klapaucius / 1.hs

Created July 04, 2012


    
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            Prelude Control.Monad> :set -XDefaultSignatures
 
Prelude Control.Monad> 
newtype Box a = Box a deriving Show
 
Prelude Control.Monad> 
instance Monad Box where
    return = Box
    (Box x) >>= f = f x
    
Prelude Control.Monad> join (Box (Box 2))
Box 2
Prelude Control.Monad> 
class DFunctor f where
    dmap :: (a -> b) -> f a -> f b
    default dmap :: Monad f => (a -> b) -> f a -> f b
    dmap f = ((return . f) =<<)
    
Prelude Control.Monad> 
instance DFunctor Box
 
Prelude Control.Monad> dmap (+1) $ Box 2
Box 3
Prelude Control.Monad> 
class DApplicative f where
    dpure :: a -> f a
    default dpure :: Monad f => a -> f a
    dpure = return
    dap :: f (a -> b) -> f a -> f b
    default dap :: Monad f => f (a -> b) -> f a -> f b
    dap = ap
    
Prelude Control.Monad> 
instance DApplicative Box
 
Prelude Control.Monad> dpure (+) `dap` Box 2 `dap` Box 3
Box 5
Prelude Control.Monad> 
newtype Xob a = Xob a deriving Show
 
Prelude Control.Monad> 
instance DFunctor Xob where
    dmap f (Xob a) = Xob . f $ a
    
Prelude Control.Monad> dmap (+1) . Xob $ 41 
Xob 42

          
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            Prelude> 
class DMonad m where
    djoin :: m(m a) -> m a
    djoin = dbind id
    
    dbind :: (a -> m b) -> m a -> m b
    default dbind :: DFunctor m => (a -> m b) -> m a -> m b
    dbind f = djoin . dmap f
    
    dreturn :: a -> m a
    default dreturn :: DApplicative m => a -> m a
    dreturn = dpure
    
class DFunctor f where
    dmap :: (a -> b) -> f a -> f b
    default dmap :: DMonad f => (a -> b) -> f a -> f b
    dmap f = dbind (dreturn . f)
    
class DApplicative f where
    dpure :: a -> f a
    default dpure :: DMonad f => a -> f a
    dpure = dreturn
    dap :: f (a -> b) -> f a -> f b
    default dap :: DMonad f => f (a -> b) -> f a -> f b
    dap = undefined
    
Prelude> instance DApplicative [] where
    dpure x = [x]
    dap = Control.Monad.ap
    
Prelude> instance DFunctor [] where
    dmap = map
    
Prelude> instance DMonad [] where
    djoin = concat
    
Prelude> dbind (\x -> [x,x]) [1..3]
[1,1,2,2,3,3]
Prelude> dbind dreturn [1..3]
[1,2,3]

          
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            Prelude Control.Monad Data.Traversable Data.Foldable Control.Applicative> 
class DTFunctor f where
    tmap :: (a -> b) -> f a -> f b
    default tmap :: Monad f => (a -> b) -> f a -> f b
    tmap f = ((return . f) =<<)
    default tmap :: Traversable f => (a -> b) -> f a -> f b
    tmap = fmapDefault
    
 
<interactive>:102:5:
    Duplicate default type signature:
      <interactive>:102:5-53: default tmap ::
                                        Monad f => (a -> b) -> f a -> f b
      <interactive>:104:5-59: default tmap ::
                                        Traversable f => (a -> b) -> f a -> f b
 
<interactive>:103:5:
    Conflicting definitions for `tmap'
    Bound at: <interactive>:103:5-8
              <interactive>:105:5-8