monad-choice (empty) → 0.1.0.0

raw patch · 10 files changed

+1351/−0 lines, 10 filesdep +MonadRandomdep +basedep +invariantsetup-changed

Dependencies added: MonadRandom, base, invariant, mtl, transformers

Files

CHANGELOG.md +48/−0
LICENSE +662/−0
README.md +17/−0
Setup.hs +2/−0
monad-choice.cabal +47/−0
src/Control/Monad/Choice/Covariant.hs +44/−0
src/Control/Monad/Choice/Invariant.hs +38/−0
src/Control/Monad/Class/Choice.hs +144/−0
src/Control/Monad/Trans/Choice/Covariant.hs +164/−0
src/Control/Monad/Trans/Choice/Invariant.hs +185/−0

+ CHANGELOG.md view

@@ -0,0 +1,48 @@+# Changelog++## 0.1.0.0 (2020-02-29)+Inital version++### Additions+- `MonadChoice`+  - Created `MonadChoice` typeclass to represent that allow choices to be made by some arbitrary entity.+  - Added function `chooseM`.+  - Added instances for the `ChoiceT` both covariant and invariant.+  - Added instance for `MonadRandom` instances by using the `uniform` function.+  - Added various passthrough instances+    - `MaybeT`+    - `ExceptT`+    - `IdentityT`+    - `StateT` either lazy or strict+    - `ReaderT`+    - `WriterT` either constant space, lazy, or strict+    - `AccumT`+    - `ContT`+    - `RWST` either constant space, lazy, strict+    - `SelectT`+- `ChoiceT`+  - Added two different versions of `ChoiceT`, one a covariant functor, the other an invariant functor on the category of monads.+  - Shared additions:+    - Function `runChoiceT`+    - Instances for `Functor`, `Applicative`, `Monad`, `MonadTrans`, and `MonadChoice`+    - Various passthrough instances+      - `MonadReader`+      - `MonadState`+      - `MonadWriter`+      - `MonadRWS`+      - `MonadIO`+  - `Covariant.ChoiceT`+    - Added functions `mapChoiceT` and `runBacktrackableChoiceT`.+  - `Invariant.ChoiceT`+    - Exposed constructor `ChoiceT`.+    - Added function `invmapChoiceT`.+    - Added various passthrough instances.+      - `Contravariant`+      - `Invariant`+      - `Alternative`+      - `MonadPlus`+      - `MonadError`+- `Choice`+  - Added two different versions of `Choice` which of type aliases for each `ChoiceT` over the `Identity` monad.+  - Added function `runChoice` for each version.+  - For `Covariant.Choice` added functions `runChoiceM` and `runBacktrackableChoiceT`.

+ LICENSE view

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If not, see <https://www.gnu.org/licenses/>.++Also add information on how to contact you by electronic and paper mail.++  If your software can interact with users remotely through a computer+network, you should also make sure that it provides a way for users to+get its source.  For example, if your program is a web application, its+interface could display a "Source" link that leads users to an archive+of the code.  There are many ways you could offer source, and different+solutions will be better for different programs; see section 13 for the+specific requirements.++  You should also get your employer (if you work as a programmer) or school,+if any, to sign a "copyright disclaimer" for the program, if necessary.+For more information on this, and how to apply and follow the GNU AGPL, see+<https://www.gnu.org/licenses/>.+

+ README.md view

@@ -0,0 +1,17 @@+# The `monad-choice` package++This package provides a multipurpose monad transformer (and associated monad and class), to represent the idea of a result depending on the outcomes of a series of choices.++## Example++The following is a simple use of `MonadChoice` for creating the name of a berry.++    {-# Language FlexibleContexts #-}++    berry :: MonadChoice NonEmpty m => m String+    berry = do+      berryColor  <- choose $ "red"   :| ["blue", "orange", "yellow", "black"]+      berryFlavor <- choose $ "sweet" :| ["sour", "bitter"]+      (++ "berry") <$> choose ( berryColor :| [berryFlavor, berryColor ++ "-" ++ berryFlavor] )++This can be used with `MonadRandom` to create a random berry, used with `Gen` to create berries for unit tests, or with user input as the structure for a menu where the user selects a berry.

