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*
* Figure 7.7 A BNF (Backus-Naur Form) grammar of sentences in propositional
* logic, along with operator precedences, from highest to lowest.
*
* Note (1): While the book states 'We use symbols that start with an upper case
* letter and may contain other letters or subscripts' in this implementation we
* allow any legal java identifier to stand in for a proposition symbol.
*
* Note (2): This implementation is right associative (tends to be more
* intuitive for this language), for example:
*
*
* A & B & C & D
*
* will be parsed as:
*
* (A & (B & (C & D)))
*
*
*
* @author Ciaran O'Reilly
* @author Ravi Mohan
*
* @see SourceVersion#isIdentifier(CharSequence)
*/
public class PLParser extends Parser {
private PLLexer lexer = new PLLexer();
/**
* Default Constructor.
*/
public PLParser() {
}
@Override
public Lexer getLexer() {
return lexer;
}
//
// PROTECTED
//
@Override
protected Sentence parse() {
Sentence result = null;
ParseNode root = parseSentence(0);
if (root != null && root.node instanceof Sentence) {
result = (Sentence) root.node;
}
return result;
}
//
// PRIVATE
//
private ParseNode parseSentence(int level) {
List levelParseNodes = parseLevel(level);
ParseNode result = null;
// Now group up the tokens based on precedence order from highest to
// lowest.
levelParseNodes = groupSimplerSentencesByConnective(Connective.NOT,
levelParseNodes);
levelParseNodes = groupSimplerSentencesByConnective(Connective.AND,
levelParseNodes);
levelParseNodes = groupSimplerSentencesByConnective(Connective.OR,
levelParseNodes);
levelParseNodes = groupSimplerSentencesByConnective(
Connective.IMPLICATION, levelParseNodes);
levelParseNodes = groupSimplerSentencesByConnective(
Connective.BICONDITIONAL, levelParseNodes);
// At this point there should just be the root formula
// for this level.
if (levelParseNodes.size() == 1
&& levelParseNodes.get(0).node instanceof Sentence) {
result = levelParseNodes.get(0);
} else {
// Did not identify a root sentence for this level,
// therefore throw an exception indicating the problem.
throw new ParserException("Unable to correctly parse sentence: "
+ levelParseNodes, getTokens(levelParseNodes));
}
return result;
}
private List groupSimplerSentencesByConnective(
Connective connectiveToConstruct, List parseNodes) {
List newParseNodes = new ArrayList();
int numSentencesMade = 0;
// Go right to left in order to make right associative,
// which is a natural default for propositional logic
for (int i = parseNodes.size() - 1; i >= 0; i--) {
ParseNode parseNode = parseNodes.get(i);
if (parseNode.node instanceof Connective) {
Connective tokenConnective = (Connective) parseNode.node;
if (tokenConnective == Connective.NOT) {
// A unary connective
if (i + 1 < parseNodes.size()
&& parseNodes.get(i + 1).node instanceof Sentence) {
if (tokenConnective == connectiveToConstruct) {
ComplexSentence newSentence = new ComplexSentence(
connectiveToConstruct,
(Sentence) parseNodes.get(i + 1).node);
parseNodes.set(i, new ParseNode(newSentence,
parseNode.token));
parseNodes.set(i + 1, null);
numSentencesMade++;
}
} else {
throw new ParserException(
"Unary connective argurment is not a sentence at input position "
+ parseNode.token
.getStartCharPositionInInput(),
parseNode.token);
}
} else {
// A Binary connective
if ((i - 1 >= 0 && parseNodes.get(i - 1).node instanceof Sentence)
&& (i + 1 < parseNodes.size() && parseNodes
.get(i + 1).node instanceof Sentence)) {
// A binary connective
if (tokenConnective == connectiveToConstruct) {
ComplexSentence newSentence = new ComplexSentence(
connectiveToConstruct,
(Sentence) parseNodes.get(i - 1).node,
(Sentence) parseNodes.get(i + 1).node);
parseNodes.set(i - 1, new ParseNode(newSentence,
parseNode.token));
parseNodes.set(i, null);
parseNodes.set(i + 1, null);
numSentencesMade++;
}
} else {
throw new ParserException(
"Binary connective argurments are not sentences at input position "
+ parseNode.token
.getStartCharPositionInInput(),
parseNode.token);
}
}
}
}
for (int i = 0; i < parseNodes.size(); i++) {
ParseNode parseNode = parseNodes.get(i);
if (parseNode != null) {
newParseNodes.add(parseNode);
}
}
// Ensure no tokens left unaccounted for in this pass.
