First-order reasoning for higher-order concurrency ?
We present a practical first-order theory of a higher-order ?-calculus ? - calculus which is both sound and complete with respect to a standard semantic equivalence. The theory is a product of combining and simplifying two of the most prominent theories for HO? HO ? of Sangiorgi et al. and Jeffrey and Rathke [10]and[21], and a novel approach to scope extrusion. In this way we obtain an elementary labelled transition system where the standard theory of first-order weak bisimulation and its corresponding propositional HennessyMilner logic can be applied. The usefulness of our theory is demonstrated by straightforward proofs of equivalences between compact but intricate higher-order processes using witness first-order bisimulations, and proofs of inequivalence using the propositional HennessyMilner logic. Finally we show that contextual equivalence in a higher-order setting is a conservative extension of the first-order ?-calculus ? - calculus .
higher-order concurrency bisimulation hennessymilner logic