[plt-scheme] How to make unit functors?

I think that the proper interpretation of the prose is:

   for any values, v1 and v2,

     (eq? v1 v2)
     =>
     (and (number? (eq-hash-code v1))
          (number? (eq-hash-code v2))
          (= (eq-hash-code v1) (eq-hash-code v2)))

The reverse implication may or may not be true (it's usually true, tho.
Isn't this the usual story for hashing?)

The text goes on to guarantee that this:

     (eq? v1 v2)
     =>
     (and (number? (eq-hash-code v1))
          (number? (eq-hash-code v2))
          (eq? (eq-hash-code v1) (eq-hash-code v2)))

which, as the text notes, implies that the numbers are fixnums. Another
way to put it:

     (eq? v1 v2)
     =>
     (and (number? (eq-hash-code v1))
          (number? (eq-hash-code v2))
          (fixnum? (eq-hash-code v1))
          (fixnum? (eq-hash-code v2))
          (= (eq-hash-code v1) (eq-hash-code v2)))

where fixnum? can (I think) be defined as:

  (define (fixnum? n) 
    (and (number? n)
         (exact? n)
         (integer? n)
         (eq? (- (+ n 1) 1) n)))

I'm not sure why there isn't a fixnum predicate built in (or maybe I
just missed it?)

Robby

At Wed, 28 May 2003 18:35:05 +0200, =?Windows-1252?Q?Jens_Axel_S=F8gaard?= wrote:
>   For list-related administrative tasks:
>   http://list.cs.brown.edu/mailman/listinfo/plt-scheme
> 
> Matthew Flatt wrote:
> 
> 
> >> Is the same also true for symbols? That is does it hold for two
> >> symbols s1 and s2 that
> >>
> >>   (= (eq-hash-code s1) (eq-hash-code s2)) =  (symbol=? s1 s2)
> >>
> >> ?
> >
> > Yes. `symbol=?' is `eq?' with its domain restricted to symbols.
> 
> Sorry, I intended to ask this question:
> 
>   Is the same also true for symbols? That is does it hold for two
>   symbols s1 and s2 that
> 
>      (= (eq-hash-code s1) (eq-hash-code s2)) =>  (symbol=? s1 s2)
>   ?
> 
> [otherwise the question is a bit silly]
> 
> I interpreted the prose describing eq-hash-code as
> 
> For all fixnums f1 and f2:
> 
>   (= (eq-hash-code f1) (eq-hash-code f2)) =>  (= f1 f2)
> 
> and wanted to know if it also holds for symbols.
> 
> --
> Jens Axel Søgaard
> 
>