+ Setup.hs view

@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain

+ monad-choice.cabal view

@@ -0,0 +1,47 @@+cabal-version: 1.12++-- This file has been generated from package.yaml by hpack version 0.31.2.+--+-- see: https://github.com/sol/hpack+--+-- hash: 6b28c8a7bf1da981f4efd400c5e91cb2a160d9cc56dadee09cad68c0d7d40c6c++name:           monad-choice+version:        0.1.0.0+synopsis:       Monad, monad transformer, and typeclass representing choices.+description:    The Monad Choice library contains monads, monad transformers, and a typeclass representing a sequence of choices of objects of arbitrary types where future choices can depend on previous ones.+category:       Control+homepage:       https://gitlab.com/e-neighborhood-watch/monad-choice#readme+author:         Eamon Olive, Louis Hyde+maintainer:     ejolive97@gmail.com+copyright:      2020 Eamon Olive, Louis Hyde+license:        AGPL-3+license-file:   LICENSE+build-type:     Simple+extra-source-files:+    README.md+    CHANGELOG.md++source-repository head+  type: git+  location: https://gitlab.com/e-neighborhood-watch/monad-choice.git++library+  exposed-modules:+      Control.Monad.Choice.Covariant+      Control.Monad.Choice.Invariant+      Control.Monad.Class.Choice+      Control.Monad.Trans.Choice.Covariant+      Control.Monad.Trans.Choice.Invariant+  other-modules:+      Paths_monad_choice+  hs-source-dirs:+      src+  ghc-options: -Weverything -Wno-implicit-prelude -Wno-safe+  build-depends:+      MonadRandom >=0.5 && <0.6+    , base >=4.7 && <5+    , invariant >=0.1.0 && <0.6+    , mtl >=2.2 && <2.3+    , transformers ==0.5.*+  default-language: Haskell2010

+ src/Control/Monad/Choice/Covariant.hs view

@@ -0,0 +1,44 @@+{-# LANGUAGE RankNTypes #-}++{-|+Module     : Control.Monad.Choice.Covariant+Copyright  : (c) Eamon Olive, 2020+             (c) Louis Hyde,  2020+License    : AGPL-3+Maintainer : ejolive97@gmail.com+Stability  : experimental++-}+module Control.Monad.Choice.Covariant+  ( Choice+  , runChoice+  , runChoiceM+  , runBacktrackableChoiceM+  ) where++-- Internal imports++import Control.Monad.Trans.Choice.Covariant+  ( ChoiceT+  , mapChoiceT+  , runBacktrackableChoiceT+  , runChoiceT+  )++-- External imports++import Control.Monad.Identity+  ( Identity+  , runIdentity+  )++type Choice f = ChoiceT f Identity++runChoice :: (forall x. f x -> x) -> Choice f a -> a+runChoice chooser = runIdentity . runChoiceT (pure . chooser)++runChoiceM :: Monad m => (forall x. f x -> m x) -> Choice f a -> m a+runChoiceM chooser = runChoiceT chooser . mapChoiceT (pure . runIdentity)++runBacktrackableChoiceM :: Monad m => (forall x. f x -> m (Maybe x)) -> Choice f a -> m (Maybe a)+runBacktrackableChoiceM chooser = runBacktrackableChoiceT chooser . mapChoiceT (pure . runIdentity)

+ src/Control/Monad/Choice/Invariant.hs view

@@ -0,0 +1,38 @@+{-# LANGUAGE RankNTypes #-}++{-|+Module     : Control.Monad.Choice.Invariant+Copyright  : (c) Eamon Olive, 2020+             (c) Louis Hyde,  2020+License    : AGPL-3+Maintainer : ejolive97@gmail.com+Stability  : experimental++-}+module Control.Monad.Choice.Invariant+  ( Choice+  , runChoice+  ) where++-- Internal imports++import Control.Monad.Trans.Choice.Invariant+  ( ChoiceT+  , runChoiceT+  )++-- External imports++import Data.Functor.Identity+  ( Identity+    ( runIdentity+    )+  )++type Choice f a = ChoiceT f Identity a++runChoice ::+  (forall x . f x -> x)+    -> Choice f a+      -> a+runChoice chooser = runIdentity . runChoiceT (\options -> pure $ chooser options)

