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2013-12-16T20:20:05.100
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The definition of <code>Ord</code> itself in the <a href="http://www.haskell.org/onlinereport/standard-prelude.html">standard prelude</a> requires there already be an <code>Eq</code> instance: <pre><code>class (Eq a) => Ord a where ... </code></pre> So it would be just as wrong to violate <pre><code> x == y = compare x y == EQ x /= y = compare x y /= EQ </code></pre> As it would be to violate (from the default definitions for these operators in Ord). <pre><code> x <= y = compare x y /= GT x < y = compare x y == LT x >= y = compare x y /= LT x > y = compare x y == GT </code></pre> Edit: Use in libraries I would be quite surprised if standard libraries didn't make use of <code>Ord</code>'s <code>==</code> and <code>/=</code> operators. The specific purpose operators (<code>==</code>, <code>/=</code>, <code><=</code>, <code><</code>, <code>>=</code>, <code>></code>) are frequently more convenient than <code>compare</code>, so I'd expect to see them used in code for <code>map</code>s or <code>filter</code>s. You can <a href="http://www.haskell.org/ghc/docs/latest/html/libraries/containers-0.5.0.0/src/Data-Map-Base.html">see <code>==</code> being used in guards on keys in <code>Data.Map</code> in fromAscListWithKey</a>. This specific function only calls out for the <code>Eq</code> class, but if the key is also an <code>Ord</code> instance, <code>Ord</code>'s <code>compare</code> will be used for other functions of the resulting <code>Map</code>, which is an assumption that <code>Eq</code>'s <code>==</code> is the same as <code>Ord</code>'s <code>compare</code> and testing for <code>EQ</code>. As a library programmer, I wouldn't be surprised if any of the special purpose operators outperformed <code>compare</code> for the specific purpose. After all, that's why they are part of the <code>Eq</code> and <code>Ord</code> classes instead of being defined as polymorphic for all <code>Eq</code> or <code>Ord</code> instances. I might make a point of using them even when <code>compare</code> is more convenient. If I did, I'd probably define something like: <pre><code>compareOp :: (Ord a) => Ordering -> Bool -> a -> a -> Bool compareOp EQ True = (==) compareOp EQ False = (/=) compareOp LT True = (<) compareOp LT False = (>=) compareOp GT True = (>) compareOp GT False = (<=) </code></pre>
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