static MuFormula RewriteBoxDia(MuFormula form)
{
// We extended our grammar from the assignment by allowing regular formulas instead of single-letter actions.
// Here, we rewrite such extended formulas to their more primitive versions for which we impemented evaluators.
if (form is Diamond) {
var dia = form as Diamond;
if (dia.RegularFormula.Multiplier == "+") {
// <R+>f = <R><R*>f
var rf2 = dia.RegularFormula.Clone();
rf2.Multiplier = "*";
dia.RegularFormula.Multiplier = "";
dia.Formula = new Diamond(dia.RegularFormula, new Diamond(rf2, dia.Formula));
}
else if (dia.RegularFormula.Multiplier == "*") {
// <R*>f = mu X . (<R> X || f)
var var = new Variable(GetFreeVar());
dia.RegularFormula.Multiplier = "";
return Rewrite(new Mu(var, new Disjunction(new Diamond(dia.RegularFormula, var), dia.Formula)));
}
dia.Formula = Rewrite(dia.Formula);
}
else if (form is Box) {
var box = form as Box;
if (box.RegularFormula.Multiplier == "+") {
// [R+]f = [R][R*]f
var rf2 = box.RegularFormula.Clone();
rf2.Multiplier = "*";
box.RegularFormula.Multiplier = "";
return new Box(box.RegularFormula, new Box(rf2, box.Formula));
}
else if (box.RegularFormula.Multiplier == "*") {
// [R*]f = nu X . ([R] X && f)
var var = new Variable(GetFreeVar());
box.RegularFormula.Multiplier = "";
return Rewrite(new Nu(var, new Disjunction(new Box(box.RegularFormula, var), box.Formula)));
}
box.Formula = Rewrite(box.Formula);
}
// we also need to perform this on all subformulas
else if (form is Disjunction) form = new Disjunction(Rewrite(((Disjunction)form).Left), Rewrite(((Disjunction)form).Right));
else if (form is Conjunction) form = new Conjunction(Rewrite(((Conjunction)form).Left), Rewrite(((Conjunction)form).Right));
else if (form is Mu) form = new Mu(((Mu)form).Variable, Rewrite(((Mu)form).Formula));
else if (form is Nu) form = new Nu(((Nu)form).Variable, Rewrite(((Nu)form).Formula));
else if (form is Negation) form = new Negation(Rewrite(((Negation)form).Formula));
return form;
}
private object CreateNewObject(GOLD.Reduction r)
{
object result = null;
switch ((ProductionIndex)r.Parent.TableIndex()) {
case ProductionIndex.Nl_Newline:
// <nl> ::= NewLine <nl>
break;
case ProductionIndex.Nl_Newline2:
// <nl> ::= NewLine
break;
case ProductionIndex.Regform_Pipepipe:
// <regForm> ::= <regForm> '||' <regFormSeq>
result = new UnionFormula((RegularFormula)r[0].Data, (RegularFormula)r[2].Data);
break;
case ProductionIndex.Regform:
// <regForm> ::= <regFormSeq>
result = r[0].Data;
break;
case ProductionIndex.Regformseq_Dot:
// <regFormSeq> ::= <regFormSeq> '.' <regFormValue>
result = new SequenceFormula((RegularFormula)r[0].Data, (RegularFormula)r[2].Data);
break;
case ProductionIndex.Regformseq:
// <regFormSeq> ::= <regFormValue>
result = r[0].Data;
break;
case ProductionIndex.Regformvalue_Identifier:
// <regFormValue> ::= Identifier <Multiplier>
result = new SingleAction((string)r[0].Data, (string)r[1].Data);
break;
case ProductionIndex.Regformvalue_Not:
// <regFormValue> ::= not <regForm>
result = new NegateAction((RegularFormula)r[1].Data);
break;
case ProductionIndex.Regformvalue_Lparen_Rparen:
// <regFormValue> ::= '(' <regForm> ')' <Multiplier>
if ((string)r[3].Data != "")
return new NestedFormula((RegularFormula)r[1].Data, (string)r[3].Data);
else // small optimization
result = r[1].Data;
break;
case ProductionIndex.Multiplier_Plus:
