Since the result you're looking for depends on time, this is inevitably going to involve impure code.
It looks like System.Timeout from the base package provides the ability to run an I/O computation until some timeout. So all you need to do is write an IO computation that returns the result you're interested in. However, the tricky part is making the IO action actually compute the result, not just return an unevaluated result. For that, I think you need to evaluate from Control.Exception.
There is a small library based on those ideas that define a https://github.com/ppetr/timeout-with-resultsmonad for computations that can return partial results before returning the final one or dying on a timeout. See
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