Iteration and coiteration schemes for higher-order and nested datatypes

Theoretical Computer Science

Volumn 333, Issue 1-2, 2005, Pages 3-66

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

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

^b Inst F Informatik Ludwig M   (Germany)

^c TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

Author keywords

Coiteration; Efficient folds; Generalized folds; Higher order datatypes; Higher order polymorphism; Iteration; Strong normalization; System F

Indexed keywords

ALGEBRA; COMPUTER SCIENCE; DATA REDUCTION; FORMAL LANGUAGES; ITERATIVE METHODS; OPTIMIZATION;

COITERATION; EFFICIENT FOLDS; GENERALIZED FOLDS; HIGHER-ORDER DATATYPES; HIGHER-ORDER POLYMORPHISM; ITERATION; STRONG NORMALIZATION; SYSTEM F;

COMPUTER PROGRAMMING;

EID: 13644281245     PISSN: 03043975     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.tcs.2004.10.017     Document Type: Conference Paper

References (53)

1. A. Abel, R. Matthes, (Co-)iteration for higher-order nested datatypes, in: H. Geuvers, F. Wiedijk (Eds.), Types for Proofs and Programs, Internat. Workshop, TYPES 2002, Selected Papers, Lecture Notes in Computer Science, Vol. 2646, Springer, Berlin, 2003, pp. 1-20.
2. A. Abel, R. Matthes, T. Uustalu, Generalized iteration and coiteration for higher-order nested datatypes, in: A. Gordon (Ed.), Foundations of Software Science and Computation Structures, Proc. of the Sixth Internat. Conf., FoSSaCS 2003, Lecture Notes in Computer Science, Vol. 2620, Springer, Berlin, 2003, pp. 54-69.
3. T. Altenkirch, Logical relations and inductive/coinductive types. in: G. Gottlob, E. Grandjean, K. Seyr (Eds.), Computer Science Logic, Proc. of the 12th Internat. Workshop, CSL '98, Lecture Notes in Computer Science, Vol. 1584, Springer, Berlin, 1999, pp. 343-354.
4. T. Altenkirch, C. McBride, Generic programming within dependently typed programming, in: J. Gibbons, J. Jeuring (Eds.), Proc. of the IFIP TC2 Working Conf. on Generic Programming, Kluwer Academic Publishers, Dordrecht, 2003, pp. 1-20.
5. T. Altenkirch, B. Reus, Monadic presentations of lambda terms using generalized inductive types, in: J. Flum, M. Rodríguez-Artalejo (Eds.), Computer Science Logic, Proc. of the 13th Internat. Workshop, CSL '99, Lecture Notes in Computer Science, Vol. 1683, Springer, Berlin, 1999, pp. 453-468.
6. R. Backhouse, P. Hoogendijk, Generic properties of datatypes, in: R. Backhouse, J. Gibbons (Eds.), Generic Programming, Advanced Lectures, Lecture Notes in Computer Science, Vol. 2793, 2003, pp. 97-132.
7. R. Backhouse, P. Jansson, J. Jeuring, L. Meertens, Generic programming - an introduction, in: S.D. Swierstra, P.R. Henriques, J.N. Oliveira (Eds.), Advanced Functional Programming, Proc. of the Third Internat. School, AFP '98, Revised Lectures, Lecture Notes in Computer Science, Vol. 1608, Springer, Berlin, 1999, pp. 28-115.
8. R. Bird, O. de Moor, Algebra of Programming, Vol. 100 of Internat. Series in Computer Science, Prentice-Hall, Englewood Cliffs, NJ, 1997.
9. R. Bird, J. Gibbons, G. Jones, Program optimisation, naturally, in: J. Davies, B. Roscoe, J. Woodcock (Eds.), Millenial Perspectives in Computer Science, Proc. of the 1999 Oxford-Microsoft Symp. in Honour of Professor Sir Antony Hoare, Palgrave, 2000.
10. R. Bird, L. Meertens, Nested datatypes, in: J. Jeuring (Ed.), Mathematics of Program Construction, Proc. of the Fourth Internat. Conf., MPC'98, Lecture Notes in Computer Science, Vol. 1422, Springer, Berlin, 1998, pp. 52-67.
11. R. Bird, and R. Paterson Generalised folds for nested datatypes Formal Aspects Comput. 11 2 1999 200 222
