public static bool Match(IExpr /*!*/ expr, IFunctionSymbol /*!*/ f, params Matcher[] /*!*/ subs)
{
Contract.Requires(subs != null);
Contract.Requires(f != null);
Contract.Requires(expr != null);
IFunApp app = MatchFunctionSymbol(expr, f);
if (app != null)
{
int i = 0; // Note ***0***
foreach (Matcher /*!*/ s in subs)
{
Contract.Assert(s != null);
if (!s(cce.NonNull((IExpr)app.Arguments[i])))
{
return(false);
}
i++;
}
return(true);
}
else
{
return(false);
}
}
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
understandsCount++;
return(lattice.Understands(f, args));
}
// Ternary Binding
public static bool Match(IExpr /*!*/ expr, IFunctionSymbol /*!*/ f, out IExpr arg0, out IExpr arg1, out IExpr arg2, params Matcher[] /*!*/ subs)
{
Contract.Requires(subs != null);
Contract.Requires(f != null);
Contract.Requires(expr != null);
arg0 = null;
arg1 = null;
arg2 = null;
IFunApp app = MatchFunctionSymbol(expr, f);
if (app != null)
{
arg0 = (IExpr /*!*/)cce.NonNull(app.Arguments[0]);
arg1 = (IExpr /*!*/)cce.NonNull(app.Arguments[1]);
arg2 = (IExpr /*!*/)cce.NonNull(app.Arguments[2]);
int i = 3; // Note ***3***
foreach (Matcher /*!*/ s in subs)
{
Contract.Assert(s != null);
if (!s(cce.NonNull((IExpr /*!*/)app.Arguments[i])))
{
return(false);
}
i++;
}
return(true);
}
else
{
return(false);
}
}
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
return(f.Equals(Prop.And) ||
f.Equals(Value.Eq) ||
microLattice.Understands(f, args));
}
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
bool result = false;
for (int i = 0; i < this.lattices.Count; i++)
{
result = (result || SubLattice(i).Understands(f, args));
}
return(result);
}
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*<IExpr!>*//*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
return(f is IntSymbol ||
f.Equals(Int.Add) ||
f.Equals(Int.Sub) ||
f.Equals(Int.Negate) ||
f.Equals(Int.Mul) ||
f.Equals(Int.Eq) ||
f.Equals(Int.Neq) ||
f.Equals(Prop.Not) ||
f.Equals(Int.AtMost) ||
f.Equals(Int.Less) ||
f.Equals(Int.Greater) ||
f.Equals(Int.AtLeast));
}
private static IFunApp /*?*/ MatchFunctionSymbol(IExpr /*!*/ expr, IFunctionSymbol /*!*/ f)
{
Contract.Requires(f != null);
Contract.Requires(expr != null);
IFunApp app = expr as IFunApp;
if (app != null)
{
if (app.FunctionSymbol.Equals(f))
{
return(app);
}
else
{
return(null);
}
}
else
{
return(null);
}
}
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*<IExpr!>*//*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
bool isEq = f.Equals(Microsoft.AbstractInterpretationFramework.Value.Eq);
if (isEq || f.Equals(Microsoft.AbstractInterpretationFramework.Value.Subtype))
{
Contract.Assert(args.Count == 2);
IExpr /*!*/ arg0 = (IExpr /*!*/)cce.NonNull(args[0]);
IExpr /*!*/ arg1 = (IExpr /*!*/)cce.NonNull(args[1]);
// Look for $typeof(var) == t or t == $typeof(var) or $typeof(var) <: t
if (isEq && factory.IsTypeConstant(arg0))
{
// swap the arguments
IExpr /*!*/ tmp = arg0;
arg0 = arg1;
arg1 = tmp;
}
else if (!factory.IsTypeConstant(arg1))
{
return(false);
}
IFunApp typeofExpr = arg0 as IFunApp;
if (typeofExpr != null &&
typeofExpr.FunctionSymbol.Equals(Microsoft.AbstractInterpretationFramework.Value.Typeof))
{
Contract.Assert(typeofExpr.Arguments.Count == 1);
if (typeofExpr.Arguments[0] is IVariable)
{
// we have a match
return(true);
}
}
}
return(false);
}
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*<IExpr!>*//*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
if (f.Equals(Microsoft.AbstractInterpretationFramework.Value.Eq) ||
f.Equals(Microsoft.AbstractInterpretationFramework.Value.Neq))
{
Contract.Assert(args.Count == 2);
IExpr /*!*/ arg0 = (IExpr /*!*/)cce.NonNull(args[0]);
IExpr /*!*/ arg1 = (IExpr /*!*/)cce.NonNull(args[1]);
// Look for "x OP null" or "null OP x" where OP is "==" or "!=".
