mgsloan wrote: > On 3/24/07, Vivian McPhail <[EMAIL PROTECTED]> wrote: >> >> I agree with Sven, but... >> >> What I want to push is a 'mathematically sound' numeric prelude. A proper >> numerical prelude should have bona fide mathematical obects like groups, >> rings, and fields underlying common numerical classes. It would be >> edifying >> to the student who discovered that the particular data type he is using is >> an inhabitant of a known class and can thus take advantage of known >> properties, presupplied as class methods. Reasoning and communication >> about >> programs, data types, and functions would be enhanced. > > One problem with that is that the instances are often times not > mathematically sound - Int and Double certainly aren't.
Int is algebraically sound as a factor ring Z/nZ with n=2**k, k the number of bits (which could be implementation defined). Unfortunately the order inherited from Integer is not compatible with the algebra... Cheers Ben _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
