ANTLR4 中的动态运算符令牌
Dynamic operator tokens in ANTLR4
我正在尝试用 ANTLR4 制作一个计算器,它可以使用几乎所有可能的符号作为数学运算符。
具体:
- 用户定义由运算符和优先级组成的操作。运算符可以是除某些系统符号(括号、逗号...)之外的任何符号组合。优先级是一个正整数。操作存储在 java HashMap 中。
- 共有三种不同类型的运算:左侧(一元减,...),右侧(阶乘,...)和二元(加法,...)
- 应该在运行时请求操作,以便在解析期间可以(取消)激活操作。如果这不可能,则应在创建解析器时请求运算符。
- 对于优先级:最好是完全动态优先级(在运行时请求遇到的操作的优先级),但如果不可能,则应该有不同的优先级预设。 (乘法、加法……)
我得到的:
- 操作员识别的工作代码
- 生成正确解析树但给出错误的优先级攀登代码:规则表达式失败谓词:(getPrecedence($op) >= $_p)?
更新:修复了操作员识别代码,并找到了优先爬升机制的代码
tokens { PREOP, POSTOP, BINOP, ERROR }
@lexer::members {
private static List<String> binaryOperators;
private static List<String> prefixOperators;
private static List<String> postfixOperators;
{
binaryOperators = new ArrayList<String>();
binaryOperators.add("+");
binaryOperators.add("*");
binaryOperators.add("-");
binaryOperators.add("/");
prefixOperators = new ArrayList<String>();
prefixOperators.add("-");
postfixOperators = new ArrayList<String>();
postfixOperators.add("!");
}
private Deque<Token> deque = new LinkedList<Token>();
private Token previousToken;
private Token nextToken;
@Override
public Token nextToken() {
if (!deque.isEmpty()) {
return previousToken = deque.pollFirst();
}
Token next = super.nextToken();
if (next.getType() != SYMBOL) {
return previousToken = next;
}
StringBuilder builder = new StringBuilder();
while (next.getType() == SYMBOL) {
builder.append(next.getText());
next = super.nextToken();
}
deque.addLast(nextToken = next);
List<Token> tokens = findOperatorCombination(builder.toString(), getOperatorType());
for (int i = tokens.size() - 1; i >= 0; i--) {
deque.addFirst(tokens.get(i));
}
return deque.pollFirst();
}
private static List<Token> findOperatorCombination(String sequence, OperatorType type) {
switch (type) {
case POSTFIX:
return getPostfixCombination(sequence);
case PREFIX:
return getPrefixCombination(sequence);
case BINARY:
return getBinaryCombination(sequence);
default:
break;
}
return null;
}
private static List<Token> getPrefixCombination(String sequence) {
if (isPrefixOperator(sequence)) {
List<Token> seq = new ArrayList<Token>(1);
seq.add(0, new CommonToken(MathParser.PREOP, sequence));
return seq;
}
if (sequence.length() <= 1) {
return null;
}
for (int i = 1; i < sequence.length(); i++) {
List<Token> seq1 = getPrefixCombination(sequence.substring(0, i));
List<Token> seq2 = getPrefixCombination(sequence.substring(i, sequence.length()));
if (seq1 != null & seq2 != null) {
seq1.addAll(seq2);
return seq1;
}
}
return null;
}
private static List<Token> getPostfixCombination(String sequence) {
if (isPostfixOperator(sequence)) {
List<Token> seq = new ArrayList<Token>(1);
seq.add(0, new CommonToken(MathParser.POSTOP, sequence));
return seq;
}
if (sequence.length() <= 1) {
return null;
}
for (int i = 1; i < sequence.length(); i++) {
List<Token> seq1 = getPostfixCombination(sequence.substring(0, i));
List<Token> seq2 = getPostfixCombination(sequence.substring(i, sequence.length()));
if (seq1 != null && seq2 != null) {
seq1.addAll(seq2);
return seq1;
}
}
return null;
}
private static List<Token> getBinaryCombination(String sequence) {
for (int i = 0; i < sequence.length(); i++) { // i is number of postfix spaces
for (int j = 0; j < sequence.length() - i; j++) { // j is number of prefix spaces
String seqPost = sequence.substring(0, i);
List<Token> post = getPostfixCombination(seqPost);
String seqPre = sequence.substring(sequence.length()-j, sequence.length());
