[Haskell-cafe] Relevance and applicability of category theory

[Dan Weston]

 > Hmmm, not sure what you asking for. If you have a monad instance Set a
 > that has Eq a attached, this
 > already would do what you want, no? An example would help me to
 > understand...

Sorry, I meant uppercase (and got the constraint wrong anyway). I meant 
that Ord a => Set a was a monad (lowercase 'm') under the obvious 
semantics, but cannot be an instance of Monad. The type signature of 
Haskell's Monad class is too free (admits too many types, not just Ord a 
=> a) to have a Set instance.

[But for solutions, see
http://www.randomhacks.net/articles/2007/03/15/data-set-monad-haskell-macros
http://okmij.org/ftp/Haskell/types.html#restricted-datatypes
http://hackage.haskell.org/packages/archive/monad-param/0.0.2/doc/html/Control-Monad-Parameterized.html
]

I was just wondering if your Thrist type constructor included (e.g. in 
its first argument) a mechanism for embedding a Set monad, since this is 
already a subject of some interest to many people.

Dan

Gabor Greif wrote:
> Am 31.01.2008 um 18:13 schrieb Dan Weston:
> 
>> Even though you cannot "dive into this matter now", maybe when you get 
>> time you can update your blog with an explicit embedding of Haskell 
>> monads and arrows in your Thrist construction. Concrete examples will 
>> help me (and probably others) more quickly see the novelty, increased 
>> generality, and usefulness of a Thrist.
> 
> Okay, I took my time and came up with:
> 
> http://heisenbug.blogspot.com/2008/01/embeddings-part-one-arrow-thrist.html
> 
> Comments welcome.
> 
> 
>>
>> Also, although you say that thrists are the moral equivalent of a free 
>> category, it appears (at least to me) possible that the first Thrist 
>> argument enables the construction of a restricted domain monad, e.g. 
>> (Eq a => Set a) monad. Is this so?
> 
> Hmmm, not sure what you asking for. If you have a monad instance Set a 
> that has Eq a attached, this
> already would do what you want, no? An example would help me to 
> understand...
> 
> 
>>
>> Dan
> 
> Cheers,
> 
>     Gabor
> 
> 
>>
>>
> 
>