monadLib-3.8: src/MonadLib.hs

{-# LANGUAGE CPP, MultiParamTypeClasses, FunctionalDependencies,
             UndecidableInstances, FlexibleInstances #-}
{-# LANGUAGE DataKinds, TypeFamilies, TypeOperators #-}
{-# LANGUAGE Rank2Types #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE Safe #-}
{-| This library provides a collection of monad transformers that
    can be combined to produce various monads.
-}
module MonadLib (
  -- * Types
  -- $Types
  Id, Lift, IdT, ReaderT, WriterT,
  StateT,
  ExceptionT,
  --
  -- $WriterM_ExceptionT
  ChoiceT, ContT,

  -- * Lifting
  -- $Lifting
  MonadT(..), BaseM(..),

  -- * Effect Classes
  -- $Effects
  ReaderM(..), WriterM(..), StateM(..), ExceptionM(..), ContM(..), AbortM(..),
  Label, labelCC, labelCC_, jump, labelC, callCC,

  -- * Execution

  -- ** Eliminating Effects
  -- $Execution
  runId, runLift,
  runIdT, runReaderT, runWriterT,
  runStateT, runExceptionT, runContT,
  runChoiceT, findOne, findAll,
  RunM(..),

  -- ** Nested Execution
  -- $Nested_Exec
  RunReaderM(..), RunWriterM(..), RunExceptionM(..),

  -- * Utility functions
  asks, puts, sets, sets_, raises,
  mapReader, mapWriter, mapException,
  handle,
  WithBase,

  -- * Miscellaneous
  version,
  module Control.Monad
) where


import Control.Applicative
import Control.Monad
import Control.Monad.Fix
import Control.Monad.ST (ST)
import qualified Control.Exception as IO (throwIO,try)
#ifdef USE_BASE3
import qualified Control.Exception as IO (Exception)
#else
import qualified Control.Exception as IO (SomeException)
#endif
import System.Exit(ExitCode,exitWith)
import Data.Monoid
import Data.Kind(Type)
import Prelude hiding (Ordering(..))

-- | The current version of the library.
version :: (Int,Int,Int)
version = (3,5,2)


-- $Types
--
-- The following types define the representations of the
-- computation types supported by the library.
-- Each type adds support for a different effect.

-- | Computations with no effects.
newtype Id a              = I a

-- | Computation with no effects (strict).
data Lift a               = L a

-- | Adds no new features.  Useful as a placeholder.
newtype IdT m a           = IT (m a)

-- | Add support for propagating a context of type @i@.
newtype ReaderT i m a     = R (i -> m a)

-- | Add support for collecting values of type @i@.
-- The type @i@ should be a monoid, whose unit is used to represent
-- a lack of a value, and whose binary operation is used to combine
-- multiple values.
-- This transformer is strict in its output component.
newtype WriterT i m a = W { unW :: m (P a i) }
data P a i = P a !i

-- | Add support for threading state of type @i@.
newtype StateT     i m a  = S (i -> m (a,i))

-- | Add support for exceptions of type @i@.
newtype ExceptionT i m a  = X (m (Either i a))

-- | Add support for multiple answers.
data ChoiceT m a          = NoAnswer
                          | Answer a
                          | Choice (ChoiceT m a) (ChoiceT m a)
                          | ChoiceEff (m (ChoiceT m a))

-- | Add support for continuations within a prompt of type @i@.
newtype ContT i m a  = C ((a -> m i) -> m i)

-- $Execution
--
-- The following functions eliminate the outermost effect
-- of a computation by translating a computation into an
-- equivalent computation in the underlying monad.
-- (The exceptions are 'Id' and 'Lift' which are not transformers
-- but ordinary monads and so, their run operations simply
-- eliminate the monad.)