List<Token> pre = getPrefixCombination(seqPre);
String seqBin = sequence.substring(i, sequence.length()-j);
if ((post != null || seqPost.isEmpty()) &&
(pre != null || seqPre.isEmpty()) &&
isBinaryOperator(seqBin)) {
List<Token> res = new ArrayList<Token>();
if (post != null)
res.addAll(post);
res.add(new CommonToken(MathParser.BINOP, seqBin));
if (pre != null)
res.addAll(pre);
return res;
}
}
}
return null;
}
/**
* Returns the expected operator type based on the previous and next token
*/
private OperatorType getOperatorType() {
if (isValueEnd(previousToken.getType())) {
if (isValueStart(nextToken.getType())) {
return OperatorType.BINARY;
}
return OperatorType.POSTFIX;
}
return OperatorType.PREFIX;
}
private enum OperatorType { BINARY, PREFIX, POSTFIX };
/**
* Checks whether the given token is a token found at the start of value elements
* @param tokenType
* @return
*/
private static boolean isValueStart(int tokenType) {
return tokenType == MathParser.INT;
}
/**
* Checks whether the given token is a token found at the end of value elements
* @param tokenType
* @return
*/
private static boolean isValueEnd(int tokenType) {
return tokenType == MathParser.INT;
}
private static boolean isBinaryOperator(String operator) {
return binaryOperators.contains(operator);
}
private static boolean isPrefixOperator(String operator) {
return prefixOperators.contains(operator);
}
private static boolean isPostfixOperator(String operator) {
return postfixOperators.contains(operator);
}
}
优先爬升代码:
@parser::members {
static Map<String, Integer> precedenceMap = new HashMap<String, Integer>();
static {
precedenceMap.put("*", 2);
precedenceMap.put("+", 1);
precedenceMap.put("^", 4);
precedenceMap.put("-", 3);
precedenceMap.put("!", 5);
}
public static Integer getPrecedence(Token op) {
return precedenceMap.get(op.getText());
}
public static Integer getNextPrecedence(Token op) {
Integer p = getPrecedence(op);
if (op.getType() == PREOP) return p;
else if (op.getText().equals("^")) return p;
else if (op.getType() == BINOP) return p+1;
else if (op.getType() == POSTOP) return p+1;
throw new IllegalArgumentException(op.getText());
}
}
prog
: expr[0]
;
expr [int _p]
: aexpr
( {getPrecedence(_input.LT(1)) >= $_p}? op=BINOP expr[getNextPrecedence($op)]
| {getPrecedence(_input.LT(1)) >= $_p}? POSTOP
)*
;
atom
: INT
| '(' expr[0] ')'
| op=PREOP expr[getNextPrecedence($op)]
;
所以现在的问题是如何处理这个谓词失败错误
您无法在运行时为 Antlr 定义 precedence/associativity 规则。但是,您可以将所有运算符(语言内置或用户定义的)解析为解析中的单个链表(如 ArrayList<>
),然后应用您自己的优先级和关联性算法在访问者中(或者在语法操作中,如果你真的想要的话)。
如果多次迭代列表,算法本身并不难。例如,您可以首先获取列表中每个运算符的优先级,然后检查具有最高优先级的那个,看看它是右结合还是左结合,然后从那里构建您的第一个(最底部的)树节点。继续应用,直到列表为空,并且您已经构建了自己的 "parse tree",但没有解析(您不再使用抽象输入字符串)。
或者,在运行时使外部调用 Antlr 编译 .g4
并调用 javac
编译生成的 Antlr 代码,然后使用反射调用它。然而,它可能要慢得多,而且可以说更难实现。
根据某些符号优先级的运行时定义,'correctly' 可以使用的解析器规则是可能的。虽然最初看起来不是一个惯用的选择,但将语义分析从解析器中延迟出来的标准替代方案会产生非常差的解析树——这使它成为标准设计规则的合理例外。
在(过于简化的)形式中,解析器规则为:
expr : LParen expr RParen # group
| expr Symbol expr # binary
| expr Symbol # postfix
| Symbol expr # prefix
| Int+ # value
;
要消除歧义,请添加内联谓词:
expr : LParen expr RParen # group
| expr s=Symbol { binary($s) }? expr # binary
| expr s=Symbol { postfix($s) }? # postfix
| s=Symbol { prefix($s) }? expr # prefix
| Int+ # value
;
对于任何给定的 Symbol,单个谓词方法的计算结果应为真。
扩展到多个 Symbol 字符串会增加一些复杂性(例如,将二进制与后缀后跟前缀区分开来),但机制基本保持不变。
我认为你的方法是正确的。我建议使用以下语法:
grammar Op;
options {
superClass=PrecedenceParser;
}
prog : expr[0] ;
