Overture Tool

Formal Modelling in VDM

Overture Tool

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Author: John Fitzgerald and Peter Gorm Larsen

This is the alarm example from the VDM++ book, John Fitzgerald, Peter Gorm Larsen, Paul Mukherjee, Nico Plat and Marcel Verhoef. Validated Designs for Object-oriented Systems, Springer, New York. 2005, ISBN 1-85233-881-4. The example is inspired by a subcomponent of a large alarm system developed by IFAD A/S. It is modelling the management of alarms for an industrial plant. The purpose of the model is to clarify the rules governing the duty roster and calling out of experts to deal with alarms. A comparable model of this example also exists in VDM-SL.

Properties Values
Language Version: vdm10
Entry point : new Test1().Run()


class Test1

instance variables

a1   : Alarm  := new Alarm(<Mech>,"Mechanical fault");
a2   : Alarm  := new Alarm(<Chem>,"Tank overflow");
ex1  : Expert := new Expert({<Mech>,<Bio>});
ex2  : Expert := new Expert({<Elec>});
ex3  : Expert := new Expert({<Chem>,<Bio>,<Mech>});
ex4  : Expert := new Expert({<Elec>,<Chem>});
plant: Plant  := new Plant({a1},{p1 |-> {ex1,ex4},
                                 p2 |-> {ex2,ex3}});


p1: Plant`Period = mk_token("Monday day");
p2: Plant`Period = mk_token("Monday night");
p3: Plant`Period = mk_token("Tuesday day");
p4: Plant`Period = mk_token("Tuesday night");


pure public Run: () ==> set of Plant`Period * Expert
Run() == 
  let periods = plant.ExpertIsOnDuty(ex1),
      expert  = plant.ExpertToPage(a1,p1)
    return mk_(periods,expert);

end Test1


class Alarm

public String = seq of char;

instance variables 

descr    : String;
reqQuali : Expert`Qualification;

public Alarm: Expert`Qualification * String ==> Alarm
Alarm(quali,str) ==
( descr := str;
  reqQuali := quali
pure public GetReqQuali: () ==> Expert`Qualification
GetReqQuali() ==
  return reqQuali;
end Alarm


class Expert

instance variables

quali : set1 of Qualification;
public Qualification = <Mech> | <Chem> | <Bio> | <Elec>;

public Expert: set1 of Qualification ==> Expert
Expert(qs) ==
  quali := qs;
pure public GetQuali: () ==> set of Qualification
GetQuali() ==
  return quali;
end Expert


class Plant

instance variables

alarms   : set of Alarm;
schedule : map Period to set of Expert;
inv PlantInv(alarms,schedule);


PlantInv: set of Alarm * map Period to set of Expert -> 
PlantInv(as,sch) ==
  (forall p in set dom sch & sch(p) <> {}) and
  (forall a in set as &
     forall p in set dom sch &
       exists expert in set sch(p) &
         a.GetReqQuali() in set expert.GetQuali());


public Period = token;


pure public ExpertToPage: Alarm * Period ==> Expert
ExpertToPage(a, p) ==
  let expert in set schedule(p) be st
      a.GetReqQuali() in set expert.GetQuali()
    return expert
pre a in set alarms and
    p in set dom schedule
post let expert = RESULT
       expert in set schedule(p) and
       a.GetReqQuali() in set expert.GetQuali();
pure public NumberOfExperts: Period ==> nat
NumberOfExperts(p) ==
  return card schedule(p)
pre p in set dom schedule;

pure public ExpertIsOnDuty: Expert ==> set of Period
ExpertIsOnDuty(ex) ==
  return {p | p in set dom schedule & 
              ex in set schedule(p)};

public Plant: set of Alarm * 
              map Period to set of Expert ==> Plant
Plant(als,sch) ==
( alarms := als;
  schedule := sch
pre PlantInv(als,sch);

end Plant