Hello Nick,
Am 02.11.2006 um 20:51 schrieb Nicolas Frisby:
OI has been lingering in the back of my mind during my own
comonadic adventures.
Did you enjoy them?
One thing that's bothered me is the signature of comain.
comain :: OI () -> ()
If the OI comonad is to represent values "in the context of the
RealWorld", and yet we can have multiple and differing copies of the
RealWorld context, then this seems to match the multiple worlds
perspective (which is why I think Kieburtz' experimental
implementation was doomed to violate referential transparency). That
is I want any deterministic program to be of top-level type:
comain :: OI () -> OI ()
The intuition is that the program as a whole receives the initial
world description, then is allowed to duplicate and manipulate that
world in any number of ways, but it has to choose one final world as
its choice. All other real worlds are discarded. The OI () -> ()
signature doesn't allow for the program to tell me what the resulting
RealWorld ought to be.
I think of signature OI a -> b as a constraint: there's no hidden
agenda inside the comonad.
The future of the comonad doesn't depend on its history. In a comonad
using OI a -> OI b, anything can be hidden. So, if the comonad hasn't
a hidden agenda,
there's no point in choosing a final world. Hence, OI a -> b seems
adequate to me.
An implementation of this doesn't seem impossible (as opposed to
improbable) for file IO or references (your filesystem/cell store
would have to be transactional and "multi-ported"). It does become a
bit mind boggling for concurrency or any other multi-agent paradigm
(networking, screen and keyboard IO, etc.)--it seems that the other
agents would have to be savvy to the multiple worlds perspective.
What is "multi-ported"?
Transactional systems certainly seem like a ripe application area for
the Product comonad with a RealWorld abstract data type as the carried
context.
My apologies for not actually commenting on your code.
Thank you for use comments.
Nick
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