Completely iterative algebras and completely iterative monads

Information and Computation

Volumn 196, Issue 1, 2005, Pages 1-41

  Milius, Stefan ^a  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Coalgebra; Completely iterative algebra; Completely iterative theory; Monad

Indexed keywords

COMPUTATIONAL METHODS; ITERATIVE METHODS; POLYNOMIALS; RECURSIVE FUNCTIONS; TREES (MATHEMATICS);

COALGEBRA; COMPLETELY ITERATIVE ALGEBRA; COMPLETELY ITERATIVE THEORY; MONADS;

ALGEBRA;

EID: 10644296224     PISSN: 08905401     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ic.2004.05.003     Document Type: Article

References (21)

1. P. Aczel, J. Adárnek, S. Milius, J. Velebil, Infinite trees and completely iterative theories: a coalgebraic view, Theoret. Comput. Sci. 300 (2003) 1-45.
2. J. Adámek, S. Milius, J. Velebil, Free iterative theories - a coalgebraic view, Math. Struct. Comp. Sci. 13 (2003) 259-320.
3. J. Adámek, S. Milius, J. Velebil, On rational monads and free iterative theories, Electron. Notes Theor. Comput. Sci. 69 (2003).
4. J. Adámek, S. Milius, J. Velebil, From iterative algebras to iterative theories, preprint, 2004, extended abstract to appear in Electron. Notes Theor. Comput. Sci.
5. J. Adámek, S. Milius, J. Velebil, On iterative algebras and Elgot algebras, 2004 (submitted).
6. P. America, J.J.M.M. Rutten, Solving reflexive domain equations in a category of complete metric spaces, J. Comp. Syst. Sci. 39 (1989) 343-375.
7. J. Barwise, L.S. Moss, Vicious Circles, CSLI Public. Notes, vol. 60, Stanford, 1996.
8. B. Courcelle, Fundamental properties of infinite trees, Theoret. Comput. Sci. 25 (1983) 95-169.
9. C.C. Elgot, Monadic computation and iterative algebraic theories, in: H.E. Rose, J.C. Shepherdson (Eds.), Logic Colloquium '73, North-Holland Publishers, Amsterdam, 1975.
10. C.C. Elgot, S.L. Bloom, R. Tindell, On the algebraic structure of rooted trees, J. Comp. Syst. Sci. 16 (1978) 361-399.
11. N. Ghani, T. Uustalu, Coproducts of ideal monads, Theor. Inform. Appl. 38 (4) (2004) 321-342.
12. J. Lambek, A fixpoint theorem for complete categories, Math. Z. 103 (1968) 151-161.
13. F.W. Lawvere, Functorial semantics of algebraic theories, dissertation, Columbia University, 1963.
14. F.E.J. Linton, Some aspects of equational categories, in: Proceedings of the Conference on Categorical Algebra, Springer, Berlin, 1966, pp. 84-94.
15. S. Mac Lane, Categories for the Working Mathematician, second ed., Springer, Berlin, 1998.
16. S. Milius, On iteratable endofunctors, Electron. Notes Theor. Comput. Sci. 69 (2003).
17. L.S. Moss, Parametric corecursion, Theoret. Comput. Sci. 260 (1-2) (2001) 139-163.
18. E. Nelson, Iterative algebras, Theoret. Comput. Sci. 25 (1983) 67-94.
19. G. Osius, Categorical set theory: a characterization of the category of sets, J. Pure Appl. Algebra 4 (1974) 79-119.
20. J. Tiuryn, Unique fixed points vs. least fixed points, Theoret. Comput. Sci. 12 (1980) 229-254.
21. J. Worrell, On the final sequence of a finitary set functor, Theoret. Comput. Sci. (accepted).