[Haskell-cafe] Restricted categories

[Nick Rudnick]

Alexander Solla wrote:
> You specifically ask withConstraintsOf to accept only Suitable2's when 
> you say
>> withConstraintsOf :: Suitable2 m a b => m a b -> (Constraints m a b 
>> -> k) -> k
>
> But you aren't saying that the argument of withConstraintsOf IS a 
> Suitable2, when you say:
>> instance (RCategory c1, RCategory c2) => RCategory (c1 :***: c2) where
>> id = withResConstraints $ \ProdConstraints -> id :***: id
>> -- f@(f1 :***: f2) . g@(g1 :***: g2) =
>> -- withResConstraints $ \ProdConstraints ->
>> -- withConstraintsOf f $ \ProdConstraints ->
>> -- withConstraintsOf g $ \ProdConstraints ->
>> -- (f1 . g1) :***: (f2 . g2) 
As I understand, Sjoerd expects this to be done at the definition of (.) 
in the type class RCategory, so that an instance method can relay on the 
constraints collected by it:
> class RCategory (~>) where
>   id :: Suitable2 (~>) a a => a ~> a
>   (.) :: (Suitable2 (~>) b c, Suitable2 (~>) a b, Suitable2 (~>) a c) => b ~> c -> a ~> b -> a ~> c
>   
A simple example: 

class Show el=> ExceptionNote el where
comment:: Show exception=> exception-> el-> String

instance ExceptionNote Int where
comment exception refId = show refId ++ ": " ++ show exception

Here you don't need to constrain ?exception? to be of ?Show? at the 
instance declaration. So it does not appear wrong for Sjoerd to expect f 
and g to already be of Suitable2...

This is exciting stuff, I am really a little astonished about the giant 
leap Haskell has made since my efforts to translate the examples of 
Rydeheart & Burstall, which actually was my intro to categories, from ML 
to Haskell. This looks very elegant... Maybe it's time for a second 
edition of the unique approach of Rydeheart & Burstall on basis of 
Haskell? Wow, really cool stuff... :-)

Cheers,

Nick
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