[plt-scheme] When does eqv? differ from eq? , from equal?

Woodhouse Gregory wrote:
>
> I almost always perform tests with eq? or equal?, seldom (if ever) 
> with eqv? . The Reference is a bit mysterious, saying (in section 3.1)
>
> Two values are eqv? 
> <file:///Applications/PLT%20Scheme%20Full%20v4.1.0.3/doc/reference/booleans.html#%28def._%28%28quote._%7E23%7E25kernel%29._eqv%7E3f%29%29> 
> if and only if they are eq? 
> <file:///Applications/PLT%20Scheme%20Full%20v4.1.0.3/doc/reference/booleans.html#%28def._%28%28quote._%7E23%7E25kernel%29._eq%7E3f%29%29>, 
> unless otherwise specified for a particular datatype.
>
Which means you ought to use eqv? for characters and numbers.

A heuristic: If a members of a datatype have a unique representation on 
the machine level,
then it is safe to use eq?.  If two different representations can 
represent the same (abstract) value,
then use eqv?.

For floating point numbers +0.0 and -0.0 have different representaions, 
but both represent zero.
The fixnum 0 and the bignum 0 also have different representation, but 
represent the same number.
Conclusion: Always use eqv? instead of eq? when comparing numbers.
Exception:   If you in an algorithm can prove all numbers are 
representable as, say, fixnums, then
                    you can use eq? -- but remember that the range of 
fixnums may be different on other
                    implementations.

Characters can also have different representations - at least in some 
implementations.

The subject pops up once in a while in comp.lang.scheme. One example of 
such a thread
is:

http://groups.google.com/group/comp.lang.scheme/browse_thread/thread/201fd2d0723731c5/c57f5868525aa811?lnk=gst&q=eq%3F+eqv%3F#c57f5868525aa811



-- 
Jens Axel Søgaard