I am going to take a guess and say that the library policy is that (Num Integer) and (Ratio Integer) are known to follow the axioms, but anyone who uses (Num Int) and (Ratio Int) did so to get the size and performance and does not want to cast to Integer. Just as someone who uses (Word8) really wants to conserve space, much as the Array of Bool is usually implemented as bitpacked in memory. David Benbennick wrote:
The Ratio data type suffers from numeric overflow. For example, consider the Ord declaration in the Haskell 98 Report (I'm looking at page 153, section 12.1 of http://haskell.org/definition/haskell98-report.pdf):
(x:%y) <= (x':%y') = x * y' <= x' * y
It is easy to see that Ratio Int is not well-ordered under this definition, because of overflow. This is a self-contradiction in the Report, since page 84 (section 6.3.2) says that "The Ord class is used for totally ordered datatypes".
I think the best way to resolve this contradiction is to avoid overflow. For example, the following definition works:
(x:%y) <= (x':%y') = (toInteger x) * (toInteger y') <= (toInteger x') * (toInteger y)
I submitted a complete patch at http://hackage.haskell.org/trac/ghc/ticket/1517, but that was apparently the wrong place, since the bug was closed as wontfix.
Is there a chance of getting this contradiction resolved? I'll be happy to provide unit tests for the change if that will help get it applied. _______________________________________________ Libraries mailing list Libraries@haskell.org http://www.haskell.org/mailman/listinfo/libraries