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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