diff --git a/DeepControl/Applicative.hs b/DeepControl/Applicative.hs --- a/DeepControl/Applicative.hs +++ b/DeepControl/Applicative.hs @@ -351,8 +351,8 @@ -- [Just 3] -- >>> [1] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2 -- [Just 3,Just (-1),Just 2,Nothing] --- >>> [0,1] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2 --- [Just 2,Just 3,Just (-2),Just (-1),Just 0,Just 2,Nothing,Nothing] +-- >>> [1,2] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2 +-- [Just 3,Just (-1),Just 2,Nothing,Just 4,Just 0,Just 4,Nothing] -- -- >>> print 1 -*|return [\_ _ -> 3]|-* print 2 -- 1 diff --git a/DeepControl/Arrow.hs b/DeepControl/Arrow.hs --- a/DeepControl/Arrow.hs +++ b/DeepControl/Arrow.hs @@ -20,6 +20,7 @@ ) where import DeepControl.Applicative +import DeepControl.Commutative import DeepControl.Monad import Control.Arrow import Prelude hiding (id, (.)) @@ -30,11 +31,11 @@ newtype Kleisli2 m1 m2 a b = Kleisli2 { runKleisli2 :: a -> m1 (m2 b) } -instance (Applicative m1, Monad m1, Monad2 m2) => Category (Kleisli2 m1 m2) where +instance (Monad m1, Monad m2, Commutative m2) => Category (Kleisli2 m1 m2) where id = Kleisli2 $ (**:) (Kleisli2 g) . (Kleisli2 f) = Kleisli2 $ f >==> g -instance (Applicative m1, Monad m1, Monad2 m2) => Arrow (Kleisli2 m1 m2) where +instance (Monad m1, Monad m2, Commutative m2) => Arrow (Kleisli2 m1 m2) where arr f = Kleisli2 $ (**:) . f first (Kleisli2 f) = Kleisli2 $ \ ~(b,d) -> f b >>== \c -> (**:) (c,d) second (Kleisli2 f) = Kleisli2 $ \ ~(d,b) -> f b >>== \c -> (**:) (d,c) @@ -44,11 +45,11 @@ newtype Kleisli3 m1 m2 m3 a b = Kleisli3 { runKleisli3 :: a -> m1 (m2 (m3 b)) } -instance (Applicative m1, Monad m1, Monad2 m2, Monad3 m3) => Category (Kleisli3 m1 m2 m3) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => Category (Kleisli3 m1 m2 m3) where id = Kleisli3 $ (***:) (Kleisli3 g) . (Kleisli3 f) = Kleisli3 $ f >===> g -instance (Applicative m1, Monad m1, Monad2 m2, Monad3 m3) => Arrow (Kleisli3 m1 m2 m3) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => Arrow (Kleisli3 m1 m2 m3) where arr f = Kleisli3 $ (***:) . f first (Kleisli3 f) = Kleisli3 $ \ ~(b,d) -> f b >>>== \c -> (***:) (c,d) second (Kleisli3 f) = Kleisli3 $ \ ~(d,b) -> f b >>>== \c -> (***:) (d,c) @@ -58,11 +59,11 @@ newtype Kleisli4 m1 m2 m3 m4 a b = Kleisli4 { runKleisli4 :: a -> m1 (m2 (m3 (m4 b))) } -instance (Applicative m1, Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => Category (Kleisli4 m1 m2 m3 m4) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => Category (Kleisli4 m1 m2 m3 m4) where id = Kleisli4 $ (****:) (Kleisli4 g) . (Kleisli4 f) = Kleisli4 $ f >====> g -instance (Applicative m1, Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => Arrow (Kleisli4 m1 m2 m3 m4) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => Arrow (Kleisli4 m1 m2 m3 m4) where arr f = Kleisli4 $ (****:) . f first (Kleisli4 f) = Kleisli4 $ \ ~(b,d) -> f b >>>>== \c -> (****:) (c,d) second (Kleisli4 f) = Kleisli4 $ \ ~(d,b) -> f b >>>>== \c -> (****:) (d,c) @@ -72,13 +73,12 @@ newtype Kleisli5 m1 m2 m3 m4 m5 a b = Kleisli5 { runKleisli5 :: a -> m1 (m2 (m3 (m4 (m5 b)))) } -instance (Applicative m1, Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => Category (Kleisli5 m1 m2 m3 m4 m5) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => Category (Kleisli5 m1 m2 m3 m4 m5) where id = Kleisli5 $ (*****:) (Kleisli5 g) . (Kleisli5 f) = Kleisli5 $ f >=====> g -instance (Applicative m1, Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => Arrow (Kleisli5 m1 m2 m3 m4 m5) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => Arrow (Kleisli5 m1 m2 m3 m4 m5) where arr f = Kleisli5 $ (*****:) . f first (Kleisli5 f) = Kleisli5 $ \ ~(b,d) -> f b >>>>>== \c -> (*****:) (c,d) second (Kleisli5 f) = Kleisli5 $ \ ~(d,b) -> f b >>>>>== \c -> (*****:) (d,c) - diff --git a/DeepControl/Commutative.hs b/DeepControl/Commutative.hs --- a/DeepControl/Commutative.hs +++ b/DeepControl/Commutative.hs @@ -47,7 +47,7 @@ -- | [], Maybe, Either, Except and Writer are all commutative each other. -- So these monads can be deepened to Monad2, Monad3, Monad4 and Monad5. -- -class (Applicative c) => Commutative c where +class (Functor c) => Commutative c where -- | This method is equivalent for @'Data.Traversable.sequenceA'@ except the name. -- The only difference is the name "commute", that is to say from which no action kind of concepts smell. -- @@ -88,10 +88,8 @@ instance Commutative (Except e) where commute x = ExceptT . Identity |$> commute (runExcept x) -{- instance Commutative (Const m) where commute (Const m) = (*:) $ Const m --} {- instance Commutative ((->) r) where @@ -126,7 +124,7 @@ -- >>> sink2 $ Right (Just [1]) -- Just [Right 1] -- -sink2 :: (Commutative m1, Commutative m2, Applicative m3) => +sink2 :: (Commutative m1, Applicative m2, Applicative m3) => m1 (m2 (m3 a)) -> m2 (m3 (m1 a)) sink2 = (commute|$>) . commute @@ -147,7 +145,7 @@ -- >>> sink3 $ Right [Just [1]] -- [Just [Right 1]] -- -sink3 :: (Commutative m1, Commutative m2, Commutative m3, Applicative m4) => +sink3 :: (Commutative m1, Applicative m2, Applicative m3, Applicative m4) => m1 (m2 (m3 (m4 a))) -> m2 (m3 (m4 (m1 a))) sink3 = (sink2|$>) . commute @@ -163,7 +161,7 @@ ------------------------------------------------------------------------------ -- Level-4 -sink4 :: (Commutative m1, Commutative m2, Commutative m3, Commutative m4, Applicative m5) => +sink4 :: (Commutative m1, Applicative m2, Applicative m3, Applicative m4, Applicative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> m2 (m3 (m4 (m5 (m1 a)))) sink4 = (sink3|$>) . commute @@ -174,7 +172,7 @@ ------------------------------------------------------------------------------ -- Level-5 -sink5 :: (Commutative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5, Applicative m6) => +sink5 :: (Commutative m1, Applicative m2, Applicative m3, Applicative m4, Applicative m5, Applicative m6) => m1 (m2 (m3 (m4 (m5 (m6 a))))) -> m2 (m3 (m4 (m5 (m6 (m1 a))))) sink5 = (sink4|$>) . commute diff --git a/DeepControl/Monad.hs b/DeepControl/Monad.hs --- a/DeepControl/Monad.hs +++ b/DeepControl/Monad.hs @@ -8,12 +8,12 @@ Portability : --- This module enables you to program in Monad for more __deeper__ level than the usual 'Control.Monad' module expresses. -You would soon realize exactly what __/more deeper level/__ means by reading the example codes in order, which are attached on the Monadx(Monad2, Monad3, etc) classes below. +You would soon realize exactly what __/more deeper level/__ means by reading the example codes in order, which are attached on the Monadx(Monad, Monad, etc) classes below. Note: - * This module never makes mlt(monad-transformer-library) unnessasary. - The range in which this module is helpful is regrettably confined to the range of deep monads (namely Monad2, Monad3, etc). + * This module never makes mtl(monad-transformer-library) unnessasary. + The range in which this module is helpful is regrettably confined to the range of deep monads (namely Monad, Monad, etc). * In my opinion this bad confinement is hard-wired with the ability of the compiler, that is to say GHC doesn't parse @(r->)@ or @((->) r)@ as a data constructor; thus some fundamental expressions such as @(r->)|$>@ or @fmap (r->)@ are useless. @@ -33,7 +33,7 @@ -- * Level-2 -- ** bind - Monad2(..), + (>>==), -- ** sequence (>>~), -- ** cover-bind @@ -45,7 +45,7 @@ -- * Level-3 -- ** bind - Monad3(..), + (>>>==), -- ** sequence (>>>~), -- ** cover-bind @@ -57,7 +57,7 @@ -- * Level-4 -- ** bind - Monad4(..), + (>>>>==), -- ** sequence (>>>>~), -- ** cover-bind @@ -73,7 +73,7 @@ -- * Level-5 -- ** bind - Monad5(..), + (>>>>>==), -- ** sequence (>>>>>~), -- ** cover-bind @@ -88,10 +88,11 @@ (->>>>~), (>->>>~), (>>->>~), (>>>->~), (>>>>-~), -- ** composite (>=====>), - + ) where import DeepControl.Applicative +import