Abstract
In this paper we study the development of (algebraic) specifications. The main issues are the following: 1) We are able to work with "incomplete" specifications, i.e. specifications in which some objects (data sorts or operations) are not fully described. Technically, this is handled by means of loose semantics with data constraints. Two basic kinds of refinements are used or the specification building: horizontal and vertical refinements. Horizontal refinements are defined as loose extensions, whether vertical refinements are defined by means of refinement morphisms. The combination of both kinds of refinements (horizontal composition) provides a form of parameter passing, in fact the results obtained here generalize the results of the standard approach. A notion of relative persistency is introduced allowing to obtain full compatibility between the model and the specification level semantics for the kind of specification building operations used here. Moreover, proof-theoretic sufficient conditions are given for checking this property.
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Orejas, F., Sacristán, V., Clerici, S. (1989). Development of algebraic specifications with constraints. In: Ehrig, H., Herrlich, H., Kreowski, H.J., Preuß, G. (eds) Categorical Methods in Computer Science With Aspects from Topology. Lecture Notes in Computer Science, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51722-7_7
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DOI: https://doi.org/10.1007/3-540-51722-7_7
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