On 14 Apr 2010, at 09:17, Ashley Yakeley wrote:
Thomas Davie wrote:
Certainly bottom is a value, and it's a value in *all* Haskell types.
This is a matter of interpretation. If you consider bottom to be a value, then all the laws fail. For instance, (==) is supposed to be reflexive, but "undefined == undefined" is not True for almost any type.
For this reason I recommend "fast and loose reasoning": http://www.cs.nott.ac.uk/~nad/publications/danielsson-et-al-popl2006.html
It might be nice to have a definition of whether we consider bottom to be a value in Haskell then, because the definition of second and fmap on tuples are different because of this consideration: fmap f (x,y) = (x,f y) second f ~(x,y) = (x,f y) Because we consider that the Functor laws must hold for all values in the type (including bottom). Bob