On Mon, Feb 2, 2009 at 11:51 AM, Lennart Augustsson <lenn...@augustsson.net>wrote:
> If we're talking Haskell types here I think it's reasonable to talk > about the values of a type as those that we can actually express in > the Haskell program, any other values are really besides the point. > Well, if you have a more philosophical view of types then I guess > there is a point, but I thought you wanted to know about Haskell > types? > The metaphysics thereof. ;) I want to situate them in the larger intellectual context to get a more precise answer to "what is a type, really?" > > There's nothing mysterious about _|_ being a member of a set. Say > that you have a function (Int->Bool). What are the possible results > when you run this function? You can get False, you can get True, and > the function can fail to terminate (I'll include any kind of runtime > error in this). > So now we want to turn this bit of computing into mathematics, so we > say that the result must belong to the set {False,True,_|_} where > we've picked the name _|_ for the computation that doesn't terminate. > Note that is is mathematics, there's no notion of non-termination > here. The function simply maps to one of three values. > I like that, thanks. -gregg
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