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Logical relations for monadic types†

Published online by Cambridge University Press:  01 December 2008

JEAN GOUBAULT-LARRECQ ,
SŁAWOMIR LASOTA  and
DAVID NOWAK
JEAN GOUBAULT-LARRECQ
Affiliation:
LSV, ENS Cachan, CNRS, INRIA
SŁAWOMIR LASOTA
Affiliation:
Institute of Informatics, Warsaw University
DAVID NOWAK
Affiliation:
Research Center for Information Security, AIST
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Abstract

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

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 18 , Issue 6 , December 2008 , pp. 1169 - 1217
Copyright
Copyright © Cambridge University Press 2008

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