Transformation of combined data type and process specifications using projection algebras

  • M. Große-Rhode
  • H. Ehrig
Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 430)


The concept of projection specifications was recently introduced as a purely algebraic approach to the specification of continuous algebras in the framework of metric spaces. It allows to combine data type- and process specifications within one formalism. Parameterized projection specifications, corresponding to usual algebraic parameterized specifications, carry over compositionality to combined data type and process specifications. The parameter part may contain data types as well as process types. Transformation concepts for algebraic specifications are shown to apply also to projection specifications; i.e. extension and refinement, and different notions of implementation can be generalized to projection specifications.


Projection Specification Projection Algebra (Continuous Algebra) Parameterized Projection Specification Horizontal and Vertical Operations Refinement R-Implementation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /AMRW85/.
    E.Astesiano, G.F.Mascari, G.Reggio, M.Wirsing: On the Parameterized Algebraic Specification of Concurrent Systems, Proc. CAAP85 — TAPSOFT Conference, Springer LNCS 185, 1985Google Scholar
  2. /AR87/.
    E.Astesiano, G.Reggio: An Outline of the SMoLCS Methodology, Mathematical Models for the Semantics of Parallelism, Springer LNCS 280, 1987Google Scholar
  3. /BEP87/.
    E.K. Blum, H. Ehrig, F. Parisi-Presicce: Algebraic Specification of Modules and Their Basic Interconnections, in JCCS Vol.34, No.2/3, pp.293–339, 1987Google Scholar
  4. /BG80/.
    R.M.Burstall, J.A.Goguen: CAT, a System for the Structured Elaboration of Correct Programs from Structured Specifications, unpublished draft, University of Edinburgh / SRI International, March 1980Google Scholar
  5. /BK83/.
    J.A. Bergstra, J.W. Klop: The Algebra of Recursively Defined Processes and the Algebra of Regular Processes, Report IW 235/83, Math. Centrum, Amsterdam 1983Google Scholar
  6. /BK86/.
    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, p. 89–138, Amsterdam 1986Google Scholar
  7. /Bro85/.
    M. Broy: Specification and Top Down Design of Distributed Systems, Proc. of TAPSOFT, Joint Concerence of Theory and Practice of Software Development, Berlin, Springer LNCS 185, 1985Google Scholar
  8. /Bro86/.
    M. Broy: A Theory for Nondeterminism, Parallelism, Communication and Concurrency, Habilitation, Fakultät für Mathematik und Informatik der Technischen Universität München, 1982, revised version in Theoretical Computer Science 45, pp 1–61, 1986Google Scholar
  9. /Bro87/.
    M.Broy: Algebraic and Functional Specification of a Serializable Database Interface, Technical Report, Universität Passau, MIP-8718, 1987Google Scholar
  10. /BZ82a/.
    J.W.DeBakker, J.I.Zucker: Denotational Semantics of Concurrency Proc. 14th. ACM Symp. on Theory of Computing, p.153–158, 1982Google Scholar
  11. /BZ82b/.
    J.W. DeBakker, J.I. Zucker: Processes and the Denotational Semantics of Concurrency, Information and Control, Vol.54, No.1/2, p.70–120, 1982CrossRefGoogle Scholar
  12. /COMPASS89/.
    COMPASS Working Group: A Comprehenisve Approach to System Specification and Development, B.Krieg Brückner (ed.), Technical Report No 6/89, Universität Bremen 1989Google Scholar
  13. /DEGR87/.
    C.Dimitrovici, H.Ehrig, M.Große-Rhode, C.Rieckhoff: Projektionsräume und Projektionsalgebren: Eine Algebraisierung von ultrametrischen Räume, Technical Report No. 87-7, TU Berlin, 1987Google Scholar
  14. /Dim89/.
    C.Dimitrovici: Projection Module Specifications and Their Basic Interconnections, Technical Report No. 89-5, TU Berlin 1989Google Scholar
  15. /EFH83/.
    H.Ehrig,W.Fey,H.Hansen: ACT ONE: An Algebraic Specification Language with Two Levels of Semantics, TUB Bericht Nr.83-01Google Scholar
  16. /Ehr89/.
    H.Ehrig: Concepts and Compatibility Requirements for Implementations and Transformations of Specifications, Algebraic Specification Column Part 6, EATCS Bulletin 38, April 1989Google Scholar
