public ImpliesProposition(ASTOpBinary ast) : base(ast)
{
if (ast.value != Language.Symbol.IMPLICA)
{
throw new Exception("An ImpliesProposition can only be created from an AST if this is a ASTOpBinary of type IMPLICA.");
}
}
/// <summary>
/// Formula extraction.
/// </summary>
/// <param name="branch">The current branch to extract from</param>
private void Extract(AST branch = null)
{
if (m_formulas == null)
{
m_formulas = new List <AST>();
}
AST current = branch != null ? branch : m_formula;
switch (current.GetType().Name)
{
case "ASTProp":
case "ASTOpUnary":
m_formulas.Add(current);
break;
case "ASTOpBinary":
ASTOpBinary binOp = (ASTOpBinary)current;
switch (binOp.value)
{
case Language.Symbol.E: // Extraction must continue.
Extract(binOp.left);
Extract(binOp.right);
break;
case Language.Symbol.OU: // Already a disjuction. Extraction must return.
m_formulas.Add(current);
break;
default: // There should not be other symbols in an CNF formula.
break;
}
break;
}
}
public EquivalentProposition(ASTOpBinary ast) : base(ast)
{
if (ast.value != Language.Symbol.EQUIVALE)
{
throw new Exception("An EquivalentProposition can only be created from an AST if this is a ASTOpBinary of type EQUIVALE.");
}
}
public DisjunctiveProposition(ASTOpBinary ast) : base(ast)
{
if (ast.value != Language.Symbol.OU)
{
throw new Exception("A DisjunctiveProposition can only be created from an AST if this is a ASTOpBinary of type OU.");
}
}
protected IEnumerable <Proposition> ConvertFromAST(AST ast, Language.Symbol oper)
{
if (ast == null)
{
return(null);
}
List <Proposition> result = new List <Proposition>();
string type = ast.GetType().Name;
if (type == "ASTOpBinary")
{
ASTOpBinary opBin = ast as ASTOpBinary;
if (opBin.value == oper)
{
result.AddRange(ConvertFromAST(opBin.left, oper));
result.AddRange(ConvertFromAST(opBin.right, oper));
return(result);
}
}
// else
result.Add(Proposition.FromAST(ast));
return(result);
}
private static string StrPlain(AST ast, bool innerOR = false)
{
if (ast == null)
{
return("CLAÚSULA NULA");
}
switch (ast.GetType().Name)
{
case "ASTProp":
return(((ASTProp)ast).value.ToString().ToLower());
case "ASTOpUnary":
return("(~" + StrPlain(((ASTOpUnary)ast).ast) + ")");
case "ASTOpBinary":
ASTOpBinary opBin = (ASTOpBinary)ast;
bool nextOR = (opBin.value == Language.Symbol.OU);
string plain =
StrPlain(opBin.left, nextOR) + " " +
opBin.value + " " +
StrPlain(opBin.right, nextOR);
if (!innerOR)
{
plain = "(" + plain + ")";
}
return(plain);
} // switch
return("");
}
public override bool Equals(object obj)
{
if (obj == null || GetType() != obj.GetType())
{
return(false);
}
ASTOpBinary other = obj as ASTOpBinary;
return
(this.left.Equals(other.left) &&
this.right.Equals(other.right) &&
this.value == other.value
);
}
/// <summary>
/// Separates a formula in CNF in its OR components clauses.
/// </summary>
/// <param name="astInCnf">An AST in CNF form.</param>
/// <returns>A enumerable of CnfOr clauses.</returns>
public static IEnumerable <CnfOr> Separate(AST astInCnf, bool order = false)
{
if (astInCnf == null)
{
return(null);
}
List <CnfOr> result = new List <CnfOr>(1);
switch (astInCnf.GetType().Name)
{
case "ASTProp":
case "ASTOpUnary":
result.Add(new CnfOr(astInCnf));
break;
case "ASTOpBinary":
ASTOpBinary opBin = (ASTOpBinary)astInCnf;
switch (opBin.value)
{
case Language.Symbol.OU: // Form (A|B).
result.Add(new CnfOr(astInCnf));
break;
case Language.Symbol.E: // Form (A&B).
