Logical Relations for Monadic Types

  • Jean Goubault-Larrecq
  • Slawomir Lasota
  • David Nowak
Conference paper

DOI: 10.1007/3-540-45793-3_37

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2471)
Cite this paper as:
Goubault-Larrecq J., Lasota S., Nowak D. (2002) Logical Relations for Monadic Types. In: Bradfield J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg

Abstract

Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi’s computational lambda-calculus. The treatment is categorical, and is based on notions of subsconing and distributivity laws for monads. Our approach has a number of interesting applications, including cases for lambda-calculi with non-determinism (where being in logical relation means being bisimilar), dynamic name creation, and probabilistic systems.

Keywords

logical relations monads semantics typed lambda-calculus 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jean Goubault-Larrecq
    • 1
  • Slawomir Lasota
    • 1
    • 2
  • David Nowak
    • 1
  1. 1.LSV, CNRS & ENSCachanFrance
  2. 2.Institute of InformaticsWarsaw UniversityPoland

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