[Haskell-cafe] Re: Laws and partial values

[Lennart Augustsson]

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.
Ordinary programming languages include non-termination, so that has to
be captured somehow in the semantics.
And that's what bottom does.

  -- Lennart

On Sat, Jan 24, 2009 at 9:31 PM, Thomas Davie <tom.davie at gmail.com> wrote:
>
> On 24 Jan 2009, at 22:19, Henning Thielemann wrote:
>
>>
>> On Sat, 24 Jan 2009, Thomas Davie wrote:
>>
>>> On 24 Jan 2009, at 21:31, Dan Doel wrote:
>>>
>>>> For integers, is _|_ equal to 0? 1? 2? ...
>>>
>>> Hypothetically (as it's already been pointed out that this is not the
>>> case in Haskell), _|_ in the integers would not be known, until it became
>>> more defined.  I'm coming at this from the point of view that bottom would
>>> contain all the information we could possibly know about a value  while
>>> still being the least value in the set.
>>>
>>> In such a scheme, bottom for Unit would be (), as we always know that the
>>> value in that type is (); bottom for pairs would be (_|_, _|_), as all pairs
>>> look like that (this incidentally would allow fmap and second to be equal on
>>> pairs); bottom for integers would contain no information, etc.
>>
>> Zero- and one-constructor data types would then significantly differ from
>> two- and more-constructor data types, wouldn't they?
>
> Yes, they would, but not in any way that's defined, or written in, the fact
> that they have a nice property of being able to tell something about what
> bottom looks like is rather nice actually.
>
> Bob
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