[Haskell-cafe] "show" for functional types
lemming at henning-thielemann.de
Sat Apr 1 02:43:28 EST 2006
On Fri, 31 Mar 2006, Greg Buchholz wrote:
> In section 5 of _Fun with Phantom Types_, Hinze states...
> "Let us move on to one of the miracles of theoretical computer
> science. In Haskell, one cannot show values of functional types. For
> reasons of computability, there is no systematic way of showing
> functions and any ad-hoc approach would destroy referential transparency
> (except if show were a constant function). For instance, if show yielded
> the text of a function definition, we could distinguish, say, quick sort
> from merge sort. Substituting one for the other could then possibly
> change the meaning of a program."
I find this statement misleading. I do not expect that (2+2::Int) is shown
as "2+2", but as "4". Analogously I don't expect 'toLower' to be shown as
"toLower". There are certainly several descriptions of the same value,
independent from whether the value is a number or a function. So what _is_
a function? A function is a set of assignments from arguments to function
values. That is, a natural way to show a function would be to print all
[('A','a'), ('a','a'), ('1', '1'), ...
In principle this instance of 'show' could be even implemented, if there
would be a function that provides all values of a type.
Prelude> sort :: [Int] -> [Int]
[(,), ([0,1],[0,1], ([1,0],[0,1]), ...
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