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class InterlockingSystem
types
public Coordinate = nat * nat;
public NonEmptyString = seq1 of char;
-- // Tracks //
public TrackKind = <Underwater> | <Underground> | <Overground> | <Elevated>;
public Track :: location: Coordinate
kind: TrackKind
capacity:- nat1; -- Number of parallel tracks/rails at this track section.
public CapacityMap = map Track to int;
-- // Metro lines //
public MetroLineName = NonEmptyString;
public MetroLine :: name: MetroLineName
tracks: seq1 of Track
-- Metro lines are assumed to be circular (i.e. the first and last track are the same).
inv mk_MetroLine(-, t) == IsCircular(t);
values
private trackPriorities: seq of TrackKind = [ <Underwater>, <Underground>, <Elevated>, <Overground> ]; -- Highest to lowest.
instance variables
private lines: inmap MetroLineName to MetroLine := { |-> };
private units: inmap MetroUnit`MetroUnitId to MetroUnit := { |-> };
-- All metro units with metro line associations must be associated with existing metro lines.
inv forall u in set rng units &
u.GetLine() <> nil => u.GetLine() in set rng lines;
-- All tracks must accommodate all metro units. If any track exceeds its capacity, it is overloaded and metro units may collide.
inv TracksAccommodateAllMetroUnits();
functions
-- // Metro lines and tracks //
private static AllTracks: set of MetroLine -> set of Track
AllTracks(allLines) == dunion { elems line.tracks | line in set allLines };
public static IsCircular: seq1 of Track -> bool
IsCircular(tracks) == hd tracks = tracks(len tracks);
public static InRangeOfTracks: [MetroLine] * nat1 -> bool
InRangeOfTracks(line, trackIndex) == line <> nil => trackIndex <= len line.tracks;
public static NextTrackIndex: [MetroLine] * nat1 -> nat1
NextTrackIndex(line, currentTrackIndex) ==
if line = nil then
currentTrackIndex
elseif currentTrackIndex < len line.tracks - 1 then
currentTrackIndex + 1
else
1
post InRangeOfTracks(line, RESULT);
public static TrackAt: [MetroLine] * nat1 -> [Track]
TrackAt(line, trackIndex) ==
if line <> nil then
line.tracks(trackIndex)
else
nil
pre InRangeOfTracks(line, trackIndex);
public static CreateCircularLine: MetroLineName * seq1 of Track -> MetroLine
CreateCircularLine(name, tracks) == mk_MetroLine(name, tracks)
pre IsCircular(tracks);
public static CreateReversedCircularLine: MetroLineName * seq1 of Track -> MetroLine
CreateReversedCircularLine(name, tracks) == mk_MetroLine(name, Reverse(tracks))
pre IsCircular(tracks);
public static CreateLinearLine: MetroLineName * seq1 of Track -> MetroLine
CreateLinearLine(name, tracks) == mk_MetroLine(name, LinearToCircularLine(tracks));
public static LinearToCircularLine: seq1 of Track -> seq1 of Track
LinearToCircularLine(tracks) == tracks ^ (tl Reverse(tracks))
post IsCircular(RESULT);
public static Reverse: seq of Track -> seq of Track
Reverse(tracks) ==
if tracks = [ ] then
[ ]
else
Reverse(tl tracks) ^ [ hd tracks ]
measure Length;
private static Length: seq of Track -> nat
Length(tracks) == len tracks;
-- // Units //
private static UnitSetToSequence: set of MetroUnit -> seq of MetroUnit
UnitSetToSequence(unitSet) ==
if unitSet = { } then
[ ]
else
let unit in set unitSet
in
[ unit ] ^ UnitSetToSequence(unitSet \ { unit })
measure Card;
private static Card: set of MetroUnit -> nat
Card(unitSet) == card unitSet;
operations
public AddUnit: MetroUnit ==> ()
AddUnit(unit) == units := units munion { unit.GetId() |-> unit }
pre unit.GetId() not in set dom units and
(unit.GetLine() <> nil => unit.GetLine() in set rng lines) and
