This is pretty close to fundamentally a monadic approach. Arrow approaches to effect management are sometimes similar and sometimes very different. It's hard to be more clear since unifying these things as effects is perhaps tenuous than trying to find their common points.
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Recent work related to free and "freer" monads: http://okmij.org/ftp/Haskell/extensible/
What is the difference between this and arrows in terms of composition of effects?
This is pretty close to fundamentally a monadic approach. Arrow approaches to effect management are sometimes similar and sometimes very different. It's hard to be more clear since unifying these things as effects is perhaps tenuous than trying to find their common points.
The freer the monads...