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# Re: Circular structures [was Re: IEEE 754 floating-point arithmetic is not completely ordered]

This page is part of the web mail archives of SRFI 67 from before July 7th, 2015. The new archives for SRFI 67 contain all messages, not just those from before July 7th, 2015.

```Bradley Lucier wrote:
```
```On Apr 16, 2005, at 10:53 AM, Jens Axel Søgaard wrote:
```
```
```
```Well, it depends on what your goal is. ...
```
```
Here are some potential goals:
...
```
3) default-compare should define a total order on almost all Scheme values
```
What is "almost all"?  How do a and b compare in the following?

[descartes:~/programs/folding/2] lucier% gsc
loading /usr/local/Gambit-C/gambcext.scm
Gambit Version 4.0 beta 12

> (define a (cons #f #f))
> (set-car! a a)
> (set-cdr! a a)
> (define b (cons #f #f))
> (set-car! b b)
> (set-cdr! b b)
> (equal? a b)   ;;; doesn't terminate
```
```
In the proposal default-compare is not defined on circular structures.
Theoretically I think (I am not sure though) it is possible to
define an order on graphs.

```
```Is default-compare compatible with equal?
```
```
The current proposal for default-compare is:

(define (default-compare x y)
(select-compare x y
(null?    0)
(pair?    (default-compare (car x) (car y))
(default-compare (cdr x) (cdr y)))
(boolean? (compare-boolean x y))
(char?    (compare-char    x y))
(string?  (compare-string  x y))
(symbol?  (compare-symbol  x y))
(number?  (compare-number  x y))
(vector?  (compare-vector default-compare x y))
(else (error "unrecognized types" x y))))

Which means they are almost compatible :-)

The return value of equal? of two non-eq? symbols with the
same spelling is left unspecified by R5RS where as
default-compare is required to return #t.

Similary the return value of equal? of an exact number
and an inexact number that are numerically equal unspecified.

Apart from that, the domain of default-compare doesn't include
e.g. procedures as equal? does.

--
Jens Axel Søgaard

```