-- | Get the result of a pure computation.
runId         :: Id a -> a
runId (I a) = a

-- | Get the result of a pure strict computation.
runLift       :: Lift a -> a
runLift (L a) = a


-- | Remove an identity layer.
runIdT        :: IdT m a -> m a
runIdT (IT a)  = a

-- | Execute a reader computation in the given context.
runReaderT    :: i -> ReaderT i m a -> m a
runReaderT i (R m) = m i

-- | Execute a writer computation.
-- Returns the result and the collected output.
runWriterT :: (Monad m) => WriterT i m a -> m (a,i)
runWriterT (W m) = liftM to_pair m
  where to_pair ~(P a w) = (a,w)

-- | Execute a stateful computation in the given initial state.
-- The second component of the result is the final state.
runStateT     :: i -> StateT i m a -> m (a,i)
runStateT i (S m) = m i

-- | Execute a computation with exceptions.
-- Successful results are tagged with 'Right',
-- exceptional results are tagged with 'Left'.
runExceptionT :: ExceptionT i m a -> m (Either i a)
runExceptionT (X m) = m

-- | Execute a computation that may return multiple answers.
-- The resulting computation returns 'Nothing'
-- if no answers were found, or @Just (answer,new_comp)@,
-- where @answer@ is an answer, and @new_comp@ is a computation
-- that may produce more answers.
-- The search is depth-first and left-biased with respect to the
-- 'mplus' operation.
runChoiceT :: (Monad m) => ChoiceT m a -> m (Maybe (a,ChoiceT m a))
runChoiceT (Answer a)     = return (Just (a,NoAnswer))
runChoiceT NoAnswer       = return Nothing
runChoiceT (Choice l r)   = do x <- runChoiceT l
                               case x of
                                 Nothing      -> runChoiceT r
                                 Just (a,l1)  -> return (Just (a,Choice l1 r))
runChoiceT (ChoiceEff m)  = runChoiceT =<< m

-- | Execute a computation that may return multiple answers,
-- returning at most one answer.
findOne :: (Monad m) => ChoiceT m a -> m (Maybe a)
findOne m = fmap fst `liftM` runChoiceT m

-- | Execute a computation that may return multiple answers,
-- collecting all possible answers.
findAll :: (Monad m) => ChoiceT m a -> m [a]
findAll m = all_res =<< runChoiceT m
  where all_res Nothing       = return []
        all_res (Just (a,as)) = (a:) `liftM` findAll as

-- | Execute a computation with the given continuation.
runContT      :: (a -> m i) -> ContT i m a -> m i
runContT i (C m) = m i


-- | Generalized running.
class Monad m => RunM m a r | m a -> r where
  runM :: m a -> r

instance RunM Id a a where
  runM = runId

instance RunM Lift a a where
  runM = runLift

instance RunM IO a (IO a) where
  runM = id

instance RunM m a r => RunM (IdT m) a r where
  runM = runM . runIdT

instance RunM m a r => RunM (ReaderT i m) a (i -> r) where
  runM m i = runM (runReaderT i m)

instance (Monoid i, RunM m (a,i) r) => RunM (WriterT i m) a r where
  runM = runM . runWriterT

instance RunM m (a,i) r => RunM (StateT i m) a (i -> r) where
  runM m i = runM (runStateT i m)

instance RunM m (Either i a) r => RunM (ExceptionT i m) a r where
  runM = runM . runExceptionT

instance RunM m i r => RunM (ContT i m) a ((a -> m i) -> r) where
  runM m k = runM (runContT k m)

instance RunM m (Maybe (a,ChoiceT m a)) r => RunM (ChoiceT m) a r where
  runM = runM . runChoiceT


-- $Lifting
--
-- The following operations allow us to promote computations
-- in the underlying monad to computations that support an extra
-- effect.  Computations defined in this way do not make use of
-- the new effect but can be combined with other operations that
-- utilize the effect.


class MonadT t where
  -- | Promote a computation from the underlying monad.
  lift :: (Monad m) => m a -> t m a

