Monad to also measure side effects

Question

How can I count the number of times bind is applied on a Monad - Example given a state monad, I'd like to count the number of times state changed. How can i best encapsulate this? Should this logic be part of bind operator (with side effect since it increments count) or is there a better way of doing it?

Answer 1

You can't. One of the monad laws is

return x >>= f = f x

which has one bind on the left and none on the right, so no law-abiding monad can observe how many bindings there are.

At best you may have an action

increment :: M ()

in your monad which bumps a counter. (This could be implemented, as you say, using StateT or similar, or in a couple other essentially isomorphic ways.)