int toSubtract = 0;
if (connectiveToConstruct == Connective.NOT) {
toSubtract = (numSentencesMade * 2) - numSentencesMade;
} else {
toSubtract = (numSentencesMade * 3) - numSentencesMade;
}
if (parseNodes.size() - toSubtract != newParseNodes.size()) {
throw new ParserException(
"Unable to construct sentence for connective: "
+ connectiveToConstruct + " from: " + parseNodes,
getTokens(parseNodes));
}
return newParseNodes;
}
private List parseLevel(int level) {
List tokens = new ArrayList();
while (lookAhead(1).getType() != LogicTokenTypes.EOI
&& lookAhead(1).getType() != LogicTokenTypes.RPAREN
&& lookAhead(1).getType() != LogicTokenTypes.RSQRBRACKET) {
if (detectConnective()) {
tokens.add(parseConnective());
} else if (detectAtomicSentence()) {
tokens.add(parseAtomicSentence());
} else if (detectBracket()) {
tokens.add(parseBracketedSentence(level));
}
}
if (level > 0 && lookAhead(1).getType() == LogicTokenTypes.EOI) {
throw new ParserException(
"Parser Error: end of input not expected at level " + level,
lookAhead(1));
}
return tokens;
}
private boolean detectConnective() {
return lookAhead(1).getType() == LogicTokenTypes.CONNECTIVE;
}
private ParseNode parseConnective() {
Token token = lookAhead(1);
Connective connective = Connective.get(token.getText());
consume();
return new ParseNode(connective, token);
}
private boolean detectAtomicSentence() {
int type = lookAhead(1).getType();
return type == LogicTokenTypes.TRUE || type == LogicTokenTypes.FALSE
|| type == LogicTokenTypes.SYMBOL;
}
private ParseNode parseAtomicSentence() {
Token t = lookAhead(1);
if (t.getType() == LogicTokenTypes.TRUE) {
return parseTrue();
} else if (t.getType() == LogicTokenTypes.FALSE) {
return parseFalse();
} else if (t.getType() == LogicTokenTypes.SYMBOL) {
return parseSymbol();
} else {
throw new ParserException(
"Error parsing atomic sentence at position "
+ t.getStartCharPositionInInput(), t);
}
}
private ParseNode parseTrue() {
Token token = lookAhead(1);
consume();
return new ParseNode(new PropositionSymbol(PropositionSymbol.TRUE_SYMBOL),
token);
}
private ParseNode parseFalse() {
Token token = lookAhead(1);
consume();
return new ParseNode(new PropositionSymbol(PropositionSymbol.FALSE_SYMBOL),
token);
}
private ParseNode parseSymbol() {
Token token = lookAhead(1);
String sym = token.getText();
consume();
return new ParseNode(new PropositionSymbol(sym), token);
}
private boolean detectBracket() {
return lookAhead(1).getType() == LogicTokenTypes.LPAREN
|| lookAhead(1).getType() == LogicTokenTypes.LSQRBRACKET;
}
private ParseNode parseBracketedSentence(int level) {
Token startToken = lookAhead(1);
String start = "(";
String end = ")";
if (startToken.getType() == LogicTokenTypes.LSQRBRACKET) {
start = "[";
end = "]";
}
match(start);
ParseNode bracketedSentence = parseSentence(level + 1);
match(end);
return bracketedSentence;
}
private Token[] getTokens(List parseNodes) {
Token[] result = new Token[parseNodes.size()];
for (int i = 0; i < parseNodes.size(); i++) {
result[i] = parseNodes.get(i).token;
}
return result;
}
private class ParseNode {
public Object node = null;
public Token token = null;
public ParseNode(Object node, Token token) {
this.node = node;
this.token = token;
}
public String toString() {
return node.toString() + " at "
+ token.getStartCharPositionInInput();
}
}
}
