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In several places this has (A, W), but (W, A) seems like it would line up more nicely with our WriterT. Is there any particular reason you went with the former?
Do people have experience using listen and listens? I will admit to never using MonadWriter, but it seems to me like working with the tuples could be a bit of a hassle. I find myself wondering if it would often be simpler to discard the A component and let people use flatMap and then a method like these if they want a reference to the A component. Just a brain dump: I'm curious about the experience of people who have actually used MonadWriter.
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Other instances are possible: https://hackage.haskell.org/package/mtl-2.2.1/docs/Control-Monad-Writer-Class.html
But I realized we also don't have similar instances for the other MTL type classes, so I'll add it all in one fell swoop