Representing nested inductive types using W-types

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

Volumn 3142, Issue , 2004, Pages 59-71

  Abbott, Michael ^a   Altenkirch, Thorsten ^b   Ghani, Neil ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; COMPUTERS;

CARTESIAN CLOSED CATEGORY; EXPONENTIATIONS; INDUCTIVE-TYPE; POLYNOMIAL FUNCTORS; W-TYPES;

ARTIFICIAL INTELLIGENCE;

EID: 35048886479     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-27836-8_8     Document Type: Article

References (15)

1. M. Abbott. Categories of Containers. PhD thesis, University of Leicester, 2003.
2. M. Abbott, T. Altenkirch, and N. Ghani. Categories of containers. In Proceedings of Foundations of Software Science and Computation Structures, volume 2620 of Lecture Notes in Computer Science, 2003.
3. M. Abbott, T. Altenkirch, and N. Ghani. Representing strictly positive types. Presented at APPSEM annual meeting, invited for submission to Theoretical Computer Science, 2004.
4. A. Abel and T. Altenkirch. A predicative strong normalisation proof for a λ-calculus with interleaving inductive types. In Types for Proof and Programs, TYPES '99, volume 1956 of Lecture Notes in Computer Science, 2000.
5. P. Dybjer. Representing inductively defined sets by wellorderings in Martin-Löfs type theory. Theoretical Computer Science, 176:329-335, 1997.
6. P. Dybjer and A. Setzer. A finite axiomatization of inductive-recursive definitions. In Typed Lambda Calculus and Applications, pages 129-146, 1999.
7. P. Dybjer and A. Setzer. Indexed induction-recursion. Lecture Notes in Computer Science, 2183, 2001.
8. N. Gambino and M. Hyland. Wellfounded trees and dependent polynomial functors. In S. Berardi, M. Coppo, and F. Damiani, editors, Types for Proofs and Programs (TYPES 2003), Lecture Notes in Computer Science, 2004.
9. M. Hofmann. On the interpretation of type theory in locally cartesian closed categories. In CSL, pages 427-441, 1994.
10. B. Jacobs. Categorical Logic and Type Theory. Number 141 in Studies in Logic and the Foundations of Mathematics. Elsevier, 1999.
11. P. T. Johnstone. Topos Theory. Academic Press, 1977.
12. P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis, Napoli, 1984.
13. I. Moerdijk and E. Palmgren. Wellfounded trees in categories. Annals of Pure and Applied Logic, 104:189-218, 2000.
14. B. Nordström, K. Petersson, and J. M. Smith. Programming in Martin-Löf's Type Theory. Number 7 in International Series of Monographs on Computer Science. Oxford University Press, 1990.
15. T. Streicher. Semantics of Type Theory. Progress in Theoretical Computer Science. Birkhäuser Verlag, 1991.