Ratio Int is not well ordered
Ratio Int is declared to be in class Ord, which means (according to http://haskell.org/ghc/docs/latest/html/libraries/base/Data-Ord.html\#t%3AOrd) that < should be a total ordering. Yet consider the following interactive session in GHCI (on a 32 bit computer!):
Prelude> :m + Ratio Prelude Ratio> let a = 1 % (2 :: Int) Prelude Ratio> let b = 883177231 % (662415279 :: Int) Prelude Ratio> let c = 1616076535 % (430549561 :: Int) Prelude Ratio> a < b && b < c True Prelude Ratio> a < c False
The problem is that overflow occurs in Real.lhs (from the GHC source code), in the definition
(x:%y) < (x':%y') = x * y' < x' * y
That works for unbounded types (such as Integer). But to define a total order on bounded types, a more complicated method is necessary.
See http://boost.cvs.sourceforge.net/boost/boost/boost/rational.hpp?revision=1.21&view=markup, line 374, for a correct implementation in C++.