result.AddRange(Separate(opBin.left));
result.AddRange(Separate(opBin.right));
break;
case Language.Symbol.IMPLICA: // Form (P->Q).
case Language.Symbol.EQUIVALE: // Form (P<->Q).
throw new System.Exception("AST in CNF separation failed. There can't be other binary operator beside & or | in a formula in CNF.");
}
break;
}
if (order)
{
result.Sort();
}
return(result);
}
private void Extract(AST astInCNF)
{
switch (astInCNF.GetType().Name)
{
case "ASTProp":
char letter = (astInCNF as ASTProp).value;
m_content.Add(new Component(letter));
break;
case "ASTOpUnary":
ASTOpUnary astNeg = astInCNF as ASTOpUnary;
if (astNeg.ast.GetType().Name != "ASTProp")
{ // In CNF form, the negation can only refers to a simple proposition.
throw new Exception("Error creating a CnfOr : In CNF form, the negation can only refers to a simple proposition.");
}
letter = (astNeg.ast as ASTProp).value;
m_content.Add(new Component(letter, true));
break;
case "ASTOpBinary":
ASTOpBinary opBin = astInCNF as ASTOpBinary;
switch (opBin.value)
{
case Language.Symbol.OU: // Form (A|B).
Extract(opBin.left);
Extract(opBin.right);
break;
case Language.Symbol.E: // Form (A&B).
case Language.Symbol.IMPLICA: // Form (P->Q).
case Language.Symbol.EQUIVALE: // Form (P<->Q).
throw new Exception("Error creating a CnfOr : In CNF form, OR formulas can't contain other operators than OR.");
}
break;
}
}
// Transitional function. Convert from AST.
public static Proposition FromAST(AST ast)
{
switch (ast.GetType().Name)
{
case "ASTProp":
return(new SingleProposition(ast as ASTProp));
case "ASTOpUnary":
return(new NegationProposition(ast as ASTOpUnary));
case "ASTOpBinary":
ASTOpBinary opBin = ast as ASTOpBinary;
switch (opBin.value)
{
case Language.Symbol.E:
return(new ConjunctiveProposition(opBin));
case Language.Symbol.OU:
return(new DisjunctiveProposition(opBin));
case Language.Symbol.IMPLICA:
return(new ImpliesProposition(opBin));
case Language.Symbol.EQUIVALE:
return(new EquivalentProposition(opBin));
default:
throw new Exception(string.Format(
"The operation {0} is not supported for conversion to Proposition",
opBin.value
));
}
}
return(null);
}
/// <summary>
/// Parsing recursive implementation.
/// </summary>
/// <param name="precede">does precedence must be considered in this recursive call?</param>
/// <returns>the resulting AST node.</returns>
AST Walk(bool precede = false)
{
// Increment the global index.
m_idx++;
if (m_idx >= Tokens.Count)
{
return(null);
}
// Read the current index's token value.
Token token = Tokens[m_idx];
AST ast = null;
switch (token.type)
{
case Language.Symbol.PROP: // a propositional letter.
ast = new ASTProp(token.value);
break;
case Language.Symbol.NAO: // negation operation.
ast = new ASTOpUnary(Walk(true), token.type);
break;
case Language.Symbol.E: // conjunction operation.
case Language.Symbol.OU: // disjunction operation.
ast = new ASTOpBinary(m_current, Walk(true), token.type);
break;
case Language.Symbol.IMPLICA: // implication operation.
case Language.Symbol.EQUIVALE: // double implication operation.
// double implication has lesser precedence over single implication.
bool bi = token.type == Language.Symbol.EQUIVALE;
// must continue to parse?
bool forward = // we continue parsing if...
m_implFlag == 0 || // ... there is no implications awaiting or ...
(m_implFlag == 2 && !bi); // ... a double implication awaits and the current is a single implication.
if (forward)
{ // must continue the parsing.
