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Formal Modelling in VDM

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CMSeqPP

Author: Peter Gorm Larsen and Marcel Verhoef

This example is used in the guidelines for developing distributed real time systems using the VICE extension to VDM++. This model is available in a sequential version, a concurrent version as well as in a distributed real-time VICE version. This is the distributed real time version of this example.

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

missiledetector.vdmpp

              
class MissileDetector is subclass of GLOBAL

-- the primary task of the MissileDetector is to
-- collect all sensor data and dispatch each event
-- to the appropriate FlareController

instance variables

-- maintain a link to each controller
ranges : map nat to (Angle * Angle) := {|->};
controllers : map nat to FlareController := {|->};
inv dom ranges = dom controllers;

-- collects the observations from all attached sensors
threats : seq of (EventId * MissileType * Angle * Time) := [];

-- status of the missile detector
busy : bool := false

operations

-- addController is only used to instantiate the model
public addController: FlareController ==> ()
addController (pctrl) ==
  (dcl nid : nat := card dom ranges + 1;
   atomic
    (ranges := ranges munion {nid |-> pctrl.getAperture()};
     controllers := controllers munion {nid |-> pctrl}
    );
  );

public Step: () ==> ()
Step() ==
  (if threats <> []
   then def mk_ (evid,pmt, pa, pt) = getThreat() in
          for all id in set dom ranges do
            def mk_(papplhs, pappsize) = ranges(id) in
              if canObserve(pa, papplhs, pappsize)
              then controllers(id).addThreat(evid,pmt,pa,pt);
    busy := len threats > 0;
    for all id in set dom controllers do
      controllers(id).Step()
  );
 
-- addThreat is a helper operation to modify the event
-- list. currently events are stored first come first served.
-- one could imagine using a different ordering instead.
public addThreat: EventId * MissileType * Angle * Time ==> ()
addThreat (evid,pmt,pa,pt) == 
  (threats := threats ^ [mk_ (evid,pmt,pa,pt)];
   busy := true );

-- getThreat is a local helper operation to modify the event list
private getThreat: () ==> EventId * MissileType * Angle * Time
getThreat () ==
  (dcl res : EventId * MissileType * Angle * Time := hd threats;
   threats := tl threats;
   return res );

public isFinished: () ==> bool
isFinished () ==
  return forall id in set dom controllers &
            controllers(id).isFinished();

pure public getAperture: () ==> Angle * Angle
getAperture () == return mk_(0,0);

end MissileDetector
              

CM.vdmpp

              
class CM

instance variables

-- maintain a link to the detector
public static detector : MissileDetector := new MissileDetector();

public static sensor0 : Sensor := new Sensor(detector,0);
public static sensor1 : Sensor := new Sensor(detector,90);
public static sensor2 : Sensor := new Sensor(detector,180);
public static sensor3 : Sensor := new Sensor(detector,270);

public static controller0 : FlareController := new FlareController(0);
public static controller1 : FlareController := new FlareController(120);
public static controller2 : FlareController := new FlareController(240);

public static dispenser0 : FlareDispenser := new FlareDispenser(0);
public static dispenser1 : FlareDispenser := new FlareDispenser(30);
public static dispenser2 : FlareDispenser := new FlareDispenser(60);
public static dispenser3 : FlareDispenser := new FlareDispenser(90);

public static dispenser4 : FlareDispenser := new FlareDispenser(0);
public static dispenser5 : FlareDispenser := new FlareDispenser(30);
public static dispenser6 : FlareDispenser := new FlareDispenser(60);
public static dispenser7 : FlareDispenser := new FlareDispenser(90);

public static dispenser8 : FlareDispenser := new FlareDispenser(0);
public static dispenser9 : FlareDispenser := new FlareDispenser(30);
public static dispenser10 : FlareDispenser := new FlareDispenser(60);
public static dispenser11 : FlareDispenser := new FlareDispenser(90);