if (arg0 is IVariable && arg1 is IFunApp && ((IFunApp)arg1).FunctionSymbol == Ref.Null)
{
return(true);
}
else if (arg1 is IVariable && arg0 is IFunApp && ((IFunApp)arg0).FunctionSymbol == Ref.Null)
{
return(true);
}
}
return(false);
}
public static bool Match(IExpr/*!*/ expr, IFunctionSymbol/*!*/ f, params Matcher[]/*!*/ subs){
Contract.Requires(subs != null);
Contract.Requires(f != null);
Contract.Requires(expr != null);
IFunApp app = MatchFunctionSymbol(expr,f);
if (app != null)
{
int i = 0; // Note ***0***
foreach(Matcher/*!*/ s in subs){
Contract.Assert(s != null);
if (!s(cce.NonNull((IExpr)app.Arguments[i]))) { return false; }
i++;
}
return true;
}
else { return false; }
}
private static IFunApp/*?*/ MatchFunctionSymbol(IExpr/*!*/ expr, IFunctionSymbol/*!*/ f){
Contract.Requires(f != null);
Contract.Requires(expr != null);
IFunApp app = expr as IFunApp;
if (app != null)
{
if (app.FunctionSymbol.Equals(f))
return app;
else
return null;
}
else
return null;
}
/// <summary>
/// Is this a boolean field that monotonically goes from false to true?
/// </summary>
public static bool IsBooleanMonotonicallyWeakening(IFunctionSymbol/*!*/ f) {
Contract.Requires(f != null);
return f.Equals(Allocated);
}
public override bool Understands(IFunctionSymbol/*!*/ f, IList/*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
understandsCount++;
return lattice.Understands(f, args);
}
public override bool Understands(IFunctionSymbol f, IList args) {
Contract.Requires(f != null);
Contract.Requires(args != null);
throw new NotImplementedException();
}
public override bool Understands(IFunctionSymbol/*!*/ f, IList/*<IExpr!>*//*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
if (f.Equals(Microsoft.AbstractInterpretationFramework.Value.Eq) ||
f.Equals(Microsoft.AbstractInterpretationFramework.Value.Neq)) {
Contract.Assert(args.Count == 2);
IExpr/*!*/ arg0 = (IExpr/*!*/)cce.NonNull(args[0]);
IExpr/*!*/ arg1 = (IExpr/*!*/)cce.NonNull(args[1]);
// Look for "x OP null" or "null OP x" where OP is "==" or "!=".
