The correct by construction paradigm is an important component of modern Formal Methods, and here we use the probabilistic Guarded-Command Language $mathit{pGCL}$ to illustrate its application to $mathit{probabilistic}$ programming. $mathit{pGCL}$ extends Dijkstras guarded-command language $mathit{GCL}$ with probabilistic choice, and is equipped with a correctness-preserving refinement relation $(sqsubseteq)$ 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 Yaos optimal solution.
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