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Algebraic data type and process specifications based on projection spaces

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Recent Trends in Data Type Specification (ADT 1987)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 332))

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Abstract

The algebraic approach to the semantics of (nonterminating) processes based on the metric completion of process algebras is extended in two directions. Instead of adopting the predefined metric, it is proposed to define the metric internally, using a suitable family of projections as part of the specification and deal with projection spaces rather than metric spaces. It is also proposed to define the data type along with the processes, to allow nonconstant actions and internally defined communication functions. Combined data type and process specifications find a suitable basis for their algebraic semantics in projection algebras.

This report was partly supported by the DFG-project "Algebraische Spezifikation verteilter Systeme und asynchron operationale Semantik (DAO)", the project "Kategorielle Methoden in Topologie und Informatik (KAMITI)" and done in cooperation with the University of Southern California. A previous version appeared as TUB-Report Nr. 87-7 (1987).

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Abbreviations

Cat(SPEC):

Category of SPEC-algebras with algebra homomorphisms

Cat(CSPEC):

Category of (constrained) projection-SPEC-algebras with projection-SPEC-algebra homomorphisms

CatCompl(CSPEC):

Category of complete projection-SPEC-algebras with projection-SPEC-algebra homomorphisms

{ie23-1}:

completion by standard construction of A (for projection spaces and projection algebras)

TSPEC :

Initial SPEC-algebra

CTSPEC :

Complete initial projection-SPEC-algebra

Hom(A):

process space

5. References

  1. J.A. Goguen, J.W. Thatcher, E.G. Wagner, J.B. Wright: Initial Algebra Semantics as Continuous Algebras, Journal ACM 24, 68–95, 1977

    Google Scholar 

  2. J.B. Wright, E.G. Wagner, J.W. Thatcher: A Uniform Approach to Inductive Posets and Inductive Closure, Theoretical Computer Science 7, 57–77, 1978

    Google Scholar 

  3. A. Arnold, M. Nivat: The metric space of infinite trees. Algebraic and topological properties, Societatis Mathematicae Polonae, Series IV:Fundamenta Informatica III, 4 p. 445–476, 1980

    Google Scholar 

  4. E.K.Blum, H.Ehrig,F.Parisi-Presicce: Algebraic Specifications of Modules and Their Basic Interconnections, Journal of Computer and System Sciences Vol 34, April/June 1987

    Google Scholar 

  5. J.A. Bergstra, J.W. Klop, 1983: The Algebra of recursively defined processes and the algebra of regular processes, Report IW 235/83, Math. Centrum, Amsterdam 1983

    Google Scholar 

  6. J.A. Bergstra, J.W. Klop: Algebra of Communicating Processes, in: CWI Monographs I Series, Proceedings of the CWI Symposium Mathematics and Computer Science, North-Holland, Amsterdam 1986, p. 89–138

    Google Scholar 

  7. M.N. Bleicher, H. Schneider: Completions of Partially Ordered Sets and Universal Algebras, Acta Math. Acad. Sci. Hung. Tomus 17 (3–4), 271–301, 1966

    Google Scholar 

  8. J.W. De Bakker, J.I. Zucker: Denotational semantics of concurrency Proc. 14th. ACM Symp. on Theory of Computing, p. 153–158, 1982

    Google Scholar 

  9. J.W. De Bakker, J.I. Zucker: Processes and the denotational semantics of concurrency, Information and Control, Vol.54, No.1/2, p.70–120, 1982

    Google Scholar 

  10. C.Dimitrovici, H.Ehrig, M.Große-Rhode, C.Rieckhoff: Projektionsräume und Projektions-algebren: Eine Algebraisierung von ultrametrischen Räumen, Technical Report No. 87–7, TU Berlin, 1987

    Google Scholar 

  11. H. Ehrig, W. Fey, F. Parisi-Presicce, E.K. Blum: Algebraic Theory of Module Specifications with Constraints, invited paper for MFCS'86, LNCS 233 (1986), 59–77

