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?