By Julia Seiter, Robert Wille, Rolf Drechsler

This ebook presents a accomplished evaluation of computerized version refinement, which is helping readers shut the space among preliminary textual specification and its wanted implementation. The authors let readers to stick with “directions” for refinement: Vertical refinement, for including element and precision to unmarried description for a given version and Horizontal refinement, which considers a number of perspectives on one point of abstraction, refining the procedure specification through devoted descriptions for constitution or habit. The dialogue contains a number of tools which help designers of digital platforms during this refinement method, together with verification the right way to fee instantly even if a refinement has been performed as intended.

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Invr = str engthen(inv a ) Each invariant of the model may be strengthened or extended. 1 Refinement Relation Fig. 2 Example of a vertical refinement step. a Abstract model. b Refined model 35 (a) Phone credit: Integer charge() context Phone::charge() post: credit ¿ credit@pre (b) RPhone credit: Integer charge(cr: Integer) context RPhone::charge(cr: Integer) post: credit = credit@pre + cr the previous rule, strengthening of invariants only includes sharpening existing constraints or constraining newly introduced attributes.

2 In the first refinement step in Fig. 1, only the operation Phone::charge() has been altered whereas Phone::call() remains unchanged. Still, since the postcondition of charge was altered, both operations have to be checked for executability again. This is due to the fact that the executability of call might depend on a state created by calling charge. On the other hand, the model’s consistency does not have to be proven again as no invariants or multiplicities have been added or changed. 2 Consistency in Vertical Refinement 27 Verifying a refinement step requires a formalization of the relation between abstract and refined model.

Invr = str engthen(inv a ) Each invariant of the model may be strengthened or extended. 1 Refinement Relation Fig. 2 Example of a vertical refinement step. a Abstract model. b Refined model 35 (a) Phone credit: Integer charge() context Phone::charge() post: credit ¿ credit@pre (b) RPhone credit: Integer charge(cr: Integer) context RPhone::charge(cr: Integer) post: credit = credit@pre + cr the previous rule, strengthening of invariants only includes sharpening existing constraints or constraining newly introduced attributes.

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