Abstract
Rooted, labeled, directed graphs (RLDs) are taken as the basis for describing data structures. A constructive formalism is set up to describe RLDs, generate them by means of grammars, and carry out operations such as accessing nodes, inserting and deleting data items, and recognizing graph patterns. It is shown how the formalism can be translated into languages for data definition and data manipulation, of the type associated with data-base systems. The availability of the formalism allows a systematic development of such languages, and provides a method of incorporating consistency preconditions to structural operations and proving the correctness of the data structures that arise in using such languages.
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References
CODASYL,Feature Analysis of Generalized Data Base Management Systems, Association for Computing Machinery (1971).
J. Earley, “Toward an understanding of data structures,”Commun. ACM 14(10):617–627 (1971).
A. Rosenberg, “Data graphs and addressable schemes,”J. Comput. Syst. Sci. 5(6):193–238 (1971).
C. Hoare, “Notes on Data Structuring,” inStructured Programming, Dahl and Dijkstra, eds. (Academic Press, New York, 1972).
T. A. Standish, “Data Structures-An Axiomatic Approach,” Technical Report 2639, Bolt, Beranek and Newman (1973).
E. F. Codd, “A relational model for large shared data banks,”Commun. ACM 13(6): 377–387 (1970).
T. A. Standish, “A Data Definition Facility for Programming Languages,” Ph.D. thesis, Carnegie Institute of Technology (1971).
CODASYL,Data Base Task Group Report (1971).
E. F. Codd, “A Data Base Sublanguage Founded on the Relational Calculus,”Proceedings of the ACM/SIGFIDET Workshop on Data Description, Access and Control (1971), pp. 35–68.
J. Pfaltz and A. Rosenfeld, “Web Grammars,” Technical Report 69–84, University of Maryland (1969).
A. Shaw, “Parsing of graph-representable pictures,”JACM 17(3):453–481 (1970).
J. Mylopoulos, “On the Relation of Graph Grammars and Graph Automata,”Proceedings of the 13th SWAT (1912), pp. 108–120.
D. L. Milgram, “Web Automata,” Technical Report 271, University of Maryland (1973).
F. Harary,Graph Theory (Addison-Wesley, Reading, Massachusetts, 1969).
J. Hopcroft and J. Ullman,Formal Languages and Their Relation to Automata (Addison-Wesley, Reading, Massachusetts, 1969).
W. Pratt and D. Friedman, “A language extension for graph processing and its formal semantics,”Commun. ACM 14(7):460–467 (1971).
J. A. Feldman and P. D. Rovner, “An algol based associative language,”Commun. ACM 12(8):439–449 (1969).
M. F. C. Crick and A. J. Symonds, “A Software Associative Memory for Complex Data Structures,” IBM Document G320-2060 (1970).
Datapro Research Corporation, “ADABAS-Software AG,” Datapro 70 (1973).
H. Love and D. Savitt, “An Iterative Cell Processor for the ASP Language,” inAssociative Information Techniques, Jacks, ed. (Elsevier, New York, 1971).
R. E. Griswold, J. E. Poage, and I. P. Polonsky,The SNOBOL 4 Programming Language (Prentice-Hall, Englewood Cliffs, New Jersey, 1968).
J. Mylopoulos, N. Badler, L. Melli, and N. Roussopoulos, “1.pak: A SNOBOL-Based Programming Language for Artificial Intelligence Applications,”Proceedings of the Third International Joint Conference on Artificial Intelligence (1973), pp. 691–696.
C. C. Gotlieb and A. L. Furtado, “Data Schemata Based on Directed Graphs,” Technical Report 70, University of Toronto (1974).
U. G. Montanari, “Separable graphs, planar graphs and web grammars,”Inf. Control 16:243–267 (1970).
C. J. Date and E. F. Codd, “The Relational and Network Approaches: Comparison of the Application Programming Interfaces,” IBM Document RJ 1401 (1974).
B. Wegbreit, “The treatment of data types in ELI,”Commun. ACM 17(5):251–264 (1974).
O. Dahl, “Hierarchical Program Structures,” inStructured Programming, Hoare and Dijkstra, eds. (Academic Press, New York, 1972).
B. Liskov and S. Zilles, “Programming with Abstract Data Types,”Proceedings of a Symposium on Very High Level Languages, ACM/SIGPLAN (1974), pp. 50–59.
P. B. Barroso and A. L. Furtado, “Implementing a data definition facility driven by graph grammars,”J. Comput. Lang. 3(2):65–74 (1978).
B. Shneiderman and P. Scheuermann, “Structured data structures,”Commun. ACM 17(10):566–574 (1974).
A. L. Furtado, “Characterizing data structures by the connectivity relation,”Int. J. Comput. Inf. Sci. 5(2):89–109 (1976).
E. F. Codd, “Further Normalization of the Data Base Relational Model,” inData Base Systems, Rustin, ed. (Prentice-Hall, Englewood Cliffs, New Jersey, 1972).
J. S. Brown, “Steps Toward Automatic Theory Formation,”Proceedings of the Third International Joint Conference on Artificial Intelligence (1973), pp. 121–129.
N. Minsky, “Toward ‘Intelligent’ Rotating Storage Devices,” Technical Report 73-2, University of Minnesota (1973).
C. Christensen, “An Example of the Manipulation of Directed Graphs in the AMBIT/G Programming Language,” inInteractive Systems for Experimental Applied Mathematics, Klerer and Reinfelds, eds. (Academic Press, New York, 1968).
C. C. Gotlieb and F. W. Tompa, “Choosing a storage schema,”Acta Inform. 3:297–319 (1974).
G. M. Nijssen, “Set and codasyl Set or Coset,” inData Base Description, Douqué and Nijssen, eds. (North-Holland/American Elsevier, New York, 1975).
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Gotlieb, C.C., Furtado, A.L. Data schemata based on directed graphs. International Journal of Computer and Information Sciences 8, 39–73 (1979). https://doi.org/10.1007/BF00995427
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DOI: https://doi.org/10.1007/BF00995427