-- Notes:
--   * It is interesting to note that these use something the resembles
--     the non-transformer 'return's.
--   * These are more general then the lift in the MonadT class because
--     most of them can lift arbitrary functors (some, even arbitrary type ctrs)
instance MonadT IdT            where lift m = IT m
instance MonadT (ReaderT    i) where lift m = R (\_ -> m)
instance MonadT (StateT     i) where lift m = S (\s -> liftM (\a -> (a,s)) m)
instance (Monoid i)
      => MonadT (WriterT i)    where lift m = W (liftM (\a -> P a mempty) m)
instance MonadT (ExceptionT i) where lift m = X (liftM Right m)
instance MonadT ChoiceT        where lift m = ChoiceEff (liftM Answer m)
instance MonadT (ContT      i) where lift m = C (\k -> m >>= k)


-- Definitions for some of the methods that are the same for all transformers

t_inBase   :: (MonadT t, BaseM m n) => n a -> t m a
t_inBase m  = lift (inBase m)

t_return   :: (MonadT t, Monad m) => a -> t m a
t_return x  = lift (return x)

t_fail     :: (MonadT t, Monad m) => String -> t m a
t_fail x    = lift (fail x)

t_mzero    :: (MonadT t, MonadPlus m) => t m a
t_mzero     = lift mzero

t_ask      :: (MonadT t, ReaderM m i) => t m i
t_ask       = lift ask

t_put      :: (MonadT t, WriterM m i) => i -> t m ()
t_put x     = lift (put x)

t_get      :: (MonadT t, StateM m i) => t m i
t_get       = lift get

t_set      :: (MonadT t, StateM m i) => i -> t m ()
t_set i     = lift (set i)

t_raise    :: (MonadT t, ExceptionM m i) => i -> t m a
t_raise i   = lift (raise i)

t_abort    :: (MonadT t, AbortM m i) => i -> t m a
t_abort i   = lift (abort i)
--------------------------------------------------------------------------------


class (Monad m, Monad n) => BaseM m n | m -> n where
  -- | Promote a computation from the base monad.
  inBase :: n a -> m a

instance BaseM IO IO         where inBase = id
instance BaseM Maybe Maybe   where inBase = id
instance BaseM [] []         where inBase = id
instance BaseM Id Id         where inBase = id
instance BaseM Lift Lift     where inBase = id
instance BaseM (ST s) (ST s) where inBase = id


instance (BaseM m n) => BaseM (IdT          m) n where inBase = t_inBase
instance (BaseM m n) => BaseM (ReaderT    i m) n where inBase = t_inBase
instance (BaseM m n) => BaseM (StateT     i m) n where inBase = t_inBase
instance (BaseM m n,Monoid i)
                     => BaseM (WriterT i m) n    where inBase = t_inBase
instance (BaseM m n) => BaseM (ExceptionT i m) n where inBase = t_inBase
instance (BaseM m n) => BaseM (ChoiceT      m) n where inBase = t_inBase
instance (BaseM m n) => BaseM (ContT      i m) n where inBase = t_inBase


instance Monad Id where
  return x = I x
  fail x   = error x
  m >>= k  = k (runId m)

instance Monad Lift where
  return x  = L x
  fail x    = error x
  L x >>= k = k x     -- Note: the pattern is important here
                      -- because it makes things strict


-- Note: None of the transformers make essential use of the 'fail' method.
-- Instead, they delegate its behavior to the underlying monad.

instance (Monad m) => Monad (IdT m) where
  return  = t_return
  fail    = t_fail
  m >>= k = IT (runIdT m >>= (runIdT . k))

instance (Monad m) => Monad (ReaderT i m) where
  return  = t_return
  fail    = t_fail
  m >>= k = R (\r -> runReaderT r m >>= \a -> runReaderT r (k a))

instance (Monad m) => Monad (StateT i m) where
  return  = t_return
  fail    = t_fail
  m >>= k = S (\s -> runStateT s m >>= \ ~(a,s') -> runStateT s' (k a))

instance (Monad m,Monoid i) => Monad (WriterT i m) where
  return  = t_return
  fail    = t_fail
  m >>= k = W $ unW m     >>= \ ~(P a w1) ->
                unW (k a) >>= \ ~(P b w2) ->
                return (P b (mappend w1 w2))

instance (Monad m) => Monad (ExceptionT i m) where
  return  = t_return
  fail    = t_fail
  m >>= k = X $ runExceptionT m >>= \e ->
                case e of
                  Left x  -> return (Left x)
                  Right a -> runExceptionT (k a)

instance (Monad m) => Monad (ChoiceT m) where
  return x  = Answer x
  fail x    = lift (fail x)

