There seems to be a sensible notion of a traversable type-aligned sequence, for traversing what McBride calls a Path in the context of an Atkey-style indexed applicative functor. There's also a related notion of folding one up in the context of a Category. This notion of traversability generalizes your mapMR and makes traversability stronger than mappability and foldability, as we'd expect.
There seems to be a sensible notion of a traversable type-aligned sequence, for traversing what McBride calls a
Path
in the context of an Atkey-style indexed applicative functor. There's also a related notion of folding one up in the context of aCategory
. This notion of traversability generalizes yourmapMR
and makes traversability stronger than mappability and foldability, as we'd expect.