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For higher-order (process) languages, characterising contextual equivalence is a long-standing issue. In the setting of a higher-order π -calculus with session types, we develop characteristic bisimilarity, a typed bisimilarity which fully characterises contextual equivalence. To our knowledge, ours is the first characterisation of its kind. Using simple values inhabiting (session) types, our approach distinguishes from untyped methods for characterising contextual equivalence in higher-orderdoi:10.1007/s00236-016-0289-7 pmid:32103830 pmcid:PMC7010397 fatcat:2mhbxewq3rczdjjtbpqsl4if4q