Parameterisations of Monads
So I was thinking how dull and uninspiring the current definiton of Monad really is and came up with some more interesting parameterisations. The only problem with this one is I'm a) not sure if it still is a Monad and b) very unsure if it's of any use. There's the possibility that chucking Cont in there or using newtype to simultate multiple arrows / type lambdas may lead to more interesting instances, but can anyone think of exciting use cases for this stuff? Feel free to fill in the instances! It's also not a parameterisation I've seen before. Matthew
class SuperMonad (m1 :: * -> * -> *) (m2 :: * -> *) where (>>~) :: m1 (m2 a) (m1 (m2 b) (m2 b)) (>>=~) :: m1 (m2 a) (m1 (m1 a (m2 b)) (m2 b)) returns :: m1 a (m2 a)
instance (Monad m) => SuperMonad ((->)) m where (>>~) :: m a -> m b -> m b (>>~) = (>>) (>>=~) :: m a -> (a -> m b) -> m b (>>=~) = (>>=) returns :: a -> m a returns = return
instance (Monad m) => SuperMonad ((,)) m where (>>~) :: (m a, (m b, m b)) (>>=~) :: (m a, ((a, m b), m b)) returns :: (a, m a)
instance (Monad m) => SuperMonad Either m where (>>~) :: Either (m a) (Either (m a) (m b)) (>>=~) :: Either (m a) (Either (Either a (m b)) (m b)) returns :: Either a (m a)
instance (Monad m) => SuperMonad State m where (>>~) :: State (m a) (State (m a) (m b)) (>>=~) :: State (m a) (State (State a (m b)) (m b)) returns :: State a (m a)
On Feb 5, 2008 7:48 AM, Matthew Sackman
So I was thinking how dull and uninspiring the current definiton of Monad really is and came up with some more interesting parameterisations. The only problem with this one is I'm a) not sure if it still is a Monad and b) very unsure if it's of any use. There's the possibility that chucking Cont in there or using newtype to simultate multiple arrows / type lambdas may lead to more interesting instances, but can anyone think of exciting use cases for this stuff?
Feel free to fill in the instances! It's also not a parameterisation I've seen before.
I can't! That's because all the instances except for (->) have free type variables in a covariant position, so I'd be forced to used undefined all over the place. And the State instance just confuses me... :-) However, I think most Arrows would work as the first parameter, it's just not clear they would be useful. Luke
Matthew, Your SuperMonad seems remarkably similar to Gabor Greif's Thrist datatype [1,2] reported only six days ago on this list [3]. Can you compare/contrast your class approach with his polymorphic type approach? Or have I completely confused the two because of the similar kind of their arguments? data Thrist :: (* -> * -> *) -> * -> * -> * where Nil :: Thrist p a a Cons :: p a b -> Thrist p b c -> Thrist p a c data Arrow' :: (* -> * -> *) -> * -> * -> * where Arr :: Arrow a => a b c -> Arrow' a b c First :: Arrow a => Arrow' a b c -> Arrow' a (b, d) (c, d) [1] http://heisenbug.blogspot.com/2007/11/trendy-topics.html [2] http://heisenbug.blogspot.com/2008/01/embeddings-part-one-arrow-thrist.html [3] http://thread.gmane.org/gmane.comp.lang.haskell.cafe/35907/focus=35957 Dan Matthew Sackman wrote:
So I was thinking how dull and uninspiring the current definiton of Monad really is and came up with some more interesting parameterisations. The only problem with this one is I'm a) not sure if it still is a Monad and b) very unsure if it's of any use. There's the possibility that chucking Cont in there or using newtype to simultate multiple arrows / type lambdas may lead to more interesting instances, but can anyone think of exciting use cases for this stuff?
Feel free to fill in the instances! It's also not a parameterisation I've seen before.
Matthew
class SuperMonad (m1 :: * -> * -> *) (m2 :: * -> *) where (>>~) :: m1 (m2 a) (m1 (m2 b) (m2 b)) (>>=~) :: m1 (m2 a) (m1 (m1 a (m2 b)) (m2 b)) returns :: m1 a (m2 a)
instance (Monad m) => SuperMonad ((->)) m where (>>~) :: m a -> m b -> m b (>>~) = (>>) (>>=~) :: m a -> (a -> m b) -> m b (>>=~) = (>>=) returns :: a -> m a returns = return
instance (Monad m) => SuperMonad ((,)) m where (>>~) :: (m a, (m b, m b)) (>>=~) :: (m a, ((a, m b), m b)) returns :: (a, m a)
instance (Monad m) => SuperMonad Either m where (>>~) :: Either (m a) (Either (m a) (m b)) (>>=~) :: Either (m a) (Either (Either a (m b)) (m b)) returns :: Either a (m a)
instance (Monad m) => SuperMonad State m where (>>~) :: State (m a) (State (m a) (m b)) (>>=~) :: State (m a) (State (State a (m b)) (m b)) returns :: State a (m a)
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Am 05.02.2008 um 21:27 schrieb Dan Weston:
Matthew,
Your SuperMonad seems remarkably similar to Gabor Greif's Thrist datatype [1,2] reported only six days ago on this list [3].
Can you compare/contrast your class approach with his polymorphic type approach? Or have I completely confused the two because of the similar kind of their arguments?
data Thrist :: (* -> * -> *) -> * -> * -> * where Nil :: Thrist p a a Cons :: p a b -> Thrist p b c -> Thrist p a c
data Arrow' :: (* -> * -> *) -> * -> * -> * where Arr :: Arrow a => a b c -> Arrow' a b c First :: Arrow a => Arrow' a b c -> Arrow' a (b, d) (c, d)
For the record, I have done the monad into thrist embedding now: http://heisenbug.blogspot.com/2008/02/embeddings-part-two-monad- thrist.html Will start pondering about mfix and restricted monads now. Cheers, Gabor
participants (4)
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Dan Weston -
Gabor Greif -
Luke Palmer -
Matthew Sackman