[r6rs-discuss] Comparison procedures' number of arguments

[Andre van Tonder]

On Thu, 23 Oct 2008, Ken Dickey wrote:

> Assuming a condition is true without requiring existence is something one
> should do very carefully.  It would seem much more natural to prove
> properties of entities that exist than for those that don't exist.

Empty and singleton lists certainly exist and, according to the very common 
mathematical definition of orderedness Mr Kowalczyk cited, satisfy the 
condition of being ordered according to the various predicates.  Mr Kowaczyk's 
definition has nicer properties.  For example, orderedness is preserved 
under truncation, and unnecessary special cases causing potential errors and 
fragility in all kinds of sorting applications are minimized.  The alternative 
point of view you propose is gratuitously more complicated and less useful, and 
would certainly be considered very odd by most mathematicians or computer 
scientists, who commonly found inductions on degenerate base cases that are 
vacuously true.