  Answer a  >>= k     = k a
  NoAnswer >>= _      = NoAnswer
  Choice m1 m2 >>= k  = Choice (m1 >>= k) (m2 >>= k)
  ChoiceEff m >>= k   = ChoiceEff (liftM (>>= k) m)

instance (Monad m) => Monad (ContT i m) where
  return  = t_return
  fail    = t_fail
  m >>= k = C $ \c -> runContT (\a -> runContT c (k a)) m

instance                       Functor Id               where fmap = liftM
instance                       Functor Lift             where fmap = liftM
instance (Monad m)          => Functor (IdT          m) where fmap = liftM
instance (Monad m)          => Functor (ReaderT    i m) where fmap = liftM
instance (Monad m)          => Functor (StateT     i m) where fmap = liftM
instance (Monad m,Monoid i) => Functor (WriterT i m)    where fmap = liftM
instance (Monad m)          => Functor (ExceptionT i m) where fmap = liftM
instance (Monad m)          => Functor (ChoiceT      m) where fmap = liftM
instance (Monad m)          => Functor (ContT      i m) where fmap = liftM

-- Applicative support ---------------------------------------------------------

-- NOTE: It may be possible to make these more general
-- (i.e., have Applicative, or even Functor transformers)

instance              Applicative Id            where (<*>) = ap; pure = return
instance              Applicative Lift          where (<*>) = ap; pure = return
instance (Monad m) => Applicative (IdT m)       where (<*>) = ap; pure = return
instance (Monad m) => Applicative (ReaderT i m) where (<*>) = ap; pure = return
instance (Monad m) => Applicative (StateT i m)  where (<*>) = ap; pure = return
instance (Monad m,Monoid i)
                   => Applicative (WriterT i m) where (<*>) = ap; pure = return
instance (Monad m) => Applicative (ExceptionT i m)
                                                where (<*>) = ap; pure = return
instance (Monad m) => Applicative (ChoiceT m)   where (<*>) = ap; pure = return
instance (Monad m) => Applicative (ContT i m)   where (<*>) = ap; pure = return

instance (MonadPlus m)
           => Alternative (IdT m)           where (<|>) = mplus; empty = mzero
instance (MonadPlus m)
           => Alternative (ReaderT i m)     where (<|>) = mplus; empty = mzero
instance (MonadPlus m)
           => Alternative (StateT i m)      where (<|>) = mplus; empty = mzero
instance (MonadPlus m,Monoid i)
           => Alternative (WriterT i m)     where (<|>) = mplus; empty = mzero
instance (MonadPlus m)
           => Alternative (ExceptionT i m)  where (<|>) = mplus; empty = mzero
instance (Monad m)
           => Alternative (ChoiceT m)       where (<|>) = mplus; empty = mzero
instance (MonadPlus m)
           => Alternative (ContT i m)       where (<|>) = mplus; empty = mzero



-- $Monadic_Value_Recursion
--
-- Recursion that does not duplicate side-effects.
-- For details see Levent Erkok's dissertation.
--
-- Monadic types built with 'ContT' and 'ChoiceT' do not support
-- monadic value recursion.

instance MonadFix Id where
  mfix f  = let m = f (runId m) in m

instance MonadFix Lift where
  mfix f  = let m = f (runLift m) in m

instance (MonadFix m) => MonadFix (IdT m) where
  mfix f  = IT (mfix (runIdT . f))

instance (MonadFix m) => MonadFix (ReaderT i m) where
  mfix f  = R $ \r -> mfix (runReaderT r . f)

instance (MonadFix m) => MonadFix (StateT i m) where
  mfix f  = S $ \s -> mfix (runStateT s . f . fst)

instance (MonadFix m,Monoid i) => MonadFix (WriterT i m) where
  mfix f  = W $ mfix (unW . f . val)
    where val ~(P a _) = a

-- No instance for ChoiceT

instance (MonadFix m) => MonadFix (ExceptionT i m) where
  mfix f  = X $ mfix (runExceptionT . f . fromRight)
    where fromRight (Right a) = a
          fromRight _         = error "ExceptionT: mfix looped."

