Dan Piponi wrote:
Marc asked:
<http://xkcd.com/c248.html>
( join /= coreturn )
IMHO this could be a beautiful and easy way to explain monads.
comments?
I'll eat my hat if there isn't a formal way of looking at this. I'm
not qualified to put it together coherently but it goes something like
this: modal logic has Kripke semantics based on the notion of many
worlds. For the right modal logic, the many worlds idea captures the
notion of counterfactual worlds. We can also extend the Curry-Howard
isomorphism to include modal logic. Some of the laws of modal logic
(or their duals) correspond to monad (or comonad) laws (see laws 4 and
t here: http://en.wikipedia.org/wiki/Kripke_semantics). These laws
translate into rules about what worlds 'accessible' from what other
worlds. So that cartoon may have a formal interpretation in terms of
monads...
Unfortunately that interpretation would have to rely on an equivocation
of 'accessible'. In modal logic (and in the transition from the first to
the second situation in the comic), it's a logical relationship; in the
transition from the second to the third situation it's meant to ground
the possibility of physical interaction, which normally is not thought
to be possible between possible worlds. You'd probably have to ship a
lot of extra physics (and metaphysics) to have an intelligible
interpretation that connects both senses :-)
Ciao,
Leif
--
Dan
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