The gentle art of levitation

Proceedings of the ACM SIGPLAN International Conference on Functional Programming, ICFP

Volumn , Issue , 2010, Pages 3-14

  Chapman, James ^a   Dagand, Pierre Évariste ^b   McBride, Conor ^b   Morris, Peter ^c  

^a TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^c UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

data structure; metaprogramming; monads; proof assistants; type systems

Indexed keywords

DATA TYPE; DEPENDENT TYPE THEORY; EXISTING SYSTEMS; GENERIC PROGRAMMING; INDUCTIVE-TYPE; META PROGRAMMING; MONADS; PROOF ASSISTANT; TYPE SYSTEMS;

DATA STRUCTURES;

FUNCTIONAL PROGRAMMING;

EID: 78249243417     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1863543.1863547     Document Type: Conference Paper

References (47)

1. A. Abel, T. Coquand, and M. Pagano. A modular type-checking algorithm for type theory with singleton types and proof irrelevance. In TLCA.
2. R. Adams. Pure type systems with judgemental equality. JFP, 2006.
3. T. Altenkirch and C. McBride. Generic programming within dependently typed programming. In Generic Programming, 2002.
4. T. Altenkirch and B. Reus. Monadic presentations of lambda terms using generalized inductive types. In Computer Science Logic. 1999.
5. T. Altenkirch, C. McBride, and W. Swierstra. Observational equality, now! In PLPV, 2007.
6. L. Augustsson and M. Carlsson. An exercise in dependent types: A well-typed interpreter. Available at http://www.cs.chalmers.se/~augustss/ cayenne/interp.ps, 1999.
7. M. Benke, P. Dybjer, and P. Jansson. Universes for generic programs and proofs in dependent type theory. Nordic Journal of Computing, 2003.
8. E. Brady, J. Chapman, P.-E. Dagand, A. Gundry, C. McBride, P. Morris, and U. Norell. An Epigram implementation.
9. E. Brady, C. McBride, and J. McKinna. Inductive families need not store their indices. In TYPES, 2003.
10. J. Cheney and R. Hinze. First-class phantom types. Technical report, Cornell University, 2003.
11. T. Coquand. An algorithm for type-checking dependent types. SCP, 1996.
12. J. Courant. Explicit universes for the calculus of constructions. In TPHOLs, 2002.
13. N. A. Danielsson. The Agda standard library, 2010.
14. P. Dybjer. Inductive sets and families in Martin-Löf's type theory. In Logical Frameworks. 1991.
15. P. Dybjer and A. Setzer. A finite axiomatization of inductive-recursive definitions. In TLCA, 1999.
16. P. Dybjer and A. Setzer. Induction-recursion and initial algebras. In Annals of Pure and Applied Logic, 2000.
17. P. Dybjer and A. Setzer. Indexed induction-recursion. In Proof Theory in Computer Science. 2001.
18. R. Garcia, J. Jarvi, A. Lumsdaine, J. Siek, and J. Willcock. A comparative study of language support for generic programming. In OOPSLA, 2003.
19. H. Geuvers. Induction is not derivable in second order dependent type theory. In TLCA, 2001.
20. H. Goguen, C. McBride, and J. McKinna. Eliminating dependent pattern matching. In Algebra, Meaning and Computation. 2006.
21. R. Harper and R. Pollack. Type checking with universes. In TAPSOFT'89.
22. R. Hinze. Polytypic values possess polykinded types. In MPC. 2000.
23. R. Hinze, J. Jeuring, and A. Löh. Type-indexed data types. In MPC, 2002.
24. R. Hinze, J. Jeuring, and A. Löh. Comparing approaches to generic programming in Haskell. In Datatype-Generic Programming. 2007.
25. S. Holdermans, J. Jeuring, A. Löh, and A. Rodriguez. Generic views on data types. In MPC. 2006.
26. P. Jansson and J. Jeuring. PolyP - a polytypic programming language extension. In POPL, 1997.
27. R. Lämmel and S. Peyton Jones. Scrap your boilerplate: a practical design pattern for generic programming. In TLDI, 2003.
28. D. R. Licata and R. Harper. A universe of binding and computation. In ICFP, 2009.
29. Z. Luo. Computation and Reasoning. Oxford University Press, 1994.
30. P. Martin-Löf. Intuitionistic Type Theory. Bibliopolis· Napoli, 1984.
31. C. McBride and J. McKinna. The view from the left. JFP, 2004.
32. P. Morris. Constructing Universes for Generic Programming. PhD thesis, University of Nottingham, 2007.
33. P. Morris and T. Altenkirch. Indexed containers. In LICS, 2009.
34. P. Morris, T. Altenkirch, and C. McBride. Exploring the regular tree types. In TYPES, 2004.
35. P. Morris, T. Altenkirch, and N. Ghani. A universe of strictly positive families. IJCS, 2009.
36. U. Norell. Functional generic programming and type theory. Master's thesis, Chalmers University of Technology, 2002.
37. U. Norell. Towards a practical programming language based on dependent type theory. PhD thesis, Chalmers University of Technology, 2007.
38. N. Oury and W. Swierstra. The power of Pi. In ICFP, 2008.
39. C. Paulin-Mohring. Définitions inductives en théorie des types d'ordre supérieur. thèse d'habilitation, ENS Lyon, 1996.
40. B. C. Pierce and D. N. Turner. Local type inference. In POPL, 1998.
41. A. Rodriguez, J. Jeuring, P. Jansson, A. Gerdes, O. Kiselyov, and B. C. d. S. Oliveira. Comparing libraries for generic programming in Haskell. In Haskell Symposium, 2008.
42. The Coq Development Team. The Coq Proof Assistant Reference Manual.
43. W. Verbruggen, E. de Vries, and A. Hughes. Polytypic programming in Coq. In WGP, 2008.
44. W. Verbruggen, E. de Vries, and A. Hughes. Polytypic properties and proofs in Coq. In WGP, 2009.
45. S. Weirich and C. Casinghino. Arity-generic datatype-generic programming. In PLPV, 2010.
46. H. Xi, C. Chen, and G. Chen. Guarded recursive datatype constructors. In POPL, 2003.
47. A. R. Yakushev, S. Holdermans, A. Löh, and J. Jeuring. Generic programming with fixed points for mutually recursive datatypes. In ICFP, 2009.