DeepControl.Commutative import Control.Monad import Control.Monad.Writer (Writer, WriterT(..), runWriter) @@ -152,7 +153,7 @@ infixr 1 ->==, >-== infixr 1 ->~, >-~ --- | The 'Monad2' class defines the bind function for level-2 types @m1 (m2 a)@ such as [[a]], Maybe [a], Either () (Maybe a), a -> [b], IO [a], etc. +-- | The level-2 bind function, analogous for @'>>='@. -- -- >>> :{ -- -- List-List monad @@ -174,69 +175,39 @@ -- in [averageM [10, 25, 70], averageM []] -- :} -- [Just 35.0,Nothing] --- -class (Monad m2) => Monad2 m2 where - -- | The level-2 bind function, analogous for @'>>='@. - (>>==) :: (Monad m1) => m1 (m2 a) -> (a -> m1 (m2 b)) -> m1 (m2 b) +-- +(>>==) :: (Monad m1, Monad m2, Commutative m2) => m1 (m2 a) -> (a -> m1 (m2 b)) -> m1 (m2 b) +m >>== f = m >>= \x -> join |$> (commute $ f |$> x) -- | The level-2 composite function, analogous for @'>=>'@. -(>==>) :: (Monad m1, Monad2 m2) => (a -> m1 (m2 b)) -> (b -> m1 (m2 c)) -> a -> m1 (m2 c) +(>==>) :: (Monad m1, Monad m2, Commutative m2) => (a -> m1 (m2 b)) -> (b -> m1 (m2 c)) -> a -> m1 (m2 c) f >==> g = \x -> f x >>== g -- | The level-2 sequence function, analogous for @'>>'@. -- -- Definition: @ m >>~ f = m >>== \\_ -> f @ -(>>~) :: (Monad m1, Monad2 m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b) +(>>~) :: (Monad m1, Monad m2, Commutative m2) => m1 (m2 a) -> m1 (m2 b) -> m1 (m2 b) m >>~ f = m >>== \_ -> f -- | A level-2 cover-bind function, analogous for @'>>='@. -- -- Definition: @ m >-== f = (-*) m >>== f @ -(>-==) :: (Monad m1, Monad2 m2) => m1 a -> (a -> m1 (m2 b)) -> m1 (m2 b) +(>-==) :: (Monad m1, Monad m2, Commutative m2) => m1 a -> (a -> m1 (m2 b)) -> m1 (m2 b) m >-== f = (-*) m >>== f -- | A level-2 cover-bind function, analogous for @'>>='@. -- -- Definition: @ m ->== f = (*:) m >>== f @ -(->==) :: (Monad m1, Monad2 m2) => m2 a -> (a -> m1 (m2 b)) -> m1 (m2 b) +(->==) :: (Monad m1, Monad m2, Commutative m2) => m2 a -> (a -> m1 (m2 b)) -> m1 (m2 b) m ->== f = (*:) m >>== f -- | A level-2 cover-sequence function, analogous for @'>>'@. -- -- Definition: @ m >-~ f = (-*) m >>~ f @ -(>-~) :: (Monad m1, Monad2 m2) => m1 a -> m1 (m2 b) -> m1 (m2 b) +(>-~) :: (Monad m1, Monad m2, Commutative m2) => m1 a -> m1 (m2 b) -> m1 (m2 b) m >-~ f = (-*) m >>~ f -- | A level-2 cover-sequence function, analogous for @'>>'@. -- -- Definition: @ m ->~ f = (*:) m >>~ f @ -(->~) :: (Monad m1, Monad2 m2) => m2 a -> m1 (m2 b) -> m1 (m2 b) +(->~) :: (Monad m1, Monad m2, Commutative m2) => m2 a -> m1 (m2 b) -> m1 (m2 b) m ->~ f = (*:) m >>~ f -instance Monad2 Maybe where - mv >>== f = - mv >>= \mv -> - case mv of - Nothing -> (*:) Nothing - Just a -> f a - -instance Monad2 [] where - mv >>== f = - mv >>= \xs -> - foldr (\x acc -> f x <$|(++)|*> acc) ((*:) []) xs - -instance Monad2 (Either e) where - mv >>== f = - mv >>= \mv -> - case mv of - Left l -> (*:) (Left l) - Right r -> f r - -instance Monad2 (Except e) where - m >>== f = (ExceptT . Identity |$>) $ (runExcept |$> m) >>== runExcept |$>> f - -instance (Monoid w) => Monad2 (Writer w) where - mv >>== f = - mv >>= \x -> runWriterT x >- \(Identity (a, w)) -> - f a <$| (\x -> runWriterT x >- \(Identity (b, w')) -> - WriterT $ Identity (b, w <> w')) - - ------------------------------------------------------------------------------- -- Level-3 functions @@ -245,7 +216,7 @@ infixr 1 >--==, ->-==, -->==, >>-==, >->==, ->>== infixr 1 >--~, ->-~, -->~, >>-~, >->~, ->>~ --- | The 'Monad3' class defines the bind function for level-3 types @m1 (m2 (m3 a)@. +-- | The level-3 bind function, analogous for @'>>='@. -- -- >>> :{ -- -- IO-List-List monad @@ -262,7 +233,7 @@ -- ("b",2) -- [["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]] -- --- This messy code above can be neatly rewritten to the code below with cover functions. +-- This messy code above can be neatly rewritten to the code below by grace of the cover functions. -- -- >>> :{ -- -- IO-List-List monad @@ -279,68 +250,39 @@ -- ("b",2) -- [["a0","b0"],["a0","b1","b2"],["a1","a2","b0"],["a1","a2","b1","b2"]] -- -class (Monad2 m3) => Monad3 m3 where - -- | The level-3 bind function, analogous for @'>>='@. - (>>>==) :: (Monad m1, Monad2 m2) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +m >>>== f = m >>== \x -> join |$>> (sink2 $ f |$> x) -(>===>) :: (Monad m1, Monad2 m2, Monad3 m3) => (a -> m1 (m2 (m3 b))) -> (b -> m1 (m2 (m3 c))) -> a -> m1 (m2 (m3 c)) +(>===>) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => (a -> m1 (m2 (m3 b))) -> (b -> m1 (m2 (m3 c))) -> a -> m1 (m2 (m3 c)) f >===> g = \x -> f x >>>== g -(>>>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 (m3 a)) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m >>>~ k = m >>>== \_ -> k -(>--==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) m >--== k = (-**) m >>>== k -(->-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) m ->-== k = (*-*) m >>>== k -(-->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m3 a -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) m -->== k = (**:) m >>>== k -(>>-==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) m >>-== k = (--*) m >>>== k -(->>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) m ->>== k = (*:) m >>>== k -(>->==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) +(>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m3 a) -> (a -> m1 (m2 (m3 b))) -> m1 (m2 (m3 b)) m >->== k = (-*) m >>>== k -(-->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m3 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m -->~ k = (**:) m >>>~ k -(->-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m ->-~ k = (*-*) m >>>~ k -(>--~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 a -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m >--~ k = (-**) m >>>~ k -(->>~) :: (Monad m1, Monad2 m2, Monad3 m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m2 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m ->>~ k = (*:) m >>>~ k -(>->~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m3 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m >->~ k = (-*) m >>>~ k -(>>-~) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) +(>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => m1 (m2 a) -> m1 (m2 (m3 b)) -> m1 (m2 (m3 b)) m >>-~ k = (--*) m >>>~ k -instance Monad3 Maybe where - mv >>>== f = - mv >>== \mv -> - case mv of - Nothing -> (**:) Nothing - Just a -> f a - -instance Monad3 [] where - mv >>>== f = - mv >>== \xs -> - foldr (\x acc -> f x <<$|(++)|*>> acc) ((**:) []) xs - -instance Monad3 (Either e) where - mv >>>== f = - mv >>== \mv -> - case mv of - Left l -> (**:) (Left l) - Right r -> f r - -instance Monad3 (Except e) where - m >>>== f = (ExceptT . Identity |$>>) $ (runExcept |$>> m) >>>== runExcept |$>>> f - -instance (Monoid w) => Monad3 (Writer w) where - mv >>>== f = - mv >>== \x -> runWriterT x >- \(Identity (a, w)) -> - f a <<$| (\x -> runWriterT x >- \(Identity (b, w')) -> - WriterT $ Identity (b, w <> w')) - ------------------------------------------------------------------------------- -- Level-4 functions @@ -353,104 +295,76 @@ infixr 1 -->>~, ->->~, >-->~, >->-~, ->>-~, >>--~ infixr 1 ->>>~, >->>~, >>->~, >>>-~ -class (Monad3 m4) => Monad4 m4 where - (>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +m >>>>== f = m >>>== \x -> join |$>>> (sink3 $ f |$> x) -(>====>) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => (a -> m1 (m2 (m3 (m4 b)))) -> (b -> m1 (m2 (m3 (m4 c)))) -> a -> m1 (m2 (m3 (m4 c))) +(>====>) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => (a -> m1 (m2 (m3 (m4 b)))) -> (b -> m1 (m2 (m3 (m4 c)))) -> a -> m1 (m2 (m3 (m4 c))) f >====> g = \x -> f x >>>>== g -(>>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >>>>~ k = m >>>>== \_ -> k -(--->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m4 