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Session Types with Arithmetic Refinements

Authors Ankush Das , Frank Pfenning

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  • 18 pages

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Author Details

Ankush Das
  • Carnegie Mellon University, Pittsburgh, PA, USA
Frank Pfenning
  • Carnegie Mellon University, Pittsburgh, PA, USA

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Ankush Das and Frank Pfenning. Session Types with Arithmetic Refinements. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 13:1-13:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


Session types statically prescribe bidirectional communication protocols for message-passing processes. However, simple session types cannot specify properties beyond the type of exchanged messages. In this paper we extend the type system by using index refinements from linear arithmetic capturing intrinsic attributes of data structures and algorithms. We show that, despite the decidability of Presburger arithmetic, type equality and therefore also subtyping and type checking are now undecidable, which stands in contrast to analogous dependent refinement type systems from functional languages. We also present a practical, but incomplete algorithm for type equality, which we have used in our implementation of Rast, a concurrent session-typed language with arithmetic index refinements as well as ergometric and temporal types. Moreover, if necessary, the programmer can propose additional type bisimulations that are smoothly integrated into the type equality algorithm.

Subject Classification

ACM Subject Classification
  • Theory of computation → Process calculi
  • Theory of computation → Linear logic
  • Theory of computation → Logic and verification
  • Computing methodologies → Concurrent programming languages
  • Theory of computation → Type theory
  • Session Types
  • Refinement Types
  • Type Equality


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