public void SetParents(MuFormula parent)
{
Parent = parent;
foreach (var f in SubFormulas)
{
f.SetParents(this);
}
}
private static void OutputResult(MuFormula f, LTS lts)
{
Log("Formula {0}", f);
Log("\t ND: {0}, AD: {1}, DAD: {2}", f.NestingDepth, f.AlternationDepth, f.DependentAlternationDepth);
var naiveSol = NaiveSolver.Solve(f, lts, new Environment());
Log("\tNAIVE: {0}", naiveSol.Contains(lts.InitialState));
var emersonLeiSol = EmersonLei.Solve(f, lts, new Environment());
Log("\tEMLEI: {0}", emersonLeiSol.Contains(lts.InitialState));
}
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;
}
public bool IsBound(MuFormula subFormula)
{
// returns whether this variable is bound in the given subformula
var parent = Parent;
do
{
if (parent is Mu && ((Mu)parent).Formula.Equals(this))
{
return(true);
}
else if (parent is Nu && ((Nu)parent).Formula.Equals(this))
{
return(true);
}
parent = parent.Parent;
} while (parent != subFormula);
return(false);
}
public void SetParents(MuFormula parent)
{
Parent = parent;
foreach (var f in SubFormulas)
f.SetParents(this);
}
public Diamond(RegularFormula regForm, MuFormula formula)
{
RegularFormula = regForm;
Formula = formula;
}
public Disjunction(MuFormula left, MuFormula right)
{
Left = left;
Right = right;
}
public Nu(Variable var, MuFormula pred)
{
Variable = var;
Formula = pred;
}
public Box(RegularFormula regForm, MuFormula formula)
{
RegularFormula = regForm;
Formula = formula;
}
public Mu(Variable var, MuFormula pred)
{
Variable = var;
Formula = pred;
}
public Disjunction(MuFormula left, MuFormula right)
{
Left = left;
Right = right;
}
public static MuFormula Rewrite(MuFormula form)
{
form = RewriteBoxDia(form);
form = RewriteRFs(form);
return(form);
}
// rewrite regular formulas inside box/diamond to multiple boxes/diamonds
static MuFormula RewriteRFs(MuFormula form)
{
// connectives on regular formulas
// <a.rf>f = <a><rf>f
if (form is Box)
{
var box = form as Box;
// [rf1+rf2]f = [rf1]f || [rf2]f
/*if (box.RegularFormula is UnionFormula) {
* var un = box.RegularFormula as UnionFormula;
* return Rewrite(new Disjunction(new Box(un.Left, box.Formula), new Box(un.Right, box.Formula)));
* }*/
// directly supported by RegularFormula now!
// [a.rf]f = [a][rf]f
if (box.RegularFormula is SequenceFormula)
{
var seq = box.RegularFormula as SequenceFormula;
return(Rewrite(new Box(seq.First, new Box(seq.Sequence, RewriteRFs(box.Formula)))));
}
// by now all *s should be gone, so we can rewrite
// [(a.b)] to [a.b]
else if (box.RegularFormula is NestedFormula)
{
var nested = box.RegularFormula as NestedFormula;
if (nested.Multiplier != "")
{
throw new InvalidProgramException("by now all multipliers should have been removed");
}
box.RegularFormula = nested.Inner;
return(Rewrite(box));
}
}
else if (form is Diamond)
{
var dia = form as Diamond;
// <rf1+rf2>f = <[rf1>f || <rf2>f
/*if (dia.RegularFormula is UnionFormula) {
* var un = dia.RegularFormula as UnionFormula;
* return Rewrite(new Disjunction(new Diamond(un.Left, dia.Formula), new Diamond(un.Right, dia.Formula)));
* }*/
// directly supported now!