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(--->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m4 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m --->== k = (***:) m >>>>== k -(-->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(-->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m -->-== k = (**-*) m >>>>== k -(->--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(->--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m ->--== k = (*-**) m >>>>== k -(>---==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>---==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 a -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >---== k = (-***) m >>>>== k -(-->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(-->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m -->>== k = (**:) m >>>>== k -(->->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(->->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m ->->== k = (*-*) m >>>>== k -(>-->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >-->== k = (-**) m >>>>== k -(>->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >->-== k = (-*-*) m >>>>== k -(->>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(->>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m ->>-== k = (*--*) m >>>>== k -(>>--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >>--== k = (--**) m >>>>== k -(->>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(->>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m ->>>== k = (*:) m >>>>== k -(>->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >->>== k = (-*) m >>>>== k -(>>->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >>->== k = (--*) m >>>>== k -(>>>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) +(>>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 b)))) -> m1 (m2 (m3 (m4 b))) m >>>-== k = (---*) m >>>>== k -(--->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m4 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(--->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m4 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m --->~ k = (***:) m >>>>~ k -(-->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(-->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m -->-~ k = (**-*) m >>>>~ k -(->--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(->--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m ->--~ k = (*-**) m >>>>~ k -(>---~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>---~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 a -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >---~ k = (-***) m >>>>~ k -(-->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m3 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(-->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m3 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m -->>~ k = (**:) m >>>>~ k -(->->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(->->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m ->->~ k = (*-*) m >>>>~ k -(>-->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m4 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >-->~ k = (-**) m >>>>~ k -(>->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >->-~ k = (-*-*) m >>>>~ k -(->>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(->>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m ->>-~ k = (*--*) m >>>>~ k -(>>--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 a) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >>--~ k = (--**) m >>>>~ k -(->>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(->>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m ->>>~ k = (*:) m >>>>~ k -(>->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >->>~ k = (-*) m >>>>~ k -(>>->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >>->~ k = (--*) m >>>>~ k -(>>>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) +(>>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 b))) -> m1 (m2 (m3 (m4 b))) m >>>-~ k = (---*) m >>>>~ k -instance Monad4 Maybe where - mv >>>>== f = - mv >>>== \mv -> - case mv of - Nothing -> (***:) Nothing - Just a -> f a - -instance Monad4 [] where - mv >>>>== f = - mv >>>== \xs -> - foldr (\x acc -> f x <<<$|(++)|*>>> acc) ((***:) []) xs - -instance Monad4 (Either e) where - mv >>>>== f = - mv >>>== \mv -> - case mv of - Left l -> (***:) (Left l) - Right r -> f r - -instance Monad4 (Except e) where - m >>>>== f = (ExceptT . Identity |$>>>) $ (runExcept |$>>> m) >>>>== runExcept |$>>>> f - -instance (Monoid w) => Monad4 (Writer w) where - mv >>>>== f = - mv >>>== \x -> runWriterT x >- \(Identity (a, w)) -> - f a <<<$| (\x -> runWriterT x >- \(Identity (b, w')) -> - WriterT $ Identity (b, w <> w')) - ------------------------------------------------------------------------------- -- Level-5 functions @@ -466,168 +380,140 @@ infixr 1 -->>>~, ->->>~, >-->>~, >->->~, ->>->~, >>-->~, >>->-~, >->>-~, ->>>-~, >>>--~ infixr 1 ->>>>~, >->>>~, >>->>~, >>>->~, >>>>-~ -class (Monad4 m5) => Monad5 m5 where - (>>>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 (m5 a)))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +m >>>>>== f = m >>>>== \x -> join |$>>>> (sink4 $ f |$> x) -(>=====>) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (a -> m1 (m2 (m3 (m4 (m5 b))))) -> (b -> m1 (m2 (m3 (m4 (m5 c))))) -> a -> m1 (m2 (m3 (m4 (m5 c)))) +(>=====>) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => (a -> m1 (m2 (m3 (m4 (m5 b))))) -> (b -> m1 (m2 (m3 (m4 (m5 c))))) -> a -> m1 (m2 (m3 (m4 (m5 c)))) f >=====> g = \x -> f x >>>>>== g -(>>>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m4 (m5 a)))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 (m5 a)))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>>>~ k = m >>>>>== \_ -> k -(---->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m5 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(---->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m5 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ---->== k = (****:) m >>>>>== k -(--->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(--->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m --->-== k = (***-*) m >>>>>== k -(-->--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->--== k = (**-**) m >>>>>== k -(->---==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->---==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->---== k = (*-***) m >>>>>== k -(>----==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>----==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 a -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >----== k = (-****) m >>>>>== k -(--->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(--->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m --->>== k = (***:) m >>>>>== k -(-->->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->->== k = (**-*) m >>>>>== k -(->-->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->-->== k = (*-**) m >>>>>== k -(>--->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>--->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m5 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >--->== k = (-***) m >>>>>== k -(>-->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>-->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >-->-== k = (-**-*) m >>>>>== k -(->->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->->-== k = (*-*-*) m >>>>>== k -(-->>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->>-== k = (**--*) m >>>>>== k -(->>--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>--== k = (*--**) m >>>>>== k -(>->--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->--== k = (-*-**) m >>>>>== k -(>>---==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>---==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 a) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>---== k = (--***) m >>>>>== k -(-->>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->>>== k = (**:) m >>>>>== k -(->->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->->>== k = (*-*) m >>>>>== k -(>-->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>-->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >-->>== k = (-**) m >>>>>== k -(>->->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->->== k = (-*-*) m >>>>>== k -(->>->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>->== k = (*--*) m >>>>>== k -(>>-->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>-->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m5 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>-->== k = (--**) m >>>>>== k -(>>->-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>->-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>->-== k = (--*-*) m >>>>>== k -(>->>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->>-== k = (-*--*) m >>>>>== k -(->>>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>>-== k = (*---*) m >>>>>== k -(>>>--==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>--==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 a)) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>--== k = (---**) m >>>>>== k -(->>>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>>>== k = (*:) m >>>>>== k -(>->>>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->>>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->>>== k = (-*) m >>>>>== k -(>>->>==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>->>==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>->>== k = (--*) m >>>>>== k -(>>>->==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>->==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m5 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>->== k = (---*) m >>>>>== k -(>>>>-==) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>>-==) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 a))) -> (a -> m1 (m2 (m3 (m4 (m5 b))))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>>-== k = (----*) m >>>>>== k -(---->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m5 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(---->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m5 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ---->~ k = (****:) m >>>>>~ k -(--->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(--->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m --->-~ k = (***-*) m >>>>>~ k -(-->--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->--~ k = (**-**) m >>>>>~ k -(->---~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->---~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->---~ k = (*-***) m >>>>>~ k -(>----~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>----~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 a -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >----~ k = (-****) m >>>>>~ k -(--->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m4 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(--->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m4 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m --->>~ k = (***:) m >>>>>~ k -(-->->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->->~ k = (**-*) m >>>>>~ k -(->-->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->-->~ k = (*-**) m >>>>>~ k -(>--->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>--->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m5 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >--->~ k = (-***) m >>>>>~ k -(>-->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>-->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >-->-~ k = (-**-*) m >>>>>~ k -(->->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->->-~ k = (*-*-*) m >>>>>~ k -(-->>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->>-~ k = (**--*) m >>>>>~ k -(->>--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>--~ k = (*--**) m >>>>>~ k -(>->--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->--~ k = (-*-**) m >>>>>~ k -(>>---~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>---~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 a) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>---~ k = (--***) m >>>>>~ k -(-->>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m3 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(-->>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m3 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m -->>>~ k = (**:) m >>>>>~ k -(->->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->->>~ k = (*-*) m >>>>>~ k -(>-->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>-->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m4 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >-->>~ k = (-**) m >>>>>~ k -(>->->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->->~ k = (-*-*) m >>>>>~ k -(->>->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>->~ k = (*--*) m >>>>>~ k -(>>-->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>-->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m5 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>-->~ k = (--**) m >>>>>~ k -(>>->-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>->-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>->-~ k = (--*-*) m >>>>>~ k -(>->>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->>-~ k = (-*--*) m >>>>>~ k -(->>>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>>-~ k = (*---*) m >>>>>~ k -(>>>--~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>--~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 a)) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>--~ k = (---**) m >>>>>~ k -(->>>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m2 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(->>>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m2 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m ->>>>~ k = (*:) m >>>>>~ k -(>->>>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>->>>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m3 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >->>>~ k = (-*) m >>>>>~ k -(>>->>~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>->>~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m4 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>->>~ k = (--*) m >>>>>~ k -(>>>->~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>->~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m5 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>->~ k = (---*) m >>>>>~ k -(>>>>-~) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) +(>>>>-~) :: (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => m1 (m2 (m3 (m4 a))) -> m1 (m2 (m3 (m4 (m5 b)))) -> m1 (m2 (m3 (m4 (m5 b)))) m >>>>-~ k = (----*) m >>>>>~ k - -instance Monad5 Maybe where - mv >>>>>== f = - mv >>>>== \mv -> - case mv of - Nothing -> (****:) Nothing - Just a -> f a - -instance Monad5 [] where - mv >>>>>== f = - mv >>>>== \xs -> - foldr (\x acc -> f x <<<<$|(++)|*>>>> acc) ((****:) []) xs - -instance Monad5 (Either e) where - mv >>>>>== f = - mv >>>>== \mv -> - case mv of - Left l -> (****:) (Left l) - Right r -> f r - -instance Monad5 (Except e) where - m >>>>>== f = (ExceptT . Identity |$>>>>) $ (runExcept |$>>>> m) >>>>>== runExcept |$>>>>> f - -instance (Monoid w) => Monad5 (Writer w) where - mv >>>>>== f = - mv >>>>== \x -> runWriterT x >- \(Identity (a, w)) -> - f a <<<<$| (\x -> runWriterT x >- \(Identity (b, w')) -> - WriterT $ Identity (b, w <> w')) diff --git a/DeepControl/Monad/Trans.hs b/DeepControl/Monad/Trans.hs --- a/DeepControl/Monad/Trans.hs +++ b/DeepControl/Monad/Trans.hs @@ -197,31 +197,28 @@ -- Level-2 class MonadTrans2 t where - liftT2 :: (Monad m1, Monad2 m2) => m1 (m2 