The Higher-Order, Call-by-Value Applied Pi-Calculus

We define a higher-order process calculus with algebraic operations such as encryption and decryption, and develop a bisimulation proof method for behavioral equivalence in this calculus. Such development has been notoriously difficult because of the subtle interactions among generative names, processes as data, and the algebraic operations. We handle them by carefully defining the calculus and adopting Sumii et al.’s environmental bisimulation, and thereby give (to our knowledge) the first “useful” proof method in this setting. We demonstrate the utility of our method through examples involving both higher-order processes and asymmetric cryptography.