Obviously you know what your talking about and I don't, so this is a question purely out of ignorance. It seems to me that Tomorrow cannot be parametrically polymorphic, or else I could wrap it again (Tomorrow (Tomorrox x)). An unwrapping fixpoint operator needs to reflect the type to know when not to go too far. One solution is to guarantee that it can go as far as it wants with a comonad (stopping when the function argument wants to, not when the data type runs out of data): import Control.Comonad import Control.Monad.Fix tfix :: Comonad tomorrow => (tomorrow x -> x) -> x tfix = extract . (\f -> fix (extend f)) To quote Cabaret, if tomorrow belongs to me, then surely the day after belongs to me as well. Otherwise, to stop the fixpoint, it seems you need a more restricted type to encode some stopping sentinel (my own parametrically polymorphic attempts all end in infinite types, so maybe ad hoc polymorphism or a type witness is needed?) Do you have a blog post on this problem? Dan Conor McBride wrote:
On 2 Nov 2009, at 00:11, Ross Paterson wrote:
On Sun, Nov 01, 2009 at 04:20:18PM +0000, Conor McBride wrote:
On 31 Oct 2009, at 10:39, Conor McBride wrote:
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 Yes, but if you will know tomorrow that you will know something tomorrow, then you will know that thing tomorrow.
That depends on what "tomorrow" means tomorrow.
The applicative does coincide with a monad, just not the one you first thought of (or/max rather than plus).
True, but it's not the notion I need to analyse circular programs. I'm looking for something with a fixpoint operator
fix :: (Tomorrow x -> x) -> x
which I can hopefully use to define things like
repmin :: Tree Int -> (Int, Tomorrow (Tree Int))
so that the fixpoint operator gives me a Tomorrow Int which I can use to build the second component, but ensures that the black-hole-tastic Tomorrow (Tomorrow (Tree Int)) I also receive is too late to be a serious temptation.
All the best
Conor
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