if (arg0 is IVariable && arg1 is IFunApp && ((IFunApp)arg1).FunctionSymbol == Ref.Null) {
return true;
} else if (arg1 is IVariable && arg0 is IFunApp && ((IFunApp)arg0).FunctionSymbol == Ref.Null) {
return true;
}
}
return false;
}
/// <summary>
/// For the moment consider just equalities. Other case must be considered
/// </summary>
public override bool Understands(IFunctionSymbol/*!*/ f, IList /*<IExpr*//*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
return f.Equals(Microsoft.AbstractInterpretationFramework.Value.Eq);
}
/// <summary>
/// For the moment consider just equalities. Other case must be considered
/// </summary>
public override bool Understands(IFunctionSymbol /*!*/ f, IList /*<IExpr*//*!*/ args)
{
//Contract.Requires(args != null);
//Contract.Requires(f != null);
return(f.Equals(Microsoft.AbstractInterpretationFramework.Value.Eq));
}
// Ternary Binding
public static bool Match(IExpr/*!*/ expr, IFunctionSymbol/*!*/ f, out IExpr arg0, out IExpr arg1, out IExpr arg2, params Matcher[]/*!*/ subs){
Contract.Requires(subs != null);
Contract.Requires(f != null);
Contract.Requires(expr != null);
arg0 = null;
arg1 = null;
arg2 = null;
IFunApp app = MatchFunctionSymbol(expr,f);
if (app != null)
{
arg0 = (IExpr/*!*/)cce.NonNull(app.Arguments[0]);
arg1 = (IExpr/*!*/)cce.NonNull(app.Arguments[1]);
arg2 = (IExpr/*!*/)cce.NonNull(app.Arguments[2]);
int i = 3; // Note ***3***
foreach(Matcher/*!*/ s in subs){
Contract.Assert(s != null);
if (!s(cce.NonNull((IExpr/*!*/)app.Arguments[i]))) { return false; }
i++;
}
return true;
}
else { return false; }
}
private static IList/*<IExpr!>*//*!*/ BreakJuncts(IExpr/*!*/ e, IFunctionSymbol/*!*/ sym) {
Contract.Requires(sym != null);
Contract.Requires(e != null);
Contract.Ensures(Contract.Result<IList>() != null);
Contract.Ensures(Contract.ForAll(0, Contract.Result<IList>().Count, i => {
var sub = Contract.Result<IList>()[i];
return (sub is IFunApp) || !((IFunApp)sub).FunctionSymbol.Equals(sym);
}));
ArrayList/*<IExpr!>*//*!*/ result = new ArrayList();
IFunApp f = e as IFunApp;
if (f != null) {
// If it is a sym, go down into sub-expressions.
if (f.FunctionSymbol.Equals(sym)) {
foreach (IExpr/*!*/ arg in f.Arguments) {
Contract.Assert(arg != null);
result.AddRange(BreakJuncts(arg, sym));
}
}
// Otherwise, stop.
else {
result.Add(e);
}
} else {
result.Add(e);
}
return result;
}
public override bool Understands(IFunctionSymbol/*!*/ f, IList/*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
bool result = false;
for (int i = 0; i < this.lattices.Count; i++) {
result = (result || SubLattice(i).Understands(f, args));
}
return result;
}
public override bool Understands(IFunctionSymbol f, IList args)
{
Contract.Requires(f != null);
Contract.Requires(args != null);
throw new NotImplementedException();
}
/// <summary> /// Allows the lattice to specify whether it understands a particular function symbol. /// /// The lattice is always allowed to return "true" even when it really can't do anything /// with such functions; however, it is advantageous to say "false" when possible to /// avoid being called to do certain things. /// /// The arguments to a function are provided for context so that the lattice can say /// true or false for the same function symbol in different situations. For example, /// a lattice may understand the multiplication of a variable and a constant but not /// of two variables. The implementation of a lattice should not hold on to the /// arguments. /// </summary> /// <param name="f">The function symbol.</param> /// <param name="args">The argument context.</param> /// <returns>True if it may understand f, false if it does not understand f.</returns> public abstract bool Understands(IFunctionSymbol /*!*/ f, IList /*<IExpr!>*//*!*/ args);
