[Haskell-cafe] Re: Laws and partial values

[Jake McArthur]

Thomas Davie wrote:
> But, as there is only one value in the Unit type, all values we have no information about must surely be that value

The flaw in your logic is your assumption that the Unit type has only 
one value. Consider

     bottom :: ()
     bottom = undefined

Oviously, bottom is not (), but its type, nonetheless, is Unit. Unit 
actually has both () and _|_. More generally, _|_ inhabits every Haskell 
type, even types with no constructors (which itself requires a GHC 
extension, of course):

     data Empty

     bottom' :: Empty
     bottom' = undefined

If you only ever use total functions then you can get away with not 
accounting for _|_. Perhaps ironically a function that doesn't account 
for _|_ may be viewed philosophically as a partial function since its 
contract doesn't accommodate all possible values.

- Jake