> m [a]
    , mapAndUnzipM  -- :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
    , zipWithM      -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
    , zipWithM_     -- :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
    , foldM         -- :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a 
    , foldM_        -- :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m ()
    , replicateM    -- :: (Monad m) => Int -> m a -> m [a]
    , replicateM_   -- :: (Monad m) => Int -> m a -> m ()

    -- ** Conditional execution of monadic expressions

    , guard         -- :: (MonadPlus m) => Bool -> m ()
    , when          -- :: (Monad m) => Bool -> m () -> m ()
    , unless        -- :: (Monad m) => Bool -> m () -> m ()

    -- ** Monadic lifting operators
    -- $lifting

    , liftM         -- :: (Monad m) => (a -> b) -> (m a -> m b)
    , liftM2        -- :: (Monad m) => (a -> b -> c) -> (m a -> m b -> m c)
    , liftM3        -- :: ...
    , liftM4        -- :: ...
    , liftM5        -- :: ...

    , ap            -- :: (Monad m) => m (a -> b) -> m a -> m b

    ) where

import Data.Maybe

-- -----------------------------------------------------------------------------
-- |The MonadPlus class definition

class Monad m => MonadPlus m where
   mzero :: m a
   mplus :: m a -> m a -> m a

instance MonadPlus [] where
   mzero = []
   mplus = (++)

instance MonadPlus Maybe where
   mzero = Nothing

   Nothing `mplus` ys  = ys
   xs      `mplus` _ys = xs

-- -----------------------------------------------------------------------------
-- Functions mandated by the Prelude

guard           :: (MonadPlus m) => Bool -> m ()
guard True      =  return ()
guard False     =  mzero

-- This subsumes the list-based filter function.

filterM          :: (Monad m) => (a -> m Bool) -> [a] -> m [a]
filterM _ []     =  return []
filterM p (x:xs) =  do
   flg <- p x
   ys  <- filterM p xs
   return (if flg then x:ys else ys)

-- This subsumes the list-based concat function.

msum        :: MonadPlus m => [m a] -> m a

msum        =  foldr mplus mzero

-- -----------------------------------------------------------------------------
-- Other monad functions

-- | The 'join' function is the conventional monad join operator. It is used to
-- remove one level of monadic structure, projecting its bound argument into the
-- outer level.
join              :: (Monad m) => m (m a) -> m a
join x            =  x >>= id

-- | The 'mapAndUnzipM' function maps its first argument over a list, returning
-- the result as a pair of lists. This function is mainly used with complicated
-- data structures or a state-transforming monad.
mapAndUnzipM      :: (Monad m) => (a -> m (b,c)) -> [a] -> m ([b], [c])
mapAndUnzipM f xs =  sequence (map f xs) >>= return . unzip

-- | The 'zipWithM' function generalises 'zipWith' to arbitrary monads.
zipWithM          :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m [c]
zipWithM f xs ys  =  sequence (zipWith f xs ys)

-- | 'zipWithM_' is the extension of 'zipWithM' which ignores the final result.
zipWithM_         :: (Monad m) => (a -> b -> m c) -> [a] -> [b] -> m ()
zipWithM_ f xs ys =  sequence_ (zipWith f xs ys)

encapsulated in a monad. Note that 'foldM' works from left-to-right over
the list arguments. This could be an issue where '(>>)' and the `folded
function' are not commutative.

>	foldM f a1 [x1, x2, ..., xm ]

==  

>	do
>	  a2 <- f a1 x1
>	  a3 <- f a2 x2
>	  ...
>	  f am xm

If right-to-left evaluation is required, the input list should be reversed.
-}

foldM             :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m a
foldM _ a []      =  return a
foldM f a (x:xs)  =  f a x >>= \fax -> foldM f fax xs

foldM_            :: (Monad m) => (a -> b -> m a) -> a -> [b] -> m ()
foldM_ f a xs     = foldM f a xs >> return ()

replicateM        :: (Monad m) => Int -> m a -> m [a]
replicateM n x    = sequence (replicate n x)

replicateM_       :: (Monad m) => Int -> m a -> m ()
replicateM_ n x   = sequence_ (replicate n x)

>	when debug (putStr "Debugging\n")

will output the string @Debugging\\n@ if the Boolean value @debug@ is 'True',
and otherwise do nothing.
-}

when              :: (Monad m) => Bool -> m () -> m ()
when p s          =  if p then s else return ()

-- | The reverse of 'when'.

unless            :: (Monad m) => Bool -> m () -> m ()
unless p s        =  if p then return () else s

The monadic lifting operators promote a function to a monad.
The function arguments are scanned left to right. For example, 

>	liftM2 (+) [0,1] [0,2] = [0,2,1,3]
>	liftM2 (+) (Just 1) Nothing = Nothing

-}

liftM   :: (Monad m) => (a1 -> r) -> m a1 -> m r
liftM2  :: (Monad m) => (a1 -> a2 -> r) -> m a1 -> m a2 -> m r
liftM3  :: (Monad m) => (a1 -> a2 -> a3 -> r) -> m a1 -> m a2 -> m a3 -> m r
liftM4  :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m r
liftM5  :: (Monad m) => (a1 -> a2 -> a3 -> a4 -> a5 -> r) -> m a1 -> m a2 -> m a3 -> m a4 -> m a5 -> m r

liftM f m1              = do { x1 <- m1; return (f x1) }
liftM2 f m1 m2          = do { x1 <- m1; x2 <- m2; return (f x1 x2) }
liftM3 f m1 m2 m3       = do { x1 <- m1; x2 <- m2; x3 <- m3; return (f x1 x2 x3) }
liftM4 f m1 m2 m3 m4    = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; return (f x1 x2 x3 x4) }
liftM5 f m1 m2 m3 m4 m5 = do { x1 <- m1; x2 <- m2; x3 <- m3; x4 <- m4; x5 <- m5; return (f x1 x2 x3 x4 x5) }

'ap', which promotes function application. 

>	return f `ap` x1 `ap` ... `ap` xn

is equivalent to 

>	liftMn f x1 x2 ... xn

-}

ap                :: (Monad m) => m (a -> b) -> m a -> m b
ap                =  liftM2 id

The functions in this library use the following naming conventions: 

* A postfix \`M\' always stands for a function in the Kleisli category:
  @m@ is added to function results (modulo currying) and nowhere else.
  So, for example, 

>  filter  ::              (a ->   Bool) -> [a] ->   [a]
>  filterM :: (Monad m) => (a -> m Bool) -> [a] -> m [a]

* A postfix \`_\' changes the result type from @(m a)@ to @(m ())@.
  Thus (in the "Prelude"): 

>  sequence  :: Monad m => [m a] -> m [a] 
>  sequence_ :: Monad m => [m a] -> m () 

* A prefix \`m\' generalises an existing function to a monadic form.
  Thus, for example: 

>  sum  :: Num a       => [a]   -> a
>  msum :: MonadPlus m => [m a] -> m a

-}