public override bool Understands(IFunctionSymbol/*!*/ f, IList/*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
return f.Equals(Prop.And) ||
f.Equals(Value.Eq) ||
microLattice.Understands(f, args);
}
static /*maybe null*/ LinearCondition GetCond(IExpr e, bool positive) /* throws ArithmeticException */
{
IFunApp funapp = e as IFunApp;
if (funapp == null)
{
return(null);
}
IFunctionSymbol /*!*/ s = funapp.FunctionSymbol;
Contract.Assert(s != null);
if ((positive && s.Equals(Prop.False)) ||
(!positive && s.Equals(Prop.True)))
{
return(new LCBottom());
}
else if (s.Equals(Prop.Not))
{
Contract.Assert(funapp.Arguments.Count == 1);
return(GetCond((IExpr /*!*/)cce.NonNull(funapp.Arguments[0]), !positive));
}
else if (funapp.Arguments.Count == 2)
{
IExpr /*!*/ arg0 = (IExpr /*!*/)cce.NonNull(funapp.Arguments[0]);
IExpr /*!*/ arg1 = (IExpr /*!*/)cce.NonNull(funapp.Arguments[1]);
LinearExpr le0 = AsExpr(arg0);
if (le0 == null)
{
return(null);
}
LinearExpr le1 = AsExpr(arg1);
if (le1 == null)
{
return(null);
}
LinearConstraint constraint = null;
bool sense = true;
if ((positive && s.Equals(Int.Less)) || (!positive && s.Equals(Int.AtLeast)))
{
constraint = MakeConstraint(le0, le1, LinearConstraint.ConstraintRelation.LE, BigNum.ONE);
}
else if ((positive && s.Equals(Int.AtMost)) || (!positive && s.Equals(Int.Greater)))
{
constraint = MakeConstraint(le0, le1, LinearConstraint.ConstraintRelation.LE, BigNum.ZERO);
}
else if ((positive && s.Equals(Int.AtLeast)) || (!positive && s.Equals(Int.Less)))
{
constraint = MakeConstraint(le1, le0, LinearConstraint.ConstraintRelation.LE, BigNum.ZERO);
}
else if ((positive && s.Equals(Int.Greater)) || (!positive && s.Equals(Int.AtMost)))
{
constraint = MakeConstraint(le1, le0, LinearConstraint.ConstraintRelation.LE, BigNum.ONE);
}
else if (s.Equals(Int.Eq))
{
constraint = MakeConstraint(le0, le1, LinearConstraint.ConstraintRelation.EQ, BigNum.ZERO);
sense = positive;
}
else if (s.Equals(Int.Neq))
{
constraint = MakeConstraint(le0, le1, LinearConstraint.ConstraintRelation.EQ, BigNum.ZERO);
sense = !positive;
}
if (constraint != null)
{
if (constraint.coefficients.Count != 0)
{
return(new LinearConditionLiteral(sense, constraint));
}
else if (constraint.IsConstantSatisfiable())
{
return(null);
}
else
{
return(new LCBottom());
}
}
}
return(null);
}
/// <summary>
/// Builds a linear expression from "e", if possible; returns null if not possible.
/// </summary>
/// <param name="e"></param>
/// <returns></returns>
public static /*maybe null*/ LinearExpr AsExpr(IExpr /*!*/ e) /* throws ArithmeticException */
{
Contract.Requires(e != null);
if (e is IVariable)
{
// Note, without a type for the variable, we don't know if the identifier is intended to hold an integer value.
// However, it seems that no harm can be caused by here treating the identifier as if it held an
// integer value, because other parts of this method will reject the expression as a linear expression
// if non-numeric operations other than equality are applied to the identifier.