  17. /EKMP82/.
    H. Ehrig, H.J. Kreowski, B. Mahr, P. Padawitz: Algebraic Implementation of Abstract Data Types, Theor. Comp. Science 20, pp.209–263, 1982Google Scholar
  18. /EKP80/.
    H. Ehrig, H.J. Kreowski, P. Padawitz: Algebraic Implementation of Abstract Data Types: Concept, Syntax, Semantics and Correctness. Proc. ICALP 80, Springer LNCS 85, pp. 142–156, 1980Google Scholar
  19. /EM85/.
    H. Ehrig, B. Mahr: Fundamentals of Algebraic Specifications 1: Equations and Initial Semantics, Springer Verlag, Berlin-Heidelberg-NewYork-Tokyo 1985Google Scholar
  20. /EM89/.
    H. Ehrig, B. Mahr: Fundamentals of Algebraic Specifications 2: Modules and Constraints, Springer Verlag, Berlin-Heidelberg-NewYork-Tokyo 1989Google Scholar
  21. /EPBRDG88/.
    H. Ehrig, F. Parisi-Presicce, P. Boehm, C. Rieckhoff, C. Dimitrovici, M. Große-Rhode: Algebraic Data Type and Process Specifications Based on Projection Spaces, Springer LNCS 332, p.23–43, 1988Google Scholar
  22. /EPO89/.
    H.Ehrig, P.Pepper, F.Orejas: On Recent Trends in Algebraic Specification, Invited paper for ICALP'89, StresaGoogle Scholar
  23. /Gro88/.
    M. Große-Rhode: Specification of Projection Algebras, Diploma Thesis, TU Berlin, 1988Google Scholar
  24. /Gro89/.
    M.Große-Rhode: Parameterized Data Type and Process Specifications Using Projection Algebras, in: Categorical Methods in Computer Science with Aspects from Topology, H.Ehrig, M.Herrlich, H.J.Kreowski G.Preuß (eds.), Springer LNCS 393, 1989Google Scholar
  25. /HE88/.
    H.Herrlich, H.Ehrig: The Construct PRO of Projection Spaces: Its Internal Structure, in: Categorical Methods in Computer Science with Aspects from Topology, H.Ehrig, M.Herrlich, H.J.Kreowski G.Preuß (eds.), Springer LNCS 393, 1989Google Scholar
  26. /HS73/.
    H. Herrlich, G.E. Strecker: Category Theory, Allyn and Bacon, Boston 1973Google Scholar
  27. /Hum87/.
    U.Hummert: High Level Netze, Technical Report No. 87-10, TU Berlin 1987Google Scholar
  28. /Hum89/.
    U. Hummert: Algebraische Theorie von High Level Netzen, Dissertation, TU Berlin, 1989Google Scholar
  29. /ISODIS86/.
    ISO-DIS 8807, ISO/TC97/SC21/WG1-FDT/SC-C, "LOTOS, a formal description technique based on the temporal ordering of observational behaviour", December 1986Google Scholar
  30. /Jen86/.
    K.Jensen: Coloured Petri Nets, Advances in Petri Nets, Springer LNCS 255, 1986Google Scholar
  31. /KHGB87/.
    B.Krieg-Brückner, B.Hoffmann, H.Ganzinger, M.Broy, R.Wilhelm, U.Möncke, B.Weisgerber, A.McGettrick, I.G. Campbell, G.Winterstein: PROgram development by SPECification and TRAnsformation. In: M.W.Roger (ed.): Results and Achievements, Proc. ESPRIT Conf. 86, North Holland (1987) 301–312Google Scholar
  32. /KP87/.
    S.Kaplan, A.Pnueli: Specification and Implementation of Concurrently Accessed Data Structures: An Abstract Data Type Approach, Proc. Symp. on Theoretical Aspects of Computer Science '87, Springer LNCS 247, 1987Google Scholar
  33. /MD86/.
    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, 178–195Google Scholar
  34. /Mil80/.
    R.Milner: CCS, A Calculus of Communicating Systems, Springer LNCS 92, 1980Google Scholar
  35. /Rei85/.
    Reisig: Petri Nets, Springer Berlin Heidelberg New York 1985Google Scholar
  36. /Smy88/.
    M.Smyth: Quasi-Uniformities: Reconciling Domains and Metric Spaces, Third Workshop on Mathematical Foundations of Programming Language Semantics (Tulane 1987), to appear: Springer LNCS, 1988Google Scholar
  37. /TW86/.
    A.Tarlecki, M.Wirsing: Continuous abstract data types, Fundamenta Informaticae IX (1986) 95–126, North-HollandGoogle Scholar
  38. /Vau86/.
    J.Vautherin: Parallel System Specifications with Coloured Petri Nets and Algebraic Abstract Data Types, 7th European Workshop on Applications and Theory of Petri Nets, Oxford 1986Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • M. Große-Rhode
    • 1
  • H. Ehrig
    • 1
  1. 1.TU Berlin, Fachbereich Informatik (20)Berlin 10

Personalised recommendations