Jeremy Gibbons wrote:
If you want "a < b < c" to mean "(a < b) && (b < c)" but "a + b + c"
to mean "(a + b) + c", you're going to have to treat "<" differently
from "+", which goes against the spirit of considering them both
simply functions.
I've wanted to chime in here for a while now. I stron
On Tuesday 01 February 2005 02:41, Jeremy Gibbons wrote:
> <[EMAIL PROTECTED]> wrote:
> > BTW, 'sigma sin' is not a function.
>
> I'm missing something here. I don't have an integral symbol to hand,
> which is what I meant by the "sigma",
I understood it that way. But let us use '\int' or '\integ
On 1 Feb 2005, at 05:20, Cale Gibbard wrote:
Statements like "a < b < c" are perfectly clear to everyone present,
and if anyone has a type error in their head when reading that which
they can't get past, they are most likely just being stubborn.
Actually, that's another nice example of what I was t
Cale Gibbard wrote:
Another common thing which is done whenever convenient is to treat
Cartesian product as associative, and naturally identify the spaces (A
x A) x A and A x (A x A), along with perhaps A^3 which might be
functions f: {0,1,2} -> A,
It's fine to identify (A x A) x A with A x (A x A
I agree, as an undergraduate student of pure mathematics, I have been
finding fairly large parts of the discussion about mathematical
notation to be somewhat silly and uninformed. (Really it was more the
previous thread, but it seems to have been continued here). One thing
to keep in mind about mat
Jacques Carette:
>Yes, I am aware that this untypeable in Haskell, because polymorphism is
>straight-jacketed by structural rules. But
>in mathematics, it is convenient and extremely common to:
>1) look at the type a -> b as being a *subtype* of b (though I have never seen
>it phrased that
On Monday 31 January 2005 04:24, Jeremy Gibbons wrote:
> Despite being a fan of generic programming, I have my doubts about
> this kind of automatic lifting. It works fine in "ordinary
> mathematics", because there is no fear of confusion - one hardly ever
> deals with functions as entities in thei
Despite being a fan of generic programming, I have my doubts about this
kind of automatic lifting. It works fine in "ordinary mathematics",
because there is no fear of confusion - one hardly ever deals with
functions as entities in their own right. (Witness "sigma sin(x) dx",
involving a term sin(x
Tomasz Zielonka <[EMAIL PROTECTED]> wrote:
It's not as bad as you think. You can do this:
{-# OPTIONS -fglasgow-exts #-}
module Apply where
class Apply f a b | f -> a, f -> b where
apply :: f -> a -> b
instance Apply (a -> b) a b where
apply f a = f a
instance Ap
On Fri, Jan 28, 2005 at 10:01:33AM -0500, Jacques Carette wrote:
> The previous post on record syntax reminded me of some 'problems' I had
> noticed where Haskell and mathematics have a (deep) usage mismatch.
>
> First, consider a syntax for other component-wise function application?
> For exam
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