Proof Techniques for Behavioural Relations Based on Unique-Solutions of Equations and Inequations

We give an overview of recent work aiming at strengthening Milner’s technique of unique-solution of equations. This technique, originally introduced for CCS, is used to establish weak bisimilarity of processes. We review two improvements of the technique. The first one builds on the contraction behavioural preorder. The second one relaxes the conditions under which unique-solution can be applied by focusing on divergence in processes. We present applications of these techniques to reason about higher-order languages. We discuss how the two approaches, involving contractions and divergences, have been adapted and enriched, and compare them to each other.