Property Verification Sample Clauses

Property Verification. ‌ For analysis and verification, we prove relevant invariant properties of the abstract co-simulation model. As explained in Section 3.2, these properties can subsequently be lifted to reactive contracts that constrain observable behaviours of co-simulation steps by an environment. Figure 17: Global typing invariant of the centralised railways model. We distinguish local invariants of FMUs that can be proved in isolation, and shared invariants that require the consideration of multiple FMUs at the same time. Our proof strategy first consists of identifying relevant local invariants of each FMU and proving that the respective FMU preserves them, using our mechanisation of Hoare logic in Isabelle/UTP. { − } A particular kind of local invariant concerns typing of state components. For instance, train locations, given by the state component current track[1/2], must either be in the range 1-13, or otherwise in the set 0, 1 . We proved that train FMUs satisfy this invariant. Similar type invariants have also been checked for the other FMUs, and their conjunction implies the global typing invariant of the system included in Fig. 17. The typing invariant in Fig. 17 is indeed also a shared invariant, since we have to consider the behaviour of all FMUs simultaneously to establish it. The proof, however, can be carried out in a modular fashion, since it is possible to decompose this global invariant into conjuncts I1, I2, and so on, that are local invariants of the respective FMUs. The above observation leads us to further distinguish shared invariants into decomposable and non-decomposable (holistic) ones. The former are easier to prove since they facilitate a compositional approach in which a property proved for individual FMUs can be lifted to a property of their parallel com- position, by virtue of the (basic) Hoare-logic rules for parallelism. Namely, all that needs to be shown for {Is}FMU1 FMU2 . . . FMUn{Is} is that {Ii}FMU1{Ii} for 1 ≤ i ≤ n, supposing that Is ⇔ I1 ∧ I2 ∧ . . . ∧ In. Proof of the invariant property in Fig. 17 provides a first validation of our model that prevents, for instance, undefined terms from arising. For instance, it guarantees that vectors have the expected size, so that indexed access is always well defined. A more interesting local invariant constrains the possible settings of relays by the interlocking FMU. At any point in time, relays must be set so that the routes they enable do not cross each other. This is a fundamental propert...
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