An example of non-trivial interaction of effects, handling of two effects together Non-determinism with control (cut) For the explanation of cut, see Section 5 of Hinze ICFP 2000 paper. Hinze suggests expressing cut in terms of cutfalse:

= return () `mplus` cutfalse
where
 cutfalse :: m a

satisfies the following laws:

 cutfalse >>= k  = cutfalse              (F1)
 cutfalse | m    = cutfalse              (F2)

(note: m `mplus` cutfalse is different from cutfalse `mplus` m). In other words, cutfalse is the left zero of both bind and mplus.

Hinze also introduces the operation call :: m a -> m a that delimits the effect of cut: call m executes m. If the cut is invoked in m, it discards only the choices made since m was called. Hinze postulates the axioms of call:

 call false = false                          (C1)
 call (return a | m) = return a | call m     (C2)
 call (m | cutfalse) = call m                (C3)
 call (lift m >>= k) = lift m >>= (call . k) (C4)

call m behaves like m except any cut inside m has only a local effect, he says.

Hinze noted a problem with the "mechanical" derivation of backtracing monad transformer with cut: no axiom specifying the interaction of call with bind; no way to simplify nested invocations of call.

We use exceptions for cutfalse Therefore, the law cutfalse >>= k = cutfalse is satisfied automatically since all exceptions have the above property.