+ src/Control/Monad/Class/Choice.hs view

@@ -0,0 +1,144 @@+{-# Language MultiParamTypeClasses #-}+{-# Language FlexibleInstances #-}++{-|+Module     : Control.Monad.Class.Choice+Copyright  : (c) Eamon Olive, 2020+             (c) Louis Hyde,  2020+License    : AGPL-3+Maintainer : ejolive97@gmail.com+Stability  : experimental++-}+module Control.Monad.Class.Choice+  ( MonadChoice (..)+  , chooseM+  )+  where++import Control.Monad+  ( join+  )+import Control.Monad.Random.Class+  ( MonadRandom+  , uniform+  )+import Control.Monad.Trans+  ( lift+  )+import Control.Monad.Trans.Accum+  ( AccumT+  )+import Control.Monad.Trans.Cont+  ( ContT+  )+import Control.Monad.Trans.Except+  ( ExceptT+  )+import Control.Monad.Trans.Identity+  ( IdentityT+  )+import Control.Monad.Trans.Maybe+  ( MaybeT+  )+import Control.Monad.Trans.Reader+  ( ReaderT+  )+import Control.Monad.Trans.RWS.CPS as RWS.CPS+  ( RWST+  )+import Control.Monad.Trans.RWS.Lazy as RWS.Lazy+  ( RWST+  )+import Control.Monad.Trans.RWS.Strict as RWS.Strict+  ( RWST+  )+import Control.Monad.Trans.Select+  ( SelectT+  )+import Control.Monad.Trans.State.Lazy as State.Lazy+  ( StateT+  )+import Control.Monad.Trans.State.Strict as State.Strict+  ( StateT+  )+import Control.Monad.Trans.Writer.CPS as Writer.CPS+  ( WriterT+  )+import Control.Monad.Trans.Writer.Lazy as Writer.Lazy+  ( WriterT+  )+import Control.Monad.Trans.Writer.Strict as Writer.Strict+  ( WriterT+  )++-- | A monad with a series of dependent choices.+-- It is usually desirable to have @f@ be a 'Foldable' so that a selection can be made from it.+--+-- As an example here is a simple berry name generator:+--+-- > berry :: MonadChoice NonEmpty m => m String+-- > berry = do+-- >   color  <- choose $ "red" :| ["blue", "pink", "cyan"]+-- >   prefix <- choose $ "color" :| ["straw", "rasp", "cran"]+-- >   return $ prefix ++ "berry"+--+-- Since this has a polymorphic type this could be used for a variety of purposes.+class Monad m => MonadChoice f m where+  -- | Makes a selection.+  choose :: f a -> m a++-- | Makes a selection where options are themselves selections.+chooseM ::+  ( MonadChoice f m+  )+    => f (m a) -> m a+chooseM = join . choose++instance (Foldable f, MonadRandom m) => MonadChoice f m where+  choose = uniform++instance MonadChoice f m => MonadChoice f (MaybeT m) where+  choose = lift . choose ++instance MonadChoice f m => MonadChoice f (ExceptT e m) where+  choose = lift . choose ++instance MonadChoice f m => MonadChoice f (IdentityT m) where+  choose = lift . choose ++instance MonadChoice f m => MonadChoice f (State.Lazy.StateT s m) where+  choose = lift . choose++instance MonadChoice f m => MonadChoice f (State.Strict.StateT s m) where+  choose = lift . choose++instance MonadChoice f m => MonadChoice f (ReaderT r m) where+  choose = lift . choose++instance MonadChoice f m => MonadChoice f (Writer.CPS.WriterT w m) where+  choose = lift . choose++instance (Monoid w, MonadChoice f m) => MonadChoice f (Writer.Lazy.WriterT w m) where+  choose = lift . choose++instance (Monoid w, MonadChoice f m) => MonadChoice f (Writer.Strict.WriterT w m) where+  choose = lift . choose++instance (Monoid w, MonadChoice f m) => MonadChoice f (AccumT w m) where+  choose = lift . choose++instance MonadChoice f m => MonadChoice f (ContT r m) where+  choose = lift . choose++instance (Monoid w, MonadChoice f m) => MonadChoice f (RWS.Lazy.RWST r w s m) where+  choose = lift . choose++instance (Monoid w, MonadChoice f m) => MonadChoice f (RWS.Strict.RWST r w s m) where+  choose = lift . choose++instance MonadChoice f m => MonadChoice f (RWS.CPS.RWST r w s m) where+  choose = lift . choose++instance MonadChoice f m => MonadChoice f (SelectT r m) where+  choose = lift . choose

