Abstract
Four different alternatives for the definition of standard equational algebraic specifications and the corresponding specification morphisms are studied and compared. Although intuitively the definitions may appear equivalent, they lead to three different equivalence classes of categories. It is shown, in fact, that the construction of pushouts and pullbacks is significantly different in these three cases. Although the corresponding specification logics are all semantical equivalent in a weak sense, three of them are semantical inconsistent with respect to pullback constructions. The nonequivalence of the equational categories has also significant implications for the corresponding high-level-replacement (HLR) system.
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R. Burstall, J.A. Goguen: Putting theories together to make specifications, Proc. 5th Internat. Joint Conf. on Artificial Intelligence, Cambridge Mass., 1977, pp. 1045–1058
H.D. Ehrich: On the theory of specification, implementation and parametrization of abstract data types, J. Assoc.Comput.Mach. 29 (1982) 206–227
H. Ehrig, M. Baldamus, F. Cornelius, F. Orejas: Theory of Algebraic Module Specifications including Behavioural Semantics, Constraints and Aspects of Generalized Morphisms (invited paper), Proc. AMAST91, Iowa City, May 1991
H. Ehrig, A. Habel, H.-J. Kreowski, F. Parisi-Presicce: Parallelism and Concurrency in High-Level-Replacement Systems, to appear in Math. Structures in Computer Science 1991
H. Ehrig: Introduction to the algebraic theory of graph grammars (A Survey) in: Graph Grammars and Their Application to Computer Science and Biology, Lecture Notes in Computer Science 73. Berlin: Springer 1979, pp. 1–69
H. Ehrig, B. Mahr: Fundamentals of Algebraic Specification 1. Equations and Initial Semantics. EATCS Monographs on Theoretical Computer Science, Vol. 6, Springer-Verlag, Berlin 1985
H. Ehrig, F. Parisi-Presicce: Algebraic Specification Grammars: A Junction Between Module Specifications and Graph Grammars, Proc. 4th Int. Workshop on Graph Grammars and Application to Computer Science, Lecture Notes in Computer Science 532. Berlin: Springer 1991,pp. 292–310
H. Ehrig, F. Parisi-Presicce: Nonequivalence of Categories for Equational Algebraic Specifications in view of High Level Replacement Systems, TUB Technical Report 91/16, Technische Universitat Berlin Sept 1991
J.V. Guttag, J. J. Horning: The algebraic specification of abstract data types, Acta Informatica 10 (1978) 27–52
F. Parisi-Presicce: A Rule-Based Approach to Modular System Design, Proc. 12th Int. Conf. Soft. Eng., Computer Science Press 1990,pp. 202–211
F. Parisi-Presicce: Foundations of Rule-Based Design of Modular Systems, Theoret. Comp. Sc. 83, 131–155 (1991)
J.W. Thatcher, E.G. Wagner, J.B. Wright, Data type specification: parametrization and the power of specification techniques, Proc. 10th Symp. Theory of Comput. (1978) 119–132 and Trans. Progr. Lang. and Syst. 4 (1982) 711–732
S. N. Zilles, Algebraic specification of data types, Project MAC Prograss Report 11, MIT 1974, 28–52
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© 1993 Springer-Verlag Berlin Heidelberg
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Ehrig, H., Parisi-Presicce, F. (1993). Nonequivalence of categories for equational algebraic specifications. In: Bidoit, M., Choppy, C. (eds) Recent Trends in Data Type Specification. ADT COMPASS 1991 1991. Lecture Notes in Computer Science, vol 655. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56379-2_42
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DOI: https://doi.org/10.1007/3-540-56379-2_42
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