New up-to techniques for weak bisimulation

Up-to techniques have been introduced to enhance the bisimulation proof method for establishing bisimilarity results. While up-to techniques for strong bisimilarity are well understood, the irregularities that appear in the weak case make it difficult to give a unified presentation. We propose a uniform and modular theory of up-to techniques for weak bisimulation that captures most of the existing proof technology and introduces new techniques. Some proofs rely on nontrivial – and new – commutation results based on termination guarantees. All results presented in this paper have been formally proved using the Coq proof assistant.