Perhaps if you search for Abelian Monad or so, you will find
interesting things in the category theory literature.  Some of them
may be transplantable to Haskell --- but you probably don't want a
completely commutative structure.  Arrows seem to express the
dependencies between operations more fine-grained than the sequencing
that Monads require.  (I meant to look into arrows for ages..)

Matthias.
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