private MSOFormula<BDD> ConvertEq(MonaExpr t1, MonaExpr t2, MapStack<string, MonaParam> locals)
{
if (t1.type == MonaExprType.INT)
{
MSOFormula<BDD> psi_x;
Variable x = ConvertTerm1(t1, locals, out psi_x);
MSOFormula<BDD> psi_y;
Variable y = ConvertTerm1(t2, locals, out psi_y);
return AddConstraints(psi_x, x, psi_y, y, new MSOEq<BDD>(x, y));
}
else
{
MSOFormula<BDD> psi_x;
Variable x = ConvertTerm2(t1, locals, out psi_x);
MSOFormula<BDD> psi_y;
Variable y = ConvertTerm2(t2, locals, out psi_y);
return AddConstraints(psi_x, x, psi_y, y, new MSOEq<BDD>(x, y));
}
}
private MSOFormula<BDD> ConvertIsEmpty(MonaExpr set, MapStack<string, MonaParam> locals)
{
MSOFormula<BDD> psi_X;
Variable X = ConvertTerm2(set, locals, out psi_X);
MSOFormula<BDD> isempty = new MSOIsEmpty<BDD>(X);
if (psi_X != null)
isempty = new MSOExists<BDD>(X, new MSOAnd<BDD>(psi_X, isempty));
return isempty;
}
internal MonaNegatedFormula(Token token, MonaExpr formula)
: base(token, MonaExprType.BOOL, new MonaExpr[]{formula})
{
}
internal MonaLet(Token letkind, Cons<Tuple<Token, MonaExpr>> lets, MonaExpr formula, Dictionary<string, MonaParam> let_vars)
: base(letkind, MonaExprType.BOOL, new MonaExpr[]{formula})
{
this.lets = lets;
this.let_vars = let_vars;
}
internal MonaFormulaDecl(MonaExpr formula)
: base(MonaDeclKind.formula)
{
this.formula = formula;
}
internal MonaExecuteDecl(MonaExpr psi)
: base(MonaDeclKind.execute)
{
this.psi = psi;
}
internal MonaConstDecl(Token name, MonaExpr def)
: base(MonaDeclKind.constant)
{
this.name = name;
this.def = def;
}
internal MonaBinaryAtom(Token token, MonaExpr term1, MonaExpr term2)
: base(token, MonaExprType.BOOL, new MonaExpr[]{term1, term2})
{
}
private MSOFormula<BDD> ConvertEq(bool fo, MonaExpr t1, MonaExpr t2, MapStack<string, MonaParam> locals)
{
MSOFormula<BDD> psi_x;
Variable x = (fo ? ConvertTerm1(t1, locals, out psi_x) : ConvertTerm2(t1, locals, out psi_x));
MSOFormula<BDD> psi_y;
Variable y = (fo ? ConvertTerm1(t2, locals, out psi_y) : ConvertTerm2(t1, locals, out psi_y));
return AddConstraints(psi_x, x, psi_y, y, new MSOEq<BDD>(x, y));
}
/// <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 Variable ConvertUnion(MonaExpr set1, MonaExpr set2, MapStack<string, MonaParam> locals, out MSOFormula<BDD> pred)
{
MSOFormula<BDD> psi1;
var X1 = ConvertTerm2(set1, locals, out psi1);
MSOFormula<BDD> psi2;
var X2 = ConvertTerm2(set2, locals, out psi2);
var X = MkNewVar2();
var x = MkNewVar1();
MSOFormula<BDD> union = new MSOForall<BDD>(x,
new MSOEquiv<BDD>(new MSOIn<BDD>(x, X),
new MSOOr<BDD>(new MSOIn<BDD>(x, X1),
new MSOIn<BDD>(x, X2))));
pred = AddConstraints(psi2, X2, psi1, X1, union);
return X;
}
/// <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());
}
}
private MSOFormula<BDD> ConvertSubset(MonaExpr t1, MonaExpr t2, MapStack<string, MonaParam> locals)
{
MSOFormula<BDD> psi_x;
Variable x = ConvertTerm2(t1, locals, out psi_x);
MSOFormula<BDD> psi_y;
Variable y = ConvertTerm2(t2, locals, out psi_y);
return AddConstraints(psi_x, x, psi_y, y, new MSOSubset<BDD>(x, y));
}
private Variable ConvertSet(MonaExpr set, MapStack<string, MonaParam> locals, out MSOFormula<BDD> psi)
{
if (set.NrOfSubexprs == 0)
return ConvertEmptyset(out psi);
MSOFormula<BDD> disj = null;
Variable x = MkNewVar1();
Variable X = MkNewVar2();
for (int i=0; i < set.NrOfSubexprs; i++)
