Trustworthy Systems

Correctness by construction for probabilistic programs

Authors

Annabelle McIver and Carroll Morgan

    School of Computer Science and Engineering
    UNSW,
    Sydney 2052, Australia

Abstract

The “correct by construction” paradigm can be applied to the development of probabilistic programs; here we use the well known semantics for pGCL, the probabilistic guarded-command language, to illustrate it. That language’s refinement relation enables compact, abstract specifications of probabilistic properties to be transformed gradually to concrete, executable code by applying mathematical insights in a systematic, layered way — and as far as possible, the reasoning in each 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 constructed algorithm is “within spitting distance” of Knuth and Yao's optimal solution.

BibTeX Entry

  @inproceedings{McIver_Morgan_20,
    paperurl         = {https://trustworthy.systems/publications/papers/McIver_Morgan_20.pdf},
    doi              = {10.1007/978-3-030-61362-4\_12},
    publisher        = {Springer},
    volume           = {12476},
    editor           = {Tiziana Margaria and Bernhard Steffen},
    series           = {Lecture Notes in Computer Science},
    booktitle        = {Leveraging Applications of Formal Methods, Verification and Validation: Verification
                        Principles---9th International Symposium on Leveraging Applications of Formal Methods, ISoLA 2020,
                        Rhodes, Greece, October 20-30, 2020, Proceedings, Part {I}},
    title            = {Correctness by Construction for Probabilistic Programs},
    pages            = {216--239},
    author           = {Annabelle McIver and Carroll Morgan},
    year             = {2020},
    url              = {https://doi.org/10.1007/978-3-030-61362-4\_12}
  }

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