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Partial abstract types

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Summary

Hierarchical abstract types, where particular sorts, operations, and axioms are designated as primitive, with conditional equational formulas are studied. Introducing notions of different homomorphisms particular models of this class can be distinguished as initial or (weakly) terminal. Sufficient conditions for the existence of such models are given and their relationship to the principle of fully abstract semantics is investigated. By this the concept of algebraic specification is extended to specify the semantics of programming languages in a completely abstract algebraic way as it is demonstrated for two toy languages.

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References

  1. Andréka, H., Burmeister, B., Németi, I.: Quasivarieties of partial algebras — a unifying approach towards a two-valued model theory for partial algebras. TH Darmstadt, FB Mathematik, Preprint Nr. 557

  2. Bauer, F.L., Wössner, H.: Algorithmische Sprache und Programmentwicklung. Berlin-Heidelberg-New York: Springer 1981

    Google Scholar 

  3. Bergstra, J.A., Broy, M., Tucker, J.V., Wirsing, M.: On the power of algebraic specifications. In: Gruska, J. (ed.): 10th MFCS, Strbske Pleso, CSSR, Sept. 1981. LNCS118, 193–204 (1981)

  4. Bergstra, J.A., Tucker, J.V.: A characterization of computable data types by means of a finite, equational specification method. Math. Centr. Rep. IWi24/79, 1979

  5. Bertoni, A., Mauri, G., Miglioli, P.A., Wirsing, M.: On different approaches to abstract data types and the existence of recursive models. EATCS Bulletin No.9, 47–57 (1979)

    Google Scholar 

  6. Broy, M.: Transformational semantics for concurrent programs. IPL11, 87–91 (1980)

    Google Scholar 

  7. Broy, M., Wirsing, M.: Algebraic definition of a functional programming language. TU München, Tech. Rep. TUM-I8008, to appear in RAIRO Computer Science

  8. Broy, M., Wirsing, M.: Programming languages as abstract data types. In: Dauchet, M. (ed.): 5ème Coll. sur les Arbres en Algèbre et Programmation, Lille 1980, Univ. de Lille, 160–177 (1980)

  9. Broy, M., Wirsing, M.: Partial recursive functions and abstract data types. EATCS Bulletin11, 34–41 (1980)

    Google Scholar 

  10. Broy, M., Wirsing, M.: On the algebraic specification of nondeterministic programming languages. In: Astesiano, E., Böhm, C. (eds.): 6th Colloquium on Trees in Algebra and Programming. LNCS112, 162–179 (1981)

  11. Broy, M., Wirsing, M.: On the algebraic extension of abstract data types. In: Diaz, J., Ramos, I. (eds.): Formalization of Programming Concepts. LNCS107, 244–251 (1981)

  12. Broy, M., Wirsing, M.: On the algebraic specification of finitary infinite communicating sequential processes. In: Bjørner, D. (ed.): IFIP Wkng. Conf. on Formal Description of Programming Language Concepts, Garmisch, June 1982 (to appear)

  13. Broy, M., Pair, C., Wirsing, P.: A systematic study of models of abstract data types. Centre de Recherche en Informatique de Nancy, Rapport 81-R-042, 1981

  14. Burstall, R.M., Goguen, J.A.: Putting theories together to make specifications. 5th Int. Conf. en Artificial Intelligence, Cambridge, Mass., pp. 1045–1058, 1977

  15. Courcelle, B., Nivat, M: The algebraic semantics of programm schemas. In: Winkowski, J. (ed.): 7th MFCS (1978), LNCS64, 16–30 (1978)

  16. Ehrich, H.D., Lipeck, U.: Proving implementations correct — two alternative approaches. In: Lavington, D. (ed.): IFIP-Congress 80. Amsterdam: North-Holland, pp. 83–88 (1980)

    Google Scholar 

  17. Ehrig, H., Kreowski, H.J., Thatcher, J.W., Wagner, E.G., Wright, J.B.: Parameterized data types in algebraic specification languages. In: De Bakker, J., van Leenwen, J. (eds.): 7th ICALP (1980), LNCS85, 157–168 (1980)

  18. Gaudel, M.C.: Génération et preuve de compilateurs basés sur une sémantique formelle des langages de programmation. Thèse d'Etat, Nancy, March 1980

  19. Giarratana, V., Gimona, F., Montanari, U.: Observability concepts in abstract data type specifications. In: A. Mazurkiewicz (ed.): 5th MFCS (1976), LNCS45, 576–587 (1976)

