The answer is traverse, but the corollory is: if you try enough random combinations of traverse, map, mapN and flatTraverse, it will eventually compile and work
I was thinking it would be possible to write a macro to always do the right thing. Only one of those methods' signatures will typecheck! We would need a good name for that method, though: the hard part.
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As for the naming, I think either a species of monkey or a brand of typewriter would be apt
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