[r6rs-discuss] [Formal] Formal Comment: NaN should be considered a number, not a real

From: Thomas Lord <lord>
Date: Fri, 22 Jun 2007 13:49:33 -0700

Arthur Smyles wrote:
> Changes
>
> (real? nan.0) => false
> (complex? nan.0) => false
>

Honestly? No.

It would make more logical sense to add a new value
to the language, "#NaB" (pronounced, "not a boolean"),
and have:

    (real? nan.0) => #NaB
    (complex? nan.0) => #NaB


The following should be (an example of) an error:

    (if #NaB 'yes 'no) => ...error...


NaN is a bottom value and (ordinary) type predicates are strict in
the type of their arguments. Bottom values have no
type other than "bottom".

       (real? _|_) => _|_

therefore

      (real? nan.0) => #f

is bogus.





> These would still hold
> (number? nan.0) => true
>

No way, please. A NaN result from an
FPU signals that no proof has been found that any
number exists which is the requested result.

The most logical thing would be to have two procedures:

   NUMERIC?
and
  NUMBER?

NUMERIC? returns #t only if its argument can be
passed to math operations without causing an error.

NUMBER? returns #t only if there exists a number
consistent with the history of how its argument was
computed.


   (number? nan.0) => #NaB
   (numeric? nan.0) => #t



> (nan? nan.0) => true
> All IEEE-754 mathematical operations with nan.0
>
>

Yes. NaN is a bottom value but there can still be some
type structure among bottom values that can be effectively
recognized.

-t
Received on Fri Jun 22 2007 - 16:49:33 UTC