[plt-scheme] Predicates from Types

On Thu, Apr 2, 2009 at 8:35 AM, Paulo J. Matos <pocmatos at gmail.com> wrote:
> On Wed, Apr 1, 2009 at 11:43 PM, Sam TH <samth at ccs.neu.edu> wrote:
>> On Wed, Apr 1, 2009 at 7:01 PM, Paulo J. Matos <pocmatos at gmail.com> wrote:
>>> Is there then a way to extract a predicate from a type? Given I assume
>>> the answer is no, what's the best solution for this?
>>> Right now I had to define :
>>> (: Predicate? (Any -> Boolean))
>>> (define (Predicate? u)
>>>     (or (Quantifier? u) (Logic-Predicate? u) ...))
>>
>> This is the right solution, but you probably want the type:
>>
>> (: Predicate? (Any -> Boolean : Predicate))
>>
>
> Now you lost me here... Why do I need the ": Predicate" part? and what
> does it do?

If a function has the type (Any -> Boolean : T), then that function is
a "predicate" for T (no relation to the "Predicate" in your mail).
This means that using that function checks if a value of of that type.
 `number?' is an excellent example here.  For example:

(if (number? x) (add1 x) 7)

always has type `Number'.

Similarly, if you give `Predicate?' the type I described, then you can
use `Predicate?' to check membership in the type `Predicate' in the
same way.
-- 
sam th
samth at ccs.neu.edu