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. _______________________________________________ r6rs-discuss mailing list [email protected] http://lists.r6rs.org/cgi-bin/mailman/listinfo/r6rs-discuss
