On 13-04-05 04:56 AM, Tom Ellis wrote:
"any" is very ambiguous. Doesn't the problem go away if you replace it with "all"?
Yes, that is even better. The world would be simple and elegant if it did things your way, and would still be not too shabby if it did things my way, no? «Learn You a Haskell for Great Good!» by Miran Lipovača: http://learnyouahaskell.com/types-and-typeclasses#type-variables "Because it's not in capital case it's actually a type variable. That means that a can be of any type." «The Haskell School of Expression» by Paul Hudak: page 57 "Intuitively, what we'd like to say is that, for any type a, the type of length is [a] -> Integer." "So length can be applied to a list containing elements of any type." (Does [True, 'x'] count as a list containing elements of any type?) At this point, you may be rightful to accuse me of taking sentences out of context. I acknowledge it. The contexts have examples and other words on using this new freedom of "any"; hopefully, readers pick up the unsaid message: who has that freedom. It is correct to say: the accompanying examples and words make it sufficiently clear. The flip side is: look how many examples and words you have to set up to make it sufficiently clear. This thread began with the omission vs inclusion of syntax "forall t" or equivalent. It also, clearly, set the beginner classroom context. If someone replied, "since it is a rank-1 language, the omission is syntactically simpler, the inclusion would be syntactically repetitive", I would agree. In fact I hold that opinion. But that has not been the reply. The reply has been, "the omission is semantically simpler", and that's what I object to. All I see is evidence against it. Look how many examples and words you have to set up to teach it. Their length testifies the semantic complexity or complication. You have saved teaching syntax, but you haven't saved teaching semantics, semantics of something unrepresented by syntax. As for what mathematicians self-inflict on themselves, I should have, right at the beginning, just dismissed them and said: the context is beginner classroom, I don't care what happens between grad students and their thesis supervisors, it's their own business. If they just needed to wink-wink nudge-nudge and that finished transmitting a proof of P=NP, good for them.