[aklug] Re: Further constraining types

On 08/03/2011 08:58 PM, Christopher Howard wrote:
> Let's say I have "f", which is a function of the following type:
>
> f :: Int -> Int
>
> However, let's say f is only capable of handling positive integers.
> Let's say that I'm committed to making f a complete function in the
> sense that (1) the pattern matching of the function is always complete
> and (2) there are no internal aborts, like an "error" call or an
> "undefined" expression. Obviously I could change the type to
>
> f :: Int -> Maybe Int
>
> ...to deal with the case where a negative parameter is passed in. But it
> seems like what I really want is something like this:
>
> f :: Positive Int -> Int
>
> I.e., the "positiveness" is hard-coded into the parameter type. But how
> do I do this? I was thinking it would involve some kind of "Positive
> Int" type, and some kind of "constructor" function like so:
>
> positiveNum :: Int -> Positive Int
>
> However, then this constructor function must deal with the problem of
> receiving a negative integer, and thus I have only shifted the problem.
> It is still an improvement, but yet it seems like I am missing some
> important concept here...
>

Um... sorry, wrong list. *insert embarrassed emoticon here*

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