no. 4-5
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. 
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     title = {Rewriting on cyclic structures : equivalence between the operational and the categorical description},
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     publisher = {EDP-Sciences},
     volume = {33},
     number = {4-5},
     year = {1999},
     mrnumber = {1748667},
     zbl = {0940.18002},
     language = {en},
     url = {http://archive.numdam.org/item/ITA_1999__33_4-5_467_0/}
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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://archive.numdam.org/item/ITA_1999__33_4-5_467_0/

[1] Z. M. Ariola and J. W. Klop, Equational term graph rewriting. Fund. Inform. 26 (1996) 207-240. | MR | Zbl

[2] Z. M. Ariola, J. W. Klop and D. Plump, 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

[3] H. P. Barendregt, M. C. J. D. Van Eekelen, J. R. W. Glauert, J. R. Kennaway, M. J. Plasrneijer and M. R. Sleep, 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

[4] L. Bernátsky and Z. Ésik, Semantics of flowchart programs and the free Conway theories. Theoret. Informatics Appl. 32 (1998) 35-78. | Numdam | MR

[5] G. Berry and J.-J. Lévy, Minimal and optimal computations of recursive programs. J. ACM 26 (1979) 148-175. | MR | Zbl

[6] S. Bloom and Z. Ésik, Axiomatizing schemes and their behaviors. J. Comput. System Sci. 31 (1985) 375-393. | MR | Zbl

[7] S. Bloom and Z. Ésik, Iteration Theories. EATCS Monographs on Theoretical Computer Science. Springer Verlag (1993). | MR | Zbl

[8] S. Bloom and Z. Ésik, The equational logic of fixed points. Theoret. Comput. Sci. 179 (1997) 1-60. | MR | Zbl

[9] S. L. Bloom, Z. Ésik, A. Labella and E. G. Manes, Iteration 2-theories, M. Johnson, Ed., Algebraic Methodology and Software Technology. Springer Verlag, Lecture Notes in Comput. Sci. 1349 (1997) 30-44. | MR | Zbl

[10] G. Boudol, 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] A. Corradini, 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] A. Corradini and F. Drewes, (Cyclic) term graph rewriting is adequate for rational parallel term rewriting, Technical Report TR-97-14. Dipartimento di Informatica, Pisa (1997).

[13] A. Corradini and F. Gadducci, 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

[14] A. Corradini and F. Gadducci, 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

[15] A. Corradini and F. Gadducci, An algebraic presentation of term graphs, via gs-monoidal categories. Applied Categorical Structures, to appear. | MR | Zbl

[16] A. Corradini, U. Montanari, F. Rossi, H. Ehrig, R. Heckel and M. Löwe, 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

[17] A. Corradini and F. Rossi, Hyperedge replacement jungle rewriting for term rewriting Systems and logic programming. Theoret. Comput Sci. 109 (1993) 7-48. | MR | Zbl

[18] Gh. Ştefănescu, On flowchart theories: Part II. The nondeterministic case. Theoret. Comput. Sci. 52 (1987307-340. | MR | Zbl

[19] Gh. Ştefănescu, Algebra of flownomials. Technical Report SFB-Bericht 342/16/94 A. Technical University of München, Institut für Informatik (1994).

[20] V.-E. Căzănescu and Gh. Ştefănescu, Towards a new algebraic foundation of nowchart scheme theory. Fund. Inform. 13 (1990) 171-210. | MR | Zbl

[21] V.-E. Căzănescu and Gh. Ştefănescu, 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

[22] V.-E. Căzănescu and Gh. Ştefănescu, Feedback, iteration and repetition, Gh. Paun, Ed., Mathematical Aspects of Natural and Formal Languages. World Scientific (1995) 43-62.

[23] C. C. Elgot, 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] C. C. Elgot, Structured programming with and without GO TO statements. IEEE Trans. Software Engrg. 2 (1976) 41-54. | MR | Zbl

[25] C. C. Elgot, C. C. Bloom and R. Tindell, The algebraic structure of rooted trees. J. Comput. System Sci. 16 (1978) 362-339. | MR | Zbl

[26] Z. Ésik, Identities in iterative theories and rational algebraic theories. Computational Linguistics and Computer Languages 14 (1980) 183-207. | MR | Zbl

[27] Z. Ésik, Group axioms for iteration. Inform. and Comput 148 (1999) 131-180. | MR | Zbl

[28] Z. Ésik and A. Labella, Equational properties of iteration in algebraically complete categories. Theoret Comput. Sci. 195 (1998) 61-89. | MR | Zbl

[29] W. M. Farmer, J. D. Ramsdell and R. J. Watro, A correetness proof for combinator reduction with cycles. ACM Trans. Program. Lang. Syst 12 (1990) 123-134.

