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{-# LANGUAGE RebindableSyntax, MultiParamTypeClasses,
FlexibleInstances, FlexibleContexts #-}
-- Tests of the do-notation for the restricted monads
-- We demonstrate that all ordinary monads are restricted monads,
-- and show the frequently requested implementation
-- of MonadPlus in terms of Data.Set.
--
-- The tests are based on the code
-- http://okmij.org/ftp/Haskell/types.html#restricted-datatypes
module DoRestrictedM where
import Data.List
import Prelude (const, String, ($), (.), Maybe(..))
import qualified Prelude
import qualified Data.Set as Set
-- Defining the restricted monad
class MN2 m a where
return :: a -> m a
fail :: String -> m a
class (MN2 m a, MN2 m b) => MN3 m a b where
(>>=) :: m a -> (a -> m b) -> m b
m1 >> m2 = m1 >>= (const m2)
-- All regular monads are the instances of the restricted monad
newtype RegularM m a = RegularM{unRM :: m a}
instance Prelude.MonadFail m => MN2 (RegularM m) a where
return = RegularM . Prelude.return
fail = fail
instance Prelude.MonadFail m => MN3 (RegularM m) a b where
m >>= f = RegularM ((Prelude.>>=) (unRM m) (unRM . f))
-- We try to inject Maybe (as the regular monad) into Restricted Monad
test1s () = return "a" >>= (\x -> return $ "b" ++ x)
test1f () = fail "" >>= (\x -> return $ "b" ++ x)
-- the same with the do-notation
test1s_do () = do
x <- return "a"
return $ "b" ++ x
{-
whose inferred type is
*DoRestrictedM> :t test1s
test1s :: (MN3 m [Prelude.Char] [Prelude.Char]) => () -> m [Prelude.Char]
-}
test1sr :: Maybe String
test1sr = unRM $ test1s ()
-- Just "ba"
test1fr :: Maybe String
test1fr = unRM $ test1f ()
-- Nothing
test1sr_do :: Maybe String
test1sr_do = unRM $ test1s_do ()
-- Just "ba"
-- As often requested, we implement a MonadPlus `monad'
-- in terms of a Set. Set requires the Ord constraint.
newtype SMPlus a = SMPlus{unSM:: Set.Set a}
instance MN2 SMPlus a where
return = SMPlus . Set.singleton
fail x = SMPlus $ Set.empty
instance Prelude.Ord b => MN3 SMPlus a b where
m >>= f = SMPlus (Set.fold (Set.union . unSM . f) Set.empty (unSM m))
-- We cannot forget the Ord constraint, because the typechecker
-- will complain (and tell us exactly what we have forgotten).
-- Now we can instantiate the previously written test1s and test1d
-- functions for this Set monad:
test2sr :: Set.Set String
test2sr = unSM $ test1s ()
-- fromList ["ba"]
test2fr :: Set.Set String
test2fr = unSM $ test1f ()
-- fromList []
test2sr_do :: Set.Set String
test2sr_do = unSM $ test1s_do ()
-- fromList ["ba"]
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