@article{ITA_1999__33_4-5_467_0, author = {Corradini, Andrea and Gadducci, Fabio}, title = {Rewriting on cyclic structures : equivalence between the operational and the categorical description}, journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications}, pages = {467--493}, publisher = {EDP-Sciences}, volume = {33}, number = {4-5}, year = {1999}, mrnumber = {1748667}, zbl = {0940.18002}, language = {en}, url = {http://www.numdam.org/item/ITA_1999__33_4-5_467_0/} }
TY - JOUR AU - Corradini, Andrea AU - Gadducci, Fabio TI - Rewriting on cyclic structures : equivalence between the operational and the categorical description JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 1999 SP - 467 EP - 493 VL - 33 IS - 4-5 PB - EDP-Sciences UR - http://www.numdam.org/item/ITA_1999__33_4-5_467_0/ LA - en ID - ITA_1999__33_4-5_467_0 ER -
%0 Journal Article %A Corradini, Andrea %A Gadducci, Fabio %T Rewriting on cyclic structures : equivalence between the operational and the categorical description %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 1999 %P 467-493 %V 33 %N 4-5 %I EDP-Sciences %U http://www.numdam.org/item/ITA_1999__33_4-5_467_0/ %G en %F ITA_1999__33_4-5_467_0
Corradini, Andrea; Gadducci, Fabio. Rewriting on cyclic structures : equivalence between the operational and the categorical description. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 33 (1999) no. 4-5, pp. 467-493. http://www.numdam.org/item/ITA_1999__33_4-5_467_0/
[1] Equational term graph rewriting. Fund. Inform. 26 (1996) 207-240. | MR | Zbl
and ,[2] Confluent rewriting of bisimilar term graphs, C. Palamidessi and J. Parrow, Eds., Expressiveness in Concurrency. Elsevier Sciences, Electron. Notes Theoret. Comput. Sci. 7 (1997). Available at http://www.elsevier.nl/locate/entcs/volume7.html/. | MR | Zbl
, and ,[3] Term graph reduction, J. W. de Bakker, A. J. Nijman and P. C. Treleaven, Eds., Parallel Architectures and Languages Europe. Springer Verlag, Lecture Notes in Comput Sci. 259 (1987) 141-158. | MR
, , , , and ,[4] Semantics of flowchart programs and the free Conway theories. Theoret. Informatics Appl. 32 (1998) 35-78. | Numdam | MR
and ,[5] Minimal and optimal computations of recursive programs. J. ACM 26 (1979) 148-175. | MR | Zbl
and ,[6] Axiomatizing schemes and their behaviors. J. Comput. System Sci. 31 (1985) 375-393. | MR | Zbl
and ,[7] Iteration Theories. EATCS Monographs on Theoretical Computer Science. Springer Verlag (1993). | MR | Zbl
and ,[8] The equational logic of fixed points. Theoret. Comput. Sci. 179 (1997) 1-60. | MR | Zbl
and ,[9] Iteration 2-theories, M. Johnson, Ed., Algebraic Methodology and Software Technology. Springer Verlag, Lecture Notes in Comput. Sci. 1349 (1997) 30-44. | MR | Zbl
, , and ,[10] Computational semantics of term rewriting Systems, M. Nivat and J. Reynolds, Eds., Algebraic Methods in Semantics. Cambridge University Press (1985) 170-235. | MR | Zbl
,[11] Term rewriting in CT∑, M.-C.. Gaudel and J.-P. Jouannaud, Eds., Trees in Algebra and Programming. Springer Verlag, Lecture Notes in Comput. Sci. 668 (1993) 468-484. | MR
,[12] (Cyclic) term graph rewriting is adequate for rational parallel term rewriting, Technical Report TR-97-14. Dipartimento di Informatica, Pisa (1997).
and ,[13] A 2-categorical presentation of term graph rewriting, E. Moggi and G. Rosolini, Eds., Category Theory and Computer Science. Springer Verlag, Lecture Notes in Comput Sci. 1290 (1997) 87-105. | MR | Zbl
and ,[14] Rational term rewriting, M. Nivat, Ed., Foundations of Software Science and Computation Structures. Springer Verlag, Lecture Notes in Comput. Sci. 1378 (1998) 156-171. | MR | Zbl
and ,[15] An algebraic presentation of term graphs, via gs-monoidal categories. Applied Categorical Structures, to appear. | MR | Zbl
and ,[16] Algebraic approaches to graph transformation I: Basic concepts and double pushout approach, G. Rozenberg, Ed., Handbook of Graph Grammars and Computing by Graph Transformation 1. World Scientific (1997). | MR
, , , , and ,[17] Hyperedge replacement jungle rewriting for term rewriting Systems and logic programming. Theoret. Comput Sci. 109 (1993) 7-48. | MR | Zbl
and ,[18] On flowchart theories: Part II. The nondeterministic case. Theoret. Comput. Sci. 52 (1987307-340. | MR | Zbl
,[19] Algebra of flownomials. Technical Report SFB-Bericht 342/16/94 A. Technical University of München, Institut für Informatik (1994).
