On Sun, Nov 1, 2009 at 11:20 AM, Conor McBride
On 31 Oct 2009, at 10:39, Conor McBride wrote:
On 30 Oct 2009, at 16:14, Yusaku Hashimoto wrote:
Hello cafe, Do you know any data-type which is Applicative but not Monad?
[can resist anything but temptation]
I have an example, perhaps not a datatype: tomorrow-you-will-know
Elaborating, one day later,
if you know something today, you can arrange to know it tomorrow if will know a function tomorrow and its argument tomorrow, you can apply them tomorrow but if you will know tomorrow that you will know something the day after, that does not tell you how to know the thing tomorrow
Put otherwise, unit-delay is applicative but not monadic. I've been using this to organise exactly what happens when in those wacky miraculous-looking circular programs. It seems quite promising, so far...
Can you do that with just applicative functors, or do you need arrows?
According to "Idioms are oblivious, arrows are meticulous, monads are
promiscuous"[1], an arrow (~>) that's equivalent to an applicative
functor has the property that "a ~> b" is isomorphic to "() ~> (a ->
b)".
A typical delay arrow has the form delay :: a -> (a ~> a), so if (~>)
is equivalent to some applicative functor f, we can rewrite that as
delay :: a -> f (a -> a), which seems too limited to have the proper
behavior.
[1] http://homepages.inf.ed.ac.uk/wadler/topics/links.html#arrows-and-idioms
--
Dave Menendez