On the Expressivity of Total Reversible Programming Languages

SRL is a reversible programming language conceived as a restriction of imperative programming languages. Each SRL program that mentions n registers defines a bijection on n-tuples of integers. Despite its simplicity, SRL is strong enough to grasp a wide class of computable bijections and to rise non-trivial programming issues. We advance in the study of its expressivity. We show how to choose among alternative program-branches by checking if a given value is positive or negative. So, we answer some longstanding questions that the literature poses. In particular, we prove that SRL is primitive recursive complete and that its program equivalence is undecidable.