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       I can't test it right now, but wouldn't the following do the job in the Identity monad?

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forkExec :: Identity a -> Identity (Identity a) forkExec k = let result = runIdentity k             in result `par` return (Identity result)

Since Identity is a newtype, would that be equivalent to "result `par` result"? The forkExec in the IO monad let's other computations keep going until I need the result from the forked computation.

You're right, it doesn't seem to work the way I hoped. The equivalent function on Maybe monad works, though, so it is possible to write forkExec in monads other than IO.

In a pure computation, I can already get the same result with `par` and laziness, right?

Yes. The goal is to enable writing monadic parallel computations which work under any parallelizable monad. For example, I'm using it to run two trampolining producer/consumer coroutines in parallel. A large majority of interesting coroutines I have are completely agnostic with respect to the underlying monad.