a) -> t m1 m2 a + liftT2 :: (Monad m1, Monad m2) => m1 (m2 a) -> t m1 m2 a liftTT2 - :: (Monad m1, Monad (t2 m1 m2), Monad2 m2, + :: (Monad m1, Monad (t2 m1 m2), Monad m2, MonadTrans t1, MonadTrans2 t2) => m1 (m2 a) -> t1 (t2 m1 m2) a liftTT2 = liftT.liftT2 liftTTT2 - :: (Monad m1, Monad (t1 (t2 m1 m2)), Monad (t2 m1 m2), - Monad2 m2, + :: (Monad m1, Monad (t1 (t2 m1 m2)), Monad (t2 m1 m2), Monad m2, MonadTrans t, MonadTrans t1, MonadTrans2 t2) => m1 (m2 a) -> t (t1 (t2 m1 m2)) a liftTTT2 = liftT.liftT.liftT2 liftTTTT2 - :: (Monad m1, Monad (t1 (t1' (t2 m1 m2))), Monad (t1' (t2 m1 m2)), Monad (t2 m1 m2), - Monad2 m2, + :: (Monad m1, Monad (t1 (t1' (t2 m1 m2))), Monad (t1' (t2 m1 m2)), Monad (t2 m1 m2), Monad m2, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans2 t2) => m1 (m2 a) -> t (t1 (t1' (t2 m1 m2))) a liftTTTT2 = liftT.liftT.liftT.liftT2 liftTTTTT2 - :: (Monad m1, Monad (t1 (t1' (t1'' (t2 m1 m2)))), Monad (t1' (t1'' (t2 m1 m2))), Monad (t1'' (t2 m1 m2)), Monad (t2 m1 m2), - Monad2 m2, + :: (Monad m1, Monad (t1 (t1' (t1'' (t2 m1 m2)))), Monad (t1' (t1'' (t2 m1 m2))), Monad (t1'' (t2 m1 m2)), Monad (t2 m1 m2), Monad m2, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans t1'', MonadTrans2 t2) => m1 (m2 a) -> t (t1 (t1' (t1'' (t2 m1 m2)))) a liftTTTTT2 = liftT.liftT.liftT.liftT.liftT2 @@ -248,10 +245,10 @@ infixl 3 |-*|, |*-|, |**| class (MonadTransCover (Trans2Down t2)) => MonadTransCover2 t2 where - (|-*|) :: (Monad m1, Monad2 m2) => (Trans2Down t2) m1 a -> t2 m1 m2 a - (|*-|) :: (Monad m1, Monad2 m2) => (Trans2Down t2) m2 a -> t2 m1 m2 a + (|-*|) :: (Monad m1, Monad m2) => (Trans2Down t2) m1 a -> t2 m1 m2 a + (|*-|) :: (Monad m1, Monad m2) => (Trans2Down t2) m2 a -> t2 m1 m2 a -(|**|) :: (Monad m1, Monad2 m2, MonadTransCover2 t2) => +(|**|) :: (Monad m1, Monad m2, MonadTransCover2 t2) => (M_ t2) a -> t2 m1 m2 a (|**|) = (|*-|) . (|*|) @@ -268,30 +265,28 @@ -- Level-3 class MonadTrans3 t where - liftT3 :: (Monad m1, Monad2 m2, Monad3 m3) => m1 (m2 (m3 a)) -> t m1 m2 m3 a + liftT3 :: (Monad m1, Monad m2, Monad m3) => m1 (m2 (m3 a)) -> t m1 m2 m3 a liftTT3 - :: (Monad m1, Monad (t3 m1 m2 m3), Monad2 m2, Monad3 m3, + :: (Monad m1, Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t3 m1 m2 m3) a liftTT3 = liftT.liftT3 liftTTT3 - :: (Monad m1, Monad (t1 (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad2 m2, Monad3 m3, + :: (Monad m1, Monad (t1 (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans t1, MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t1 (t3 m1 m2 m3)) a liftTTT3 = liftT.liftT.liftT3 liftTTTT3 - :: (Monad m1, Monad (t1 (t1' (t3 m1 m2 m3))), Monad (t1' (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), - Monad2 m2, Monad3 m3, + :: (Monad m1, Monad (t1 (t1' (t3 m1 m2 m3))), Monad (t1' (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t1 (t1' (t3 m1 m2 m3))) a liftTTTT3 = liftT.liftT.liftT.liftT3 liftTTTTT3 - :: (Monad m1, Monad (t1 (t1' (t1'' (t3 m1 m2 m3)))), Monad (t1' (t1'' (t3 m1 m2 m3))), Monad (t1'' (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), - Monad2 m2, Monad3 m3, + :: (Monad m1, Monad (t1 (t1' (t1'' (t3 m1 m2 m3)))), Monad (t1' (t1'' (t3 m1 m2 m3))), Monad (t1'' (t3 m1 m2 m3)), Monad (t3 m1 m2 m3), Monad m2, Monad m3, MonadTrans t, MonadTrans t1, MonadTrans t1', MonadTrans t1'', MonadTrans3 t3) => m1 (m2 (m3 a)) -> t (t1 (t1' (t1'' (t3 m1 m2 m3)))) a liftTTTTT3 = liftT.liftT.liftT.liftT.liftT3 @@ -319,22 +314,22 @@ infixl 3 |--*|, |-*-|, |*--| class (MonadTransCover2 (Trans3Down t3)) => MonadTransCover3 t3 where - (|--*|) :: (Monad m1, Monad2 m2, Monad3 m3) => (Trans3Down t3) m1 m2 a -> t3 m1 m2 m3 a - (|-*-|) :: (Monad m1, Monad2 m2, Monad3 m3) => (Trans3Down t3) m1 m3 a -> t3 m1 m2 m3 a - (|*--|) :: (Monad m1, Monad2 m2, Monad3 m3) => (Trans3Down t3) m2 m3 a -> t3 m1 m2 m3 a + (|--*|) :: (Monad m1, Monad m2, Monad m3) => (Trans3Down t3) m1 m2 a -> t3 m1 m2 m3 a + (|-*-|) :: (Monad m1, Monad m2, Monad m3) => (Trans3Down t3) m1 m3 a -> t3 m1 m2 m3 a + (|*--|) :: (Monad m1, Monad m2, Monad m3) => (Trans3Down t3) m2 m3 a -> t3 m1 m2 m3 a infixl 3 |***| -(|***|) :: (Monad m1, Monad2 m2, Monad3 m3, MonadTransCover3 t3) => +(|***|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (M__ t3) a -> t3 m1 m2 m3 a infixl 3 |-**|, |*-*|, |**-| (|***|) = (|--*|) . (|**|) -(|-**|) :: (Monad m1, Monad2 m2, Monad3 m3, MonadTransCover3 t3) => +(|-**|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (T__ t3) m1 a -> t3 m1 m2 m3 a (|-**|) = (|--*|) . (|-*|) -(|*-*|) :: (Monad m1, Monad2 m2, Monad3 m3, MonadTransCover3 t3) => +(|*-*|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (T__ t3) m2 a -> t3 m1 m2 m3 a (|*-*|) = (|--*|) . (|*-|) -(|**-|) :: (Monad m1, Monad2 m2, Monad3 m3, MonadTransCover3 t3) => +(|**-|) :: (Monad m1, Monad m2, Monad m3, MonadTransCover3 t3) => (T__ t3) m3 a -> t3 m1 m2 m3 a (|**-|) = (|-*-|) . (|*-|) @@ -351,7 +346,7 @@ -- Level-4 class MonadTrans4 t where - liftT4 :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => m1 (m2 (m3 (m4 a))) -> t m1 m2 m3 m4 a + liftT4 :: (Monad m1, Monad m2, Monad m3, Monad m4) => m1 (m2 (m3 (m4 a))) -> t m1 m2 m3 m4 a class (MonadTrans3 (Trans4Down t4), MonadTrans4 t4) => MonadTrans4Down t4 where type Trans4Down t4 :: (* -> *) -> (* -> *) -> (* -> *) -> * -> * @@ -378,45 +373,45 @@ infixl 3 |---*|, |--*-|, |-*--|, |*---| class (MonadTransCover3 (Trans4Down t4)) => MonadTransCover4 t4 where - (|---*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => (Trans4Down t4) m1 m2 m3 a -> t4 m1 m2 m3 m4 a - (|--*-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => (Trans4Down t4) m1 m2 m4 a -> t4 m1 m2 m3 m4 a - (|-*--|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => (Trans4Down t4) m1 m3 m4 a -> t4 m1 m2 m3 m4 a - (|*---|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => (Trans4Down t4) m2 m3 m4 a -> t4 m1 m2 m3 m4 a + (|---*|) :: (Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m1 m2 m3 a -> t4 m1 m2 m3 m4 a + (|--*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m1 m2 m4 a -> t4 m1 m2 m3 m4 a + (|-*--|) :: (Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m1 m3 m4 a -> t4 m1 m2 m3 m4 a + (|*---|) :: (Monad m1, Monad m2, Monad m3, Monad m4) => (Trans4Down t4) m2 m3 m4 a -> t4 m1 m2 m3 m4 a infixl 3 |****| -(|****|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|****|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (M___ t4) a -> t4 m1 m2 m3 m4 a (|****|) = (|---*|) . (|***|) infixl 3 |--**|, |-*-*|, |-**-|, |*-*-|, |**--|, |*--*| -(|--**|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|--**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m1 m2 a -> t4 m1 m2 m3 m4 a (|--**|) = (|---*|) . (|--*|) -(|-*-*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|-*-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m1 m3 a -> t4 m1 m2 m3 m4 a (|-*-*|) = (|---*|) . (|-*-|) -(|-**-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|-**-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m1 m4 a -> t4 m1 m2 m3 m4 a (|-**-|) = (|--*-|) . (|-*-|) -(|*-*-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|*-*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m2 m4 a -> t4 m1 m2 m3 m4 a (|*-*-|) = (|--*-|) . (|*--|) -(|**--|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|**--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m3 m4 a -> t4 m1 m2 m3 m4 a (|**--|) = (|-*--|) . (|*--|) -(|*--*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|*--*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T2__ t4) m2 m3 a -> t4 m1 m2 m3 m4 a (|*--*|) = (|---*|) . (|*--|) infixl 3 |-***|, |*-**|, |**-*|, |***-| -(|-***|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|-***|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m1 a -> t4 m1 m2 m3 m4 a (|-***|) = (|---*|) . (|-**|) -(|*-**|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|*-**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m2 