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++.

Trac metadata

Trac field	Value
Version	6.6.1
Type	Bug
TypeOfFailure	OtherFailure
Priority	normal
Resolution	Unresolved
Component	libraries/base
Test case
Differential revisions
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Blocking
CC
Operating system	Multiple
Architecture	Multiple