{
MonaExpr t = set[i];
if (t.symbol.Kind == Tokens.RANGE)
{
MSOFormula<BDD> from_psi;
Variable from = ConvertTerm1(t[0], locals, out from_psi);
MSOFormula<BDD> to_psi;
Variable to = ConvertTerm1(t[1], locals, out to_psi);
MSOFormula<BDD> range = AddConstraints(from_psi, from, to_psi, to,
new MSOAnd<BDD>(new MSOLe<BDD>(from, x), new MSOLe<BDD>(x, to)));
if (disj == null)
disj = range;
else
disj = new MSOOr<BDD>(disj, range);
}
else
{
MSOFormula<BDD> y_psi;
Variable y = ConvertTerm1(t, locals, out y_psi);
MSOFormula<BDD> elem = new MSOEq<BDD>(x, y);
if (y_psi != null)
elem = new MSOExists<BDD>(y, new MSOAnd<BDD>(y_psi, elem));
if (disj == null)
disj = elem;
else
disj = new MSOOr<BDD>(disj, elem);
}
}
var pred = new MSOForall<BDD>(x, new MSOEquiv<BDD>(new MSOIn<BDD>(x, X), disj));
psi = pred;
return X;
}
internal MonaAssertDecl(MonaExpr psi)
: base(MonaDeclKind.assert)
{
this.psi = psi;
}
internal MonaPconst(Token pconst, MonaExpr elem)
: base(pconst, MonaExprType.SET, new MonaExpr[]{elem})
{
}
internal MonaVarWhere(Token token, MonaExpr where)
{
this.token = token;
this.where = where;
}
internal MonaPredDecl(Token name, Cons<MonaParam> parameters, Dictionary<string,MonaParam> pmap, MonaExpr formula, bool isMacro = false)
: base(isMacro ? MonaDeclKind.macro : MonaDeclKind.pred)
{
this.pmap = (pmap == null ? new Dictionary<string,MonaParam>() : pmap);
this.isMacro = isMacro;
this.name = name;
this.parameters = (parameters == null ? Cons<MonaParam>.Empty : parameters);
this.formula = formula;
}
internal MonaBinaryBooleanFormula(Token token, MonaExpr formula1, MonaExpr formula2)
: base(token, MonaExprType.BOOL, new MonaExpr[]{formula1, formula2})
{
}
internal MonaQBFormula(Token quantifier, Cons<Token> vars, MonaExpr formula, Dictionary<string, MonaParam> varmap)
: base(quantifier, MonaExprType.BOOL, new MonaExpr[]{formula})
{
this.varmap = varmap;
this.vars = vars;
}
internal MonaDefaultWhereDecl(bool isSecondOrder, Token param, MonaExpr formula)
: base(isSecondOrder ? MonaDeclKind.defaultwhere2 : MonaDeclKind.defaultwhere1)
{
this.isSecondOrder = isSecondOrder;
this.param = param;
this.formula = formula;
}
internal MonaQFormula(Token quantifier, Cons<MonaVarWhere> vars, MonaExpr formula, Cons<Token> universes, Dictionary<string, MonaParam> varmap)
: base(quantifier, MonaExprType.BOOL, new MonaExpr[] { formula })
{
this.varmap = varmap;
this.universes = universes;
this.vars = vars;
}
internal MonaExpr(Token token, MonaExprType type, MonaExpr[] subexprs)
{
this.token = token;
this.type = type;
this.subexprs = subexprs;
}
internal MonaRange(Token dots, MonaExpr from, MonaExpr to)
: base(dots, MonaExprType.SET, new MonaExpr[]{from, to})
{
}
public MonaIsEmpty(Token token, MonaExpr term)
: base(token, MonaExprType.BOOL, new MonaExpr[]{term})
{
}
internal MonaRestrict(Token token, MonaExpr formula)
: base(token, MonaExprType.BOOL, new MonaExpr[]{formula})
{
}
public MonaMinOrMax(Token minormax, MonaExpr set)
: base(minormax, MonaExprType.INT, new MonaExpr[]{set})
{
}
internal MonaSetOp(Token op, MonaExpr arg1, MonaExpr arg2)
: base(op, MonaExprType.SET, new MonaExpr[]{arg1, arg2})
{
}
internal MonaArithmFuncApp(Token func, MonaExpr arg1, MonaExpr arg2)
: base(func, MonaExprType.INT, new MonaExpr[]{arg1, arg2})
{
}
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());
}
}