// <a.rf>f = <a><rf>f
if (dia.RegularFormula is SequenceFormula)
{
var seq = dia.RegularFormula as SequenceFormula;
dia.RegularFormula = seq.First;
dia.Formula = new Diamond(seq.Sequence, dia.Formula);
return(Rewrite(dia));
}
else if (dia.RegularFormula is NestedFormula)
{
var nested = dia.RegularFormula as NestedFormula;
if (nested.Multiplier != "")
{
throw new InvalidProgramException("by now all multipliers should have been removed");
}
dia.RegularFormula = nested.Inner;
return(Rewrite(dia));
}
}
// 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));
}
return(form);
}
private static void OutputResult(MuFormula f, LTS lts)
{
Log("Formula {0}", f);
Log("\t ND: {0}, AD: {1}, DAD: {2}", f.NestingDepth, f.AlternationDepth, f.DependentAlternationDepth);
var naiveSol = NaiveSolver.Solve(f, lts, new Environment());
Log("\tNAIVE: {0}", naiveSol.Contains(lts.InitialState));
var emersonLeiSol = EmersonLei.Solve(f, lts, new Environment());
Log("\tEMLEI: {0}", emersonLeiSol.Contains(lts.InitialState));
}
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);
}
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");
}
public Box(RegularFormula regForm, MuFormula formula)
{
RegularFormula = regForm;
Formula = formula;
}
public Negation(MuFormula formula)
{
Formula = formula;
}
public Negation(MuFormula formula)
{
Formula = formula;
}
public bool IsBound(MuFormula subFormula)
{
// returns whether this variable is bound in the given subformula
var parent = Parent;
do {
if (parent is Mu && ((Mu)parent).Formula.Equals(this)) return true;
else if (parent is Nu && ((Nu)parent).Formula.Equals(this)) return true;
parent = parent.Parent;
} while (parent != subFormula);
return false;
}
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 MuFormula Rewrite(MuFormula form)
{
form = RewriteBoxDia(form);
form = RewriteRFs(form);
return form;
}
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");
}
// rewrite regular formulas inside box/diamond to multiple boxes/diamonds
static MuFormula RewriteRFs(MuFormula form)
{
// connectives on regular formulas
// <a.rf>f = <a><rf>f
if (form is Box) {
var box = form as Box;
// [rf1+rf2]f = [rf1]f || [rf2]f
/*if (box.RegularFormula is UnionFormula) {
var un = box.RegularFormula as UnionFormula;
return Rewrite(new Disjunction(new Box(un.Left, box.Formula), new Box(un.Right, box.Formula)));
}*/
// directly supported by RegularFormula now!
// [a.rf]f = [a][rf]f
if (box.RegularFormula is SequenceFormula) {
var seq = box.RegularFormula as SequenceFormula;
return Rewrite(new Box(seq.First, new Box(seq.Sequence, RewriteRFs(box.Formula))));
}
// by now all *s should be gone, so we can rewrite
// [(a.b)] to [a.b]
else if (box.RegularFormula is NestedFormula) {
var nested = box.RegularFormula as NestedFormula;
if (nested.Multiplier != "")
throw new InvalidProgramException("by now all multipliers should have been removed");
box.RegularFormula = nested.Inner;
return Rewrite(box);
}
}
else if (form is Diamond) {
var dia = form as Diamond;
// <rf1+rf2>f = <[rf1>f || <rf2>f
/*if (dia.RegularFormula is UnionFormula) {
var un = dia.RegularFormula as UnionFormula;
return Rewrite(new Disjunction(new Diamond(un.Left, dia.Formula), new Diamond(un.Right, dia.Formula)));
}*/
// directly supported now!
// <a.rf>f = <a><rf>f
if (dia.RegularFormula is SequenceFormula) {
var seq = dia.RegularFormula as SequenceFormula;
dia.RegularFormula = seq.First;
dia.Formula = new Diamond(seq.Sequence, dia.Formula);
return Rewrite(dia);
}
else if (dia.RegularFormula is NestedFormula) {
var nested = dia.RegularFormula as NestedFormula;
if (nested.Multiplier != "")
throw new InvalidProgramException("by now all multipliers should have been removed");
dia.RegularFormula = nested.Inner;
return Rewrite(dia);
}
}
// 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));
return form;
}
public Diamond(RegularFormula regForm, MuFormula formula)
{
RegularFormula = regForm;
Formula = formula;
}