12. R.S. Bird, and R. Paterson De Bruijn notation as a nested datatype J. Funct. Programming 9 1 1999 77 91
13. C. Chen, D. Zhu, H. Xi, Implementing cut elimination: a case study of simulating dependent types in Haskell, in: B. Jayaraman (Ed.), Practical Aspects of Declarative Languages, Proc. of the Sixth Internat. Symp., PADL 2004, Lecture Notes in Computer Science, Vol. 3057, Springer, Berlin, 2004, pp. 239-254.
14. D. Clarke, J. Jeuring, A. Löh, The Generic Haskell user's guide - version 1.23, Technical Report UU-CS-2002-047, Department of Computer Science, Utrecht University, 2002.
15. T. Hagino, A typed lambda calculus with categorical type constructors, in: D.H. Pitt, A. Poigné, D.E. Rydeheard (Eds.), Category Theory and Computer Science, Proc. of the Second Internat. Conf., CTCS '87, Lecture Notes in Computer Science, Vol. 283, Springer, Berlin, 1987, pp. 140-157.
16. R. Harper, G. Morrisett, Compiling polymorphism using intensional type analysis, in: Conf. Record of POPL'95, Proc. of the 22nd ACM SIGPLAN-SIGACT Symp. on Principles of Programming Languages, ACM Press, New York, 1995, pp. 130-141.
17. Haskell Mailing List, Markus Schnell's message slide: useful function? July 25 2002, URL http://www.mail-archive.com/haskell@haskell.org/.
18. F. Henglein Type inference with polymorphic recursion ACM Trans. Programming Languages Systems 15 2 1993 253 289
19. R. Hinze, Numerical representations as higher-order nested datatypes, Technical Report IAI-TR-98-12, Institut für Informatik III, Universität Bonn, 1998.
20. R. Hinze, Polytypic values possess polykinded types, Technical Report IAI-TR-99-15, Institut für Informatik III, Universität Bonn, 1999.
21. R. Hinze, Efficient generalized folds, in: J. Jeuring (Ed.), Proc. of the Second Workshop on Generic Programming, WGP 2000, Technical Report UU-CS-2000-19, Department of Computer Science, Utrecht Univ, 2000.
22. R. Hinze Generalizing generalized tries J. Funct. Programming 10 4 2000 327 351
23. R. Hinze Manufacturing datatypes J. Funct. Programming 11 5 2001 424 493
24. R. Hinze Polytypic values possess polykinded types Sci. Comput. Programming 43 2-3 2002 129 159
25. R. Hinze, J. Jeuring, Generic Haskell: applications, in: R. Backhouse, J. Gibbons (Eds.), Generic Programming, Advanced Lectures, Lecture Notes in Computer Science, Vol. 2793, Springer, Berlin, 2003, pp. 57-97.
26. R. Hinze, J. Jeuring, Generic Haskell: practice and theory, in: R. Backhouse, J. Gibbons (Eds.), Generic Programming, Advanced Lectures, Lecture Notes in Computer Science, Vol. 2793, Springer, Berlin, 2003, pp. 1-56.
27. R. Hinze, J. Jeuring, and A. Löh Type-indexed data types Sci. Comput. Programming 51 1-2 2004 117 151
28. P. Jansson, J. Jeuring, PolyP - a polytypic programming language extension, in: Conf. Record of POPL '97, Proc. of the 24th ACM SIGPLAN-SIGACT Symp. on Principles of Programming Languages, ACM Press, New York, 1997, pp. 470-482.
29. C.B. Jay, Distinguishing data structures and functions: the constructor calculus and functorial types, in: S. Abramsky (Ed.), Typed Lambda-Calculi and Applications, Proc. of the Fifth Internat. Conf., TLCA 2001, Lecture Notes in Computer Science, Vol. 2044, Springer, Berlin, 2001, pp. 217-239.
30. S. Kahrs Red-black trees with types J. Funct. Programming 11 4 2001 425 432
31. A. Kfoury, J. Tiuryn, and P. Urzyczyn Type reconstruction in the presence of polymorphic recursion ACM Trans. Programming Languages Systems 15 2 1993 290 311
32. A. Kfoury, J. Tiuryn, and P. Urzyczyn The undecidability of the semi-unification problem Inform. Comput. 102 1 1993 83 101
