不依赖yacc如何实现表达式按优先级解析

总结

无意发现一个非常有意思的简单语法解析器，不依赖lex/yacc，本文对其中比较难理解的表达式解析（带优先级）部分做一些分析和记录。

（理解本文需要调试后面的代码部分，have fun！）

理解表达式解析部分

这段代码的功能是解析a+b+(c+d)*e*f+g;，包含符号优先级处理的功能。

static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {// If this is a binop, find its precedence.while (1) {int TokPrec = GetTokPrecedence();// If this is a binop that binds at least as tightly as the current binop,// consume it, otherwise we are done.if (TokPrec < ExprPrec)return LHS;// Okay, we know this is a binop.int BinOp = CurTok;getNextToken();// eat binop// Parse the primary expression after the binary operator.ExprAST *RHS = ParsePrimary();if (!RHS) return 0;// If BinOp binds less tightly with RHS than the operator after RHS, let// the pending operator take RHS as its LHS.int NextPrec = GetTokPrecedence();if (TokPrec < NextPrec) {RHS = ParseBinOpRHS(TokPrec+1, RHS);if (RHS == 0) return 0;}// Merge LHS/RHS.LHS = new BinaryExprAST(BinOp, LHS, RHS);}}

解析流程：

1. 解析：a+b+(c+d)*e*f+g;
2. 进入函数时，ExprPrec为0，LHS是a。
3. 第一轮：解析+b
   1. TokPrec < ExprPrec 即 20 < 0：不退出递归
   2. TokPrec < NextPrec 即 20 < 20：不进入递归
   3. 符号+、RHS=b被合入LHS=a，LHS变为a+b
4. 第二轮：解析+(c+d)
   1. TokPrec < ExprPrec 即 20 < 0：不退出递归
   2. TokPrec < NextPrec 即 20 < 40：进入递归，当前RHS=(c+d)、符号为+
      1. 递归ParseBinOpRHS第一轮：当前LHS被设为外面的RHS=(c+d)，也就是(c+d)被当做后面乘号的左值了。
         1. 解析*e
         2. 进入后ExprPrec=21（因为加1后面在遇到+可以退出递归，后面在遇到比加号高的不会退出递归，很巧妙的做法），TokPrec < ExprPrec 即 40 < 21：不进入
         3. TokPrec < NextPrec 即 40 < 40：不退出递归
         4. 符号*、RHS=e被合入LHS=(c+d)，LHS变为(c+d)*e
      2. 递归ParseBinOpRHS第二轮：当前LHS变为(c+d)*e、符号为*
         1. TokPrec < ExprPrec 即 40 < 21：不退出递归
         2. TokPrec < NextPrec即 40 < 20：不进入递归
         3. 符号*、RHS=f被合入LHS=(c+d)*e，LHS变为(c+d)*e*f
      3. 递归ParseBinOpRHS第三轮：当前LHS变为(c+d)*e*f、符号为+
         1. TokPrec < ExprPrec 即 20 < 21：退出递归！（非常重要）
         2. 返回(c+d)*e*f
   3. 外层还在处理第二个加号，通过递归得到RHS=(c+d)*e*f
   4. 合并+、LHS=a+b、RHS=(c+d)*e*f得到：a+b+(c+d)*e*f
5. 第三轮：解析+g
   1. TokPrec < ExprPrec 即 20 < 0：不退出递归
   2. TokPrec < NextPrec 即 20 < 20：不进入递归
   3. 符号+、RHS=g被合入LHS=a+b+(c+d)*e*f，LHS变为a+b+(c+d)*e*f+g

解析流程总结：

a+b+(c+d)*e*f+g;的解析过程分了三部分，循环一次解析一组，一组的定义是：【符号+数字】或【符号+(表达式)】，也就是{+b}、{+(c+d)}、{*e}、{*f}、{+g}，解析每一组的时候，都是不断把rhs拼入lhs的过程，rhs到底是什么，需要判断是否递归解析，比如前面是+b+(c+d)*e，在解析第二个加号的时候，rhs就不能是(c+d)了，需要递归的把后面乘号也解了，rhs应该是(c+d)*e*f。

三步解析：

1. （外侧函数解析a）
2. 解析+b
3. 递归解析+(c+d)ef
4. 解析+g

整个解析流程就是不断把RHS拼到LHS中，最终返回LHS的过程。

中间比较重要的就是乘号和+号的优先级问题，上述代码中，进入递归的含义为：把优先级高于当前符号的所有后续表达式一块解析出来，直到遇到当前符号为止，那么这里就涉及递归进入条件和递归退出条件了：

• 递归进入条件：遇到的符号优先级比上一个符号高：if (TokPrec < NextPrec)
• 递归退出条件：遇到的符号优先级和上一个符号相同：if (TokPrec < ExprPrec)

假设当前符号为+遇到*后，TokPrec=20、NextPrec=40会进入递归。
假设当前符号为*遇到+后，TokPrec=20、ExprPrec=21会退出递归，而遇到*的话ExprPrec=40无法退出递归，代码比较巧妙，不容易理解。