// <Multiplier> ::= '+'
result = "+";
break;
case ProductionIndex.Multiplier_Times:
// <Multiplier> ::= '*'
result = "*";
break;
case ProductionIndex.Multiplier:
// <Multiplier> ::=
result = "";
break;
case ProductionIndex.Muform_Identifier:
// <muForm> ::= Identifier
result = new Proposition((string)r[0].Data);
break;
case ProductionIndex.Muform_Variable:
// <muForm> ::= Variable
result = new Variable((string)r[0].Data);
break;
case ProductionIndex.Muform_Lparen_Pipepipe_Rparen:
// <muForm> ::= '(' <muForm> '||' <muForm> ')'
result = new Disjunction((MuFormula)r[1].Data, (MuFormula)r[3].Data);
break;
case ProductionIndex.Muform_Lparen_Ampamp_Rparen:
// <muForm> ::= '(' <muForm> '&&' <muForm> ')'
result = new Conjunction((MuFormula)r[1].Data, (MuFormula)r[3].Data);
break;
case ProductionIndex.Muform_Lt_Gt:
// <muForm> ::= '<' <regForm> '>' <muForm>
result = new Diamond((RegularFormula)r[1].Data, (MuFormula)r[3].Data);
break;
case ProductionIndex.Muform_Lbracket_Rbracket:
// <muForm> ::= '[' <regForm> ']' <muForm>
result = new Box((RegularFormula)r[1].Data, (MuFormula)r[3].Data);
break;
case ProductionIndex.Muform_Mu_Variable_Dot:
// <muForm> ::= mu Variable '.' <muForm>
result = new Mu(new Variable((string)r[1].Data), (MuFormula)r[3].Data);
break;
case ProductionIndex.Muform_Nu_Variable_Dot:
// <muForm> ::= nu Variable '.' <muForm>
result = new Nu(new Variable((string)r[1].Data), (MuFormula)r[3].Data);
break;
case ProductionIndex.Muform_Not:
// <muForm> ::= not <muForm>
result = new Negation((MuFormula)r[1].Data);
break;
case ProductionIndex.Muform_Lparen_Rparen:
result = r[1].Data as MuFormula;
break;
case ProductionIndex.Line_Commentl:
// <Line> ::= CommentL <nl>
break;
case ProductionIndex.Line:
// <Line> ::= <muForm> <nl>
var form = (MuFormula)r[0].Data;
FormulaRewriter.ResetFreeVars();
form = FormulaRewriter.Rewrite(form);
form.SetParents(null /* root has no parent */);
formulas.Add(form);
break;
case ProductionIndex.Line2:
// <Line> ::= <nl>
break;
case ProductionIndex.Lines:
// <Lines> ::= <Line> <Lines>
break;
case ProductionIndex.Lines2:
// <Lines> ::=
break;
} //switch
return result;
}
public static HashSet <LTSState> Solve(MuFormula formula, LTS lts, Environment env, bool init = true)
{
if (init)
{
var allVariables = new List <Variable>();
if (formula is Variable)
{
allVariables.Add((Variable)formula);
}
allVariables.AddRange(formula.AllSubFormulas.OfType <Variable>());
allVariables.AddRange(formula.AllSubFormulas.OfType <Mu>().Select(mu => mu.Variable));
allVariables.AddRange(formula.AllSubFormulas.OfType <Nu>().Select(nu => nu.Variable));
Init(allVariables.Distinct(), lts, env);
}
if (formula is Proposition)
{
var prop = formula as Proposition;
return(bool.Parse(prop.Value) ? lts.States : new HashSet <LTSState>());
}
else if (formula is Variable)
{
return(env.GetVariable(formula as Variable));
}
else if (formula is Negation)
{
var neg = formula as Negation;
return(new HashSet <LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env, false))));
}
else if (formula is Conjunction)
{
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env, false);
var rightStates = Solve(conj.Right, lts, env, false);
return(new HashSet <LTSState>(leftStates.Intersect(rightStates)));
}
else if (formula is Disjunction)
{
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env, false);
var rightStates = Solve(disj.Right, lts, env, false);
