Program extraction for mutable arrays

Abstract

We present a lightweight method to represent, verify, and extract efficient programs involving mutable arrays in the Coq proof assistant. Our method mainly consists of a library for handling mutable arrays and an improved extraction plugin. Our library provides a monadic domain specific language for modeling computations involving mutable arrays, a simple reasoning method based on the Ssreflect extension and the Mathematical Components library, and an extraction method to efficient OCaml programs using in-place updates. Our extraction plugin improves the performance of our extracted programs, or more appropriately, through the application of simple program transformations for purely functional programs, it reduces both construction and destruction costs of inductive and coinductive objects and function call costs. As concrete applications for our method, we provide efficient implementations, correctness proofs, and benchmarks of the union–find data structure and the quicksort algorithm.