-- No instance for ContT

instance (MonadPlus m) => MonadPlus (IdT m) where
  mzero               = t_mzero
  mplus (IT m) (IT n) = IT (mplus m n)

instance (MonadPlus m) => MonadPlus (ReaderT i m) where
  mzero             = t_mzero
  mplus (R m) (R n) = R (\r -> mplus (m r) (n r))

instance (MonadPlus m) => MonadPlus (StateT i m) where
  mzero             = t_mzero
  mplus (S m) (S n) = S (\s -> mplus (m s) (n s))

instance (MonadPlus m,Monoid i) => MonadPlus (WriterT i m) where
  mzero               = t_mzero
  mplus (W m) (W n) = W (mplus m n)

instance (MonadPlus m) => MonadPlus (ExceptionT i m) where
  mzero             = t_mzero
  mplus (X m) (X n) = X (mplus m n)

instance (Monad m) => MonadPlus (ChoiceT m) where
  mzero             = NoAnswer
  mplus m n         = Choice m n

-- Alternatives share the continuation.
instance (MonadPlus m) => MonadPlus (ContT i m) where
  mzero             = t_mzero
  mplus (C m) (C n) = C (\k -> m k `mplus` n k)


-- $Effects
--
-- The following classes define overloaded operations
-- that can be used to define effectful computations.


-- | Classifies monads that provide access to a context of type @i@.
class (Monad m) => ReaderM m i | m -> i where
  -- | Get the context.
  ask :: m i

instance (Monad m) => ReaderM (ReaderT i m) i where
  ask = R return

instance (ReaderM m j) => ReaderM (IdT m) j           where ask = t_ask
instance (ReaderM m j,Monoid i)
                       => ReaderM (WriterT i m) j     where ask = t_ask
instance (ReaderM m j) => ReaderM (StateT i m) j      where ask = t_ask
instance (ReaderM m j) => ReaderM (ExceptionT i m) j  where ask = t_ask
instance (ReaderM m j) => ReaderM (ChoiceT m) j       where ask = t_ask
instance (ReaderM m j) => ReaderM (ContT i m) j       where ask = t_ask


-- | Classifies monads that can collect values of type @i@.
class (Monad m) => WriterM m i | m -> i where
  -- | Add a value to the collection.
  put  :: i -> m ()

instance (Monad m,Monoid i) => WriterM (WriterT i m) i where
  put x = W (return (P () x))

instance (WriterM m j) => WriterM (IdT          m) j where put = t_put
instance (WriterM m j) => WriterM (ReaderT    i m) j where put = t_put
instance (WriterM m j) => WriterM (StateT     i m) j where put = t_put
instance (WriterM m j) => WriterM (ExceptionT i m) j where put = t_put
instance (WriterM m j) => WriterM (ChoiceT      m) j where put = t_put
instance (WriterM m j) => WriterM (ContT      i m) j where put = t_put

-- | Classifies monads that propagate a state component of type @i@.
class (Monad m) => StateM m i | m -> i where
  -- | Get the state.
  get :: m i
  -- | Set the state.
  set :: i -> m ()

instance (Monad m) => StateM (StateT i m) i where
  get   = S (\s -> return (s,s))
  set s = S (\_ -> return ((),s))

instance (StateM m j) => StateM (IdT m) j where
  get = t_get; set = t_set
instance (StateM m j) => StateM (ReaderT i m) j where
  get = t_get; set = t_set
instance (StateM m j,Monoid i) => StateM (WriterT i m) j where
  get = t_get; set = t_set
instance (StateM m j) => StateM (ExceptionT i m) j where
  get = t_get; set = t_set
instance (StateM m j) => StateM (ChoiceT m) j where
  get = t_get; set = t_set
instance (StateM m j) => StateM (ContT i m) j where
  get = t_get; set = t_set

