/// <summary>
/// Converts expression to only use negation, conjunction, and disjunction operators
/// </summary>
/// <param name="node"></param>
/// <param name="steps"></param>
void ConvertOperators(ref BoolExpr node, IList <ConversionStep> steps)
{
if (node == null || node.Op == OperatorType.LEAF)
{
return;
}
if (Rewrite.Implication(ref node))
{
if (node.Parent == null)
{
Root = node;
}
steps.Add(new ConversionStep(ToString(), "Implication"));
}
if (Rewrite.Equivalence(ref node))
{
if (node.Parent == null)
{
Root = node;
}
steps.Add(new ConversionStep(ToString(), "Equivalence"));
}
if (Rewrite.XOR(ref node))
{
if (node.Parent == null)
{
Root = node;
}
steps.Add(new ConversionStep(ToString(), "Xor"));
}
var right = node.Right;
var left = node.Left;
ConvertOperators(ref left, steps);
ConvertOperators(ref right, steps);
node.Right = right;
node.Left = left;
}
/// <summary>
/// Applies the distribution rule to an expression
/// </summary>
/// <param name="node"></param>
/// <param name="steps"></param>
void ApplyDistribution(ref BoolExpr node, IList <ConversionStep> steps)
{
if (node == null || node.Op == OperatorType.LEAF)
{
return;
}
// try to apply distribution
if (Rewrite.Distribution(ref node))
{
if (node.Parent == null)
{
Root = node;
}
steps.Add(new ConversionStep(ToString(), "Distribution"));
}
var right = node.Right;
var left = node.Left;
ApplyDistribution(ref left, steps);
ApplyDistribution(ref right, steps);
node.Right = right;
node.Left = left;
}
/// <summary>
/// Converts expression to negation normal form
/// </summary>
/// <param name="node"></param>
/// <param name="steps"></param>
void ConvertToNNF(ref BoolExpr node, IList <ConversionStep> steps)
{
if (node == null || node.Op == OperatorType.LEAF)
{
return;
}
// try to apply DN as many times as possible
while (Rewrite.DN(ref node))
{
if (node.Parent == null)
{
Root = node;
}
steps.Add(new ConversionStep(ToString(), "Double Negation"));
}
// try to apply DeM
if (Rewrite.DeM(ref node))
{
if (node.Parent == null)
{
Root = node;
}
steps.Add(new ConversionStep(ToString(), "DeMorgan's"));
}
var right = node.Right;
var left = node.Left;
ConvertToNNF(ref left, steps);
ConvertToNNF(ref right, steps);
node.Right = right;
node.Left = left;
}