Wolfram wrote:
My arguments consistently assume the following specification: \begin{spec} forall a . (Ord a, Bounded a) => forall x :: a . minBound <= x && x <= maxBound \end{spec}
That sounds like a great thing to suggest for Haskell'. It is not true currently. Ord and Bounded are independent of each other. Current discussions on this list make it clear that forcibly enforcing such a restriction, e.g. by introducing Bounded instances in libraries, would break people's existing programs. Your restriction implies, among other things, that Ord may only be used for natural universal orderings of a type, not for arbitrary artificial orderings introduced for technical reasons. Because otherwise, why restrict people from using a natural Bounded instance if there is one, or a Bounded instance that is needed for some other technical reason? A good migration path towards your idea would be to fix the current most prominent offenders, the Data.<collection> modules, by providing an additional version of each that uses Indexable instead of Ord for artificial orderings, as suggest by Henning. And, of course, there is nothing to stop us from suggesting that people adhere to your specification by adding it to the documentation. I wrote:
Where are these axioms?
...it could be argued that the sentence: "The Bounded class is used to name the upper and lower limits of a type." might be understood to imply it
Given the current usage of Ord in the libraries, there is no reason to think that the upper and lower limits *of a type* necessarily have anything to do with Ord. -Yitz