In article <200305130355.h4D3ttcB013484@adric.fnmoc.navy.mil>, oleg@pobox.com wrote:
Just for the record: yet another way to introduce negative numbers is through an explicit constructor Neg. For example: http://pobox.com/~oleg/ftp/Computation/type-arithmetics.html (sorry, the code uses C++ templates. The idea is just the same however: a mere Prolog in a more verbose notation). The above example demonstrates division of signed Peano numbers. The Neg constructor becomes quite handy then.
I prefer NegativeSucc, i.e. -(n+1) or -n-1. My integer types are thus T or NegativeSucc T for any natural type T, and the two don't overlap. Another trick is to use the same class for addition and subtraction: class Add a b ab | a b -> ab, ab a -> b; I found you can't build the instances if you have all three possible fundeps (because of overlaps), but you can with two. <http://cvs.sourceforge.net/cgi-bin/viewcvs.cgi/hbase/Source/HBase/TypeCa lc/>. As for dimensions, what would be most interesting would be to allow the user to add their own "basis" units, so for instance: module MyModule where import PhysicalUnits -- new basis unit type Cost = [whatever] dollar :: Cost dollar = [whatever] goldValue :: (Div Mass Cost t) => t goldValue = ... ...but that may be hard and/or messy. -- Ashley Yakeley, Seattle WA