you can notice a difference if you think about strict vs non-strict evaluation. the first implementation can be more efficient for implementing isPositive

you can notice a difference if you think about strict vs non-strict evaluation. the first implementation can be more efficient for implementing isPositive isPositive x = case x when 0 = false when S _ = true then isPositive P(SSS0, SSSSS0) = isPositive S(P(SSS0, SSSS0)) and we can terminate right there the other formulation of plus is "strict" in the 2nd argument, you need to evaluate P |b| times to get a natural number out to case on, prior to that, you have a function call