expr[int _p] locals[Token op]: INT ({$op = _input.LT(1);} {getPrecedence($op) >= $_p}? OP expr[getPrecedence($op)])*;
INT : ( '0'..'9' )+ ;
OP : '+' | '*'; // all allowed symbols, should be extended
WS : [ \t\r\n]+ -> skip ; // skip spaces, tabs, newlines
op 规则应包含所有允许的运算符符号。我对 +
和 *
的限制只是为了简单起见。解析器 super class 将是:
public abstract class PrecedenceParser extends Parser {
private Map<String, Integer> precedences;
public PrecedenceParser(TokenStream input) {
super(input);
this.precedences = new HashMap<>();
}
public PrecedenceParser putOperator(String op, int p) {
precedences.put(op, p);
return this;
}
public int getPrecedence(Token operator) {
Integer p = precedences.get(operator.getText());
if (p == null) {
return Integer.MAX_VALUE;
} else {
return p;
}
}
}
结果
优先{+ : 4, * : 3 }
(prog (expr 1 + (expr 2) * (expr 3 + (expr 4))))
优先{+ : 3, * : 4 }
(prog (expr 1 + (expr 2 * (expr 3) + (expr 4))))
从左到右评估这些序列等同于按优先顺序评估它们。
这种方法应该适用于更大的运算符集。 ANTLR4 在内部将这种方法用于优先级攀升,但 ANTLR 使用常量而不是优先级映射(因为它假定优先级是在解析器构建时确定的)。
感谢其他贡献者,我找到了一个完整的(实际上相当干净的)解决方案来解决我的问题。
运算符匹配:
通过查看遇到的一系列符号前后的标记,可以检测运算符的固定性。之后,应用一种算法来检测符号系列中的一系列有效运算符。然后将这些令牌注入令牌流(在 nextToken() 中)。
只需确保在 SYMBOL 定义之前定义所有硬编码标记即可。
优先级攀升:
其实这并不难,它与ANTLR4 的内部策略完全相同。
grammar Math;
tokens { PREOP, POSTOP, BINOP, ERROR }
@header {
import java.util.*;
}
@lexer::members {
private static List<String> binaryOperators;
private static List<String> prefixOperators;
private static List<String> postfixOperators;
{
binaryOperators = new ArrayList<String>();
binaryOperators.add("+");
binaryOperators.add("*");
binaryOperators.add("-");
binaryOperators.add("/");
System.out.println(binaryOperators);
prefixOperators = new ArrayList<String>();
prefixOperators.add("-");
System.out.println(prefixOperators);
postfixOperators = new ArrayList<String>();
postfixOperators.add("!");
System.out.println(postfixOperators);
}
private Deque<Token> deque = new LinkedList<Token>();
private Token previousToken;
private Token nextToken;
@Override
public Token nextToken() {
if (!deque.isEmpty()) {
return previousToken = deque.pollFirst();
}
Token next = super.nextToken();
if (next.getType() != SYMBOL) {
return previousToken = next;
}
StringBuilder builder = new StringBuilder();
while (next.getType() == SYMBOL) {
builder.append(next.getText());
next = super.nextToken();
}
deque.addLast(nextToken = next);
List<Token> tokens = findOperatorCombination(builder.toString(), getOperatorType());
for (int i = tokens.size() - 1; i >= 0; i--) {
deque.addFirst(tokens.get(i));
}
return deque.pollFirst();
}
private static List<Token> findOperatorCombination(String sequence, OperatorType type) {
switch (type) {
case POSTFIX:
return getPostfixCombination(sequence);
case PREFIX:
return getPrefixCombination(sequence);
case BINARY:
return getBinaryCombination(sequence);
default:
break;
}
return null;
}
private static List<Token> getPrefixCombination(String sequence) {
if (isPrefixOperator(sequence)) {
List<Token> seq = new ArrayList<Token>(1);
seq.add(0, new CommonToken(MathParser.PREOP, sequence));
return seq;
}
if (sequence.length() <= 1) {
return null;
}
for (int i = 1; i < sequence.length(); i++) {
List<Token> seq1 = getPrefixCombination(sequence.substring(0, i));
List<Token> seq2 = getPrefixCombination(sequence.substring(i, sequence.length()));
if (seq1 != null & seq2 != null) {
seq1.addAll(seq2);
return seq1;
}
}
return null;
}
private static List<Token> getPostfixCombination(String sequence) {
