Invariants Sample Clauses

Invariants. ‌ First we define Hoare triples over transition relations and then we derive proof rules to establish invariants.
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Invariants. We can now introduce the safety conditions for these hazards as invariants on the properties of a train. (Since they are placed within the class train, they apply to all instances of trains, i.e. universal quantification is implicit for all thisTrain belonging to train). For H3, we introduce an invariant to say that an occupied track is never obstructed. thisTrain occupies obstructed = FALSE For H4, we introduce an invariant to say that a train’s speed is always less than the safe speed of the track it occupies. thisTrain speed < thisTrain occupies safeSpeed Initially the Rodin tools generated twelve proof obligations for this stage of the model. At the first attempt, the automatic prover, failed to prove two proof obligations. Examining these two proof obligations (e.g. obstructed(next(occupies(thisTrain)))=FALSE) we observed that they both concern the invariant associated with H3. We are fairly confident that this invariant is satisfied since we added a guard to ensure that all track segments are always unobstructed. However, the prover doesn’t know this information. We could attempt to assist the prover interactively, but in this case it is easier to add an invariant to the model to give the prover the additional information it needs so that it can break the proof in to smaller steps. The prover will first prove that this new invariant is true and then use it to prove H3. After adding this invariant, 15 proof obligations were generated by the Rodin tools, but all were then discharged automatically. thisTrack obstructed = FALSE Figure 5.6 – The refined model consists of the two refined classes with all their previous attributes and associations inherited (i.e. retained) and some new invariants added. By omission we assume that the remaining events are fully controlled by the interlocking system that is yet to be introduced. More explicitly, the interlocking system has full control over when trains can change their occupancy of track sections, when points can change (the value of next) and when a track section becomes ‘incorrect’.

Related to Invariants

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