Quasi-Open Bisimilarity with Mismatch is Intuitionistic

Quasi-open bisimilarity is the coarsest notion of bisimilarity for the π-calculus that is also a congruence. This work extends quasi-open bisimilarity to handle mismatch (guards with inequalities). This minimal extension of quasi-open bisimilarity allows fresh names to be manufactured to provide constructive evidence that an inequality holds. The extension of quasi-open bisimilarity is canonical and robust --- coinciding with open barbed bisimilarity (an objective notion of bisimilarity congruence) and characterised by an intuitionistic variant of an established modal logic. The more famous open bisimilarity is also considered, for which the coarsest extension for handling mismatch is identified. Applications to checking privacy properties are highlighted. Examples and soundness results are mechanised using the proof assistant Abella.