ajb-2 wrote:
>
> In Haskell, natural transformations are
> functions that respect the structure of functors. Since you can't
> avoid respecting the structure of functors (the language won't let you
> do otherwise), you get natural transformations for free. (Free as
> in theorems, not free as i
G'day all.
Quoting Derek Elkins <[EMAIL PROTECTED]>:
Of course, this is a concrete example using basic ideas of programming
and not some "intuitive analogy". I feel comfortable working with
adjunctions, but I don't have some general analogy that I use.
I think this is important. The concept
On Tue, 2008-03-04 at 18:30 +, Edsko de Vries wrote:
> On Tue, Mar 04, 2008 at 11:58:38AM -0600, Derek Elkins wrote:
> > On Tue, 2008-03-04 at 17:16 +, Edsko de Vries wrote:
> > > Hi,
> > >
> > > Is there an intuition that can be used to explain adjunctions to
> > > functional programmers,
Edsko asked:
> Is there an intuition that can be used to explain adjunctions to
> functional programmers, even if the match isn't necessary 100% perfect
> (like natural transformations and polymorphic functions?).
I think there's a catch because many interesting examples of
adjunctions involve
Well, we have at least one very useful example of adjunction. It's
called "curry". See, if X is some arbitrary type, you can define
type F = (,X)
instance Functor F where
fmap f (a,x) = (fa,x)
type G = (->) X
instance Functor G where
fmap f h = \x -> f (h x)
Now, we have the adjunction
On Tue, Mar 04, 2008 at 11:58:38AM -0600, Derek Elkins wrote:
> On Tue, 2008-03-04 at 17:16 +, Edsko de Vries wrote:
> > Hi,
> >
> > Is there an intuition that can be used to explain adjunctions to
> > functional programmers, even if the match isn't necessary 100% perfect
> > (like natural tra
On Tue, 2008-03-04 at 17:16 +, Edsko de Vries wrote:
> Hi,
>
> Is there an intuition that can be used to explain adjunctions to
> functional programmers, even if the match isn't necessary 100% perfect
> (like natural transformations and polymorphic functions?).
Well when you pretend Hask is S
Hi,
Is there an intuition that can be used to explain adjunctions to
functional programmers, even if the match isn't necessary 100% perfect
(like natural transformations and polymorphic functions?).
Thanks,
Edsko
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