-- | Classifies monads that support raising exceptions of type @i@.
class (Monad m) => ExceptionM m i | m -> i where
  -- | Raise an exception.
  raise :: i -> m a

#ifdef USE_BASE3
instance ExceptionM IO IO.Exception where
  raise = IO.throwIO
#else
instance ExceptionM IO IO.SomeException where
  raise = IO.throwIO
#endif

instance (Monad m) => ExceptionM (ExceptionT i m) i where
  raise x = X (return (Left x))

instance (ExceptionM m j) => ExceptionM (IdT m) j where
  raise = t_raise
instance (ExceptionM m j) => ExceptionM (ReaderT i m) j where
  raise = t_raise
instance (ExceptionM m j,Monoid i) => ExceptionM (WriterT i m) j where
  raise = t_raise
instance (ExceptionM m j) => ExceptionM (StateT  i m) j where
  raise = t_raise
instance (ExceptionM m j) => ExceptionM (ChoiceT   m) j where
  raise = t_raise
instance (ExceptionM m j) => ExceptionM (ContT   i m) j where
  raise = t_raise


-- The following instances differ from the others because the
-- liftings are not as uniform (although they certainly follow a pattern).

-- | Classifies monads that provide access to a computation's continuation.
class Monad m => ContM m where
  -- | Capture the current continuation.
  callWithCC :: ((a -> Label m) -> m a) -> m a


-- This captures a common pattern in the lifted definitions of `callWithCC`.
liftJump :: (ContM m, MonadT t) =>
  (a -> b) ->
  ((a -> Label (t m)) -> t m a) ->
  ((b -> Label    m ) -> t m a)
liftJump ans f l = f $ \a -> Lab (lift $ jump $ l $ ans a)


instance (ContM m) => ContM (IdT m) where
  callWithCC f = IT $ callWithCC $ \k -> runIdT $ liftJump id f k

instance (ContM m) => ContM (ReaderT i m) where
  callWithCC f = R $ \r -> callWithCC $ \k -> runReaderT r $ liftJump id f k

instance (ContM m) => ContM (StateT i m) where
  callWithCC f = S $ \s -> callWithCC $ \k -> runStateT s $ liftJump (ans s) f k
    where ans s a = (a,s)

instance (ContM m,Monoid i) => ContM (WriterT i m) where
  callWithCC f = W $ callWithCC $ \k -> unW $ liftJump (`P` mempty) f k

instance (ContM m) => ContM (ExceptionT i m) where
  callWithCC f = X $ callWithCC $ \k -> runExceptionT $ liftJump Right f k

instance (ContM m) => ContM (ChoiceT m) where
  callWithCC f = ChoiceEff $ callWithCC $ \k -> return $ liftJump Answer f k
    -- ??? What does this do ???

instance (Monad m) => ContM (ContT i m) where
  callWithCC f = C $ \k -> runContT k $ f $ \a -> Lab (C $ \_ -> k a)

-- $Nested_Exec
--
-- The following classes define operations that are overloaded
-- versions of the @run@ operations.   Unlike the @run@ operations,
-- these functions do not change the type of the computation (i.e., they
-- do not remove a layer).  Instead, they perform the effects in
-- a ``separate effect thread''.

-- | Classifies monads that support changing the context for a
-- sub-computation.
class (ReaderM m i) => RunReaderM m i | m -> i where
  -- | Change the context for the duration of a sub-computation.
  local        :: i -> m a -> m a
  -- prop(?): local i (m1 >> m2) = local i m1 >> local i m2

instance (Monad m)        => RunReaderM (ReaderT    i m) i where
  local i m     = lift (runReaderT i m)

instance (RunReaderM m j) => RunReaderM (IdT m) j where
  local i (IT m) = IT (local i m)
instance (RunReaderM m j,Monoid i) => RunReaderM (WriterT i m) j where
  local i (W m) = W (local i m)
instance (RunReaderM m j) => RunReaderM (StateT     i m) j where
  local i (S m) = S (local i . m)
instance (RunReaderM m j) => RunReaderM (ExceptionT i m) j where
  local i (X m) = X (local i m)

instance (RunReaderM m j) => RunReaderM (ContT i m) j where
  local i (C m) = C (local i . m)