end CM
             

flaredispenser.vdmpp

              
class FlareDispenser is subclass of GLOBAL

values

responseDB : map MissileType to Plan =
  {<MissileA> |-> [mk_(<FlareOneA>,900),
                   mk_(<FlareTwoA>,500),
                   mk_(<DoNothingA>,100),
                   mk_(<FlareOneA>,500)],
   <MissileB> |-> [mk_(<FlareTwoB>,500),
                   mk_(<FlareTwoB>,700)],
   <MissileC> |-> [mk_(<FlareOneC>,400),
                   mk_(<DoNothingC>,100),
                   mk_(<FlareTwoC>,400),
                   mk_(<FlareOneC>,500)] };

missilePriority : map MissileType to nat =
  {<None>     |-> 0,
   <MissileA> |-> 1,
   <MissileB> |-> 2,
   <MissileC> |-> 3 }

types

public Plan = seq of PlanStep;

public PlanStep = FlareType * Time;

instance variables

public curplan : Plan := [];
curprio        : nat := 0;
busy           : bool := false;
aperture       : Angle;
eventid        : [EventId];

operations

public FlareDispenser: nat ==> FlareDispenser
FlareDispenser(ang) ==
  aperture := ang;
  
public Step: () ==> ()
Step() ==
  if len curplan > 0
  then (dcl curtime : Time := World`timerRef.GetTime(),
            first : PlanStep := hd curplan,
            next : Plan := tl curplan;
        let mk_(fltp, fltime) = first in
          (if fltime <= curtime
           then (releaseFlare(eventid,fltp,fltime,curtime);
                 curplan := next;
                 if len next = 0
                 then (curprio := 0; 
                       busy := false ) )
           )
    );

pure public GetAngle: () ==> nat
GetAngle() ==
  return aperture;

public addThreat: EventId * MissileType * Time ==> ()
addThreat (evid, pmt, ptime) ==
  if missilePriority(pmt) > curprio
  then (dcl newplan : Plan :=  [],
            newtime : Time := ptime;
        -- construct an absolute time plan
        for mk_(fltp, fltime) in responseDB(pmt) do
          (newplan := newplan ^ [mk_ (fltp, newtime)];
           newtime := newtime + fltime );
        -- immediately release the first action
        def mk_(fltp, fltime) = hd newplan;
            t = World`timerRef.GetTime() in
          releaseFlare(evid,fltp,fltime,t);
        -- store the rest of the plan
        curplan := tl newplan;
        eventid := evid;
        curprio := missilePriority(pmt);
        busy := true )
pre pmt in set dom missilePriority and
    pmt in set dom responseDB;

private releaseFlare: EventId * FlareType * Time * Time ==> ()
releaseFlare (evid,pfltp, pt1, pt2) == 
  World`env.handleEvent(evid,pfltp,aperture,pt1,pt2);

public isFinished: () ==> bool
isFinished () == 
  return not busy;

pure public getAperture: () ==> Angle * Angle
getAperture () == return mk_(0,0);

end FlareDispenser
               

sensor.vdmpp

              
class Sensor is subclass of GLOBAL

instance variables

-- the missile detector this sensor is connected to
private detector : MissileDetector;

-- the left hand-side of the viewing angle of the sensor
private aperture : Angle;

operations

public Sensor: MissileDetector * Angle ==> Sensor
Sensor (pmd, psa) == ( detector := pmd; aperture := psa);

-- get the left hand-side start point and opening angle
pure public getAperture: () ==> GLOBAL`Angle * GLOBAL`Angle
getAperture () == return mk_ (aperture, SENSOR_APERTURE);

-- trip is called asynchronously from the environment to
-- signal an event. the sensor triggers if the event is
-- in the field of view. the event is stored in the
-- missile detector for further processing
public trip: EventId * MissileType * Angle ==> ()
trip (evid, pmt, pa) ==
  -- log and time stamp the observed threat
  detector.addThreat(evid, pmt,pa,World`timerRef.GetTime())
pre canObserve(pa, aperture, SENSOR_APERTURE)

end Sensor
                                                                               

flarecontroller.vdmpp

              
class FlareController is subclass of GLOBAL

instance variables

-- the left hand-side of the working angle
private aperture : Angle;