  20. Goguen, J.A.: Abstract errors for abstract data types. UCLA Semantics and Theory of Computation Report 46, Proc. IFIP Wkng. Confr. Formal Description of Programming Language Concepts, St. Andrews, 21.1–21.32, 1977

  21. Goguen, J.A., Thatcher, J.W., Wagner, E.G.: An initial algebra approach to the specification, correctness and implementation of abstract data types. In: Current Trends in Programming Methodology IV: Data Structuring (R. Yeh, ed.), pp. 80–144, Englewood Cliffs: Prentice Hall 1978

    Google Scholar 

  22. Grätzer, G.: Universal algebra. Princeton: Van Nostrand 1968

    Google Scholar 

  23. Greif, L, Meyer, A.: Specifying programming language semantics. 6th POPL (1979)

  24. Guttag, J.V.: The specification and application to programming of abstract data types. Ph.D. Thesis, University of Toronto, 1975

  25. Hennessy, M., Milner, R.: On observing nondeterminism and concurrency. In: De Bakker, J., van Leeuwen, J. (eds.): 7th ICALP, LNCS85, 299–309 (1980)

  26. Hennessy, M., Plotkin, G.: A term model for CCS. In: Dembinski, P. (ed): 9th MFCS (1980), LNCS88, 261–274 (1980)

  27. Hornung, G., Raulefs, P.: Terminal algebra semantics and retractions for abstract data types. In: De Bakker, J, van Leeuwen, J. (eds.): 7th ICALP (1980), LNCS85, 310–323 (1980)

  28. Kamin, S.: Final data type specifications: a new data type specification method. 7th POPL, Las Vegas 1979

  29. Klaeren, H.A.: Eine Klasse von Algebren mit struktureller Rekursion und ihre Anwendung bei der abstrakten Software-Spezifikation. Dissertation, RWTH Aachen, 1980

    Google Scholar 

  30. Lescanne, P.: Etude algebraique et relationelle des types abstraits et de leurs représentations. Thése d'Etat, Université de Nancy, 1979

  31. Milner, R.: Fully abstract models of typed λ-calculi. TCS4, 1–22 (1977)

    Google Scholar 

  32. Milner, R.: Synthesis of communicating behavior. In: Winkowski, J. (ed.): 7th MFCS, LNCS64, 71–83 (1978)

  33. Nourani, F.: A model theoretic approach to specification, extension, and implementation. In: Robinet, B. (ed.): 4ème Colloque Int. sur la Programmation, LNCS83, 282–297 (1980)

  34. Pair, C: Types abstraits et sémantique algébrique des langages de programmation. Centre de Recherche en Informatique de Nancy, 80-R-011, 1980

  35. Pair, C.: Sur les modèles des types abstraits algébriques. Centre de Recherche en Informatique de Nancy. 80-P-052, 1980

  36. Reichel, H.: Theorie der Aequoide, Dissertation B. Humbold-Universität Berlin, 1979

    Google Scholar 

  37. Veloso, P.A., Pequeno, T.H.: Don't write more axioms than you have to: A methodology for the complete and correct specification of abstract data types, with examples. Univ. Rio de Janeiro, Monografias en Ciencia do Computacao No. 10, 1979, Ext. Abstr. in Proc. Int. Comp. Cump., Nankang (China) 1978

  38. Wagner, E.G., Thatcher, J.W., Wright, J.B.: Programming languages as mathematical objects. In: Winkowski, J. (ed.): 7th MFCS (1978), LNCS64, 84–101 (1978)

  39. Wand, M.: Final algebra semantics and data type extensions. JCSS19, 27–44. Preliminary Version: Indiana University TR65, 1978

    Google Scholar 

  40. Wirsing, M., Pepper, P., Partsch, H., Dosch, W., Broy, M.: On hierarchies of abstract data types. Preliminary Version: TU München, Tech. Rep. TUM-I8007, 1980. (To appear in Acta Informat.)

  41. Wirsing, M., Broy, M.: An analysis of semantic models for algebraic specifications. In: Broy, M.; Schmidt, G. (eds.): Int. Summerschool on Theoretical Foundations of Programming Methodology, Marktoberdorf, August 1981 Dordrecht: Reidel, pp. 351–413 (1982)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Technische Universität München, Arcisstraße 21, 8000, München 2, Federal Republic of Germany

    Manfred Broy & Martin Wirsing

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  1. Manfred Broy
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  2. Martin Wirsing
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This research has been partially sponsored by the Sonderforschungsbereich 49 — Programmiertechnik, München

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Broy, M., Wirsing, M. Partial abstract types. Acta Informatica 18, 47–64 (1982). https://doi.org/10.1007/BF00625280

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