(unit.GetLocation() <> nil => RemainingCapacityOf(unit.GetLocation()) > 0);
public RemoveUnit: MetroUnit`MetroUnitId ==> ()
RemoveUnit(unitId) == units := { unitId } <-: units;
public AddLine: MetroLine ==> ()
AddLine(line) == lines := lines munion { line.name |-> line }
pre line.name not in set dom lines;
public RemoveLine: MetroLineName ==> ()
RemoveLine(lineName) == lines := { lineName } <-: lines;
pure
public IsAnyUnitStuck: () ==> bool
IsAnyUnitStuck() ==
return exists u in set rng units &
u.IsStuck();
public FindStuckUnit: () ==> MetroUnit
FindStuckUnit() ==
let u in set rng units be st u.IsStuck()
in
return u
pre IsAnyUnitStuck();
public Tick: () ==> ()
Tick() ==
def unitsAllowedToRun: set of MetroUnit = UnitsAllowedToRun()
in
(
for all u in set rng units \ unitsAllowedToRun do
u.Stop();
for all u in set unitsAllowedToRun do
u.Run();
)
post forall track in set AllTracks(rng lines) &
NumberOfEnteringUnitsOn(track) <= RemainingCapacityOf(track);
-- // Track capacities //
pure
private TracksAccommodateAllMetroUnits: () ==> bool
TracksAccommodateAllMetroUnits() ==
return forall capacity in set rng RemainingCapacities() &
capacity >= 0;
pure
private RemainingCapacities: () ==> CapacityMap
RemainingCapacities() == return { track |-> RemainingCapacityOf(track) | track in set AllTracks(rng lines) };
pure
private RemainingCapacityOf: Track ==> int
RemainingCapacityOf(track) ==
def numberOfUnitsOnTrack: nat = card { unit | unit in set rng units & unit.GetLocation() = track }
in
return track.capacity - numberOfUnitsOnTrack;
pure
private NumberOfEnteringUnitsOn: Track ==> int
NumberOfEnteringUnitsOn(track) ==
return card { unit | unit in set rng units & unit.GetNextLocation() = track and unit.GetState() = <Running> };
-- // Interlocking mechanism //
private UnitsAllowedToRun: () ==> set of MetroUnit
UnitsAllowedToRun() ==
(
dcl capacities: CapacityMap := RemainingCapacities(),
unitsAllowedToRun: set of MetroUnit := { };
def prioritisedUnits: seq of MetroUnit = PrioritiseUnits(rng units, trackPriorities)
in
(
for unit in prioritisedUnits do
(
if MayRun(capacities, unit) then
(
capacities := Occupied(capacities, unit);
unitsAllowedToRun := unitsAllowedToRun union { unit };
);
);
return unitsAllowedToRun;
);
);
public PrioritiseUnits: set of MetroUnit * seq of TrackKind ==> seq of MetroUnit
PrioritiseUnits(unitsToPrioritise, priorities) ==
if priorities = [ ] then
return [ ]
else
def nextUnits = UnitsOn(unitsToPrioritise, hd priorities);
pendingUnits = unitsToPrioritise \ nextUnits
in
return UnitSetToSequence(nextUnits) ^ PrioritiseUnits(pendingUnits, tl priorities)
post forall unit in set elems RESULT &
unit.GetNextLocation() in set AllTracks(rng lines);
private UnitsOn: set of MetroUnit * TrackKind ==> set of MetroUnit
UnitsOn(unitsToFilter, trackKind) ==
return { unit | unit in set unitsToFilter & unit.GetLocation() <> nil and unit.GetLocation().kind = trackKind };
private MayRun: CapacityMap * MetroUnit ==> bool
MayRun(capacities, unit) == return capacities(unit.GetNextLocation()) > 0
pre unit.GetNextLocation() in set dom capacities;
private Occupied: CapacityMap * MetroUnit ==> CapacityMap
Occupied(capacities, unit) ==
def currentRemainingCapacity = capacities(unit.GetNextLocation())
in
return capacities ++ { unit.GetNextLocation() |-> currentRemainingCapacity - 1 }
pre unit.GetNextLocation() in set dom capacities and
capacities(unit.GetNextLocation()) > 0;
end InterlockingSystem
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