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

RAIRO - Theoretical Informatics and Applications

Volumn 33, Issue 4-5, 1999, Pages 309-328

  Matthes, Ralph ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

Coiteration; Iteration; Monotone coinductive type; Monotone inductive type; Monotonicity witness; Primitive corecursion; Primitive recursion; Retract type; System F

Indexed keywords

MATHEMATICAL MODELS; MATHEMATICAL OPERATORS;

LAMBDA CALCULUS;

FORMAL LOGIC;

EID: 0033295934     PISSN: 09883754     EISSN: 1290385X     Source Type: Journal    
DOI: 10.1051/ita:1999120     Document Type: Article

References (11)

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.
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.
3. H. Geuvers, Inductive and coinductive types with iteration and recursion, B. Nordstrom, K. Pettersson and G. Plotkin, Eds., Proceedings of the 1992 Workshop on Types for Proofs and Programs, Bdstad, Sweden, June 1992, pages 193-217, 1992. Only published via ftp://ftp.cs.chalmers.se/pub/cs-reports/baastad.92/proc.dvi.Z
4. J.-Y. Girard, Interprétation fonctionnelle et élimination des coupures dans l’arithmétique d’ordre supérieur. Thèse de Doctorat d’Etat, Université de Paris VII (1972).
5. J.-Y. Girard, Y. Lafont and P. Taylor, Proofs and Types. Cambridge University Press, Cambridge Tracts Theoret. Comput. Sci. 7 (1989).
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. 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/
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.
9. R. Matthes and F. Joachimski, Short proofs of normalization for the simply-typed lambda-calculus, permutative conversions and Godel’s T. Arch. Math. Logic, submitted.
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.
11. M. Takahashi, Parallel reduction in Λ-calculus. Inform. and Comput. 118 (1995) 120-127.