Logical relations for monadic types

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2471, Issue , 2002, Pages 553-568

  Goubault Larrecq, Jean ^a   Lasota, Slawomir ^a,b   Nowak, David ^a  

^a CNRS   (France)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

Logical relations; Monads; Semantics; Typed lambda calculus

Indexed keywords

BIOMINERALIZATION; CALCULATIONS; COMPUTATION THEORY; DIFFERENTIATION (CALCULUS); PATHOLOGY; SEMANTICS;

COMPUTATIONAL LAMBDA CALCULUS; FUNDAMENTAL TOOLS; LOGICAL RELATIONS; MONADS; NON DETERMINISM; OBSERVATIONAL EQUIVALENCES; PROBABILISTIC SYSTEMS; TYPED LAMBDA CALCULUS;

COMPUTER CIRCUITS;

EID: 1442333628     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45793-3_37     Document Type: Conference Paper

References (26)

1. [1] J. Adamek, H. Herrlich, and G. Strecker. Abstract and Concrete Categories. Wiley, New York, 1990.
2. [2] M. Alimohamed. A characterization of lambda definability in categorical models of implicit polymorphism. Theoretical Computer Science, 146:5–23, 1995.
3. [3] R. Crole and A. Pitts. New foundations for fixpoint computations: Fixhyperdoctrines and the fix-logic. Information and Computation, 98:171–210, 1992.
4. [4] M. Fiore and A. Simpson. Lambda definability with sums via Grothendieck logical relations. In TLCA’99, pages 147–161. Springer Verlag LNCS 1581, 1999.
5. [5] J. Goubault-Larrecq and E. Goubault. On the geometry of intuitionistic S4 proofs. Research Report LSV-01-8, LSV, CNRS & ENS Cachan, 2001. To appear in Homology, Homotopy andA pplications.
6. [6] J. Goubault-Larrecq, S. Lasota, and D. Nowak. Logical relations for monadic types. Research Report, LSV, CNRS & ENS Cachan, 2002.
7. [7] F. Honsell and D. Sannella. Pre-logical relations. In CSL’99, pages 546–561. Springer Verlag LNCS 1683, 1999.
8. [8] C. Jones. Probabilistic Non-Determinism. PhD thesis, University of Edinburgh, 1990. Technical Report ECS-LFCS-90-105.
9. [9] A. Jung and J. Tiuryn. A new characterization of lambda definability. In TLCA’93, pages 245–257. Springer Verlag LNCS 664, 1993.
10. [10] K. G. Larsen and A. Skou. Bisimulation through probabilistic testing. Information and Computation, 94:1–28, 1991.
11. [11] R. Lazić and D. Nowak. A unifying approach to data-independence. In CONCUR’ 2000, pages 581–595. Springer Verlag LNCS 1877, 2000.
12. [12] Q. Ma and J. C. Reynolds. Types, abstraction, andp arametric polymorphism, part 2. In MFPS’91, pages 1–40. Springer-Verlag LNCS 598, 1992.
13. [13] J. C. Mitchell. Foundations for Programming Languages. MIT Press, 1996.
14. [14] J.C. Mitchell and A. Scedrov. Notes on sconing andre lators. In CSL’92, pages 352–378. Springer Verlag LNCS 702, 1993.
15. [15] E. Moggi. An abstract view of programming languages. Technical Report ECSLFCS- 90-113, LFCS, Department of Computer Science, University of Edinburgh, 1990.
16. [16] E. Moggi. Notions of computation andm onads. Information and Computation, 93:55–92, 1991.
17. [17] A. Pitts and I. Stark. Observable properties of higher order functions that dynamically create local names, or: What’s new? In MFCS’93, pages 122–141. Springer- Verlag LNCS 711, 1993.
18. [18] G. Plotkin, J. Power, D. Sannella, and R. Tennent. Lax logical relations. In ICALP’2000, pages 85–102. Springer Verlag LNCS 1853, 2000.
19. [19] G.D. Plotkin. Lambda-definability in the full type hierarchy. In To H. B. Curry: Essays on Combinatory Logic, Lambda Calculus and Formalism, pages 363–373. Academic Press, 1980.
20. [20] N. Ramsey andA. Pfeffer. Stochastic lambda calculus andmon ads of probability distributions. In POPL’02, pages 154–165, 2002.
21. [21] J.C. Reynolds. Types, abstraction and parametric polymorphism. In IFIP’83, pages 513–523. North-Holland, 1983.
22. [22] J. Rutten. Relators andmetri c bisimulations. In CMCS’98, volume 11 of Electronic Notes in Theoretical Computer Science, pages 1–7. Elsevier Science, 1998.
23. [23] I. Stark. Names, equations, relations: Practical ways to reason about new. Fundamenta Informaticae, 33(4):369–396, April 1998.
24. [24] R. Statman. Logical relations andt he typed λ-calculus. Information and Control, 65(2–3):85–97, 1985.
25. [25] D. Turi. Functorial Operational Semantics and its Denotational Dual. PhDthesis, Free University, Amsterdam, June 1996.
26. [26] P. Wadler. Comprehending monads. Mathematical Structures in Computer Science, 2:461–493, 1992.