Abstract
Refinement in formal specifications has received significant attention as a method to gradually construct a rigorous model. Although refactoring methods for formal specifications have been proposed, there are no methods for refactoring of refinement structures in formal specifications. In this paper, we describe a method to restructure refinements in specifications of Event-B, a formal specification method with supports for refinement. The core of our method is decomposition of refinements. Namely, when an abstract Event-B machine A, a concrete machine C refining A, and a slicing strategy are provided, our method constructs a consistent intermediate machine B, which refines A and is refined by C. We show effectiveness of our methods through two case studies on representative usages of our method: decomposition of large-scale refinements and extraction of reusable parts of specifications.
This work is partially supported by JSPS KAKENHI Grant Number 26700005.
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Notes
- 1.
Assume that a function \(\mathrm {mod2}(n)\) that returns \(n \, \mathrm {modulo} \, 2\) is defined in a context.
- 2.
Actually static predicates (axioms) and predicates of event parameters are also included in POs. We will omit them for the sake of simplicity.
- 3.
BAPs that are expressible by \(V_{\mathrm {B}}\cup V_{\mathrm {B}}'\) are also specified, where \(V_{\mathrm {B}}'\) represents the set of after-state variables of \(V_{\mathrm {B}}\).
- 4.
Available at http://tkoba.jp/software/slice_and_merge/.
- 5.
For the sake of simplicity we did not count invariants for typing.
- 6.
There were differences in the actual specifications, because several invariants were moved in order to abstract the intermediate machines and the refinement structures of the events were changed.
- 7.
Models of this case study are at http://tkoba.jp/publications/fm2016/
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Kobayashi, T., Ishikawa, F., Honiden, S. (2016). Refactoring Refinement Structure of Event-B Machines. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds) FM 2016: Formal Methods. FM 2016. Lecture Notes in Computer Science(), vol 9995. Springer, Cham. https://doi.org/10.1007/978-3-319-48989-6_27
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