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POHaskell: do standard libraries assume Eq and Ord are compatible?
 

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  1. POHaskell: do standard libraries assume Eq and Ord are compatible?
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    <p>This is a followup question to <a href="https://stackoverflow.com/questions/17114899/inconsistent-eq-and-ord-instances">Inconsistent Eq and Ord instances?</a>.</p> <p>The question there is essentially: when declaring <code>Eq</code> and <code>Ord</code> instances for a type, must one ensure that <code>compare x y</code> returns <code>EQ</code> if and only if <code>x == y</code> returns <code>True</code>? Is it dangerous to create instances that break this assumption? It seems like a natural law one might assume, but it doesn’t appear to be explicitly stated in the Prelude, unlike e.g. the monad or functor laws.</p> <p>The basic response was: it is a bit dangerous to do this, since libraries may assume that this law holds.</p> <p>My question, now, is: <strong>do any of the standard libraries (in particular, <code>Set</code> or <code>Map</code>) make this assumption? Is it dangerous to have a type with incompatible <code>Eq</code> and <code>Ord</code>, so long as I am only relying on the standard libraries supplied with GHC?</strong> (If big-list questions were still acceptable, I would be asking: which commonly used libraries assume this law?)</p> <p><strong>Edit.</strong> My use-case is similar to that of the original question. I have a type with a custom instance of <code>Eq</code>, that I use quite a bit. The only reason I want <code>Ord</code> is so that I can use it as the domain of a <code>Map</code>; I don’t care about the specific order, and will never use it explicitly in code. So if I can use the derived instance of <code>Ord</code>, then my life will be easier and my code clearer.</p>
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    1. CO"which commonly used libraries assume this law" --- people's brains?
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    2. COIndeed, a better question would be for a (non contrieved) example where `(a == b) /= (compare a b == EQ)` would make any sense.
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    3. COIs this just idle curiosity, or do you have a use case in mind where you think it makes sense to make the two differ? If the latter, I would love to see it presented (seriously, I am curious now, and can't think of a good use case myself....)
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