On 11 Feb 2009, at 09:29, Brent Yorgey wrote:
Good. I'm not ready for _|_ yet .. :-)
There's actually nothing all that difficult about _|_; it is the value of divergent computations--i.e. infinite recursion which never actually produces any data. We usually also say that anything which results in a run-time error is _|_. For example, each of the following is _|_:
undefined error "blarg" let x = x in x let y = y + 1 in y
Note though that it's not the value of divergent computations, but instead of divergent computations that also never produce any output. For example, this divergent computation is not _|_, because it produces values: ones = 1 : ones More precisely, in haskell bottom is a value in every type which we can give no information about at all. In mathematics, bottom is a value which contains the *least* information of any value in the set, this is true in Haskell also, but also guarenteed by the fact that types are extended to include a special "I know nothing at all" value. Bob