A sheaf semantics for FOOPS expressions (extended abstract)

  • D. A. Wolfram
  • Joseph A. Goguen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 612)


We present a sheaf semantics for concurrent method expression evaluation in FOOPS. Evaluations of functions, methods, and attributes are treated in a uniform way. General E-strategies for functions, methods, attributes, and method combiners are assumed.


Function Symbol Method Combiner Constant Symbol Sheaf Theory Fourth Transition 
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  1. [1]
    J.W. Alexander, A theory of connectivity in terms of gratings, Ann. Math. 39 (1938) 883–912.Google Scholar
  2. [2]
    D.B. Benson, Global versus local enveloping behaviours of concurrent systems, Extended Abstract, Washington State University, Pullman, Washington, 1991.Google Scholar
  3. [3]
    D.B. Benson, Sheaves of Process Histories, Draft #7, Washington State University, Pullman, Washington, 1991.Google Scholar
  4. [4]
    R. Dubey, On a general definition of safety and liveness, M.Sc. thesis, Washington State University, Pullman, Washington, 1991.Google Scholar
  5. [5]
    H.-D. Ehrich, J.A. Goguen, and A. Sernadas, A categorial theory of objects as observed processes, in: Foundations of Object Oriented Languages, Proceedings of a REX/FOOL Workshop, (Noordwijkerhout, the Netherlands, May/June 1990), J.W. de Bakker, W.P. de Roever and G. Rozenberg (Eds.), Lecture Notes in Computer Science, Springer, Berlin, 489 (1991) 203–228.Google Scholar
  6. [6]
    K. Futatsugi, J.A. Goguen, J.-P. Jouannaud, and J. Meseguer, Principles of OBJ2, Proceedings of the Twelfth Symposium on Principles of Programming Languages, Association for Computing Machinery, New York, 1985, 52–66.Google Scholar
  7. [7]
    J.A. Goguen and J. Meseguer, Order-sorted algebra solves the constructor-selector, multiple representation and coercion problems, in: Proceedings of the Second IEEE Symposium on Logic in Computer Science, IEEE Computer Society, Washington, D.C., 1987, 18–29.Google Scholar
  8. [8]
    J.A. Goguen and J. Meseguer, Unifying functional, object-oriented and relational programming with logical semantics, Research Report SRI-CSL-87-7, SRI International, Menlo Park, California, 1987.Google Scholar
  9. [9]
    J.A. Goguen, Mathematical representations of hierarchically organized systems, Global Systems Dynamics, S. Karger, 1971, 112–128.Google Scholar
  10. [10]
    J.A. Goguen, Categorical foundations for general systems theory, in: Advances in Cybernetics and Systems Research, Transcripta Books, 1973, 121–130.Google Scholar
  11. [11]
    J.A. Goguen, Objects, International Journal of General Systems 1 (1975) 237–243.Google Scholar
  12. [12]
    J.A. Goguen, Sheaf semantics for concurrent interacting objects, Mathematical Structures in Computer Science, 1991, (to appear).Google Scholar
  13. [13]
    J.A. Goguen and S. Ginali, A categorical approach to general systems theory, in: Applied General Systems Research, G. Klir, (Ed.), Plenum, 1978, 257–270.Google Scholar
  14. [14]
    J.W. Gray, Fragments of the history of sheaf theory, in: Applications of Sheaves: Proceedings of the Research Symposium on Applications of Sheaf Theory to Logic, Algebra, and Analysis, M.P. Fourman, C.J. Mulvey, and D.S. Scott, (Eds.), Lecture Notes in Mathematics 753, Springer, Berlin, 1979, 1–79.Google Scholar
  15. [15]
    J. Leray, Sur la forme des espaces topologiques et sur les points fixes des représentations, Journal de Math. Ser. 9, 24 (1945) 95–167.Google Scholar
  16. [16]
    L.F. Monteiro and F.C.N. Pereira, A sheaf-theoretic model of concurrency, Proceedings of the Symposium on Logic in Computer Science, IEEE Computer Society, Washington D.C., 1986, 66–76.Google Scholar
  17. [17]
    E. Munthe-Kaas, J.A. Goguen, and J. Meseguer, Method expressions and default values for object-valued attributes, Research Report, SRI International, Menlo Park, California, 1987.Google Scholar
  18. [18]
    J.A. Goguen and D.A. Wolfram, On types and FOOPS, Proceedings of the IFIP Working Group 2.6 Working Conference on Database Semantics: Object Oriented Databases: Analysis, Design & Construction, 1990, International Federation for Information Processing, (To appear).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • D. A. Wolfram
    • 1
  • Joseph A. Goguen
    • 1
    • 2
  1. 1.Programming Research GroupUniversity of OxfordOxfordUK
  2. 2.SRI InternationalMenlo ParkUSA

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