[30] W. M. Farmer and R. J. Watro, 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

[31] S. Ginali, Regular trees and the free iterative theory. J. Comput System Sci. 18 (1979) 222-242. | MR | Zbl

[32] J. A. Goguen, J. W. Tatcher, E. G. Wagner and J. R Wright, Initial algebra semantics and continuous algebras. J. ACM 24 (1977) 68-95. | MR | Zbl

[33] I. Guessarian, Algebraic Semantics. Springer Verlag, Lecture Notes in Comput. Sci. 99 (1981). | MR | Zbl

[34] M. Hasegawa, Models of Sharing Graphs. Ph. D. Thesis, University of Edinburgh, Department of Computer Science (1997).

[35] M. Hasegawa, 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] B. Hoffmann and D. Plump, Implementing term rewriting by jungle evaluation. Theoret. Informatics Appl 25 (1991) 445-472. | Numdam | MR | Zbl

[37] A. Joyal, R. H. Street and D. Verity, Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119 (1996) 425-446. | MR | Zbl

[38] G. Kelly, Basic Concepts of Enriched Category Theory. Cambridge University Press (1982). | MR | Zbl

[39] G. M. Kelly and R. H. Street, 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

[40] J. R. Kennaway, On "On Graph Rewritings". Theoret Comput Sci. 52 (1980) 37-58. | MR | Zbl

[41] J. R. Kennaway, J. W. Klop, M. R. Sleep and F. J. De Vries, On the adequacy of graph rewriting for simulating term rewriting. ACM Trans. Program. Lang. Syst. 16 (1994) 493-523.

[42] J. W. Klop, Term rewriting Systems, S. Abramsky, D. Gabbay and T. Maibaum, Eds. Oxford University Press, Handb. Log. Comput Sci. 1 (1992) 1-116. | MR

[43] N. Martí-Oliet and J. Meseguer, From Petri nets to linear logic through categories: A survey. Intrenat J. Foundations Comput. Sci. 4 (1991) 297-399. | MR | Zbl

[44] J. Meseguer, Conditional rewriting logic as a unified model of concurrency. Theoret. Comput. Sci. 96 (1992) 73-155. | MR | Zbl

[45] J. Meseguer and U. Montanari, Petri nets are monoids. Inform. and Comput 88 (1990) 105-155. | MR | Zbl

[46] H. Miyoshi, 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] U. Montanari and F. Rossi, Contextual nets. Acta Inform. 32 (1995) 545-596. | MR | Zbl

[48] M. J. Plasmeijer and M. C. J. D. Van Eekelen, Functional Programming and Parallel Graph Rewriting. Addison Wesley (1993). | Zbl

[49] A. J. Power, 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] W. Reisig, Petri Nets: An Introduction. EACTS Monographs on Theoretical Computer Science. Springer Verlag (1985). | MR | Zbl

[51] D. E. Rydehard and E. G. Stell, 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

[52] D. Scott, 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] M. R. Sleep, M. J. Plasmeijer and M. C. Van Eekelen, Term Graph Rewriting: Theory and Practice. Wiley (1993). | MR | Zbl

[54] J. Staples, Computation of graph-like expressions. Theoret. Comput Sci. 10 (1980) 171-195. | MR | Zbl

[55] J. Staples, Optimal evaluation of graph-like expressions. Theoret. Comput. Sci. 10 (1980) 297-316. | MR | Zbl

[56] J. Staples, Speeding up subtree replacement systems. Theoret. Comput. Sci. 11 (1980) 39-47. | MR | Zbl

[57] R. H. Street, Categorical structures, M. Hazewinkel, Ed., Handbook of Algebra. Elsevier (1996) 529-577. | MR | Zbl

[58] D. A. Turner, A new implementation technique for applicative languages. Software: Practice and Experience 9 (1979) 31-49. | Zbl

[59] M. Wand, A concrete approach to abstract recursive definitions, M. Nivat, Ed., Automata, Languages and Programming. North Holland (1973) 331-341. | MR | Zbl