A calculus for collections and aggregates

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

Volumn 1290, Issue , 1997, Pages 261-280

  Lellahi, Kazem ^a   Tannen, Val ^b  

^a CNRS   (France)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AGGREGATES; ALGEBRA; DIFFERENTIATION (CALCULUS); FUNCTIONAL PROGRAMMING; QUERY LANGUAGES; QUERY PROCESSING; SEMANTICS;

AGGREGATE OPERATION; ALGEBRAIC STRUCTURES; DATABASE QUERY LANGUAGE; LAMBDA CALCULUS; PROGRAM EQUIVALENCE; SEMANTIC FOUNDATION;

CALCULATIONS;

EID: 84949202258     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/bfb0026993     Document Type: Conference Paper

References (32)

1. R. C. Backhouse. An exploration of the Bird-Meertens formalism. Technica] Report CS 8810, Groningen University, The Netherlands, 1988.
2. Val Breazu-Tannen, Peter Buneman, and Limsoon Wong. Natura~y embedded query languages. In J. Biskup and R. Hull, editors, LNCS 646: Proceedings of 4th International Conference on Database Theory, Berlin, Germany, October, 1992, pages 140-154. Springer-Verlag, October 1992.
3. Peter Buneman, Shamim Naqvi, Val Tannen, and Limsoon Wong. Principles of programming with complex objects and collection types. Theoretical Computer Science, 149(1):3-48, September 1995.
4. F. Borceux. Handbook of categorical algebra, Vol.2. Cambridge University Press, 1994.
5. V. Breazu-Tannen and R. Subrahmanyam. Logical and computational aspects of programming with Sets~Bags~Lists. In LNCS 510: Proceedings of 18th International Colloquium on Automata, Languages, and Programming, Madrid, Spain, July 1991, pages 60-75. Springer Verlag, 1991.
6. Michael Barr and Charles Wells. Toposes, Triples, and Theories. Springer-Veflag, New York, 1985.
7. R. G. G. Cattell, editor. The Object Database Standard: ODMG-93. Morgan Kaufmann, San Mateo, California, 1996.
8. R. Di Cosmo. On the power of simple diagrams. In LNCS 1103: Rewriting Techniques and Applications, New Brunswick, N J, duly 1996, Berlin, July 1996. Springer-Verlag.
9. S. Eilenberg and J. C. Moore. Adjoint functors and triples, Illinois Journal of Mathematics, 9:381-398, 1965.
10. A. Filinski. Controlling effects. PhD thesis, School of Computer Science, Carnegie Mellon University, Pittsburgh, PA 15213, May 1996. Available as CMU Technical Report CMU-CS-96-119.
11. Leonidas Fegaras and David Maier. Towards an effective calculus for object query languages. In Proceedings of ACM SIGMOD International Conference on Management of Data, pages 47-58, San Jose, California, May 1995.
12. A. Gill, J. Lannchbury, and S. Peyton Jones. A short cut to deforestation. In Proceedings of Conference on Functional Programming Languages and Computer Architecture, pages 223-232, 1993.
13. P. Hoogendijk. Relational programming laws in the Boom hierarchy of types. Technical report, Eindhoven University of Technology, The Netherlands, 1994.
14. H. Kleisli. Every standard construction is induced by a pair of adjoint functors. Proceedings of the American Mathematical Society, 16:544-546, 1965.
15. K. Lellahi. Towards a characterization of bulk types. Technical Report 94-01, Universit6 Paris 13, LIPN, 1994.
16. K. Lellahi. Type de collection et monades. In Actes des Journdes Categgories, Algébres, Esquisses et neo-esquisses, Caen, 1994.
17. J. Lambek and P. J. Scott. Introduction to Higher Order Categorical Logic, volume 7 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, London, 1986.
18. J. Launchbury and T. Sheard. Warm fusion: deriving build-catas from recursive definitions. In Proceedings of Conference on Functional Programming Languages and Computer Architecture, pages 314-323, 1995.
19. Leonid Libkin and Limsoon Wong. Aggregate flmctions, conservative extension, and finear orders. In Catriel Beeri, Atsushi Ohori, and Dennis E. Shasha, editors, Proceedings of DBPL-4, New York, August 1993, pages 282-294. Springer-Verlag, January 1994.
20. Leonid Libkin and Limsoon Wong. Some properties of query languages for bags. In Catriel Beeri, Atsushi Ohori, and Dennis E. Shasha, editors, Proceedings of DBPL-4, New York, August 1993, pages 97-114. Springer- Vertag, January 1994.
21. S. MacLane. Categories for the Working Mathematician. Springer-Verlag, Berlin, 1971.
22. Ernest G. Manes. Algebraic Theories, volume 26 of Graduate Texts in Mathematics. Springer-Verlag, Berlin, 1976.
23. Erik Meijer, Maartens Fokkinga, and Ross Paterson. Functional programming with bananas, lenses, envelopes, and barbed wires. In J. Hughes, editor, LNCS 523: 5th ACM Conference on Functional Languages and Computer Architecture, pages 124-144. Springer-Verlag, August 1991.
24. Eugenio Moggi. Notions of computation and monads. Information and Computation, 93:55-92, 1991.
25. P. Mulry. Monads and algebras in the semantics of partial data types. Theoretical Computer Science, 99:141-155, 1992.
26. P. Mulry, May 1997. Private communication.
27. Dan Suciu and Val Breazu-Tannen. A query language for NC. In Proceedings of t3th ACM Symposium on Principles of Database Systems, pages 167-178, Minneapolis, Minnesota~ May 1994. See also UPenn Technical Report MS-CIS-94-05.
28. P. W. Trinder. Comprehensions, a query notation for DBPLs. In Proceedings of 3rd International Workshop on Database Programming Languages, Nahplion, Greece, pages 49-62. Morgan Kaufmann, August 1991.
29. Philip Wadler. Comprehending monads. Mathematical Structures in Computer Science, 2:461-493, 1992.
30. Limsoon Wong. Normal forms and conservative properties for query languages over collection types. In Proceedings of 12th ACM Symposium on Principles of Database Systems, pages 26-36, Washington, D. C., May 1993. See also UPenn Technical Report MS-CIS-92-59.
31. Limsoon Wong. Querying Nested Collections. PhD thesis, Department, of Computer and Information Science, University of Pennsylvania, Philadelphia, PA 19104, August 1994. Available as University of Pennsylvania IRCS Report 94-09.
32. David A. Watt and Phil Trinder. Towards a theory of bulk types. Fide Technical Report 91/26, Glasgow University, Glasgow G12 8QQ, Scotland, July 1991.