/// <summary>
/// If t is a variable name then returns t as a f-o variable and sets psi=null.
/// Else returns a fresh f-o variable x and outputs psi(x) s.t. psi(x) iff x=t.
/// </summary>
Variable ConvertTerm1(MonaExpr t, MapStack<string, MonaParam> locals, out MSOFormula<BDD> psi)
{
switch (t.symbol.Kind)
{
case Tokens.NAME:
{
MonaParam p;
if (locals.TryGetValue(t.symbol.text, out p))
{
if (p.kind == MonaParamKind.var1)
{
psi = null;
return new Variable(t.symbol.text, true);
}
else
throw new NotImplementedException(t.ToString());
}
else
{
MonaDecl d;
if (globals.TryGetValue(t.symbol.text, out d))
{
if (d.kind == MonaDeclKind.constant)
{
int n = ((MonaConstDecl)d).def.ToInt(globals);
Variable x = MkNewVar1();
var pred = new MSOeqN<BDD>(x, n);
psi = pred;
return x;
}
else if (d.kind == MonaDeclKind.var1)
{
psi = null;
return new Variable(t.symbol.text, true);
}
else
throw new NotImplementedException(t.ToString());
}
else
throw new NotImplementedException(t.ToString());
}
}
case Tokens.PLUS:
{
Variable y = MkNewVar1();
if (t[0].symbol.Kind == Tokens.NAME)
{
int n = t[1].ToInt(globals);
Variable x = new Variable(t[0].symbol.text, true);
psi = new MSOSuccN<BDD>(x, y, n); // y = x + n
}
else
{
int n = t.ToInt(globals);
psi = new MSOeqN<BDD>(y, n); // y = n
}
return y;
}
case Tokens.MIN:
{
MSOFormula<BDD> X_psi;
Variable X = ConvertTerm2(t[0], locals, out X_psi);
Variable x = MkNewVar1();
MSOFormula<BDD> min = new MSOMin<BDD>(x, X);
if (X_psi != null)
min = new MSOExists<BDD>(X, new MSOAnd<BDD>(X_psi, min));
psi = min;
return x;
}
case Tokens.MAX:
{
MSOFormula<BDD> X_psi;
Variable X = ConvertTerm2(t[0], locals, out X_psi);
Variable x = MkNewVar1();
MSOFormula<BDD> max = new MSOMax<BDD>(x, X);
if (X_psi != null)
max = new MSOExists<BDD>(X, new MSOAnd<BDD>(X_psi, max));
psi = max;
return x;
}
case Tokens.NUMBER:
{
Variable x = MkNewVar1();
int num = t.symbol.ToInt();
psi = new MSOeqN<BDD>(x,num);
return x;
}
default:
throw new NotImplementedException(t.ToString());
}
}
/// <summary>
/// If t is a variable name then returns t as a s-o variable and sets psi=null.
/// Else returns a fresh s-o variable X and outputs psi(X) s.t. psi(X) iff X=t.
/// </summary>
private Variable ConvertTerm2(MonaExpr t, MapStack<string, MonaParam> locals, out MSOFormula<BDD> psi)
{
switch (t.symbol.Kind)
{
case Tokens.NAME:
{
psi = null;
return new Variable(t.symbol.text, false);
}
case Tokens.INTER:
return ConvertInter(t[0], t[1], locals, out psi);
case Tokens.UNION:
return ConvertUnion(t[0], t[1], locals, out psi);
case Tokens.SETMINUS:
return ConvertSetminus(t[0], t[1], locals, out psi);
case Tokens.EMPTY:
return ConvertEmptyset(out psi);
case Tokens.LBRACE:
return ConvertSet(t, locals, out psi);
default:
throw new NotImplementedException(t.ToString());
}
}
private MSOFormula<BDD> ConvertFormula(MonaExpr expr, MapStack<string,MonaParam> locals)
{
switch (expr.symbol.Kind)
{
case Tokens.TRUE:
return new MSOTrue<BDD>();
case Tokens.FALSE:
return new MSOFalse<BDD>();
case Tokens.NOT:
return new MSONot<BDD>(ConvertFormula(expr[0], locals));
case Tokens.AND:
return new MSOAnd<BDD>(ConvertFormula(expr[0], locals), ConvertFormula(expr[1], locals));
case Tokens.OR:
return new MSOOr<BDD>(ConvertFormula(expr[0], locals), ConvertFormula(expr[1], locals));
case Tokens.IMPLIES:
return new MSOImplies<BDD>(ConvertFormula(expr[0], locals), ConvertFormula(expr[1], locals));
case Tokens.EQUIV:
return new MSOEquiv<BDD>(ConvertFormula(expr[0], locals), ConvertFormula(expr[1], locals));
case Tokens.EQ:
return ConvertEq(expr[0], expr[1], locals);
case Tokens.NE:
return new MSONot<BDD>(ConvertEq(expr[0], expr[1], locals));
case Tokens.LT:
return ConvertLt(expr[0], expr[1], locals);
case Tokens.GT:
return ConvertLt(expr[1], expr[0], locals);
case Tokens.LE:
return ConvertLe(expr[0], expr[1], locals);
case Tokens.GE:
return ConvertLe(expr[1], expr[0], locals);
case Tokens.SUBSET:
return ConvertSubset(expr[1], expr[0], locals);
case Tokens.IN:
return ConvertIn(expr[0], expr[1], locals);
case Tokens.NOTIN:
return new MSONot<BDD>(ConvertIn(expr[0], expr[1], locals));
case Tokens.EMPTY:
return ConvertIsEmpty(expr[0], locals);
case Tokens.EX1:
case Tokens.EX2:
{
MonaQFormula phi = (MonaQFormula)expr;
if ((phi.universes != null && phi.universes.Count > 1) ||
phi.vars.Exists(vw => vw.where != null))
throw new NotImplementedException(expr.ToString());
MSOFormula<BDD> psi = ConvertFormula(phi.formula, locals.Push(phi.varmap));
foreach (var vw in phi.vars)
psi = new MSOExists<BDD>(new Variable(vw.name, phi.varmap[vw.name].type == MonaExprType.INT), psi);
return psi;
}
case Tokens.ALL1:
case Tokens.ALL2:
{
MonaQFormula phi = (MonaQFormula)expr;
if ((phi.universes != null && phi.universes.Count > 1) ||
phi.vars.Exists(vw => vw.where != null))
throw new NotImplementedException(expr.ToString());
MSOFormula<BDD> psi = ConvertFormula(phi.formula, locals.Push(phi.varmap));
foreach (var vw in phi.vars)
psi = new MSOForall<BDD>(new Variable(vw.name, phi.varmap[vw.name].type == MonaExprType.INT), psi);
return psi;
}
case Tokens.NAME:
{
var name = expr as MonaName;
if (name != null)
{
//must be a nullary predicate application (var0 is not supported)
var tmpPredApp = new MonaPredApp(name.symbol, Cons<MonaExpr>.Empty);
return ConvertPredApp(tmpPredApp, locals);
}
var predApp = expr as MonaPredApp;
if (predApp != null)
{
return ConvertPredApp(predApp, locals);
}
throw new NotImplementedException(expr.ToString());
}
default:
throw new NotImplementedException(expr.ToString());
}
}