33. D. Le Botlan, D. Rémy, MLF: raising ML to the power of system F, in: Proc. of the Eighth ACM SIGPLAN Internat. Conf. on Functional Programming, ICFP 2003, ACM Press, New York, 2003, pp. 27-38.
34. S. Mac Lane, Categories for the Working Mathematician, second ed., Graduate Texts in Mathematics, Vol. 5, Springer, New York, 1998.
35. C. Martin, J. Gibbons, and I. Bayley Disciplined, efficient, generalised folds for nested datatypes Formal Aspects Comput. 16 1 2004 19 35
36. R. Matthes, Extensions of system F by iteration and primitive recursion on monotone inductive types, Ph.D. Thesis, University of Munich, 1998.
37. R. Matthes Monotone (co)inductive types and positive fixed-point types Theoret. Informat. Appl. 33 4-5 1999 309 328
38. C. McBride Faking it (simulating dependent types in Haskell) J. Funct. Programming 12 4-5 2002 375 392
39. N.P. Mendler, Recursive types and type constraints in second-order lambda calculus, in: Proc. of the Second Annual IEEE Symp. on Logic in Computer Science, LICS '87, IEEE CS Press, 1987, pp. 30-36.
40. N.P. Mendler Inductive types and type constraints in the second-order lambda calculus Ann. Pure Appl. Logic 51 1-2 1991 159 172
41. M. Neubauer, P. Thiemann, Type classes with more higher-order polymorphism, in: Proc. of the Seventh ACM SIGPLAN Internat. Conf. on Functional Programming, ICFP 2002, ACM Press, New York, 2002, pp. 179-190.
42. U. Norell, P. Jansson, Polytypic programming in Haskell, in: G. Michaelson, P. Trinder (Eds.), Implementation of Functional Languages, Proc. of the 15th Internat. Workshop, IFL 2003, Lecture Notes in Computer Science, Vol. 3145, Springer, Berlin, 2004.
43. C. Okasaki, From fast exponentiation to square matrices: an adventure in types, in: Proc. of the Fourth ACM SIGPLAN Internat. Conf. Functional Programming, ICFP '99, ACM Press, New York, 1999, pp. 28-35.
44. C. Okasaki Red-black trees in a functional setting J. Funct. Programming 9 4 1999 471 477
45. F. Pfenning, P. Lee, LEAP: A language with eval and polymorphism, in: J. Díaz, F. Orejas (Eds.), TAPSOFT '89, Proc. of the Internat. Joint Conf. on Theory and Practice of Software Development, Lecture Notes in Computer Science, Vol. 2, Vol. 352, Springer, Berlin, 1989, pp. 345-359.
46. B. Pierce, S. Dietzen, S. Michaylov, Programming in higher-order typed lambda-calculi, Technical Report, School of Computer Science, Carnegie Mellon University, 1989.
47. T. Uustalu, V. Vene, A cube of proof systems for the intuitionistic predicate μ -, ν -logic, in: M. Haveraaen, O. Owe (Eds.), Selected Papers from the Eighth Nordic Workshop on Programming Theory, NWPT '96, Research Report 248, Department of Informatics, University of Oslo, 1997, pp. 237-246.
48. T. Uustalu, and V. Vene The dual of substitution is redecoration K. Hammond S. Curtis Trends in Funct. Programming 3 2002 Intellect Bristol/Portland, OR 99 110
49. P. Wadler, Theorems for free!, in: Proc. of the Fourth Internat. Conf. on Functional Programming Languages and Computer Architecture, FPCA '89, ACM Press, New York, 1989, pp. 347-359.
50. P. Wadler The Girard-Reynolds isomorphism Inform. Comput. 186 2 2003 260 284
51. P. Wadler, S. Blott, How to make ad-hoc polymorphism less ad hoc, in: Conf. Record of the 16th Annu. ACM Symp. on Principles of Programming Languages, POPL '89, ACM Press, New York, 1989, pp. 60-76.
52. S. Weirich, Higher-order intensional type analysis, in: D. Le Métayer (Ed.), Programming Languages and Systems, Proc. of the 11th European Symp. on Programming, ESOP 2002, Lecture Notes in Computer Science, Vol. 2305, Springer, Berlin, 2002, pp. 98-114.
53. J.B. Wells Typability and type checking in system F are equivalent and undecidable Ann. Pure Appl. Logic 98 1-3 1999 111 156