+ src/Control/Monad/Trans/Choice/Covariant.hs view

@@ -0,0 +1,164 @@+{-# LANGUAGE MultiParamTypeClasses #-}+{-# LANGUAGE UndecidableInstances #-}+{-# LANGUAGE ScopedTypeVariables #-}+{-# LANGUAGE FlexibleInstances #-}+{-# LANGUAGE RankNTypes #-}+{-# LANGUAGE GADTs #-}++{-|+Module     : Control.Monad.Trans.Choice.Covariant+Copyright  : (c) Eamon Olive, 2020+             (c) Louis Hyde,  2020+License    : AGPL-3+Maintainer : ejolive97@gmail.com+Stability  : experimental++-}+module Control.Monad.Trans.Choice.Covariant+  ( ChoiceT ( )+  , runChoiceT+  , mapChoiceT+  , runBacktrackableChoiceT+  ) where++-- Internal imports++import Control.Monad.Class.Choice+  ( MonadChoice (choose)+  )++-- External imports++import Control.Arrow+  ( second+  )+import Control.Monad+  ( (>=>)+  )+import Control.Monad.IO.Class+  ( MonadIO+    ( liftIO+    )+  )+import Control.Monad.Reader.Class+  ( MonadReader+    ( ask+    , local+    )+  )+import Control.Monad.RWS.Class+  ( MonadRWS+  )+import Control.Monad.State.Class+  ( MonadState+    ( state+    )+  )+import Control.Monad.Trans+  ( MonadTrans+    ( lift+    )+  )+import Control.Monad.Writer.Class+  ( MonadWriter+    ( writer+    , listen+    , pass+    )+  )++data ChoiceT f m a where+  FixedT :: a -> ChoiceT f m a+  LiftThenT :: m b -> (b -> ChoiceT f m a) -> ChoiceT f m a+  ChooseThenT :: f b -> (b -> ChoiceT f m a) -> ChoiceT f m a++instance Functor (ChoiceT f m) where+  fmap f (FixedT value) = FixedT $ f value+  fmap f (LiftThenT action next) = LiftThenT action $ fmap f . next+  fmap f (ChooseThenT options next) = ChooseThenT options $ fmap f . next++instance Applicative (ChoiceT f m) where+  pure = FixedT -- === LiftThenT (pure value) $ FixedT++  (FixedT f) <*> choice = fmap f choice+  fChoice <*> (FixedT f) = fmap ($f) fChoice+  -- Proof:+  --+  -- > LiftThenT action next = lift action >>= next+  -- > +  -- > (a >>= b) >>= (<$> c) = (a >>= b) >>= (<$> c)+  -- > (a >>= b) >>= (<$> c) = a >>= (\x -> (b x >>= (<$> c)))+  -- > (a >>= b) <*> c = a >>= (\x -> (b x <*> c))+  (LiftThenT   fAction  nextF) <*> dependentChoice = LiftThenT   fAction  $ (<*> dependentChoice) . nextF+  (ChooseThenT fOptions nextF) <*> dependentChoice = ChooseThenT fOptions $ (<*> dependentChoice) . nextF++instance Monad (ChoiceT f m) where+  (FixedT value) >>= f = f value+  (LiftThenT action next) >>= f = LiftThenT action $ next >=> f+  (ChooseThenT options next) >>= f = ChooseThenT options $ next >=> f++instance MonadChoice f (ChoiceT f m) where+  choose options = ChooseThenT options pure++instance MonadTrans (ChoiceT f) where+  lift action = LiftThenT action pure++instance MonadReader r m => MonadReader r (ChoiceT f m) where+  ask = lift ask+  local f = mapChoiceT (local f)++instance MonadState s m => MonadState s (ChoiceT f m) where+  state = lift . state++instance MonadWriter w m => MonadWriter