,[20] Towards a new algebraic foundation of nowchart scheme theory. Fund. Inform. 13 (1990) 171-210. | MR | Zbl
and ,[21] A general result on abstract flowchart schemes with applications to the study of accessibility, reduction and minimization. Theoret Comput. Sci. 99 (1992) 1-63. | MR | Zbl
and ,[22] Feedback, iteration and repetition, Gh. Paun, Ed., Mathematical Aspects of Natural and Formal Languages. World Scientific (1995) 43-62.
and ,[23] Monadic computations and iterative algebraic theories, H. E. Rose and J. C. Shepherdson, Eds., Logic Colloquium 1973. North Holland, Stud. Logic Found. Math. 80 (1975) 175-230. | MR | Zbl
,[24] Structured programming with and without GO TO statements. IEEE Trans. Software Engrg. 2 (1976) 41-54. | MR | Zbl
,[25] The algebraic structure of rooted trees. J. Comput. System Sci. 16 (1978) 362-339. | MR | Zbl
, and ,[26] Identities in iterative theories and rational algebraic theories. Computational Linguistics and Computer Languages 14 (1980) 183-207. | MR | Zbl
,[27] Group axioms for iteration. Inform. and Comput 148 (1999) 131-180. | MR | Zbl
,[28] Equational properties of iteration in algebraically complete categories. Theoret Comput. Sci. 195 (1998) 61-89. | MR | Zbl
and ,[29] A correetness proof for combinator reduction with cycles. ACM Trans. Program. Lang. Syst 12 (1990) 123-134.
, and ,[30] Redex capturing in term graph rewriting, R.V. Book, Ed., Rewriting Techniques and Applications. Springer Verlag, Lecture Notes in Comput. Sci. 488 (1991) 13-24. | MR
and ,[31] Regular trees and the free iterative theory. J. Comput System Sci. 18 (1979) 222-242. | MR | Zbl
,[32] Initial algebra semantics and continuous algebras. J. ACM 24 (1977) 68-95. | MR | Zbl
, , and ,[33] Algebraic Semantics. Springer Verlag, Lecture Notes in Comput. Sci. 99 (1981). | MR | Zbl
,[34] Models of Sharing Graphs. Ph. D. Thesis, University of Edinburgh, Department of Computer Science (1997).
,[35] Recursion from cyclic sharing: Traced monoidal categories and models of cyclic lambda-calculus, Ph. de Groote and R. Hindly, Eds., Typed Lambda Calculi and Applications. Springer Verlag, Lecture Notes in Comput. Sci. 1210 (1997) 196-213. | MR | Zbl
,[36] Implementing term rewriting by jungle evaluation. Theoret. Informatics Appl 25 (1991) 445-472. | Numdam | MR | Zbl
and ,[37] Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119 (1996) 425-446. | MR | Zbl
, and ,[38] Basic Concepts of Enriched Category Theory. Cambridge University Press (1982). | MR | Zbl
,[39] Review of the elements of 2-categories, G. M. Kelly, Ed., Sydney Category Seminar. Springer Verlag, Lecture Notes in Math. 420 (1974) 75-103. | MR | Zbl
and ,[40] On "On Graph Rewritings". Theoret Comput Sci. 52 (1980) 37-58. | MR | Zbl
,[41] On the adequacy of graph rewriting for simulating term rewriting. ACM Trans. Program. Lang. Syst. 16 (1994) 493-523.
, , and ,[42] Term rewriting Systems, S. Abramsky, D. Gabbay and T. Maibaum, Eds. Oxford University Press, Handb. Log. Comput Sci. 1 (1992) 1-116. | MR
,[43] From Petri nets to linear logic through categories: A survey. Intrenat J. Foundations Comput. Sci. 4 (1991) 297-399. | MR | Zbl
and ,[44] Conditional rewriting logic as a unified model of concurrency. Theoret. Comput. Sci. 96 (1992) 73-155. | MR | Zbl
,[45] Petri nets are monoids. Inform. and Comput 88 (1990) 105-155. | MR | Zbl
and ,[46] Rewriting logic for cyclic sharing structures, T. Sato and A. Middeldorp, Eds., Fuji International Symposium on Functional and Logic Programming. World Scientific (1998) 167-186.
,[47] Contextual nets. Acta Inform. 32 (1995) 545-596. | MR | Zbl
and ,[48] Functional Programming and Parallel Graph Rewriting. Addison Wesley (1993). | Zbl
and ,[49] An abstract formulation for rewrite Systems, D. H. Pitt, D. E. Rydehard, P. Dybjer, A. M. Pitts and A. Poigné, Eds., Category Theory and Computer Science. Springer Verlag, Lecture Notes in Comput. Sci. 389 (1989) 300-312. | MR
,[50] Petri Nets: An Introduction. EACTS Monographs on Theoretical Computer Science. Springer Verlag (1985). | MR | Zbl
,[51] Foundations of equational deductions: A categorical treatment of equational proofs and unification algorithms, D. H. Pitt, A. Poigne and D. E. Rydehard, Eds., Category Theory and Computer Science. Springer Verlag, Lecture Notes in Comput Sci. 283 (1987) 114-139. | MR | Zbl
and ,[52] The lattice of flow diagrams, E. Engeler, Ed., Semantics of Algorithmic Languages, Springer Verlag, Lecture Notes in Math. 182 (1971) 311-366. | MR | Zbl
,[53] Term Graph Rewriting: Theory and Practice. Wiley (1993). | MR | Zbl
, and ,[54] Computation of graph-like expressions. Theoret. Comput Sci. 10 (1980) 171-195. | MR | Zbl
,[55] Optimal evaluation of graph-like expressions. Theoret. Comput. Sci. 10 (1980) 297-316. | MR | Zbl
,[56] Speeding up subtree replacement systems. Theoret. Comput. Sci. 11 (1980) 39-47. | MR | Zbl
,[57] Categorical structures, M. Hazewinkel, Ed., Handbook of Algebra. Elsevier (1996) 529-577. | MR | Zbl
,[58] A new implementation technique for applicative languages. Software: Practice and Experience 9 (1979) 31-49. | Zbl
,[59] A concrete approach to abstract recursive definitions, M. Nivat, Ed., Automata, Languages and Programming. North Holland (1973) 331-341. | MR | Zbl
,