The Countdown Problem
Hutton, Graham (2002) The Countdown Problem. Journal of Functional Programming, 12 (6). pp. 609-616.
We systematically develop a functional program that solves the countdown problem, a numbers game in which the aim is to construct arithmetic expressions satisfying certain constraints. Starting from a formal specification of the problem, we present a simple but inefficient program that solves the problem, and prove that this program is correct. We then use program fusion to calculate an equivalent but more efficient program, which is then further improved by exploiting arithmetic properties.
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