Generalized iteration and coiteration for higher-order nested datatypes

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

Volumn 2620, Issue , 2003, Pages 54-69

  Abel, Andreas ^a   Matthes, Ralph ^a,b   Uustalu, Tarmo ^c  

^a UNIVERSITY OF MUNICH   (Germany)

^b CNRS   (France)

^c TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY;

COITERATION; GENERALIZED FOLDS; HIGHER-ORDER; MONOTONICITY; NESTED DATATYPES; PARAMETRIC POLYMORPHISM; RECURSIONS; STRONG NORMALIZATION;

BIRDS;

EID: 35248899419     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-36576-1_4     Document Type: Article

References (23)

1. A. Abel. Termination checking with types. Technical Report 0201, Inst. für Informatik, Ludwigs-Maximilians-Univ. München, 2002.
2. A. Abel and R. Matthes. (Co-)iteration for higher-order nested datatypes. To appear in H. Geuvers, F. Wiedijk, eds., Post-Conf. Proc. of IST WG TYPES 2nd Ann. Meeting, TYPES'02, Lect. Notes in Comput. Sci., Springer-Verlag.
3. T. Altenkirch and C. McBride. Generic programming within dependency typed programming. To appear in J. Gibbons and J. Jeuring, Proc. of IFIP TC2 WC on Generic Programming, WCGP 2002, Kluwer Acad. Publishers.
4. T. Altenkirch and B. Reus. Monadic presentations of lambda terms using generalized inductive types. In J. Flum and M. Rodriguez-Artalejo, eds., Proc. of 13th Int. Wksh. on Computer Science Logic, CSL'99, vol. 1683 of Lect. Notes in Comput. Sci., pp.53-468. Springer-Verlag, 1999.
5. G. Barthe, M. J. Frade, E. Giménez, L. Pinto, and T. Uustalu. Type-based termination of recursive definitions. Math. Struct. in Comput. Sci., to appear.
6. R. Bird, J. Gibbons, and G. Jones. Program optimisation, naturally. In J. Davies, B. Roscoe, J. Woodcock, eds., Millenial Perspectives in Computer Science. Palgrave, 2000.
7. R. Bird and L. Meertens. Nested datatypes. In J. Jeuring, ed., Proc. 4th Int. Conf. on Mathematics of Program Construction, MPC'98, vol. 1422 of Lect. Notes in Comput. Sci., pp. 52-67. Springer-Verlag, 1998.
8. R. Bird and R. Paterson. Generalised folds for nested datatypes. Formal Aspects of Comput., 11(2):200-222, 1999.
9. R. Bird and R. Paterson. De Bruijn notation as a nested datatype. J. of Funct. Program., 9(1):77-91, 1999.
10. E. Giménez. Structural recursive definitions in type theory. In Proc. of 25th Int. Coll. on Automata, Languages and Programming, ICALP'98, vol. 1443 of Lect. Notes in Comput. Sci., pp. 397-408. Springer-Verlag, 1998.
11. R. Hinze. Efficient generalized folds. In J. Jeuring, ed., Proc. of 2nd Wksh. on Generic Programming, WGP 2000, Tech. Report UU-CS-2000-19, Dept. of Comput. Sci., Utrecht Univ., pp. 1-16. 2000.
12. R. Hinze. Manufacturing datatypes. J. of Funct. Program., 11(5): 493-524, 2001.
13. R. Hinze. Polytypic values possess polykinded types. Sci. of Comput. Program., 43(2-3):129-159, 2002.
14. C. B. Jay. Distinguishing data structures and functions: The constructor calculus and functorial types. In S. Abramsky, ed., Proc. of 5th Int. Conf. on Typed Lambda Calculi and Appl., TLCA '01, vol. 2044 of Lect. Notes in Comput. Sci., pp. 217-239. Berlin, 2001.
15. C. Martin, J. Gibbons and I. Bayley. Disciplined, efficient, generalised folds for nested datatypes. Submitted.
16. R. Matthes. Extensions of System F by Iteration and Primitive Recursion on Monotone Inductive Types. PhD thesis, Ludwig-Maximilians-Univ. München, 1998.
17. R. Matthes. Monotone inductive and coinductive constructors of rank 2. In L. Fribourg, ed., Proc. of 15th Int. Wksh. on Computer Science Logic, CSL 2001, vol. 2142 of Lect. Notes in Comput. Sci., pp. 600-614. Springer-Verlag, 2001.
18. N. P. Mendier. Recursive types and type constraints in second-order lambda calculus. In Proc. of 2nd Ann. IEEE Symp. on Logic in Computer Science, LICS'87, pp. 30-36. IEEE CS Press, 1987.
19. N. P. Mendier. Inductive types and type constraints in the second-order lambda calculus. Ann. of Pure and Appl. Logic, 51(1-2):159-172, 1991.
20. S. Mac Lane. Categories for the Working Mathematician, vol. 5 of Graduate Texts in Mathematics, 2nd ed. Springer-Verlag, 1998.
21. T. Uustalu and V. Vene. A cube of proof systems for the intuitionistic predicate μ-, v-logic. In M. Haveraaen and O. Owe, eds., Selected Papers from the 8th Nordic Wksh. on Programming Theory, NWPT '96, Res. Rep. 248, Dept. of Informatics, Univ. of Oslo, pp. 237-246, 1997.
22. T. Uustalu and V. Vene. Coding recursion à la Mendier (extended abstract). In J. Jeuring, ed., Proc. of 2nd Wksh. on Generic Programming, WGP 2000, Tech. Rep. UU-CS-2000-19, Dept. of Comput. Sci., Utrecht Univ., pp. 69-85. 2000.
23. T. Uustalu and V. Vene. The dual of substitution is redecoration. In K. Hammond and S. Curtis, eds., Trends in Funct. Programming 3, pp. 99-110. Intellect, 2002.