[Haskell-cafe] matrix computations based on the GSL

[Jacques Carette]

Henning Thielemann wrote:

>On Wed, 29 Jun 2005, Jacques Carette wrote:
>  
>
>><sarcasm>Next thing you know, you'll want a different 'application'
>>symbol for every arity of function, because they are ``different''.
>></sarcasm>
>>    
>>
>
>Btw. there is less sarcasm in it as may you think. There was already a
>proposal to extend function application:
> http://www.haskell.org/pipermail/haskell/2002-October/010629.html
>  and guess - I would be very unhappy about such an extension because it
>mixes the representation of a map with the map itself.
>  
>
There are no maps in Haskell (or in any syntactic lambda calculus), only 
representations of maps.  It just turns out that things of type -> are 
builtin representations of maps, where other representations are not 
first class ``maps''.  This is a bias of all lambda-calculus based 
languages.

In ZFC, there are no maps, just sets, yet you can do lots of mathematics 
and CS in ZFC ;-). 

I happen to believe that a more structure-centric view of the world (a 
la category theory) reveals more than an object-centric view a la ZFC.  
But even arrows in a category sometimes turn out to be too restrictive.  
They are too ``functional'' instead of being more ``relational''.

Once you realize that \x.x is *not* a function, but a denotation of a 
function, then a proposal like the one you point to starts to make a lot 
of sense.  I rather like it.

Jacques