Parigot's second order λμ-calculus and inductive types

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

Volumn 2044 LNCS, Issue , 2001, Pages 329-343

  Matthes, Ralph ^a  

^a UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BIOMINERALIZATION; COMPUTATIONAL COMPLEXITY; DIFFERENTIATION (CALCULUS); EMBEDDINGS; PATHOLOGY;

ATOMIC FORMULAE; CLASSICAL LOGIC; INDUCTIVE-TYPE; INTUITIONISTIC LOGIC; LAMBDA-MU CALCULUS; POLYMORPHIC LAMBDA CALCULUS; POSITIVE FIXED POINT; STRONG NORMALIZATION; SECOND ORDERS;

CALCULATIONS;

EID: 84888868431     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45413-6_26     Document Type: Conference Paper

References (18)

1. Henk P. Barendregt. The Lambda Calculus: Its Syntax and Semantics. North-Holland, Amsterdam, second revised edition, 1984.
2. Pierre-Louis Curien and Hugo Herbelin. The duality of computation. In Proceedings of the fifth A CM SIGPLAN International Conference on Functional Programming (ICFP '00), Montréal, pages 233-243. ACM Press, 2000.
3. Philippe de Groote. A CPS-translation of the λμ-calculus. In Sophie Tison, editor, Trees in Algebra and Programming - CAAP'94, 19th International Colloquium, volume 787 of Lecture Notes in Computer Science, pages 85-99, Edinburgh, 1994. Springer Verlag.
4. Herman Geuvers. Inductive and coinductive types with iteration and recursion. In Bengt Nordstrom, Kent Pettersson, and Gordon Plotkin, editors, Proceedings of the 1992 Workshop on Types for Proofs and Programs, Bâstad, Sweden, June 1992, pages 193-217, 1992. Only published electronically: ftp://ftp.cs.chalmers.Se/pub/cs-reports/baastad.92/proc.dvi.Z
5. Jean-Yves Girard, Yves Lafont, and Paul Taylor. Proofs and Types, volume 7 of Cambridge Tracts in Theoretical Computer Science. Cambridge University Press, 1989.
6. Thierry Joly. Un plongement de la logique classique du 2nd ordre dans AF2. Unpublished manuscript. In French, 5 pp., January 1996.
7. Ralph Matthes. Extensions of System F by Iteration and Primitive Recursion on Monotone Inductive Types. Doktorarbeit (PhD thesis), University of Munich, 1998. Available via http://www.tcs.informatik.uni-muenchen.de/~matthes/.
8. Ralph Matthes. Monotone (co)inductive types and positive fixed-point types. Theoretical Informatics and Applications, 33(4/5):309-328, 1999.
9. Ralph Matthes. Monotone fixed-point types and strong normalization. In Georg Gottlob, Etienne Grandjean, and Katrin Seyr, editors, Computer Science Logic, 12th International Workshop, Brno, Czech Republic, August 24-28, 1998, Proceedings, volume 1584 of Lecture Notes in Computer Science, pages 298-312. Springer Verlag, 1999.
10. Nax P. Mendler. Recursive types and type constraints in second-order lambda calculus. In Proceedings of the Second Annual IEEE Symposium on Logic in Computer Science, Ithaca, N.Y., pages 30-36. IEEE Computer Society Press, 1987. Forms a part of [11].
11. Paul F. Mendler. Inductive definition in type theory. Technical Report 87-870, Cornell University, Ithaca, N.Y., September 1987. Ph.D. Thesis (Paul F. Mendler = Nax P. Mendler).
12. Michel Parigot. λμ-calculus: an algorithmic interpretation of classical natural deduction. In Andrei Voronkov, editor, Logic Programming and Automated Reasoning, International Conference LPAR'92, St. Petersburg, Russia, volume 624 of Lecture Notes in Computer Science, pages 190-201. Springer Verlag, 1992.
13. Michel Parigot. Strong normalization for second order classical natural deduction. In Proceedings, Eighth Annual IEEE Symposium on Logic in Computer Science, pages 39-46, Montreal, Canada, 1993. IEEE Computer Society Press.
14. Michel Parigot. Proofs of strong normalisation for second order classical natural deduction. The Journal of Symbolic Logic, 62(4):1461-1479, 1997.
15. Christine Paulin-Mohring. Definitions Inductives en Theorie des Types d'Ordre Supérieur. Habilitation a diriger les recherches, ENS Lyon, 1996.
16. Dag Prawitz. Natural Deduction. A Proof-Theoretical Study. Almquist and Wiksell, 1965.
17. Zdzislaw Splawski and Pawel Urzyczyn. Type Fixpoints: Iteration vs. Recursion. SIGPLAN Notices, 34(9):102-113, 1999. Proceedings of the 1999 International Conference on Functional Programming (ICFP), Paris, France.
18. Thomas Streicher and Bernhard Reus. Classical logic, continuation semantics and abstract machines. Journal of Functional Programming, 8(6):543-572, 1998.