return(new HashSet <LTSState>(leftStates.Union(rightStates)));
}
else if (formula is Box)
{
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env, false);
var hashSet = new HashSet <LTSState>();
foreach (var state in lts.States)
{
var outTransitions = state.GetOutTransitions(box.RegularFormula);
if (outTransitions.All(tr => fe.Contains(tr.Right)))
{
hashSet.Add(state);
}
}
return(hashSet);
}
else if (formula is Diamond)
{
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return(Solve(shorthand, lts, env, false));
}
else if (formula is Mu)
{
var mu = formula as Mu;
if (mu.Parent is Nu)
{
// surrounding binder is nu
// reset open subformulae of form mu Xk.g set env[k]=false
foreach (var innerMu in formula.AllSubFormulas.OfType <Mu>().Where(m => m.FreeVariables.Count > 0))
{
env[innerMu.Variable] = new HashSet <LTSState>();
}
}
HashSet <LTSState> Xold;
do
{
Xold = env.GetVariable(mu.Variable);
env[mu.Variable] = Solve(mu.Formula, lts, env, false);
} while (Xold.Count != env[mu.Variable].Count);
return(env[mu.Variable]);
}
else if (formula is Nu)
{
var nu = formula as Nu;
if (nu.Parent is Mu)
{
// surrounding binder is mu
// reset open subformulae of form nu Xk.g set env[k]=true
foreach (var innerNu in formula.AllSubFormulas.OfType <Nu>().Where(m => m.FreeVariables.Count > 0))
{
env[innerNu.Variable] = lts.States;
}
}
HashSet <LTSState> Xold;
do
{
Xold = env.GetVariable(nu.Variable);
env[nu.Variable] = Solve(nu.Formula, lts, env, false);
} while (Xold.Count != env[nu.Variable].Count);
return(env[nu.Variable]);
}
throw new InvalidDataException("formula not valid in our grammar");
}
public static HashSet<LTSState> Solve(MuFormula formula, LTS lts, Environment env, bool init = true)
{
if (init) {
var allVariables = new List<Variable>();
if (formula is Variable) allVariables.Add((Variable)formula);
allVariables.AddRange(formula.AllSubFormulas.OfType<Variable>());
allVariables.AddRange(formula.AllSubFormulas.OfType<Mu>().Select(mu => mu.Variable));
allVariables.AddRange(formula.AllSubFormulas.OfType<Nu>().Select(nu => nu.Variable));
Init(allVariables.Distinct(), lts, env);
}
if (formula is Proposition) {
var prop = formula as Proposition;
return bool.Parse(prop.Value) ? lts.States : new HashSet<LTSState>();
}
else if (formula is Variable) {
return env.GetVariable(formula as Variable);
}
else if (formula is Negation) {
var neg = formula as Negation;
return new HashSet<LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env, false)));
}
else if (formula is Conjunction) {
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env, false);
var rightStates = Solve(conj.Right, lts, env, false);
return new HashSet<LTSState>(leftStates.Intersect(rightStates));
}
else if (formula is Disjunction) {
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env, false);
var rightStates = Solve(disj.Right, lts, env, false);
return new HashSet<LTSState>(leftStates.Union(rightStates));
}
else if (formula is Box) {
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env, false);
var hashSet = new HashSet<LTSState>();
foreach (var state in lts.States) {
var outTransitions = state.GetOutTransitions(box.RegularFormula);
if (outTransitions.All(tr => fe.Contains(tr.Right)))
hashSet.Add(state);
}
return hashSet;
}
else if (formula is Diamond) {
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return Solve(shorthand, lts, env, false);