-- maintain a link to each dispenser
ranges : map nat to (Angle * Angle) := {|->};
dispensers : map nat to FlareDispenser := {|->};
inv dom ranges = dom dispensers;

-- the relevant events to be treated by this controller
threats : seq of (EventId * MissileType * Angle * Time) := [];

-- the status of the controller
busy : bool := false

operations

public FlareController: Angle ==> FlareController
FlareController (papp) == aperture := papp;

public addDispenser: FlareDispenser ==> ()
addDispenser (pfldisp) ==
  let angle = aperture + pfldisp.GetAngle() in
    (dcl id : nat := card dom ranges + 1;
     atomic
     (ranges := ranges munion 
                {id |-> mk_(angle, DISPENSER_APERTURE)};
      dispensers := dispensers munion {id |-> pfldisp});
     );

public Step: () ==> ()
Step() ==
  (if threats <> []
   then def mk_ (evid,pmt, pa, pt) = getThreat() in
          for all id in set dom ranges do
            def mk_(papplhs, pappsize) = ranges(id) in
              if canObserve(pa, papplhs, pappsize)
              then dispensers(id).addThreat(evid,pmt,pt);
   busy := len threats > 0;
   for all id in set dom dispensers do
     dispensers(id).Step());
 
-- get the left hand-side start point and opening angle
pure public getAperture: () ==> GLOBAL`Angle * GLOBAL`Angle
getAperture () == return mk_(aperture, FLARE_APERTURE);

-- addThreat is a helper operation to modify the event
-- list. currently events are stored first come first served.
-- one could imagine using a different ordering instead
public addThreat: EventId * MissileType * Angle * Time ==> ()
addThreat (evid,pmt,pa,pt) ==
  (threats := threats ^ [mk_ (evid,pmt,pa,pt)];
   busy := true );

-- getThreat is a local helper operation to modify the event list
private getThreat: () ==> EventId * MissileType * Angle * Time
getThreat () ==
  (dcl res : EventId * MissileType * Angle * Time := hd threats;
   threats := tl threats;
   return res );

public isFinished: () ==> bool
isFinished () ==
  return forall id in set dom dispensers &
            dispensers(id).isFinished();

end FlareController
               

environment.vdmpp

              
class Environment is subclass of GLOBAL

types

public inline  = EventId * MissileType * Angle * Time;
public outline = EventId * FlareType * Angle * Time * Time;

instance variables

-- access to the VDMTools stdio
io : IO := new IO();

-- the input file to process
inlines : seq of inline := [];

-- the output file to print
outlines : seq of outline := [];

-- maintain a link to all sensors
ranges : map nat to (Angle * Angle) := {|->};
sensors : map nat to Sensor := {|->};
inv dom ranges = dom sensors;

-- information about the latest event that has arrived
evid : [EventId] := nil;

busy : bool := true;

operations

public Environment: seq of char ==> Environment
Environment (fname) ==
  def mk_ (-,input) = io.freadval[seq of inline](fname) in
    inlines := input;

public addSensor: Sensor ==> ()
addSensor (psens) ==
  (dcl id : nat := card dom ranges + 1;
   atomic (
    ranges := ranges munion {id |-> psens.getAperture()};
    sensors := sensors munion {id |-> psens} 
   )
  );

public Run: () ==> ()
Run () == 
 (while not (isFinished() and CM`detector.isFinished()) do
    (evid := createSignal();
     CM`detector.Step();
     World`timerRef.StepTime();
    );
 showResult()
 );

private createSignal: () ==> [EventId]
createSignal () ==
  (if len inlines > 0
   then (dcl curtime : Time := World`timerRef.GetTime(), 
             done : bool := false;
         while not done do
           def mk_ (eventid, pmt, pa, pt) = hd inlines in
             if pt <= curtime
             then (for all id in set dom ranges do
                     def mk_(papplhs,pappsize) = ranges(id) in
                       if canObserve(pa,papplhs,pappsize)
                       then sensors(id).trip(eventid,pmt,pa);
                   inlines := tl inlines;
                   done := len inlines = 0;
                   return eventid )
             else (done := true;
                   return nil ))
   else (busy := false;
         return nil));

