Assumption propagation through annotated programs

Abstract

In the correct-by-construction programming methodology, programs are incrementally derived from their formal specifications, by repeatedly applying transformations to partially derived programs. At an intermediate stage in a derivation, users may have to make certain assumptions to proceed further. To ensure that the assumptions hold true at that point in the program, certain other assumptions may need to be introduced upstream as loop invariants or preconditions. Typically these other assumptions are made in an ad hoc fashion and may result in unnecessary rework, or worse, complete exclusion of some of the alternative solutions. In this work, we present rules for propagating assumptions through annotated programs. We show how these rules can be integrated in a top-down derivation methodology to provide a systematic approach for propagating the assumptions, materializing them with executable statements at a place different from the place of introduction, and strengthening of loop invariants with minimal additional proof efforts.