First-order reasoning for higher-order concurrency

  • Authors:

  • Vasileios Koutavas;Matthew Hennessy

  • Affiliations:

  • Trinity College Dublin, Dublin, Ireland;Trinity College Dublin, Dublin, Ireland

  • Venue:
  • Computer Languages, Systems and Structures
  • Year:
  • 2012

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Abstract

We present a practical first-order theory of a higher-order @p-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@p of Sangiorgi et al. and Jeffrey and Rathke [10,21], 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 Hennessy-Milner 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 Hennessy-Milner logic. Finally we show that contextual equivalence in a higher-order setting is a conservative extension of the first-order @p-calculus.