if (isPostfixOperator(sequence)) {
List<Token> seq = new ArrayList<Token>(1);
seq.add(0, new CommonToken(MathParser.POSTOP, sequence));
return seq;
}
if (sequence.length() <= 1) {
return null;
}
for (int i = 1; i < sequence.length(); i++) {
List<Token> seq1 = getPostfixCombination(sequence.substring(0, i));
List<Token> seq2 = getPostfixCombination(sequence.substring(i, sequence.length()));
if (seq1 != null && seq2 != null) {
seq1.addAll(seq2);
return seq1;
}
}
return null;
}
private static List<Token> getBinaryCombination(String sequence) {
for (int i = 0; i < sequence.length(); i++) { // i is number of postfix spaces
for (int j = 0; j < sequence.length() - i; j++) { // j is number of prefix spaces
String seqPost = sequence.substring(0, i);
List<Token> post = getPostfixCombination(seqPost);
String seqPre = sequence.substring(sequence.length()-j, sequence.length());
List<Token> pre = getPrefixCombination(seqPre);
String seqBin = sequence.substring(i, sequence.length()-j);
if ((post != null || seqPost.isEmpty()) &&
(pre != null || seqPre.isEmpty()) &&
isBinaryOperator(seqBin)) {
List<Token> res = new ArrayList<Token>();
if (post != null)
res.addAll(post);
res.add(new CommonToken(MathParser.BINOP, seqBin));
if (pre != null)
res.addAll(pre);
return res;
}
}
}
return null;
}
/**
* Returns the expected operator type based on the previous and next token
*/
private OperatorType getOperatorType() {
if (isAfterAtom()) {
if (isBeforeAtom()) {
return OperatorType.BINARY;
}
return OperatorType.POSTFIX;
}
return OperatorType.PREFIX;
}
private enum OperatorType { BINARY, PREFIX, POSTFIX };
/**
* Checks whether the current token is a token found at the start of atom elements
* @return
*/
private boolean isBeforeAtom() {
int tokenType = nextToken.getType();
return tokenType == MathParser.INT ||
tokenType == MathParser.PLEFT;
}
/**
* Checks whether the current token is a token found at the end of atom elements
* @return
*/
private boolean isAfterAtom() {
int tokenType = previousToken.getType();
return tokenType == MathParser.INT ||
tokenType == MathParser.PRIGHT;
}
private static boolean isBinaryOperator(String operator) {
return binaryOperators.contains(operator);
}
private static boolean isPrefixOperator(String operator) {
return prefixOperators.contains(operator);
}
private static boolean isPostfixOperator(String operator) {
return postfixOperators.contains(operator);
}
}
@parser::members {
static Map<String, Integer> precedenceMap = new HashMap<String, Integer>();
static {
precedenceMap.put("*", 2);
precedenceMap.put("+", 1);
precedenceMap.put("^", 4);
precedenceMap.put("-", 3);
precedenceMap.put("!", 5);
}
public static Integer getPrecedence(Token op) {
return precedenceMap.get(op.getText());
}
public static Integer getNextPrecedence(Token op) {
Integer p = getPrecedence(op);
if (op.getType() == PREOP) return p;
else if (op.getText().equals("^")) return p;
else if (op.getType() == BINOP) return p+1;
throw new IllegalArgumentException(op.getText());
}
}
prog
: expr[0]
;
expr [int _p]
: atom
( {getPrecedence(_input.LT(1)) >= $_p}? op=BINOP expr[getNextPrecedence($op)]
| {getPrecedence(_input.LT(1)) >= $_p}? POSTOP
)*
;
atom
: INT
| PLEFT expr[0] PRIGHT
| op=PREOP expr[getNextPrecedence($op)]
;
INT
: ( '0'..'9' )+
;
PLEFT : '(' ;
PRIGHT : ')' ;
WS
: [ \t\r\n]+ -> skip ; // skip spaces, tabs, newlines
SYMBOL
: .
;
注意:代码是示例,不是我的真实代码(运算符和优先级将在外部请求)