Elgot Theories: A New Perspective of Iteration Theories (Extended Abstract)

Electronic Notes in Theoretical Computer Science

Volumn 249, Issue , 2009, Pages 407-427

  Adámek, Jiří ^a   Milius, Stefan ^a   Velebil, Jiří ^b  

^a TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

^b CZECH TECHNICAL UNIVERSITY IN PRAGUE   (Czech Republic)

Author keywords

Elgot theory; iteration theory; iterative algebra; rational mona

Indexed keywords

AXIOMATIZATION; DOMAIN THEORY; ELGOT THEORY; EXTENDED ABSTRACTS; FINITE SET; ITERATION THEORY; ITERATIVE ALGEBRA; PRESHEAF; RATIONAL MONA; RECURSIVE EQUATIONS;

ALGEBRA;

SET THEORY;

EID: 68549135066     PISSN: 15710661     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.entcs.2009.07.100     Document Type: Article

References (22)

1. Adámek J. Free algebras and automata realizations in the language categories. Comment. Math. Uni. carolinæ 15 (1974) 589-602
2. Adámek J., Börger R., Milius S., and Velebil J. Iterative algebras: How iterative are they?. Theory Appl. Categ. 19 (2008) 61-92
3. Adámek J., and Milius S. Terminal coalgebras and free iterative theories. Inform. Comput. 16 (2006) 1139-1172
4. Adámek J., Milius S., and Velebil J. Iterative algebras at work. Math. Structures Comput. Sci. (2006) 1085-1131
5. Adámek J., Milius S., and Velebil J. Elgot algebras. Logic. Meth. Comput. Sci. 2 (2006) 1-31
6. Adámek J., Milius S., and Velebil J. What are iteration theories?. In: Kučera L., and Kučera A. (Eds). Proc. MFCS 2007. Lect. Notes Comput. Sci. 4708 (2007), Springer 240-252
7. J. Adámek, S. Milius and J. Velebil, Equational Properties of Iterative Monads, submitted
8. J. Adámek, S. Milius and J. Velebil, Iterative reflections of monads, to appear in Math. Structures Comput. Sci
9. J. Adámek, S. Milius and J. Velebil. Semantics of higher-order recursion schemes, submitted
10. Adámek J., and Rosický J. Locally Presentable and Accessible Categories (1994), Cambridge University Press
11. Badouel E. Terms and infinite trees as monads over a signature. Proc. TAPSOFT 1989. Lect. Notes Comput. Sci. 351 (1989), Springer 89-103
12. Bloom S.L., and Ésik Z. Iteration Theories: the equational logic of iterative processes (1993), Springer-Verlag
13. Elgot C.C. Monadic computation and iterative algebraic theories. In: Shepherdson J.C. (Ed). Logic Colloquium 1973. Studies in Logic 80 (1975) 174-250
14. Elgot C.C., Bloom S.L., and Tindell R. On the algebraic structure of rooted trees. J. Comput. System Sci. 16 (1978) 362-399
15. M. Fiore, G. Plotkin and D. Tiuri, Abstract syntax and variable binding, Proc. 14th Annual Symposium on Logic Computer Science 1999, 193-202
16. Gabriel P., and Ulmer F. Lokal präsentierbare Kategorien. Lect. Notes Math. 221 (1971), Springer-Verlag, Berlin
17. Ginali S. Regular trees and the free iterative theory. J. Comput. Syst. Sci. 18 (1979) 228-242
18. Hasegawa M. The uniformity principle on traced monoidal categories. Proc. CTCS 2002. Electron. Notes in Theoret. Comput. Sci. (2003)
19. Kelly G.M., and Power A.J. Adjunctions whose counits are coequalizers, and presentations of finitary enriched monads. J. Pure Appl. Algebra 89 (1993) 163-179
20. Mac Lane S. Categories for the working mathematician. 2nd edition (1998), Springer Verlag
21. Moss L.S. Recursion and corecursion have the same equational logic. Theoret. Comput. Sci. 294 (2003) 233-267
22. A. Simpson, and G. Plotkin, Complete axioms for categorical fixed-point operators, Proc. 15th Symposium on Logic in Computer Science LICS 2000, 30-44