Abstract
We give a fundamental notion of implementation of one algebraic data type by another one that gives a unifying framework for studying various recent approaches to algebraic implementation, and at the same time is consistent with the classical theory of finite automata realization developed by Hartmanis and Stearns. Much uniformity and simplicity is achieved by discarding reduction problems from automata realization as well as specification problems from algebraic data type implementation. As a result of our approach, we get new insights in the composability of algebraic implementations and the existence of normal forms for algebraic implementations.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Goguen, J.A./Thatcher, J.W./Wagner, E.G./Wright, J.B.: Initial Algebra Semantics and Continuous Algebras. Journal ACM 24, (1977), 68–95
Goguen, J.A./Thatcher, J.W./Wagner, E.G.: An Initial Algebra Approach to the Specification, Correctness, and Implementation of Abstract Data Types. Current Trends in Programming Methodology, Vol IV(R.T. Yeh, ed.). Prentice Hall, Englewood Cliffs 1978, 80–149
Arbib, M.A./Manes, E.G.: Arrows, Structures, and Functors. Academic Press, New York, 1975
Ehrich, H-D.: Extensions and Implementations of Abstract Data Type Specifications. Proc. 7th MFCS 1978, J. Winkowski (ed), LNCS 64, Springer-Verlag, Berlin 1978, 155–164
Ehrich,H.-D.: On the Theory of Specification, Implementation, and Parameterization of Abstract Data Types. Bericht Nr. 82/79, Abteilung Informatik, Univ. Dortmund 1979 (also to appear in Journal ACM)
Ehrig, h./Kreowski, H.-J./Mahr, B./Padawitz, P.: Compound Algebraic Implementations: an Approach to Stepwise Refinement of Software Systems. Proc. 9th MFCS (P. Dembinski, ed.), LNCS 88, Springer-Verlag, Berlin 1980, 231–245
Ehrig, H./Kreowski, H.-J./Padawitz, P.: Stepwise Specification and Implementation of Abstract Data Types. Proc. 5th ICALP (G. Ausiello/C. Boehm, eds.), LNCS 62, Springer-Verlag, Berlin 1978, 205–226
Ehrig, H./Kreowski, H.-J./Padawitz, P.: Algebraic Implementation of Abstract Data Types: Concept, Syntax, Semantics, and Correctness. Proc. 7th ICALP (J.W. deBakker/J. van Leeuwen, eds.), LNCS 85, Springer-Verlag, Berlin 1980, 142–156
Ganzinger, H.: Parameterized Specifications: Parameter Passing and Implementation. Internal Report, EECS-Comp.Sc. Division, UC Berkeley, September 1980
Guttag, J.V.: The Specification and Application to Programming of Abstract Data Types. Tech. Report CSRG-59, Univ. of Toronto, September 1975
Hartmanis, J./Stearns, R.E.: Algebraic Structure Theory of Sequential Machines. Prentice-Hall, Englewood Cliffs, 1966
Hupbach, U.L.: Abstract Implementations of Abstract Data Types. Proc 9th MFCS (P. Dembinski, ed.), LNCS 88, Springer-Verlag, Berlin 1980, 291–304
Lipeck, U.: Zum Begriff der Implementierung in der Theorie der abstrakten Datentypen. Diplomarbeit, Abteilung Informatik, Univ. Dortmund 1979
Mayoh,B.H.: Data Types as Functions. Report DAIMI PB-89, Comp. Sc.Dept. Aarhus University, July 1978
Nourani,F.: Constructive Extension and Implementation of Abstract Data Types and Algorithms. Report UCLA-ENG-7945, Comp. Sc. Dept. UC Los Angeles, August 1979
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ehrich, H.D. (1981). On realization and implementation. In: Gruska, J., Chytil, M. (eds) Mathematical Foundations of Computer Science 1981. MFCS 1981. Lecture Notes in Computer Science, vol 118. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10856-4_93
Download citation
DOI: https://doi.org/10.1007/3-540-10856-4_93
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10856-6
Online ISBN: 978-3-540-38769-5
eBook Packages: Springer Book Archive