Modular synthesis of verified verifiers of computation with STV algorithms

Single transferable vote (STV) is a family of preferential voting systems, different instances of which are used in binding elections throughout the world. We give a formal specification of this family, from which we derive fully verified tools that verify the computation for various instances of STV vote counting. These tools validate an execution of an STV vote counting algorithm, based on a transcript of the count. Our framework distils the similarities and differences of various instances of STV and gives a uniform and modular way of synthesising verifiers for its various instances, and provides the flexibility and ease for adapting and extending it to a variety of STV schemes. We minimise the trusted base in correctness of the tools produced by using the HOL4 and CakeML as the technical basis. We first formally specify and verify the tools in HOL4 and then obtain the machine executable versions for the tools by relying on the verified proof translator and the compiler of CakeML. Moreover, proofs that we establish in HOL4 and CakeML are almost completely automated so that new verified instances of STV can be created with no (or minimal) extra proof. Finally, our experimental results with executable code demonstrate feasibility of deploying the framework for verifying real size elections having an STV counting algorithm.