[Haskell-cafe] Re: Laws and partial values
lemming at henning-thielemann.de
Sat Jan 24 16:19:39 EST 2009
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?
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