Safety at speed: in-place array algorithms from pure functional programs by safely re-using storage

We present a purely functional array programming language that offers safe, purely functional and crash-free in-place array transformations. The language supports high-level abstractions for pure and efficient array computations that fully support equational reasoning. We show how to execute selected parts of these computations safely in-place, with the compiler guaranteeing that in-place execution does not change the computation’s result. Correctness is ensured by using an off-the-shelf-theorem prover to discharge safety conditions. Our main contribution is the idea of virtual copies for expressing re-use of arrays, and techniques for verifying their safety, which allow a pure language to include in-place transformations without weakening its transparency or rea- soning power