w (ChoiceT f m) where+  writer = lift . writer+  listen (FixedT value) = FixedT (value, mempty)+  listen (LiftThenT action next) = LiftThenT (listen action) $ \(result, output) -> fmap (second $ mappend output) $ listen $ next result+  listen (ChooseThenT options next) = ChooseThenT options $ listen . next+  pass = go mempty+    where+      go :: w -> ChoiceT f m (a, w -> w) -> ChoiceT f m a+      go acc (FixedT (value, f)) = writer (value, f acc)+      go acc (LiftThenT action next) = LiftThenT (listen action) (\(a,w)-> go (acc <> w) $ next a)+      go acc (ChooseThenT options next) = ChooseThenT options $ go acc . next++instance MonadRWS r w s m => MonadRWS  r w s (ChoiceT f m)++instance MonadIO m => MonadIO (ChoiceT f m) where+  liftIO = lift . liftIO++mapChoiceT :: (forall x. m x -> n x) -> ChoiceT f m a -> ChoiceT f n a+mapChoiceT _ (FixedT value) = FixedT value+mapChoiceT f (LiftThenT action next) = LiftThenT (f action) (mapChoiceT f . next)+mapChoiceT f (ChooseThenT options next) = ChooseThenT options (mapChoiceT f . next)++runChoiceT :: Monad m => (forall x. f x -> m x) -> ChoiceT f m a -> m a+runChoiceT _ (FixedT value) = pure value+runChoiceT chooser (LiftThenT action next) = action >>= (runChoiceT chooser . next)+runChoiceT chooser (ChooseThenT options next) = chooser options >>= (runChoiceT chooser . next)++-- | A variant of 'runChoiceT' that allows for the selection function to+-- output 'Nothing' to represent the desire to potentially select a different+-- option for the previous choice.+runBacktrackableChoiceT ::+  forall f m a. Monad m+    =>+      (forall x. f x -> m (Maybe x)) -- ^ The selection function.+                                     -- If the result of the outputted computation is 'Nothing' then+                                     -- 'runBacktrackableChoiceT' will backtrack to the previous choice.+                                     -- Otherwise, the result is a 'Just' then it will proceed like 'runChoiceT'.+        -> ChoiceT f m a             -- ^ The choice structure to run+          -> m (Maybe a)             -- ^ The resulting computation. If the selection function backtracks on the+                                     -- first choice the result of the computation will be 'Nothing'.+runBacktrackableChoiceT _ (FixedT firstValue) = return $ Just firstValue+runBacktrackableChoiceT chooser (LiftThenT action next) = action >>= runBacktrackableChoiceT chooser . next+runBacktrackableChoiceT chooser (ChooseThenT options next) =+  do+    maybeChoice <- chooser options+    case maybeChoice of+      Nothing -> return Nothing+      Just choice -> do+        maybeResult <- runBacktrackableChoiceT chooser $ next choice+        case maybeResult of+          Nothing -> runBacktrackableChoiceT chooser $ ChooseThenT options next+          Just result -> return $ Just result

