Skip to main content
×
Home
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 4
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Deng, Yuxin and Zhang, Yu 2015. Program equivalence in linear contexts. Theoretical Computer Science, Vol. 585, p. 71.


    Katsumata, Shin-ya 2013. Relating computational effects by ⊤⊤-lifting. Information and Computation, Vol. 222, p. 228.


    Tzevelekos, Nikos 2012. Program equivalence in a simple language with state. Computer Languages, Systems & Structures, Vol. 38, Issue. 2, p. 181.


    Møgelberg, Rasmus Simpson, Alex and Tennent, Robert 2009. Relational Parametricity for Computational Effects. Logical Methods in Computer Science, Vol. 5, Issue. 3,


    ×
  • Mathematical Structures in Computer Science, Volume 18, Issue 6
  • December 2008, pp. 1169-1217

Logical relations for monadic types

  • JEAN GOUBAULT-LARRECQ (a1), SŁAWOMIR LASOTA (a2) and DAVID NOWAK (a3)
  • DOI: http://dx.doi.org/10.1017/S0960129508007172
  • Published online: 01 December 2008
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.

Copyright
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

M. Alimohamed (1995) A characterization of lambda definability in categorical models of implicit polymorphism. Theoretical Computer Science 146 (1-2) 523.

J. Beck (1969) Distributive laws. In: Seminar on Triples and Categorical Homology Theory. Springer-Verlag Lecture Notes in Mathematics 80 119140.

R. Crole and A. Pitts (1992) New foundations for fixpoint computations: Fix-hyperdoctrines and the fix-logic. Information and Computation 98 171210.

S. Eilenberg and G. M. Kelly (1966) Closed categories. In: Proceedings of the Conference on Categorical Algebra at La Jolla, Springer-Verlag421562.

M. Fiore and A. Simpson (1999) Lambda definability with sums via Grothendieck logical relations. In: Proceedings of the 4th International Conference on Typed Lambda-Calculi and Applications (TLCA'99). Springer-Verlag Lecture Notes in Computer Science 1581 147161.

P. J. Freyd and G. M. Kelly (1972) Categories of continuous functors I. Journal of Pure and Applied Algebra 2 (3) 169191.

G. Gierz , K. H. Hofmann , K. Keimel , J. D. Lawson , M. Mislove and D. S. Scott (1980) A Compendium of Continuous Lattices, Springer Verlag.

M. Giry (1981) A categorical approach to probability theory. In: B. Banaschewski (ed.) Categorical Aspects of Topology and Analysis. Springer-Verlag Lecture Notes in Mathematics 915 6885.

J. Goubault-Larrecq and E. Goubault (2003) On the geometry of intuitionistic S4 proofs. Homology, Homotopy and Applications 5 (2) 137209.

J. Goubault-Larrecq , S. Lasota and D. Nowak (2002) Logical relations for monadic types. In: Proceedings of the 16th International Workshop on Computer Science Logic (CSL'02). Springer-Verlag Lecture Notes in Computer Science 2471.

F. Honsell and D. Sannella (2002) Prelogical relations. Information and Computation 178 2343.

P. Johnstone (1975) Adjoint lifting theorems for categories of algebras. Bulletin of the London Mathematical Society 7 294297.

A. Jung and J. Tiuryn (1993) A new characterization of lambda definability. In: Proceedings of the 1st International Conference on Typed Lambda-Calculi and Applications (TLCA'93). Springer-Verlag Lecture Notes in Computer Science 664 245257.

K. G. Larsen and A. Skou (1991) Bisimulation through probabilistic testing. Information and Computation 94 128.

R. Lazić and D. Nowak (2000) A unifying approach to data-independence. In: Proceedings of the 11th Internal Conference on Concurrency Theory (CONCUR'2000). Springer-Verlag Lecture Notes in Computer Science 1877 581595.

Q. Ma and J. C. Reynolds (1992) Types, abstraction, and parametric polymorphism, part 2. In: 7th International Conference on Mathematical Foundations of Programming Semantics (MFPS'91). Springer-Verlag Lecture Notes in Computer Science 598 140.

S. Mac Lane (1971) Categories for the Working Mathematician, Graduate Texts in Mathematics 5,Springer-Verlag.

J. C. Mitchell and A. Scedrov (1993) Notes on sconing and relators. In: E. Börger , G. Jäger , H. Kleine Büning , S. Martini and M. M. Richter (eds.) Proceedings of the 6th International Workshop on Computer Science Logic (CSL'92). Springer-Verlag Lecture Notes in Computer Science 702 352378.

E. Moggi (1991) Notions of computation and monads. Information and Computation 93 5592.

A. Pitts and I. Stark (1993) Observable properties of higher order functions that dynamically create local names, or: What's new? In: A. Borzyszkowski and S. Sokołowski (eds.) Proceedings of the 18th International Symposium on Mathematical Foundations of Computer Science (MFCS'93). Springer-Verlag Lecture Notes in Computer Science 711 122141

A. M. Pitts (1991) Evaluation logic. In: G. Birtwistle (ed.) IVth Higher Order Workshop, Banff 1990, Workshops in Computing, Springer-Verlag162189.

A. M. Pitts (1996) Relational properties of domains. Information and Computation 127 (2) 6690.

G. Plotkin , J. Power , D. Sannella and R. Tennent (2000) Lax logical relations. In: Proceedings of the 7th International Colloquium on Automata, Languages and Programming (ICALP'2000). Springer-Verlag Lecture Notes in Computer Science 1853 85102.

J. Power and H. Watanabe (2002) Combining a monad and a comonad. Theoretical Computer Science 280 (1-2) 137162.

J. Rutten (1998) Relators and metric bisimulations. In: Proceedings of the 1th Workshop on Coalgebraic Methods in Computer Science (CMCS '98). Electronic Notes in Theoretical Computer Science 11 17.

I. Stark (1996) Categorical models for local names. Lisp and Symbolic Computation 9 (1) 77107.

R. Statman (1985) Logical relations and the typed λ-calculus. Information and Control 65 (2-3) 8597.

Y. Zhang and D. Nowak (2003) Logical relation for dynamic name creation. In: Proceedings of the 17th International Workshop on Computer Science Logic (CSL'03). Springer-Verlag Lecture Notes in Computer Science 2803 575588.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×