/// <summary>
/// Checks whether the expression is in NNF
/// </summary>
/// <param name="node"></param>
/// <returns></returns>
bool IsNNF(BoolExpr node)
{
switch (node.Op)
{
case OperatorType.LEAF:
return(true);
case OperatorType.AND:
case OperatorType.OR:
return(IsNNF(node.Right) && IsNNF(node.Left));
case OperatorType.NOT:
return(node.Right.Op == OperatorType.LEAF);
default:
return(false);
}
}
/// <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>
/// Checks wheter the only operators used in the expression are the negation, disjunction, and conjunction operators
/// </summary>
/// <param name="node"></param>
/// <returns></returns>
bool BasicOperators(BoolExpr node)
{
switch (node.Op)
{
case OperatorType.LEAF:
return(true);
case OperatorType.AND:
return(BasicOperators(node.Right) && BasicOperators(node.Left));
case OperatorType.OR:
return(BasicOperators(node.Right) && BasicOperators(node.Left));
case OperatorType.NOT:
return(BasicOperators(node.Right));
default:
return(false);
}
}
/// <summary>
/// Converts the tree to CDNF
/// </summary>
/// <param name="variables"></param>
/// <param name="reverse"></param>
/// <returns></returns>
public IList <ConversionStep> Evaluate(IEnumerable <string> variables, bool reverse = false)
{
BoolExpr root;
var steps = new ObservableCollection <ConversionStep>();
steps.Add(new ConversionStep(ToString(), "Input"));
if (!BasicOperators(Root))
{
root = Root;
ConvertOperators(ref root, steps);
Root = root;
}
Debug.Assert(BasicOperators(Root));
if (!IsNNF(Root))
{
root = Root;
ConvertToNNF(ref root, steps);
Root = root;
}
Debug.Assert(IsNNF(Root));
if (!IsDNF(Root))
{
root = Root;
ConvertNNFtoDNF(ref root, steps);
Root = root;
}
Debug.Assert(IsDNF(Root));
// convert to DNFList
var d = new DNFExpression(Root, variables);
steps.Add(new ConversionStep(d.ToString(), "Association"));
d.ConvertToCDNF(steps, reverse);
return(steps);
}
public static BoolExpr CreateBinary(string op, BoolExpr left, BoolExpr right)
{
switch (op)
{
case "AND":
return(new BoolExprConjunction(left, right));
case "OR":
return(new BoolExprDisjunction(left, right));
case "CONDITIONAL":
return(new BoolExprConditional(left, right));
case "BICONDITIONAL":
return(new BoolExprBiconditional(left, right));
case "XOR":
return(new BoolExprXOR(left, right));
default:
throw new Exception();
}
}
/// <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;
}
public BoolExprXOR(BoolExpr left, BoolExpr right) : base(OperatorType.XOR, left, right)
{
Lit = LogicalSymbols.XOr.ToString();
}
public BoolExprBiconditional(BoolExpr left, BoolExpr right) : base(OperatorType.BICONDITIONAL, left, right)
{
Lit = LogicalSymbols.Biconditional.ToString();
}
public BoolExprDisjunction(BoolExpr left, BoolExpr right) : base(OperatorType.OR, left, right)
{
Lit = LogicalSymbols.Or.ToString();
}
public BoolExprConjunction(BoolExpr left, BoolExpr right) : base(OperatorType.AND, left, right)
{
Lit = LogicalSymbols.And.ToString();
}
public BoolExprNegation(BoolExpr child) : base(OperatorType.NOT, null, child)
{
}
public BoolExprBinary(OperatorType op, BoolExpr left, BoolExpr right) : base(op, left, right)
{
}
public static BoolExpr CreateNot(BoolExpr child) => new BoolExprNegation(child);