+ src/Control/Monad/Trans/Choice/Invariant.hs view

@@ -0,0 +1,185 @@+{-# Language RankNTypes #-}+{-# Language FlexibleInstances #-}+{-# Language ScopedTypeVariables #-}+{-# Language UndecidableInstances #-}+{-# Language MultiParamTypeClasses #-}++{-|+Module     : Control.Monad.Trans.Choice.Invariant+Copyright  : (c) Eamon Olive, 2020+             (c) Louis Hyde,  2020+License    : AGPL-3+Maintainer : ejolive97@gmail.com+Stability  : experimental++-}+module Control.Monad.Trans.Choice.Invariant+  ( ChoiceT+    ( ChoiceT+    )+  , runChoiceT+  , invmapChoiceT+  ) where++-- Internal imports++import Control.Monad.Class.Choice+  ( MonadChoice+  , choose+  )++-- External imports++import Control.Applicative+  ( Alternative+    ( empty+    , (<|>)+    )+  )+import Control.Monad.Except+  ( MonadError+    ( throwError+    , catchError+    )+  )+import Control.Monad+  ( MonadPlus+  )+import Control.Monad.IO.Class+  ( MonadIO+    ( liftIO+    )+  )+import Control.Monad.Reader.Class+  ( MonadReader+    ( ask+    , local+    )+  )+import Control.Monad.State.Class+  ( MonadState+    ( get+    , put+    )+  )+import Control.Monad.Trans+  ( MonadTrans+  , lift+  )+import Control.Monad.Writer.Class+  ( MonadWriter+    ( listen+    , pass+    , tell+    )+  )+import Data.Functor.Contravariant+  ( Contravariant+    ( contramap+    )+  )+import Data.Functor.Invariant+  ( Invariant+    ( invmap+    )+  )++-- | The choice monad transformer+-- It takes a monad and enriches it with choice.+newtype ChoiceT f m a = ChoiceT+  { _runChoiceT :: (forall x . f x -> m x) -> m a+  -- ^ Should not be used externally.+  -- runChoiceT has the proper argument order.+  }++-- | Transforms the computation inside the 'ChoiceT'.+-- This function differs from other map functions over the monads in monad transformers in that it requires an additional function of type @forall x . n x -> m x@.+-- This is because 'ChoiceT' is not a covariant functor over the category of monads, but rather an invariant functor.+-- +invmapChoiceT ::+  (forall x . n x -> m x)+    -> (m a -> n b)+      -> ChoiceT f m a+        -> ChoiceT f n b+invmapChoiceT f g m1 = ChoiceT (\ chooser -> g $ runChoiceT (\ options -> f $ chooser options) m1)++-- | Use a chooser to perform all the selections of a 'ChoiceT'.+-- This uses a sensible argument order unlike many of the other monad transformers.+runChoiceT ::+  (forall x . f x -> m x)+  -- ^ A chooser which can perform selections over @f@s containing arbitrary @x@s.+  -- This will be used to determine the result of each selection.+  -- +  -- This type proves the theorem :+  --+  -- > chooser (fmap f x) = fmap f (chooser x)+    -> ChoiceT f m a+    -- ^ A monad transformed by 'ChoiceT' to contain choices+      -> m a+      -- ^ The initial monad with the 'ChoiceT' removed and thus the choices resolved.+runChoiceT chooser m1 = _runChoiceT m1 chooser++-- | This acts as an map but does not go as "deep" as 'fmap'.+--+-- prop> lowMap f . lift = lift . f+--+-- prop> lowMap id = id+--+lowMap ::+  (m a -> m b)+    -> (ChoiceT f m a -> ChoiceT f m b)+lowMap f m = ChoiceT (\ chooser -> f $ runChoiceT chooser m)+    ++instance Functor m => Functor (ChoiceT f m) where+  fmap f (ChoiceT deChooser) = ChoiceT (\ chooser -> fmap f $ deChooser chooser)++instance Contravariant m => Contravariant (ChoiceT f m) where+  contramap f (ChoiceT deChooser) = ChoiceT (\ chooser -> contramap f $ deChooser chooser)++instance Invariant m => Invariant (ChoiceT f m) where+  invmap f1 f2 (ChoiceT deChooser) = ChoiceT (\ chooser -> invmap f1 f2 $ deChooser chooser)++instance Applicative m => Applicative (ChoiceT f m) where+  pure a =+    ChoiceT (\ _ -> pure a )+  (ChoiceT lDeChooser) <*> (ChoiceT rDeChooser) =+    ChoiceT (\ chooser -> lDeChooser chooser <*> rDeChooser chooser )++instance Alternative m => Alternative (ChoiceT f m) where+  empty = ChoiceT (const empty)+  m1 <|> m2 = ChoiceT (\ chooser -> runChoiceT chooser m1 <|> runChoiceT chooser m2)++instance Monad m => Monad (ChoiceT f m) where+  (ChoiceT deChooser) >>= f =+    ChoiceT (\ chooser -> deChooser chooser >>= (\ x -> runChoiceT chooser (f x)) )++instance MonadPlus m => MonadPlus (ChoiceT f m)++-- | 'ChoiceT' is a functor on the category of monads.+-- However it is an invariant functor.  Meaning the traditional @mapChoiceT@ cannot be implemented.+instance MonadTrans (ChoiceT f) where+  lift m = ChoiceT (\ _ -> m )++instance Monad m => MonadChoice f (ChoiceT f m) where+  choose f = ChoiceT (\ chooser -> chooser f )++instance MonadReader r m => MonadReader r (ChoiceT f m) where+  ask = lift ask+  local f = lowMap (local f)++instance MonadState s m => MonadState s (ChoiceT f m) where+  get = lift get+  put s = lift (put s) ++instance MonadWriter w m => MonadWriter w (ChoiceT f m) where+  tell w = lift (tell w)+  listen = lowMap listen+  pass   = lowMap pass++instance MonadIO m => MonadIO (ChoiceT f m) where+  liftIO = lift . liftIO++instance MonadError e m => MonadError e (ChoiceT f m) where+  throwError toThrow = lift (throwError toThrow)+  catchError m handler = ChoiceT (\ chooser -> catchError (runChoiceT chooser m) (runChoiceT chooser . handler))