[Haskell-cafe] matrix computations based on the GSL
carette at mcmaster.ca
Wed Jun 29 18:18:55 EDT 2005
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''.
>Btw. there is less sarcasm in it as may you think. There was already a
>proposal to extend function application:
> 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
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.
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