    Google Scholar 

  12. H. Ehrig, B. Mahr: Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics, Springer Verlag, Berlin-Heidelberg-New York-Tokyo 1985

    Google Scholar 

  13. M.Hennessy, R.Milner: Algebraic Laws for Nondeterminism and Concurrency, University of Edingburgh, Department of Computer Science, Internal Report CSR-133-83, June 1983

    Google Scholar 

  14. E. Kranakis: Approximating the Projective Model, Report CS-R8607,Centre for Mathematics and Computer Science, Amsterdam 1980, 122–133, 179–191

    Google Scholar 

  15. E.Kranakis, Fixed point equations with parameters in the projective model, CWI Report CS-R8606, Amsterdam 1986, to be published in Information and Computation

    Google Scholar 

  16. ISO-documents and draft proposals on the Specification Language LOTOS since 1983

    Google Scholar 

  17. H.Ehrig, J.Buntrock, P.Boehm, K.P.Hasler, F.Nürnberg, C.Rieckhoff, J.deMeer: Towards an Algebraic Semantics of the ISO-Specification Language LOTOS, draft version, Technische Universität Berlin, May 1986

    Google Scholar 

  18. Information processing systems-Open systems interconnection-LOTOS-A Formal Description Technique Based on the Temporal Ordering of Observational Behaviour,ISO DIS 8807 (ISO/TC97/SC21N), July 20, 1987

    Google Scholar 

  19. R.Milner, A Calculus of Communicating Systems, Springer LNCS 92, 1980

    Google Scholar 

  20. R. Milner, Lectures on a calculus for communicating systems, seminar on concurrency, Springer LNCS 197, 197–220, 1985

    Google Scholar 

  21. B. Möller, W. Dosch: On the Algebraic Specification of Domains, in Recent Trends in Data Type Specification (e.d. H.J.Kreowski), Informatik Fachberichte 116, Springer Verlag 1986, 178–195

    Google Scholar 

  22. B.Möller: Unendliche Objekte und Geflechte, Fakultät für Mathematik und Informatik der TU München, Dissertation, TUM-18213, 1982

    Google Scholar 

  23. B. Möller: On the Algebraic Specification of Objects — Ordered and Continuous Models of Algebraic Types, Acta Informatica 22, 537–578, 1985

    Google Scholar 

  24. M. Nivat: On the Interpretation of Recursive Polyadic Program Schemes, Istituto Nazionale di Alta Mathematica XV, 255–281, Academic Press, London 1975

    Google Scholar 

  25. A. Tarlecki, M. Wirsing: Continuous abstract data types, Fundamenta Informaticae IX (1986) 95–126, North-Holland

    Google Scholar 

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Author information

Authors and Affiliations

  1. TU Berlin, Germany

    Hartmut Ehrig, Francesco Parisi-Presicce, Paul Boehm, Catharina Rieckhoff, Cristian Dimitrovici & Martin Große-Rhode

  2. University of Southern California, USA

    Francesco Parisi-Presicce

  3. University of L'Aquila, Italy

    Francesco Parisi-Presicce

Authors
  1. Hartmut Ehrig
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  2. Francesco Parisi-Presicce
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  3. Paul Boehm
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  4. Catharina Rieckhoff
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  5. Cristian Dimitrovici
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  6. Martin Große-Rhode
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Editor information

D. Sannella A. Tarlecki

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© 1988 Springer-Verlag Berlin Heidelberg

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Ehrig, H., Parisi-Presicce, F., Boehm, P., Rieckhoff, C., Dimitrovici, C., Große-Rhode, M. (1988). Algebraic data type and process specifications based on projection spaces. In: Sannella, D., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT 1987. Lecture Notes in Computer Science, vol 332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50325-0_2

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  • DOI: https://doi.org/10.1007/3-540-50325-0_2

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  • Print ISBN: 978-3-540-50325-5

  • Online ISBN: 978-3-540-45970-5

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