Transforming imperative programs into bisimilar logically constrained term rewrite systems via injective functions from configurations to terms

To transform an imperative program into a logically constrained term rewrite system (LCTRS, for short), previous work transforms a list of statements into rewrite rules in a stepwise manner, and proves the correctness along the transformation and the big-step semantics of the program. On the other hand, the small-step semantics of a programming language consists of inference rules that define single transitions of configurations. Partial instances of such inference rules are almost the same as rewrite rules in the transformed LCTRS. In this paper, we aim at establishing a framework for simpler definitions and correctness proofs of transformations from programs into LCTRSs. To this end, for the transformation in previous work as an example, we show the existence of an injective function from configurations of a given program to terms, and reformulate the transformation by means of the injective function. The injective function enables us to make a one-to-one correspondence between single small-step transitions and reduction steps, and provides bisimilarity between the program and transformed LCTRS, resulting in a simpler correctness proof.