-- | Classifies monads that support collecting the output of
-- a sub-computation.
class WriterM m i => RunWriterM m i | m -> i where
  -- | Collect the output from a sub-computation.
  collect :: m a -> m (a,i)

instance (Monad m,Monoid i) => RunWriterM (WriterT i m) i where
  collect m = lift (runWriterT m)

instance (RunWriterM m j) => RunWriterM (IdT m) j where
  collect (IT m) = IT (collect m)
instance (RunWriterM m j) => RunWriterM (ReaderT i m) j where
  collect (R m) = R (collect . m)
instance (RunWriterM m j) => RunWriterM (StateT i m) j where
  collect (S m) = S (liftM swap . collect . m)
    where swap (~(a,s),w) = ((a,w),s)
instance (RunWriterM m j) => RunWriterM (ExceptionT i m) j where
  collect (X m) = X (liftM swap (collect m))
    where swap (Right a,w)  = Right (a,w)
          swap (Left x,_)   = Left x
instance (RunWriterM m j, MonadFix m) => RunWriterM (ContT i m) j where
  collect (C m) = C $ \k -> fst `liftM`
                                mfix (\ ~(_,w) -> collect (m (\a -> k (a,w))))


-- $WriterM_ExceptionT
--
-- About the 'WriterM' instance:
-- If an exception is risen while we are collecting output,
-- then the output is lost.  If the output is important,
-- then use 'try' to ensure that no exception may occur.
-- Example:
--
-- > do (r,w) <- collect (try m)
-- >    case r of
-- >      Left err -> ...do something...
-- >      Right a  -> ...do something...

-- | Classifies monads that support handling of exceptions.
class ExceptionM m i => RunExceptionM m i | m -> i where
  -- | Convert computations that may raise an exception
  -- into computations that do not raise exception but instead,
  -- yield a tagged results.  Exceptions are tagged with "Left",
  -- successful computations are tagged with "Right".
  try :: m a -> m (Either i a)

#ifdef USE_BASE3
instance RunExceptionM IO IO.Exception where
  try = IO.try
#else
instance RunExceptionM IO IO.SomeException where
  try = IO.try
#endif

instance (Monad m) => RunExceptionM (ExceptionT i m) i where
  try m = lift (runExceptionT m)

instance (RunExceptionM m i) => RunExceptionM (IdT m) i where
  try (IT m) = IT (try m)
instance (RunExceptionM m i) => RunExceptionM (ReaderT j m) i where
  try (R m) = R (try . m)
instance (RunExceptionM m i,Monoid j) => RunExceptionM (WriterT j m) i where
  try (W m) = W (liftM swap (try m))
    where swap (Right (P a w))  = P (Right a) w
          swap (Left e)         = P (Left e) mempty
instance (RunExceptionM m i) => RunExceptionM (StateT j m) i where
  try (S m) = S (\s -> liftM (swap s) (try (m s)))
    where swap _ (Right ~(a,s)) = (Right a,s)
          swap s (Left e)       = (Left e, s)

-- | Classifies monads that support aborting the program and returning
-- a given final result of type 'i'.
class Monad m => AbortM m i where

  -- | Abort the program with the given value as final result.
  abort :: i -> m a

instance Monad m => AbortM (ContT i m) i where
  abort i = C (\_ -> return i)

instance AbortM IO ExitCode where
  abort = exitWith

instance AbortM m i => AbortM (IdT m) i           where abort = t_abort
instance AbortM m i => AbortM (ReaderT j m) i     where abort = t_abort
instance (AbortM m i,Monoid j)
                    => AbortM (WriterT j m) i     where abort = t_abort
instance AbortM m i => AbortM (StateT j m) i      where abort = t_abort
instance AbortM m i => AbortM (ExceptionT j m) i  where abort = t_abort
instance AbortM m i => AbortM (ChoiceT m) i       where abort = t_abort

--------------------------------------------------------------------------------
-- Some convenient functions for working with continuations.