public handleEvent: EventId * FlareType * Angle * Time * Time ==> ()
handleEvent (newevid,pfltp,angle,pt1,pt2) ==
  (outlines := outlines ^ [mk_ (newevid,pfltp, angle,pt1, pt2)] );

public showResult: () ==> ()
showResult () ==
  def - = io.writeval[seq of outline](outlines) in skip;

public isFinished : () ==> bool
isFinished () == 
  return inlines = [] and not busy;

pure public getAperture: () ==> Angle * Angle
getAperture () == return mk_(0,0);

end Environment
              

timer.vdmpp

              
class Timer

instance variables

currentTime : nat := 0;
private static timerInstance : Timer := new Timer(); 

values

stepLength : nat = 10;

operations

private Timer: () ==> Timer
Timer() ==
  skip;
  
pure public static GetInstance: () ==> Timer
GetInstance() ==
  return timerInstance;

public StepTime : () ==> ()
StepTime() ==
  currentTime := currentTime + stepLength;

pure public GetTime : () ==> nat
GetTime() ==
  return currentTime;

end Timer
             

world.vdmpp

              
class World

instance variables
  
-- maintain a link to the environment
public static env : [Environment] := nil;
public static timerRef : Timer := Timer`GetInstance();

operations

public World: () ==> World
World () ==
  (-- set-up the sensors
   env := new Environment("scenario.txt");
   env.addSensor(CM`sensor0);
   env.addSensor(CM`sensor1);
   env.addSensor(CM`sensor2);
   env.addSensor(CM`sensor3);

   -- add the first controller with four dispensers
   CM`controller0.addDispenser(CM`dispenser0);
   CM`controller0.addDispenser(CM`dispenser1);
   CM`controller0.addDispenser(CM`dispenser2);
   CM`controller0.addDispenser(CM`dispenser3);
   CM`detector.addController(CM`controller0);

   -- add the second controller with four dispensers
   CM`controller1.addDispenser(CM`dispenser4);
   CM`controller1.addDispenser(CM`dispenser5);
   CM`controller1.addDispenser(CM`dispenser6);
   CM`controller1.addDispenser(CM`dispenser7);
   CM`detector.addController(CM`controller1);
 
   -- add the third controller with four dispensers
   CM`controller2.addDispenser(CM`dispenser8);
   CM`controller2.addDispenser(CM`dispenser9);
   CM`controller2.addDispenser(CM`dispenser10);
   CM`controller2.addDispenser(CM`dispenser11);
   CM`detector.addController(CM`controller2);
  );

-- the run function blocks the user-interface thread
-- until all missiles in the file have been processed
public Run: () ==> ()
Run () == 
  env.Run()

end World
              

global.vdmpp

              
class GLOBAL

values

public SENSOR_APERTURE = 90;
public FLARE_APERTURE = 120;
public DISPENSER_APERTURE = 30

types

-- there are three different types of missiles
public MissileType = <MissileA> | <MissileB> | <MissileC> | <None>;

-- there are nine different flare types, three per missile
public FlareType =
    <FlareOneA> | <FlareTwoA> | <DoNothingA> | 
    <FlareOneB> | <FlareTwoB> | <DoNothingB> | 
    <FlareOneC> | <FlareTwoC> | <DoNothingC>;

-- the angle at which the missile is incoming
public Angle = nat
inv num == num < 360;

public EventId = nat;

public Time = nat

operations

pure public canObserve: Angle * Angle * Angle ==> bool
canObserve (pangle, pleft, psize) ==
  def pright = (pleft + psize) mod 360 in
    if pright < pleft
    -- check between [0,pright> and [pleft,360>
    then return (pangle < pright or pangle >= pleft)
    -- check between [pleft, pright>
    else return (pangle >= pleft and pangle < pright);
       
pure public getAperture: () ==> Angle * Angle
getAperture () == is subclass responsibility;

end GLOBAL