Monotone (co)inductive types and positive fixed-point types

Ralph Matthes

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (1999)

  • Volume: 33, Issue: 4-5, page 309-328
  • ISSN: 0988-3754

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Matthes, Ralph. "Monotone (co)inductive types and positive fixed-point types." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 33.4-5 (1999): 309-328. <http://eudml.org/doc/92606>.

@article{Matthes1999,
author = {Matthes, Ralph},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},
keywords = {extensions of polymorphically typed lambda-calculus; System F; monotonicity witness; monotone inductive type; monotone coinductive type; primitive recursion; primitive corecursion; iteration; coiteration; fixed-points of monotone operators; retract types},
language = {eng},
number = {4-5},
pages = {309-328},
publisher = {EDP-Sciences},
title = {Monotone (co)inductive types and positive fixed-point types},
url = {http://eudml.org/doc/92606},
volume = {33},
year = {1999},
}

TY - JOUR
AU - Matthes, Ralph
TI - Monotone (co)inductive types and positive fixed-point types
JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
PY - 1999
PB - EDP-Sciences
VL - 33
IS - 4-5
SP - 309
EP - 328
LA - eng
KW - extensions of polymorphically typed lambda-calculus; System F; monotonicity witness; monotone inductive type; monotone coinductive type; primitive recursion; primitive corecursion; iteration; coiteration; fixed-points of monotone operators; retract types
UR - http://eudml.org/doc/92606
ER -

References

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  1. [1] T. Altenkirch, Logical relations and inductive/coinductive types, G. Gottlob, E. Grandjean and K. Seyr, Eds., Computer Science Logic, 12th International Workshop, Brno, Czech Republic, August 24.-28, 1998, Proceedings, Springer Verlag, Lecture Notes in Comput. Sci. 1584 (1999) 343-354. Zbl0934.03019MR1717502
  2. [2] H. P. Barendregt, Lambda calculi with types, S. Abramsky, D.M. Gabbay and T.S.E. Maibaum, Eds., Background: Computational Structures. Oxford University Press, Handb. Log. Comput. Sci. 2 (1993) 117-309. MR1381697
  3. [3] H. Geuvers, Inductive and coinductive types with iteration and recursion, B. Nordström, K. Pettersson and G. Piotkin, Eds., Proceedings of the 1992 Workshop on Types for Proofs and Programs, Båstad, Sweden, June 1992, pages 193-217, 1992. Only published via ftp://ftp.cs.chalmers.se/pub/cs-reports/baastad.92/proc.dvi.Z 
  4. [4] J.-Y. Girard, Interprétation fonctionnelle et élimination des coupures dans l'arithmétique d'ordre supérieur. Thèse de Doctorat d'État, Université de Paris VII (1972). 
  5. [5] J.-Y. Girard, Y. Lafont and P. Taylor, Proofs and Types. Cambridge University Press, Cambridge Tracts Theoret Comput. Set 7 (1989). Zbl0671.68002MR1003608
  6. [6] D. Leivant, Contracting proofs to programs, P. Odifreddi, Ed., Logic and Computer Science. Academic Press, APIC Studies in Data Processing 31 (1990) 279-327. 
  7. [7] R. Matthes, Extensions of System F by Iteration and Primitive Recursion on Monotone Inductive Types. Doktorarbeit (PhD thesis), University of Munich (1998). Available via the homepage http://www.tcs.informatik.uni-muenchen.de/matthes/ Zbl0943.68086
  8. [8] R. Matthes, Monotone fixed-point types and strong normalization, G. Gottlob, E. Grandjean and K. Seyr, Eds., Computer Science Logic, 12th International Workshop, Brno, Czech Republic, August 24.-28, 1998, Proceedings, Springer Verlag, Lecture Notes in Comput. Sci. 1584 (1999) 298-312. Zbl0933.03027MR1717499
  9. [9] R. Matthes and F. Joachimski, Short proofs of normalization for the simply-typed lambda-calculus, permutative conversions and Gödel's T. Arch. Math. Logic, submitted. Zbl1025.03010
  10. [10] J. C. Reynolds, Towards a theory of type structure, B. Robinet, Ed., Programming Symposium, Springer-Verlag, Lecture Notes in Comput. Sci. 19 (1974) 408-425. Zbl0309.68016MR458988
  11. [11] M. Takahashi, Parallel réduction in λ-calculus. Inform. and Comput. 118 (1995) 120-127. Zbl0827.68060MR1329243

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