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types
LampId = <L1> | <L2> | <L3>;
values
darklamps: set of LampId = {};
stoplamps: set of LampId = {<L1>,<L2>};
warninglamps: set of LampId = {<L1>,<L3>};
drivelamps: set of LampId = {<L2>,<L3>};
types
Signal = set of LampId;
LogCom = <stop> | <dark> | <drive> | <warning>;
Message = LogCom | <unknown> | <port_failure>;
Errors = set of LampId;
operations
Control: [LogCom] * set of LampId ==> Message * Errors * Trace
Control(com,failures) ==
let newstate = NormalTrans(com)
in
ErrorCorrection(com,newstate,failures)
pre AllowedCommand(com,lampstate);
functions
AllowedCommand: [LogCom] * Signal +> bool
AllowedCommand(com,signal) ==
(com = <dark> => signal in set {stoplamps,darklamps}) and
(com in set {<warning>,<drive>} => signal <> darklamps);
types
Trace = seq of set of LampId
state Dwarf of
trace : Trace
lampstate : Signal
inv mk_Dwarf(t,s) ==
MaxOneLampChange(t) and
StopToDriveOrWarning(t) and
ToAndFromDark(t) and
AlwaysDefinedState(s) -- this may change when errors are
-- taken into account
init s == s = mk_Dwarf([stoplamps],stoplamps)
end
operations
NormalTrans: [LogCom] ==> Dwarf
NormalTrans(command) ==
cases command:
nil -> return mk_Dwarf([],lampstate),
<dark> -> let t = if lampstate = stoplamps
then [{<L1>},darklamps]
else [] -- already in darksignals state
in
return mk_Dwarf(t,darklamps),
<stop> -> let t = if lampstate = darklamps
then [{<L1>},stoplamps]
elseif lampstate = warninglamps
then [{<L1>},stoplamps]
elseif lampstate = drivelamps
then [{<L2>},stoplamps]
else [] -- already in stoplamps state
in
return mk_Dwarf(t,stoplamps),
<warning> -> let t = if lampstate = drivelamps
then [{<L3>},warninglamps]
elseif lampstate = stoplamps
then [{<L1>},warninglamps]
else [] -- already in warninglamps state
in
return mk_Dwarf(t,warninglamps),
<drive> -> let t = if lampstate = warninglamps
then [{<L3>},drivelamps]
elseif lampstate = stoplamps
then [{<L2>},drivelamps]
else [] -- already in drivelamps state
in
return mk_Dwarf(t,drivelamps),
others -> error
end
pre AllowedCommand(command,lampstate);
ErrorCorrection: [LogCom] * Dwarf * set of LampId ==>
Message * Errors * Trace
ErrorCorrection(com,dwarf,failures) ==
if failures = {<L2>}
then (cases com:
nil -> if <L2> in set lampstate
then let errdwarf = NormalTrans(<warning>)
in
NoCorrection(com,errdwarf,failures)
else NoCorrection(com,dwarf,failures),
<dark> -> NoCorrection(com,dwarf,failures),
<stop> -> let errdwarf = NormalTrans(<warning>)
in
NoCorrection(com,errdwarf,failures),
<warning> -> NoCorrection(com,dwarf,failures),
<drive> -> let errdwarf = NormalTrans(<warning>)
in
NoCorrection(com,errdwarf,failures),
others -> error
end;
)
else (-- other error sitiuations have not yet been coped with
NoCorrection(com,dwarf,failures));
NoCorrection: [LogCom] * Dwarf * set of LampId ==>
Message * Errors * Trace
NoCorrection(com,mk_Dwarf(newtr,newsignals),failures) ==
(trace := trace ^ newtr;
lampstate := newsignals;
let m = if failures <> {}
then <port_failure>
elseif com = nil
then <unknown>
else com
in
return mk_(m,{},newtr));
functions
MaxOneLampChange: Trace +> bool
MaxOneLampChange(t) ==
forall i in set inds t \ {1} &
card (t(i - 1) \ t(i)) <= 1 and card (t(i) \ t(i - 1)) <= 1;
StopToDriveOrWarning: Trace +> bool
StopToDriveOrWarning(t) ==
forall i,j in set inds t &
(i < j and t(i) = stoplamps and
t(j) in set {drivelamps,warninglamps} and
not exists k in set {i+1,...,j-1} &
t(k) in set {darklamps, warninglamps,drivelamps})
=>
forall k in set {i+1,...,j-1} & card t(k) < 3 and card t(k) > 0;
ToAndFromDark: Trace +> bool
ToAndFromDark(t) ==
forall i in set inds t & t(i) = darklamps => ToOrFromStop(t,i);
ToOrFromStop: Trace * nat1 +> bool
ToOrFromStop(t,i) ==
(i > 2 => t(i - 2) = stoplamps) and
(i + 1 < len t => t(i + 2) = stoplamps);
AlwaysDefinedState: Signal +> bool
AlwaysDefinedState(sig) ==
sig in set {darklamps,
stoplamps,
warninglamps,
drivelamps};
traces
SeqTest: (let com : LogCom
in
NormalTrans(com)){5};
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