a -> t4 m1 m2 m3 m4 a (|*-**|) = (|---*|) . (|*-*|) -(|**-*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|**-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m3 a -> t4 m1 m2 m3 m4 a (|**-*|) = (|---*|) . (|**-|) -(|***-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, MonadTransCover4 t4) => +(|***-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, MonadTransCover4 t4) => (T___ t4) m4 a -> t4 m1 m2 m3 m4 a (|***-|) = (|--*-|) . (|**-|) @@ -433,7 +428,7 @@ -- Level-5 class MonadTrans5 t where - liftT5 :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => m1 (m2 (m3 (m4 (m5 a)))) -> t m1 m2 m3 m4 m5 a + liftT5 :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => m1 (m2 (m3 (m4 (m5 a)))) -> t m1 m2 m3 m4 m5 a class (MonadTrans4 (Trans5Down t5), MonadTrans5 t5) => MonadTrans5Down t5 where type Trans5Down t5 :: (* -> *) -> (* -> *) -> (* -> *) -> (* -> *) -> * -> * @@ -463,74 +458,74 @@ infixl 3 |----*|, |---*-|, |--*--|, |-*---|, |*----| class (MonadTransCover4 (Trans5Down t5)) => MonadTransCover5 t5 where - (|----*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (Trans5Down t5) m1 m2 m3 m4 a -> t5 m1 m2 m3 m4 m5 a - (|---*-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (Trans5Down t5) m1 m2 m3 m5 a -> t5 m1 m2 m3 m4 m5 a - (|--*--|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (Trans5Down t5) m1 m2 m4 m5 a -> t5 m1 m2 m3 m4 m5 a - (|-*---|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (Trans5Down t5) m1 m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a - (|*----|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => (Trans5Down t5) m2 m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a + (|----*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m2 m3 m4 a -> t5 m1 m2 m3 m4 m5 a + (|---*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m2 m3 m5 a -> t5 m1 m2 m3 m4 m5 a + (|--*--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m2 m4 m5 a -> t5 m1 m2 m3 m4 m5 a + (|-*---|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m1 m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a + (|*----|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5) => (Trans5Down t5) m2 m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a infixl 3 |*****| -(|*****|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*****|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (M____ t5) a -> t5 m1 m2 m3 m4 m5 a (|*****|) = (|----*|) . (|****|) infixl 3 |---**|, |--*-*|, |-*--*|, |*---*|, |*--*-|, |*-*--|, |**---| -(|---**|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|---**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m1 m2 m3 a -> t5 m1 m2 m3 m4 m5 a (|---**|) = (|----*|) . (|---*|) -(|--*-*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|--*-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m1 m2 m4 a -> t5 m1 m2 m3 m4 m5 a (|--*-*|) = (|----*|) . (|--*-|) -(|-*--*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|-*--*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m1 m3 m4 a -> t5 m1 m2 m3 m4 m5 a (|-*--*|) = (|----*|) . (|-*--|) -(|*---*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*---*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m2 m3 m4 a -> t5 m1 m2 m3 m4 m5 a (|*---*|) = (|----*|) . (|*---|) -(|*--*-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*--*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m2 m3 m5 a -> t5 m1 m2 m3 m4 m5 a (|*--*-|) = (|---*-|) . (|*---|) -(|*-*--|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*-*--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m2 m4 m5 a -> t5 m1 m2 m3 m4 m5 a (|*-*--|) = (|--*--|) . (|*---|) -(|**---|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|**---|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T3___ t5) m3 m4 m5 a -> t5 m1 m2 m3 m4 m5 a (|**---|) = (|-*---|) . (|*---|) infixl 3 |--***|, |-*-**|, |*--**|, |*-*-*|, |**--*|, |**-*-|, |***--| -(|--***|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|--***|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m1 m2 a -> t5 m1 m2 m3 m4 m5 a (|--***|) = (|----*|) . (|--**|) -(|-*-**|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|-*-**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m1 m3 a -> t5 m1 m2 m3 m4 m5 a (|-*-**|) = (|----*|) . (|-*-*|) -(|*--**|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*--**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m2 m3 a -> t5 m1 m2 m3 m4 m5 a (|*--**|) = (|----*|) . (|*--*|) -(|*-*-*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*-*-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m2 m4 a -> t5 m1 m2 m3 m4 m5 a (|*-*-*|) = (|----*|) . (|*-*-|) -(|**--*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|**--*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m3 m4 a -> t5 m1 m2 m3 m4 m5 a (|**--*|) = (|----*|) . (|**--|) -(|**-*-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|**-*-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m3 m5 a -> t5 m1 m2 m3 m4 m5 a (|**-*-|) = (|---*-|) . (|**--|) -(|***--|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|***--|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T2___ t5) m4 m5 a -> t5 m1 m2 m3 m4 m5 a (|***--|) = (|--*--|) . (|**--|) infixl 3 |-****|, |*-***|, |**-**|, |***-*|, |****-| -(|-****|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|-****|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m1 a -> t5 m1 m2 m3 m4 m5 a (|-****|) = (|----*|) . (|-***|) -(|*-***|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|*-***|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m2 a -> t5 m1 m2 m3 m4 m5 a (|*-***|) = (|----*|) . (|*-**|) -(|**-**|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|**-**|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m3 a -> t5 m1 m2 m3 m4 m5 a (|**-**|) = (|----*|) . (|**-*|) -(|***-*|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|***-*|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m4 a -> t5 m1 m2 m3 m4 m5 a (|***-*|) = (|----*|) . (|***-|) -(|****-|) :: (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5, MonadTransCover5 t5) => +(|****-|) :: (Monad m1, Monad m2, Monad m3, Monad m4, Monad m5, MonadTransCover5 t5) => (T____ t5) m5 a -> t5 m1 m2 m3 m4 m5 a (|****-|) = (|---*-|) . (|***-|) @@ -598,7 +593,8 @@ Here is a monad transformer example showing how to use trans-cover functions. >import DeepControl.Applicative ((|$>)) ->import DeepControl.Monad (Monad2) +>import DeepControl.Commutative (Commutative) +>import DeepControl.Monad (Monad) >import DeepControl.Monad.Morph ((|>|)) >import DeepControl.Monad.Trans (liftT, (|*|), (|-*|), (|*-|)) >import DeepControl.Monad.Trans.Identity @@ -622,12 +618,12 @@ > n <- get > liftT $ tell [n] > ->program :: StateT Int (IdentityT2 IO (Writer [Int])) () -- StateT-IdentityT2-IO-Writer monad, a level-2 monad-transform +>program :: StateT Int (IdentityT2 IO (Writer [Int])) () -- StateT-IdentityT2-IO-Writer monad, a level-2 monad-transform >program = replicateM_ 4 $ do -> ((|-*|).liftT) |>| tock -- (|-*|) is a level-2 trans-cover function, analogous for (-*) -> :: (Monad2 m) => StateT Int (IdentityT2 IO m ) () -> ((|*-|).liftT) |>| save -- (|*-|) is a level-2 trans-cover function, analogous for (*:) -> :: (Monad m) => StateT Int (IdentityT2 m (Writer [Int])) () +> ((|-*|).liftT) |>| tock -- (|-*|) is a level-2 trans-cover function, analogous for (-*) +> :: (Monad m, Commutative m) => StateT Int (IdentityT2 IO m ) () +> ((|*-|).liftT) |>| save -- (|*-|) is a level-2 trans-cover function, analogous for (*:) +> :: (Monad m ) => StateT Int (IdentityT2 m (Writer [Int])) () > >-- λ> execWriter |$> runIdentityT2 (runStateT program 0) >-- Tock! diff --git a/DeepControl/Monad/Trans/Except.hs b/DeepControl/Monad/Trans/Except.hs --- a/DeepControl/Monad/Trans/Except.hs +++ b/DeepControl/Monad/Trans/Except.hs @@ -46,28 +46,29 @@ throwError2 :: (MonadError e m2, Applicative m1) => e -> m1 (m2 a) throwError2 = (*:) |$> throwError -catchError2 :: (MonadError e m2, Commutative m1, Commutative m2) => - m1 (m2 a) -> (e -> m1 (m2 a)) -> m1 (m2 a) +catchError2 :: (MonadError e m2, Commutative m1, Applicative m1, Commutative m2, Applicative m2) => + Catch2 e m1 m2 a catchError2 = liftCatch catchError where - liftCatch :: (Commutative m1, Commutative m2) => + liftCatch :: (Commutative m1, Applicative m1, Commutative m2, Applicative m2) => (forall a. Catch e m2 a) -> Catch2 e m1 m2 a liftCatch catch m h = let m' = commute m h' = commute |$> h in commute $ catch m' h' + ---------------------------------------------------------------- -- Level-3 throwError3 :: (MonadError e m3, Applicative m1, Applicative m2) => e -> m1 (m2 (m3 a)) throwError3 = (**:) |$> throwError -catchError3 :: (MonadError e m3, Commutative m1, Commutative m2, Commutative m3) => - m1 (m2 (m3 a)) -> (e -> m1 (m2 (m3 a))) -> m1 (m2 (m3 a)) +catchError3 :: (MonadError e m3, Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3) => + Catch3 e m1 m2 m3 a catchError3 = liftCatch catchError where - liftCatch :: (Commutative m1, Commutative m2, Commutative m3) => + liftCatch :: (Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3) => (forall a. Catch e m3 a) -> Catch3 e m1 m2 m3 a liftCatch catch m h = let m' = float2 m @@ -80,11 +81,11 @@ throwError4 :: (MonadError e m4, Applicative m1, Applicative m2, Applicative m3) => e -> m1 (m2 (m3 (m4 a))) throwError4 = (***:) |$> throwError -catchError4 :: (MonadError e m4, Commutative m1, Commutative m2, Commutative m3, Commutative m4) => - m1 (m2 (m3 (m4 a))) -> (e -> m1 (m2 (m3 (m4 a)))) -> m1 (m2 (m3 (m4 a))) +catchError4 :: (MonadError e m4, Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3, Commutative m4, Applicative m4) => + Catch4 e m1 m2 m3 m4 a catchError4 = liftCatch catchError where - liftCatch :: (Commutative m1, Commutative m2, Commutative m3, Commutative m4) => + liftCatch :: (Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3, Commutative m4, Applicative m4) => (forall a. Catch e m4 a) -> Catch4 e m1 m2 m3 m4 a liftCatch catch m h = let m' = float3 m @@ -97,11 +98,11 @@ throwError5 :: (MonadError e m5, Applicative m1, Applicative m2, Applicative m3, Applicative m4) => e -> m1 (m2 (m3 (m4 (m5 a)))) throwError5 = (****:) |$> throwError -catchError5 :: (MonadError e m5, Commutative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5) => - m1 (m2 (m3 (m4 (m5 a)))) -> (e -> m1 (m2 (m3 (m4 (m5 a))))) -> m1 (m2 (m3 (m4 (m5 a)))) +catchError5 :: (MonadError e m5, Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3, Commutative m4, Applicative m4, Commutative m5, Applicative m5) => + Catch5 e m1 m2 m3 m4 m5 a catchError5 = liftCatch catchError where - liftCatch :: (Commutative m1, Commutative m2, Commutative m3, Commutative m4, Commutative m5) => + liftCatch :: (Commutative m1, Applicative m1, Commutative m2, Applicative m2, Commutative m3, Applicative m3, Commutative m4, Applicative m4, Commutative m5, Applicative m5) => (forall a. Catch e m5 a) -> Catch5 e m1 m2 m3 m4 m5 a liftCatch catch m h = let m' = float4 m diff --git a/DeepControl/Monad/Trans/Identity.hs b/DeepControl/Monad/Trans/Identity.hs --- a/DeepControl/Monad/Trans/Identity.hs +++ b/DeepControl/Monad/Trans/Identity.hs @@ -73,20 +73,20 @@ instance (Applicative m1, Applicative m2) => Applicative (IdentityT2 m1 m2) where pure x = IdentityT2 $ (**:) x (<*>) = lift2IdentityT2 (|*>>) -instance (Monad m1, Monad2 m2) => Monad (IdentityT2 m1 m2) where +instance (Monad m1, Monad m2, Commutative m2) => Monad (IdentityT2 m1 m2) where return = IdentityT2 . (**:) m >>= f = IdentityT2 $ runIdentityT2 m >>== (f >-> runIdentityT2) instance (Alternative m1, Alternative m2) => Alternative (IdentityT2 m1 m2) where empty = IdentityT2 empty (<|>) = lift2IdentityT2 (<|>) -instance (MonadPlus m1, Alternative m2, Monad2 m2) => MonadPlus (IdentityT2 m1 m2) where +instance (MonadPlus m1, Alternative m2, Monad m2, Commutative m2) => MonadPlus (IdentityT2 m1 m2) where mzero = IdentityT2 mzero mplus = lift2IdentityT2 mplus instance MonadTrans2 IdentityT2 where liftT2 = IdentityT2 -instance (MonadIO m1, Monad m1, Monad2 m2) => MonadIO (IdentityT2 m1 m2) where +instance (MonadIO m1, Monad m1, Monad m2, Commutative m2) => MonadIO (IdentityT2 m1 m2) where liftIO = liftT2 . (-*) . liftIO lift2IdentityT2 :: @@ -125,20 +125,20 @@ instance (Applicative m1, Applicative m2, Applicative m3) => Applicative (IdentityT3 m1 m2 m3) where pure x = IdentityT3 $ (***:) x (<*>) = lift3IdentityT3 (|*>>>) -instance (Monad m1, Monad2 m2, Monad3 m3) => Monad (IdentityT3 m1 m2 m3) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => Monad (IdentityT3 m1 m2 m3) where return = IdentityT3 . (***:) m >>= f = IdentityT3 $ runIdentityT3 m >>>== (f >-> runIdentityT3) instance (Alternative m1, Alternative m2, Alternative m3) => Alternative (IdentityT3 m1 m2 m3) where empty = IdentityT3 empty (<|>) = lift3IdentityT3 (<|>) -instance (MonadPlus m1, Alternative m2, Monad2 m2, Alternative m3, Monad3 m3) => MonadPlus (IdentityT3 m1 m2 m3) where +instance (MonadPlus m1, Alternative m2, Monad m2, Commutative m2, Alternative m3, Monad m3, Commutative m3) => MonadPlus (IdentityT3 m1 m2 m3) where mzero = IdentityT3 mzero mplus = lift3IdentityT3 mplus instance MonadTrans3 IdentityT3 where liftT3 = IdentityT3 -instance (MonadIO m1, Monad m1, Monad2 m2, Monad3 m3) => MonadIO (IdentityT3 m1 m2 m3) where +instance (MonadIO m1, Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3) => MonadIO (IdentityT3 m1 m2 m3) where liftIO = liftT3 . (-**) . liftIO lift3IdentityT3 :: @@ -178,20 +178,20 @@ instance (Applicative m1, Applicative m2, Applicative m3, Applicative m4) => Applicative (IdentityT4 m1 m2 m3 m4) where pure x = IdentityT4 $ (****:) x (<*>) = lift4IdentityT4 (|*>>>>) -instance (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => Monad (IdentityT4 m1 m2 m3 m4) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => Monad (IdentityT4 m1 m2 m3 m4) where return = IdentityT4 . (****:) m >>= f = IdentityT4 $ runIdentityT4 m >>>>== (f >-> runIdentityT4) instance (Alternative m1, Alternative m2, Alternative m3, Alternative m4) => Alternative (IdentityT4 m1 m2 m3 m4) where empty = IdentityT4 empty (<|>) = lift4IdentityT4 (<|>) -instance (MonadPlus m1, Alternative m2, Monad2 m2, Alternative m3, Monad3 m3, Alternative m4, Monad4 m4) => MonadPlus (IdentityT4 m1 m2 m3 m4) where +instance (MonadPlus m1, Alternative m2, Monad m2, Commutative m2, Alternative m3, Monad m3, Commutative m3, Alternative m4, Monad m4, Commutative m4) => MonadPlus (IdentityT4 m1 m2 m3 m4) where mzero = IdentityT4 mzero mplus = lift4IdentityT4 mplus instance MonadTrans4 IdentityT4 where liftT4 = IdentityT4 -instance (MonadIO m1, Monad m1, Monad2 m2, Monad3 m3, Monad4 m4) => MonadIO (IdentityT4 m1 m2 m3 m4) where +instance (MonadIO m1, Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4) => MonadIO (IdentityT4 m1 m2 m3 m4) where liftIO = liftT4 . (-***) . liftIO lift4IdentityT4 :: @@ -232,20 +232,20 @@ instance (Applicative m1, Applicative m2, Applicative m3, Applicative m4, Applicative m5) => Applicative (IdentityT5 m1 m2 m3 m4 m5) where pure x = IdentityT5 $ (*****:) x (<*>) = lift5IdentityT5 (|*>>>>>) -instance (Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => Monad (IdentityT5 m1 m2 m3 m4 m5) where +instance (Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => Monad (IdentityT5 m1 m2 m3 m4 m5) where return = IdentityT5 . (*****:) m >>= f = IdentityT5 $ runIdentityT5 m >>>>>== (f >-> runIdentityT5) instance (Alternative m1, Alternative m2, Alternative m3, Alternative m4, Alternative m5) => Alternative (IdentityT5 m1 m2 m3 m4 m5) where empty = IdentityT5 empty (<|>) = lift5IdentityT5 (<|>) -instance (MonadPlus m1, Alternative m2, Monad2 m2, Alternative m3, Monad3 m3, Alternative m4, Monad4 m4, Alternative m5, Monad5 m5) => MonadPlus (IdentityT5 m1 m2 m3 m4 m5) where +instance (MonadPlus m1, Alternative m2, Monad m2, Commutative m2, Alternative m3, Monad m3, Commutative m3, Alternative m4, Monad m4, Commutative m4, Alternative m5, Monad m5, Commutative m5) => MonadPlus (IdentityT5 m1 m2 m3 m4 m5) where mzero = IdentityT5 mzero mplus = lift5IdentityT5 mplus instance MonadTrans5 IdentityT5 where liftT5 = IdentityT5 -instance (MonadIO m1, Monad m1, Monad2 m2, Monad3 m3, Monad4 m4, Monad5 m5) => MonadIO (IdentityT5 m1 m2 m3 m4 m5) where +instance (MonadIO m1, Monad m1, Monad m2, Commutative m2, Monad m3, Commutative m3, Monad m4, Commutative m4, Monad m5, Commutative m5) => MonadIO (IdentityT5 m1 m2 m3 m4 m5) where liftIO = liftT5 . (-****) . liftIO lift5IdentityT5 :: @@ -274,5 +274,4 @@ (|--*--|) = IdentityT5 . (--*) . runIdentityT4 (|-*---|) = IdentityT5 . (-*) . runIdentityT4 (|*----|) = IdentityT5 . (*:) . runIdentityT4 - diff --git a/README.md b/README.md --- a/README.md +++ b/README.md @@ -4,7 +4,7 @@ ## Examples -### [Applicative](https://hackage.haskell.org/package/deepcontrol-0.4.2.1/docs/DeepControl-Applicative.html) +### [Applicative](https://hackage.haskell.org/package/deepcontrol-0.4.3.0/docs/DeepControl-Applicative.html) This module enables you to program in applicative style for more deeper level than the usual Applicative module expresses. You would soon realize exactly what more deeper level means by reading the example codes below in order. @@ -175,14 +175,14 @@ [Just 3] > [1] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2 [Just 3,Just (-1),Just 2,Nothing] - > [0,1] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2 - [Just 2,Just 3,Just (-2),Just (-1),Just 0,Just 2,Nothing,Nothing] + > [1,2] -*|[Just (+), Just (-), Just (*), Nothing]|*- Just 2 + [Just 3,Just (-1),Just 2,Nothing,Just 4,Just 0,Just 4,Nothing] #### Level-3, Level-4 and Level-5 Work well likewise. -### [Commutative](https://hackage.haskell.org/package/deepcontrol-0.4.2.1/docs/DeepControl-Commutative.html) +### [Commutative](https://hackage.haskell.org/package/deepcontrol-0.4.3.0/docs/DeepControl-Commutative.html) Prelude> :m DeepControl.Commutative @@ -201,9 +201,9 @@ > commute $ Just (Right 1) Right (Just 1) -So these monads can be deepened to Monad2, Monad3, Monad4 and Monad5. +So these monads can be deepened freely. -### [Monad](https://hackage.haskell.org/package/deepcontrol-0.4.2.1/docs/DeepControl-Monad.html) +### [Monad](https://hackage.haskell.org/package/deepcontrol-0.4.3.0/docs/DeepControl-Monad.html) This module enables you to program in Monad for more deeper level than the usual Monad module expresses. You would soon realize exactly what more deeper level means by reading the example codes below in order. @@ -248,7 +248,7 @@ factorial n | n < 0 = (-*) Nothing | n == 0 = (*:) $ tell [0] >> (*:) 1 | n > 0 = factorial (n-1) >>== \v -> - tell [v] ->~ -- (->~) is a level-2 cover-bind function, analogous for (>>) + tell [v] ->~ -- (->~) is a level-2 cover-sequence function, analogous for (>>) (**:) (n * v) -- > runWriter |$> factorial 5 @@ -267,8 +267,8 @@ factorial n | n < 0 = (*-*) Nothing -- (*-*) is a level-3 cover function | n == 0 = (**:) $ tell [0] >> (*:) 1 | n > 0 = factorial (n-1) >>>== \v -> -- (>>>==) is the level-3 bind function, analogous for (>>=) - print v >--~ -- (>--~) is a level-3 cover-bind function, analogous for (>>) - tell [v] -->~ -- (-->~) is a level-3 cover-bind function too, analogous for (>>) + print v >--~ -- (>--~) is a level-3 cover-sequence function, analogous for (>>) + tell [v] -->~ -- (-->~) is a level-3 cover-sequence function too, analogous for (>>) (***:) (n * v) -- > runWriter |$>> factorial 5 @@ -283,7 +283,7 @@ Work well likewise. -### [Monad-Transformer](https://hackage.haskell.org/package/deepcontrol-0.4.2.1/docs/DeepControl-Monad-Trans.html) +### [Monad-Transformer](https://hackage.haskell.org/package/deepcontrol-0.4.3.0/docs/DeepControl-Monad-Trans.html) #### Level-2 @@ -338,7 +338,8 @@ ```haskell import DeepControl.Applicative ((|$>)) -import DeepControl.Monad (Monad2) +import DeepControl.Commutative (Commutative) +import DeepControl.Monad (Monad) import DeepControl.Monad.Morph ((|>|)) import DeepControl.Monad.Trans (liftT, (|*|), (|-*|), (|*-|)) import DeepControl.Monad.Trans.Identity @@ -362,12 +363,12 @@ n <- get liftT $ tell [n] -program :: StateT Int (IdentityT2 IO (Writer [Int])) () -- StateT-IdentityT2-IO-Writer monad, a level-2 monad-transform +program :: StateT Int (IdentityT2 IO (Writer [Int])) () -- StateT-IdentityT2-IO-Writer monad, a level-2 monad-transform program = replicateM_ 4 $ do - ((|-*|).liftT) |>| tock -- (|-*|) is a level-2 trans-cover function, analogous for (-*) - :: (Monad2 m) => StateT Int (IdentityT2 IO m ) () - ((|*-|).liftT) |>| save -- (|*-|) is a level-2 trans-cover function, analogous for (*:) - :: (Monad m) => StateT Int (IdentityT2 m (Writer [Int])) () + ((|-*|).liftT) |>| tock -- (|-*|) is a level-2 trans-cover function, analogous for (-*) + :: (Monad m, Commutative m) => StateT Int (IdentityT2 IO m ) () + ((|*-|).liftT) |>| save -- (|*-|) is a level-2 trans-cover function, analogous for (*:) + :: (Monad m ) => StateT Int (IdentityT2 m (Writer [Int])) () -- λ> execWriter |$> runIdentityT2 (runStateT program 0) -- Tock! @@ -380,7 +381,7 @@ Work well likewise. -### [Monad-Morph](https://hackage.haskell.org/package/deepcontrol-0.4.2.1/docs/DeepControl-Monad-Morph.html) +### [Monad-Morph](https://hackage.haskell.org/package/deepcontrol-0.4.3.0/docs/DeepControl-Monad-Morph.html) Here is a monad-morph example, a level-2 monad-morph. @@ -427,4 +428,4 @@ Work well likewise. -### [Arrow](https://hackage.haskell.org/package/deepcontrol-0.4.2.1/docs/DeepControl-Arrow.html) +### [Arrow](https://hackage.haskell.org/package/deepcontrol-0.4.3.0/docs/DeepControl-Arrow.html) diff --git a/deepcontrol.cabal b/deepcontrol.cabal --- a/deepcontrol.cabal +++ b/deepcontrol.cabal @@ -1,5 +1,5 @@ name: deepcontrol -version: 0.4.2.1 +version: 0.4.3.0 synopsis: Provide more deeper level style of programming than the usual Control.xxx modules express description: This module enables more deeper level style of programming than the usual Control.xxx modules express, especially for Applicative and Monad. license: BSD3 diff --git a/test/unit_MonadTrans.hs b/test/unit_MonadTrans.hs --- a/test/unit_MonadTrans.hs +++ b/test/unit_MonadTrans.hs @@ -1,7 +1,8 @@ import Test.HUnit hiding (State) import DeepControl.Applicative ((|$>)) -import DeepControl.Monad (Monad2) +import DeepControl.Commutative (Commutative) +import DeepControl.Monad (Monad) import DeepControl.Monad.Morph ((|>|)) import DeepControl.Monad.Trans (liftT, (|*|), (|-*|), (|*-|)) import DeepControl.Monad.Trans.Identity @@ -25,12 +26,12 @@ n <- get liftT $ tell [n] -program :: StateT Int (IdentityT2 IO (Writer [Int])) () -- StateT-IdentityT2-IO-Writer monad, a level-2 monad-transform +program :: StateT Int (IdentityT2 IO (Writer [Int])) () -- StateT-IdentityT2-IO-Writer monad, a level-2 monad-transform program = replicateM_ 4 $ do - ((|-*|).liftT) |>| tock -- (|-*|) is a level-2 trans-cover function, analogous for (-*) - :: (Monad2 m) => StateT Int (IdentityT2 IO m ) () - ((|*-|).liftT) |>| save -- (|*-|) is a level-2 trans-cover function, analogous for (*:) - :: (Monad m) => StateT Int (IdentityT2 m (Writer [Int])) () + ((|-*|).liftT) |>| tock -- (|-*|) is a level-2 trans-cover function, analogous for (-*) + :: (Monad m, Commutative m) => StateT Int (IdentityT2 IO m ) () + ((|*-|).liftT) |>| save -- (|*-|) is a level-2 trans-cover function, analogous for (*:) + :: (Monad m ) => StateT Int (IdentityT2 m (Writer [Int])) () -- λ> execWriter |$> runIdentityT2 (runStateT program 0) -- Tock!