Correctness by construction for probabilistic programs
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The "correct by construction" paradigm is an important component of modern Formal Methods, and here we use the probabilistic Guarded-Command Language ππΊπΆπΏ to illustrate its application to ππππππππππ π‘ππ programming. ππΊπΆπΏ extends Dijkstra's guarded-command language πΊπΆπΏ with probabilistic choice, and is equipped with a correctness-preserving refinement relation (β) that enables compact, abstract specifications of probabilistic properties to be transformed gradually to concrete, executable code by applying mathematical insights in a systematic and layered way. Characteristically for "correctness by construction", as far as possible the reasoning in each refinement-step layer does not depend on earlier layers, and does not affect later ones. We demonstrate the technique by deriving a fair-coin implementation of any given discrete probability distribution. In the special case of simulating a fair die, our correct-by-construction algorithm turns out to be "within spitting distance" of Knuth and Yao's optimal solution.
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