On 25 Jan 2009, at 00:01, Benja Fallenstein wrote:
Hi Lennart,
On Sat, Jan 24, 2009 at 10:47 PM, Lennart Augustsson
<lenn...@augustsson.net> wrote:
You can dream up any semantics you like about bottom, like it has to
be () for the unit type.
But it's simply not true. I suggest you do some cursory study of
denotational semantics and domain theory.
Umh. It's certainly not Haskell, but as far as I can tell, the
semantics Bob likes are perfectly fine domain theory. (_|_, _|_) = _|_
is the *simpler* definition of domain-theoretical product (and
inl(_|_) = inr(_|_) = _|_ is the simpler definition of
domain-theoretical sum), and the unit of this product (and sum) is
indeed the type containing only bottom. Lifting everything, as Haskell
does, is extra. I suppose it's unusual that Bob wants to lift sums but
not products, but there's nothing theoretically fishy about it that I
can see.
Yep, this is part of the insight that Conal helped me have – I sense
tomorrow is gonna be spent with much blog writing.
Bob_______________________________________________
Haskell-Cafe mailing list
Haskell-Cafe@haskell.org
http://www.haskell.org/mailman/listinfo/haskell-cafe