}
else if (formula is Mu) {
var mu = formula as Mu;
if (mu.Parent is Nu) {
// surrounding binder is nu
// reset open subformulae of form mu Xk.g set env[k]=false
foreach (var innerMu in formula.AllSubFormulas.OfType<Mu>().Where(m => m.FreeVariables.Count > 0))
env[innerMu.Variable] = new HashSet<LTSState>();
}
HashSet<LTSState> Xold;
do {
Xold = env.GetVariable(mu.Variable);
env[mu.Variable] = Solve(mu.Formula, lts, env, false);
} while (Xold.Count != env[mu.Variable].Count);
return env[mu.Variable];
}
else if (formula is Nu) {
var nu = formula as Nu;
if (nu.Parent is Mu) {
// surrounding binder is mu
// reset open subformulae of form nu Xk.g set env[k]=true
foreach (var innerNu in formula.AllSubFormulas.OfType<Nu>().Where(m => m.FreeVariables.Count > 0))
env[innerNu.Variable] = lts.States;
}
HashSet<LTSState> Xold;
do {
Xold = env.GetVariable(nu.Variable);
env[nu.Variable] = Solve(nu.Formula, lts, env, false);
} while (Xold.Count != env[nu.Variable].Count);
return env[nu.Variable];
}
throw new InvalidDataException("formula not valid in our grammar");
}
public static HashSet<LTSState> Solve(MuFormula formula, LTS lts, Environment env)
{
if (formula is Proposition) {
var prop = formula as Proposition;
return bool.Parse(prop.Value) ? lts.States : new HashSet<LTSState>();
}
else if (formula is Variable) {
return env.GetVariable(formula as Variable);
}
else if (formula is Negation) {
var neg = formula as Negation;
return new HashSet<LTSState>(lts.States.Except(
Solve(neg.Formula, lts, env)));
}
else if (formula is Conjunction) {
var conj = formula as Conjunction;
var leftStates = Solve(conj.Left, lts, env);
var rightStates = Solve(conj.Right, lts, env);
return new HashSet<LTSState>(leftStates.Intersect(rightStates));
}
else if (formula is Disjunction) {
var disj = formula as Disjunction;
var leftStates = Solve(disj.Left, lts, env);
var rightStates = Solve(disj.Right, lts, env);
return new HashSet<LTSState>(leftStates.Union(rightStates));
}
else if (formula is Box) {
var box = formula as Box;
// box a f = { s | forall t. s -a-> t ==> t in [[f]]e }
// i.e. the set of states for which all a-transitions go to a state in which f holds
var fe = Solve(box.Formula, lts, env);
return new HashSet<LTSState>(lts.States.Where(
// states where, for all outtransitions with action a, the Formula holds in the direct successor
state => state.GetOutTransitions(box.RegularFormula).All(tr => fe.Contains(tr.Right))
));
}
else if (formula is Diamond) {
var diamond = formula as Diamond;
var shorthand = new Negation(
// <a>f == [a](not f)
new Box(diamond.RegularFormula, new Negation(diamond.Formula))
);
return Solve(shorthand, lts, env);
}
else if (formula is Mu) {
var mu = formula as Mu;
env[mu.Variable] = new HashSet<LTSState>();
return FixedPoint.LFP(delegate(Tuple<HashSet<LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(mu.Formula, lts, env);
env[mu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env);
}
else if (formula is Nu) {
var nu = formula as Nu;
env[nu.Variable] = lts.States;
return FixedPoint.GFP(delegate(Tuple<HashSet<LTSState>, LTS, Environment> tuple) {
// repeats tau: X := solve(f)
var X = tuple.Item1;
X = Solve(nu.Formula, lts, env);
env[nu.Variable] = X;
return Tuple.Create(X, lts, env);
}, lts, env);
}
throw new InvalidDataException("not a valid formula in our grammar");
}