return(new LinearExpr((IVariable)e));
}
else if (e is IFunApp)
{
IFunApp /*!*/ funapp = (IFunApp)e;
Contract.Assert(funapp != null);
IFunctionSymbol /*!*/ s = funapp.FunctionSymbol;
Contract.Assert(s != null);
if (s is IntSymbol)
{
return(new LinearExpr(((IntSymbol)s).Value));
}
else if (s.Equals(Int.Negate))
{
Contract.Assert(funapp.Arguments.Count == 1);
LinearExpr le = AsExpr((IExpr /*!*/)cce.NonNull(funapp.Arguments[0]));
if (le != null)
{
le.Negate();
return(le);
}
}
else if (s.Equals(Int.Add) || s.Equals(Int.Sub) || s.Equals(Int.Mul))
{
Contract.Assert(funapp.Arguments.Count == 2);
IExpr /*!*/ arg0 = (IExpr /*!*/)cce.NonNull(funapp.Arguments[0]);
IExpr /*!*/ arg1 = (IExpr /*!*/)cce.NonNull(funapp.Arguments[1]);
LinearExpr le0 = AsExpr(arg0);
if (le0 == null)
{
return(null);
}
LinearExpr le1 = AsExpr(arg1);
if (le1 == null)
{
return(null);
}
if (s.Equals(Int.Add))
{
le0.Add(le1);
return(le0);
}
else if (s.Equals(Int.Sub))
{
le1.Negate();
le0.Add(le1);
return(le0);
}
else if (s.Equals(Int.Mul))
{
BigNum x;
if (le0.AsConstant(out x))
{
le1.Multiply(x);
return(le1);
}
else if (le1.AsConstant(out x))
{
le0.Multiply(x);
return(le0);
}
}
}
}
return(null);
}
/// <summary> /// Allows the lattice to specify whether it understands a particular function symbol. /// /// The lattice is always allowed to return "true" even when it really can't do anything /// with such functions; however, it is advantageous to say "false" when possible to /// avoid being called to do certain things. /// /// The arguments to a function are provided for context so that the lattice can say /// true or false for the same function symbol in different situations. For example, /// a lattice may understand the multiplication of a variable and a constant but not /// of two variables. The implementation of a lattice should not hold on to the /// arguments. /// </summary> /// <param name="f">The function symbol.</param> /// <param name="args">The argument context.</param> /// <returns>True if it may understand f, false if it does not understand f.</returns> public abstract bool Understands(IFunctionSymbol/*!*/ f, IList/*<IExpr!>*//*!*/ args);
public override bool Understands(IFunctionSymbol/*!*/ f, IList/*<IExpr!>*//*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
bool isEq = f.Equals(Microsoft.AbstractInterpretationFramework.Value.Eq);
if (isEq || f.Equals(Microsoft.AbstractInterpretationFramework.Value.Subtype)) {
Contract.Assert(args.Count == 2);
IExpr/*!*/ arg0 = (IExpr/*!*/)cce.NonNull(args[0]);
IExpr/*!*/ arg1 = (IExpr/*!*/)cce.NonNull(args[1]);
// Look for $typeof(var) == t or t == $typeof(var) or $typeof(var) <: t
if (isEq && factory.IsTypeConstant(arg0)) {
// swap the arguments
IExpr/*!*/ tmp = arg0;
arg0 = arg1;
arg1 = tmp;
} else if (!factory.IsTypeConstant(arg1)) {
return false;
}
IFunApp typeofExpr = arg0 as IFunApp;
if (typeofExpr != null &&
typeofExpr.FunctionSymbol.Equals(Microsoft.AbstractInterpretationFramework.Value.Typeof)) {
Contract.Assert(typeofExpr.Arguments.Count == 1);
if (typeofExpr.Arguments[0] is IVariable) {
// we have a match
return true;
}
}
}
return false;
}
public override bool Understands(IFunctionSymbol/*!*/ f, IList/*<IExpr!>*//*!*/ args) {
//Contract.Requires(args != null);
//Contract.Requires(f != null);
return f is IntSymbol ||
f.Equals(Int.Add) ||
f.Equals(Int.Sub) ||
f.Equals(Int.Negate) ||
f.Equals(Int.Mul) ||
f.Equals(Int.Eq) ||
f.Equals(Int.Neq) ||
f.Equals(Prop.Not) ||
f.Equals(Int.AtMost) ||
f.Equals(Int.Less) ||
f.Equals(Int.Greater) ||
f.Equals(Int.AtLeast);
}