Towards Automated Property Discovery within Hume

Hume is a Turing-complete programming language, designed to guarantee space and time bounds whilst still working on a high-level. Formal properties of Hume programs, such as invariants and transformations, have previously been verified using the temporal logic of actions (TLA). TLA properties are verified in an inductive way, which often requires lemma discovery or generalisations. Rippling was developed for guiding inductive proofs, and supports lemmas and generalisation discovery through proof critics. In this paper we show how rippling and proof critics can be used in the verification of Hume invariants represented in TLA. Our approach is based on existing work on the problem of verifying and discovering loop invariants for an imperative program. We then extend this work to Hume program transformations.