On Tuesday 21 October 2008 12:53:32 Thomas Lord wrote: > > Ken Dickey wrote: > > Can't we just use comparison predicates to compare quantities? > > A set of binary predicates makes sense to me. > > The way the word is usually used, the consequent of the conditional > should return #t. (You're defining "monotic-and-two-or-more?") > E.g., look for math definitions of "monotonic" on the web.
OK [wikipedia again]: In mathematics, a monotonic function (or monotone function) is a function which preserves the given order. Order => two or more. I see nothing about unordered monotonicity [whatever that might mean]. > > Is there really a natural, universal, fundamental extension here that > > needs to be in the language? .. > Having an arbitrary arity predicate that returns #t iff > it's arguments (if any) are in order seems like a basic > thing. > > As it stands now the primitive < tests if a sequence > of length 2 or greater is well ordered which is a bit > exotic and tends to not come up often in math. I think this is the crux of the matter. I was trained as and engineer -- a user of mathematics, rather than as a mathematician. Looking at my undergraduate math books [Elementary Functions, Calculus, Linear Algebra, Numerical Methods, Approximation Theory, Probability, Fluid Mechanics, Differential Equations, ...] there are zero (count' em, zero) mentions of relation, transitive relation, reflexive relation, symmetric relation, partial order, or total order. You are claiming/assuming a "natural, universal, fundamental" extension to a transitive binary predicate/relation for a specialized use one may not get introduced to until graduate school. I know (<=) => #t looks normal _to you_. But I believe that you are a specialist and I think that you are trying to inject a particular logic into a "basic literacy" kind of usage. I think that high school and undergraduate students should be able to use Scheme to do math without having to understand graduate level mathematics. $0.02, -KenD _______________________________________________ r6rs-discuss mailing list r6rs-discuss@lists.r6rs.org http://lists.r6rs.org/cgi-bin/mailman/listinfo/r6rs-discuss
