public ConditionalDerivative <S> Compose(ConditionalDerivative <S> that)
{
var f = this.Condition;
var g = that.Condition;
var builder = this.PartialDerivative.builder;
var f_o_g = ComposeCounterUpdates(f, g);
var pd = builder.MkConcat(this.PartialDerivative, that.PartialDerivative);
var cd = new ConditionalDerivative <S>(f_o_g, pd);
return(cd);
}
internal IEnumerable <ConditionalDerivative <S> > EnumerateConditionalDerivatives(S elem, SymbolicRegexNode <S> node)
{
if (node == this.dotStar)
{
yield return(new ConditionalDerivative <S>(this.dotStar));
}
else if (node == this.nothing)
{
yield break;
}
else
{
switch (node.kind)
{
case SymbolicRegexKind.StartAnchor:
case SymbolicRegexKind.EndAnchor:
case SymbolicRegexKind.Epsilon:
{
yield break;
}
case SymbolicRegexKind.Singleton:
{
#region d(a,R) = epsilon if (a in R) else nothing
if (this.solver.IsSatisfiable(this.solver.MkAnd(elem, node.set)))
{
yield return(new ConditionalDerivative <S>(this.epsilon));
}
yield break;
#endregion
}
case SymbolicRegexKind.Or:
{
#region d(a,A|B) = d(a,A) U d(a,B)
//the hashset is used to eliminate duplicates
//for two different members the derivatives may be the same
var derivs = new HashSet <ConditionalDerivative <S> >();
foreach (var member in node.alts)
{
foreach (var deriv in this.EnumerateConditionalDerivatives(elem, member))
{
if (derivs.Add(deriv))
{
yield return(deriv);
}
}
}
yield break;
#endregion
}
case SymbolicRegexKind.Concat:
{
#region d(a, AB) = d(a,A)B U (if A nullable then d(a,B))
//rearrange the concat into left-associative form
//knowing that the representation initially is in
//right-associative form where none of the elements is itself a sequence
//this is crucial for correctness of nullability condition generation
var left = node.left;
var right = node.right;
while (right.kind == SymbolicRegexKind.Concat)
{
left = left.ConcatWithoutNormalizing(right.left);
right = right.right;
}
var derivs = new HashSet <ConditionalDerivative <S> >();
//observe that left will be already in the left-assoc form so the above loop will
//not be used again to normalize left to left-assoc form in the recursive call
foreach (var deriv in this.EnumerateConditionalDerivatives(elem, left))
{
var deriv1 = new ConditionalDerivative <S>(deriv.Condition,
this.MkConcat(deriv.PartialDerivative, right));
if (derivs.Add(deriv1))
{
yield return(deriv1);
}
}
var reset = GetNullabilityCondition_of_left_assoc(left);
if (reset != null)
{
var cd_reset = new ConditionalDerivative <S>(reset, this.epsilon);
foreach (var deriv in this.EnumerateConditionalDerivatives(elem, right))
{
var deriv1 = cd_reset.Compose(deriv);
if (derivs.Add(deriv1))
{
yield return(deriv1);
}
}
}
yield break;
#endregion
}
case SymbolicRegexKind.Loop:
{
#region d(a, R*) = d(a,R)R*
if (node.IsStar)
{
foreach (var step in this.EnumerateConditionalDerivatives(elem, node.left))
{
var deriv = this.MkConcat(step.PartialDerivative, node);
var cd = new ConditionalDerivative <S>(step.Condition, deriv);
yield return(cd);
}
}
//--- already normalized, this should be dead code
//else if (node.IsPlus)
//{
// var star = this.MkLoop(node.left);
// var expandedloop = this.MkConcat(node.left, star);
// foreach (var deriv in this.EnumerateConditionalDerivatives(elem, expandedloop))
// yield return deriv;
//}
//else if (node.IsMaybe)
//{
// foreach (var step in this.EnumerateConditionalDerivatives(elem, node.left))
// yield return step;
//}
//else if (node.UpperBound == int.MaxValue)
//{
// //normalize A{k,*} loop into A{k}A*
// var Ak = this.MkLoop(node.left, node.lower, node.lower);
// var Astar = this.MkLoop(node.left, 0, int.MaxValue);
// var expandedloop = this.MkConcat(Ak, Astar);
// foreach (var step in this.EnumerateConditionalDerivatives(elem, expandedloop))
// yield return step;
//}
else
{
CounterUpdate ca = new CounterUpdate(node, CounterOp.INCREMENT);
foreach (var step in this.EnumerateConditionalDerivatives(elem, node.left))
{
var deriv = this.MkConcat(step.PartialDerivative, node);
var cond = step.Condition.Append(ca);
var cd = new ConditionalDerivative <S>(cond, deriv);
yield return(cd);
}
}
yield break;
#endregion
}
default:
{
throw new NotSupportedException("Conditional derivatives not supported for " + node.kind);
}
}
}
}
