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
Dan Piponi wrote: 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
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