(Sorry I can't in-reply-to I've lost the original message) Neil Toronto ntoronto at cs.byu.edu:
While kicking around ideas for multiple dispatch, I came across one of Perl's implementations, and it reminded me of something Larry Wall said recently in his State of the Onion address about how types get together and democratically select a function to dispatch to. I immediately thought of Arrow's Theorem.
Maybe I'm wrong, but I don't think this theorem applies in the case of mulitple dispatch. The type of the argument sequence as a whole chooses the best specialisation, it's not the case that each argument expresses a preference. The set of choices is the set S of signatures of specialisations of the function (which is partially ordered), and the 'commitee' is made of one entity only: the function call's signature s. To choose the relevant specialisation, look at: { t \in S | s <= t and \forall u \in S (s < u <= t) \implies u = t } If this set is a singleton { t } then the specialization with signature t is the best fit for s, otherwise there is no best fit. -- Arnaud