-- | An explicit representation for monadic continuations.
newtype Label m     = Lab (forall b. m b)

-- | Capture the current continuation.
-- This function is like 'return', except that it also captures
-- the current continuation.  Later, we can use 'jump' to repeat the
-- computation from this point onwards but with a possibly different value.
labelCC            :: (ContM m) => a -> m (a, a -> Label m)
labelCC x           = callWithCC (\l -> let label a = Lab (jump (l (a, label)))
                                        in return (x, label))

-- | Capture the current continuation.
-- Later we can use `jump` to restart the program from this point.
labelCC_           :: forall m. (ContM m) => m (Label m)
labelCC_            = callWithCC $ \k -> let x :: m a   -- Signature matters!!!
                                             x = jump (k (Lab x))
                                         in x

-- | A version of `callWithCC` that avoids the need for an explicit
-- use of the `jump` function.
callCC             :: ContM m => ((a -> m b) -> m a) -> m a
callCC f            = callWithCC $ \l -> f $ \a -> jump $ l a

-- | Label a given continuation.
labelC             :: (forall b. m b) -> Label m
labelC k            = Lab k

-- | Restart a previously captured computation.
jump               :: Label m -> m a
jump (Lab k)       = k




--------------------------------------------------------------------------------

-- | Apply a function to the environment.
-- Useful for accessing environmnt components.
asks :: ReaderM m r => (r -> a) -> m a
asks f      = do r <- ask
                 return (f r)

-- | Add content the output and return a result.
puts :: WriterM m w => (a,w) -> m a
puts ~(a,w) = put w >> return a

-- | Update the state and return a result.
sets :: StateM m s => (s -> (a,s)) -> m a
sets f      = do s <- get
                 let (a,s1) = f s
                 set s1
                 return a

-- | Updates the state with the given function.
sets_ :: StateM m s => (s -> s) -> m ()
sets_ f     = do s <- get
                 set (f s)
-- | Either raise an exception or return a value.
-- 'Left' values signify the we should raise an exception,
-- 'Right' values indicate success.
raises :: ExceptionM m x => Either x a -> m a
raises (Right a)  = return a
raises (Left x)   = raise x

-- for ChoiceT we already have "msum"
-- for ContT, not sure if it makes sense.

-- | Modify the environment for the duration of a computation.
mapReader        :: RunReaderM m r => (r -> r) -> m a -> m a
mapReader f m     = do r <- ask
                       local (f r) m

-- | Modify the output of a computation.
mapWriter        :: RunWriterM m w => (w -> w) -> m a -> m a
mapWriter f m     = do ~(a,w) <- collect m
                       put (f w)
                       return a

-- | Modify the exception that was risen by a computation.
mapException     :: RunExceptionM m x => (x -> x) -> m a -> m a
mapException f m  = do r <- try m
                       case r of
                         Right a -> return a
                         Left x  -> raise (f x)

-- | Apply the given exception handler, if a computation raises an exception.
handle           :: RunExceptionM m x => m a -> (x -> m a) -> m a
handle m f        = do r <- try m
                       case r of
                         Right a -> return a
                         Left x  -> f x


{- | A convenience type family for defining stacks of monads.
The first entry in the list is the top-most layer of the monad stack
(i.e., the one that is furtherest from the base).  For example:

> newtype M a = M { unM ::
>   WithBase IO
>     '[ ReaderT    Int
>      , StateT     Char
>      , ExceptionT String
>      ] a
>   }

is equivalent to:

> newtype M a = M { unM ::
>   ReaderT    Int      (
>   StateT     Char     (
>   ExceptionT String
>   IO                  )) a
>   }

-}
type family WithBase base layers :: Type -> Type where
  WithBase b '[]        = b
  WithBase b (f ': fs)  = f (WithBase b fs)