Chapter

Software, Services, and Systems

Volume 8950 of the series Lecture Notes in Computer Science pp 602-618

Formalization of Invariant Patterns for the Invariant Refinement Method

  • Tomáš BurešAffiliated withFaculty of Mathematics and Physics, Charles University in Prague
  • , Ilias GerostathopoulosAffiliated withFaculty of Mathematics and Physics, Charles University in Prague
  • , Jaroslav KezniklAffiliated withFaculty of Mathematics and Physics, Charles University in Prague
  • , František PlášilAffiliated withFaculty of Mathematics and Physics, Charles University in Prague
  • , Petr TůmaAffiliated withFaculty of Mathematics and Physics, Charles University in Prague

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Abstract

Refining high-level system invariants into lower-level software obligations has been successfully employed in the design of ensemble-based systems. In order to obtain guarantees of design correctness, it is necessary to formalize the invariants in a form amenable to mathematical analysis. This paper provides such a formalization and demonstrates it in the context of the Invariant Refinement Method. The formalization is used to formally define invariant patterns at different levels of abstraction and with respect to different (soft) real-time constraints, and to provide proofs of theorems related to refinement among these patterns.

Keywords

architecture refinement requirements assume-guarantee