[Haskell-cafe] The mother of all functors/monads/categories

[Twan van Laarhoven]

Max Bolingbroke wrote:
> I don't actually know what the right name for this data type is, I
> just invented it and it seems to work:
> 
>> -- (>>>) :: forall a b. t a b -> (forall c. t b c -> t a c)
>> newtype Wotsit t a b = Wotsit { runWotsit :: forall c. t b c -> t a c }

There is of course no reason to prefer (>>>) to (<<<), so you can instead 
quantify over the first argument as opposed to second one:

     newtype Wotsit' t a b = Wotsit' { runWotsit' :: forall c. t c a -> t c b }

     liftWotsit' :: Category t => t a b -> Wotsit' t a b
     liftWotsit' t = Wotsit' ((<<<) t)

     lowerWotsit' :: Category t => Wotsit' t a b -> t a b
     lowerWotsit' t = runWotsit' t id

     instance Category (Wotsit' t) where
         id = Wotsit' id
         t1 . t2 = Wotsit' (runWotsit' t1 . runWotsit' t2)


Twan