// save current implication flag value...
int implications = m_implFlag;
// and update the global value.
m_implFlag = bi ? 2 : 1;
// enter another recursion.
ast = new ASTOpBinary(m_current, Walk(false), token.type);
// did the last recursive call finished precedence analysis?
if (m_implFlag == 0)
{
precede = false;
}
// restore previous (saved) implication flag value.
m_implFlag = implications;
}
else
{ // must not continue and must return to the last call.
m_idx--;
ast = m_current;
precede = true;
m_implFlag = 0;
break;
}
break;
case Language.Symbol.ABERTURA: // opening expression symbol.
// enter a new recursive call, as an AST node must come from the parenthesis' content analysis.
while (Walk(precede) != null)
{
ast = m_current;
}
break;
case Language.Symbol.FECHAMENTO: // closing expression symbol.
return(null);
}
// update current AST node.
m_current = ast;
// continue the processing as long as there are tokens and no precedence.
if (!precede && m_idx < Tokens.Count)
{
Walk();
}
return(m_current);
}
} // Extractor class
#endregion Inner classes
#region Public functions
/// <summary>
/// Convert the formula to conjuntive normal form.
/// </summary>
/// <param name="ast">original abstract syntatic tree representinf the formula.</param>
/// <returns>formula in CNF.</returns>
public static AST Convert(AST ast)
{
if (ast == null)
{
return(ast);
}
switch (ast.GetType().Name)
{
case "ASTProp":
return(ast);
case "ASTOpBinary":
ASTOpBinary opBin = ast as ASTOpBinary;
switch (opBin.value)
{
case Language.Symbol.E: // Form (P&Q).
AST left = Convert(opBin.left);
AST right = Convert(opBin.right);
return(new ASTOpBinary(left, right, Language.Symbol.E));
case Language.Symbol.OU: // Form (P|Q).
left = Convert(opBin.left);
right = Convert(opBin.right);
return(Distribute(left, right));
case Language.Symbol.IMPLICA: // Form (P->Q). Equivalent to (~P|Q)
return(Convert(
new ASTOpBinary(
new ASTOpUnary(opBin.left, Language.Symbol.NAO),
opBin.right, Language.Symbol.OU)
));
case Language.Symbol.EQUIVALE: // Form (P<->Q). Equivalent to (P&Q)|(~P&~Q).
left = new ASTOpBinary(opBin.left, opBin.right, Language.Symbol.E);
right = new ASTOpBinary(
new ASTOpUnary(opBin.left, Language.Symbol.NAO),
new ASTOpUnary(opBin.right, Language.Symbol.NAO),
Language.Symbol.E
);
return(Convert(new ASTOpBinary(left, right, Language.Symbol.OU)));
}
break;
case "ASTOpUnary":
AST p = (ast as ASTOpUnary).ast;
switch (p.GetType().Name)
{
case "ASTProp": // Form ~P ... return ~P
return(ast);
case "ASTOpUnary": // Form ~(~P) - double negation ... return Convert(P)
return(Convert((p as ASTOpUnary).ast));
case "ASTOpBinary":
opBin = (ASTOpBinary)p;
Language.Symbol op = opBin.value;
if (op != Language.Symbol.E && op != Language.Symbol.OU)
{ // Not yet in CNF.
AST pInNcf = Convert(p);
return(Convert(new ASTOpUnary(pInNcf, Language.Symbol.NAO)));
}
AST left = new ASTOpUnary(opBin.left, Language.Symbol.NAO);
AST right = new ASTOpUnary(opBin.right, Language.Symbol.NAO);
Language.Symbol deMorganOp = Language.Symbol.INVALIDO;
if (opBin.value == Language.Symbol.E)
{
// Form ~(P&Q): from DeMorgan's Law, return Convert(~P|~Q)
deMorganOp = Language.Symbol.OU;
}
else if (opBin.value == Language.Symbol.OU)
{
// Form ~(P|Q): from DeMorgan's Law, return Convert(~P&~Q)
deMorganOp = Language.Symbol.E;
}
return(Convert(new ASTOpBinary(left, right, deMorganOp)));
}
break;
}
return(null);
}
// transitional constructor
public BinaryOperation(ASTOpBinary ast)
{
Left = Proposition.FromAST(ast.left);
Right = Proposition.FromAST(ast.right);
}
