[Haskell-cafe] Re: Laws and partial values

[Thomas Davie]

On 25 Jan 2009, at 00:01, Benja Fallenstein wrote:

> Hi Lennart,
>
> On Sat, Jan 24, 2009 at 10:47 PM, Lennart Augustsson
> <lennart at 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