Exotic List Monads

&gt; The usual list monad is only one of infinitely many ways to turn the List functor into a monad.<p>So simple, and yet this is a point that I think is rarely made clear enough in &quot;monad explainers.&quot; For instance, they almost always talk about &quot;the Maybe monad&quot; -- but this is conflating two things: the Maybe <i>data type</i>, and the Monad <i>instance</i> defined on that type. Propagating &quot;Nothing&quot; is <i>not</i> inherent to the Maybe data type, it&#x27;s just a convenient behavior to have.<p>Talking about &quot;the List monad&quot; is even more confusing for a newcomer. When they hear &quot;the List monad implements a kind of nondeterminism,&quot; it sounds like nondeterminism is a property <i>inherent to lists themselves</i> -- but of course it is nothing of the sort. All Monad instances are, in a sense, arbitrary.

&gt; In each case return is singleton (it is not known if there exists a monad on lists with a different return).<p>The &quot;diagonal&quot; monad join [[a, b, c, ...], [1, 2, 3, ...], [x, y, z, ...], ...] = [a, 2, z, ...] has return a = [a, a, a, ...], though I guess it&#x27;s hard to define it in a way that&#x27;s well-behaved for finite lists, so you might not consider it &quot;a monad on lists&quot;.

No comments, because no one understand these (At least, I don&#x27;t).

I appreciate comment threads like this because it shows me I have a lot to learn. HN is a great place to encounter people smarter than you.

I don’t see how this has broad appeal, but at least the Mazewalk interpretation is cute.