Traced premonoidal categories

RAIRO - Theoretical Informatics and Applications

Volumn 37, Issue 4, 2003, Pages 273-299

  Benton, Nick ^a   Hyland, Martin ^b  

^a MICROSOFT RESEARCH   (United Kingdom)

^b UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Fixed point operators; Monads; Premonoidal categories; Recursion; Traces

Indexed keywords

COMPUTATIONAL METHODS; COMPUTER PROGRAMMING; FEEDBACK; PROBLEM SOLVING; SEMANTICS; THEOREM PROVING;

FUNCTIONAL PROGRAMMING; LAYERED PROTOCOL STACKS;

COMPUTER SCIENCE;

EID: 0942278562     PISSN: 09883754     EISSN: 28047346     Source Type: Journal    
DOI: 10.1051/ita:2003020     Document Type: Conference Paper

References (33)

1. R.S. Bird, Using circular programs to eliminate multiple traversals of data. Acta Informatica 21 (1984) 239-250.
2. P. Bjesse, K. Claessen, M. Sheeran and S. Singh, Lava: Hardware design in Haskell, in International Conference on Functional Programming (1998).
3. S.L. Bloom and Z. Ésik, Axiomatizing schemes and their behaviors. J. Comput. Syst. Sci. 31 (1985) 375-393.
4. S.L. Bloom and Z. Ésik, Iteration Theories. EATCS Monographs on Theoretical Computer Science, Springer-Verlag (1993).
5. V.E. Cazanescu and Gh. Stefanescu, A general result on abstract flowchart schemes with applications to the study of accessibility, reduction and minimization. Theor. Comput. Sci. 99 (1992) 1-63.
6. K. Claessen and D. Sands, Observable sharing for functional circuit description, in Asian Computing Science Conference (1999).
7. J.H. Conway, Regular Algebra and Finite Machines. Chapman Hall (1971).
8. R.L. Crole and A.M. Pitts, New foundations for fixpoint computations: FIX-hyperdoctrines and the FIX-logic. Inf. Comput. 98 (1992) 171-210.
9. L. Erkök, Value Recursion in Monadic Computations. Ph.D. thesis, Oregon Graduate Institute, OHSU (October 2002).
10. L. Erkök, J. Launchbury and A. Moran, Semantics of value recursion for monadic input/output. RAIRO Theoret. Informatics Appl. 36 (2002) 155-180.
11. Z. Ésik, Axiomatizing iteration categories. Acta Cybernet. 14 (1999).
12. Z. Ésik, Group axioms for iteration. Inf. Comput. 148 (1999) 131-180
13. D.P. Friedman and A. Sabry, Recursion is a computational effect. Technical Report 546, Computer Science Department, Indiana University (December 2000).
14. C. Fuhrmann, A. Bucalo and A. Simpson, An equational notion of lifting monad. Theor. Comput. Sci. 294 (2003) 31-60.
15. J.-Y. Girard, Towards a geometry of interaction, in Categories in Computer Science and Logic, edited by J.W. Gray and A. Scedrov. Contemp. Math. 92 (1989) 69-108.
16. M. Hasegawa, Models of Sharing Graphs (A Categorical Semantics of Let and Letrec). Distinguished Dissertations in Computer Science, Springer-Verlag (1999).
17. M. Hasegawa, The uniformity principle on traced monoidal categories, edited by R. Blute and P. Selinger. Elsevier, Electronic Notes in Theor. Comput. Sci. (2003).
18. J. Hughes, Generalising monads to arrows. Sci. Comput. Program. 37 (2000) 67-112.
19. M. Hyland and A.J. Power, Symmetric monoidal sketches, in Proc. of the 2nd Conference on Principles and Practice of declarative Programming (2000) 280-288.
20. A. Jeffrey, Premondoidal categories and a graphical view of programs. http://www.cogs.susx.ac.uk/users/alanje/premon/ (June 1998).
21. A. Joyal, R. Street and D. Verity, Traced monoidal categories. Math. Proc. Cambridge Philoso. Soc. 119 (1996).
22. J. Launchbury and L. Erkök. Recursive monadic bindings, in International Conference on Functional Programming (2000).
23. J. Launchbury, J.R. Lewis and B. Cook, On embedding a microarchitectural design language within Haskell. International Conference on Functional Programming (1999).
24. J. Launchbury and S.L. Peyton Jones, State in Haskell. Lisp and Symbolic Computation 8 (1995) 293-341.
25. E. Moggi, Notions of computation and monads. Inf. Comput. 93 (1991) 55-92.
26. E. Moggi and A. Sabry, An abstract monadic semantics for value recursion, in Proc. of the 2003 Workshop on Fixed Points in Computer Science (April 2003).
27. P.S. Mulry, Strong monads, algebras and fixed points, in Applications of Categories in Computer Science, edited by M.P. Fourman, P.T. Johnstone and A.M. Pitts. LMS Lecture Notes 177 (1992) 202-216.
28. R. Paterson, A new notation for arrows, in Proc. of the International Conference on Functional Programming. ACM Press (September 2001).
29. R. Paterson, Arrows and computation, in The Fun of Programming, edited by J. Gibbons and O. de Moor. Palgrave (2003) 201-222.
30. A.J. Power and E.P. Robinson, Premonoidal categories and notions of computation. Math. Struct. Comput. Sci. 7 (1997) 453-468.
31. A.J. Power and H. Thielecke, Closed Freyd and κ-categories. International Conference on Automata, Languages and Programming (1999).
32. A.K. Simpson and G.D. Plotkin, Complete axioms for categorical fixed-point operators, in Proc. of 15th Annual Symposium on Logic in Computer Science. IEEE Computer Society (2000).
33. P. Wadler, The essence of functional programming, in Proc. of the 19th Symposium on Principles of Programming Languages. ACM (1992).