A theory of indirection via approximation

  • Authors:

  • Aquinas Hobor;Robert Dockins;Andrew W. Appel

  • Affiliations:

  • National University of Singapore, Singapore, Singapore;Princeton University, Princeton, NJ, USA;Princeton University, Princeton, NJ, USA

  • Venue:
  • Proceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
  • Year:
  • 2010

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Abstract

Building semantic models that account for various kinds of indirect reference has traditionally been a difficult problem. Indirect reference can appear in many guises, such as heap pointers, higher-order functions, object references, and shared-memory mutexes. We give a general method to construct models containing indirect reference by presenting a "theory of indirection". Our method can be applied in a wide variety of settings and uses only simple, elementary mathematics. In addition to various forms of indirect reference, the resulting models support powerful features such as impredicative quantification and equirecursion; moreover they are compatible with the kind of powerful substructural accounting required to model (higher-order) separation logic. In contrast to previous work, our model is easy to apply to new settings and has a simple axiomatization, which is complete in the sense that all models of it are isomorphic. Our proofs are machine-checked in Coq.