That module defines two intervals to be equal if their bounds are
equal, but to be unequal only if they are disjoint.
Well, this is simply a broken implementation. Quick question: Is the Ord instance lawful or not? Hard to tell... (at least without pencil & paper)
In my eyes this speaks for the proposal, because the library author would have been
unable to write the broken instance. [...]
But this is an extremely weak argument for the proposal: One can easily write broken instances even with a single (==) method, e.g. violating symmetry etc. As another example: Given some e.g. Monad instance, can one quickly see if it is lawful? I very much doubt so, unless one tries to prove it. Laws of type classes are very much "outside of the Haskell language", anyway, so I see nothing special for Eq.