语法解析器

gcc或clang编译均可，下面makefile是clang的。

main.c

#include #include #include #include #include /* * def foo(x y) x+foo(y, 4.0); ** def foo(x y) x+y y; ** def foo(x y) x+y ); ** extern sin(a); * * def foo(x y) a+b+(c+d)*e*f+g; *///===----------------------------------------------------------------------===//// Lexer//===----------------------------------------------------------------------===//// The lexer returns tokens [0-255] if it is an unknown character, otherwise one// of these for known things.enum Token {tok_eof = -1,// commandstok_def = -2, tok_extern = -3,// primarytok_identifier = -4, tok_number = -5};static std::string IdentifierStr;// Filled in if tok_identifierstatic double NumVal;// Filled in if tok_number/// gettok - Return the next token from standard input.static int gettok() {static int LastChar = ' ';// Skip any whitespace.while (isspace(LastChar))LastChar = getchar();if (isalpha(LastChar)) { // identifier: [a-zA-Z][a-zA-Z0-9]*IdentifierStr = LastChar;while (isalnum((LastChar = getchar())))IdentifierStr += LastChar;if (IdentifierStr == "def") return tok_def;if (IdentifierStr == "extern") return tok_extern;return tok_identifier;}if (isdigit(LastChar) || LastChar == '.') { // Number: [0-9.]+std::string NumStr;do {NumStr += LastChar;LastChar = getchar();} while (isdigit(LastChar) || LastChar == '.');NumVal = strtod(NumStr.c_str(), 0);return tok_number;}if (LastChar == '#') {// Comment until end of line.do LastChar = getchar();while (LastChar != EOF && LastChar != '\n' && LastChar != '\r');if (LastChar != EOF)return gettok();}// Check for end of file.Don't eat the EOF.if (LastChar == EOF)return tok_eof;// Otherwise, just return the character as its ascii value.int ThisChar = LastChar;LastChar = getchar();return ThisChar;}//===----------------------------------------------------------------------===//// Abstract Syntax Tree (aka Parse Tree)//===----------------------------------------------------------------------===///// ExprAST - Base class for all expression nodes.class ExprAST {public:virtual ~ExprAST() {}};/// NumberExprAST - Expression class for numeric literals like "1.0".class NumberExprAST : public ExprAST {double Val;public:NumberExprAST(double val) : Val(val) {}};/// VariableExprAST - Expression class for referencing a variable, like "a".class VariableExprAST : public ExprAST {std::string Name;public:VariableExprAST(const std::string &name) : Name(name) {}};/// BinaryExprAST - Expression class for a binary operator.class BinaryExprAST : public ExprAST {char Op;ExprAST *LHS, *RHS;public:BinaryExprAST(char op, ExprAST *lhs, ExprAST *rhs): Op(op), LHS(lhs), RHS(rhs) {}};/// CallExprAST - Expression class for function calls.class CallExprAST : public ExprAST {std::string Callee;std::vector<ExprAST*> Args;public:CallExprAST(const std::string &callee, std::vector<ExprAST*> &args): Callee(callee), Args(args) {}};/// PrototypeAST - This class represents the "prototype" for a function,/// which captures its name, and its argument names (thus implicitly the number/// of arguments the function takes).class PrototypeAST {std::string Name;std::vector<std::string> Args;public:PrototypeAST(const std::string &name, const std::vector<std::string> &args): Name(name), Args(args) {}};/// FunctionAST - This class represents a function definition itself.class FunctionAST {PrototypeAST *Proto;ExprAST *Body;public:FunctionAST(PrototypeAST *proto, ExprAST *body): Proto(proto), Body(body) {}};//===----------------------------------------------------------------------===//// Parser//===----------------------------------------------------------------------===///// CurTok/getNextToken - Provide a simple token buffer.CurTok is the current/// token the parser is looking at.getNextToken reads another token from the/// lexer and updates CurTok with its results.static int CurTok;static int getNextToken() {return CurTok = gettok();}/// BinopPrecedence - This holds the precedence for each binary operator that is/// defined.static std::map<char, int> BinopPrecedence;/// GetTokPrecedence - Get the precedence of the pending binary operator token.static int GetTokPrecedence() {if (!isascii(CurTok))return -1;// Make sure it's a declared binop.int TokPrec = BinopPrecedence[CurTok];if (TokPrec <= 0) return -1;return TokPrec;}/// Error* - These are little helper functions for error handling.ExprAST *Error(const char *Str) { fprintf(stderr, "Error: %s\n", Str);return 0;}PrototypeAST *ErrorP(const char *Str) { Error(Str); return 0; }FunctionAST *ErrorF(const char *Str) { Error(Str); return 0; }static ExprAST *ParseExpression();/// identifierexpr/// ::= identifier/// ::= identifier '(' expression* ')'static ExprAST *ParseIdentifierExpr() {std::string IdName = IdentifierStr;getNextToken();// eat identifier.if (CurTok != '(') // Simple variable ref.return new VariableExprAST(IdName);// Call.getNextToken();// eat (std::vector<ExprAST*> Args;if (CurTok != ')') {while (1) {ExprAST *Arg = ParseExpression();if (!Arg) return 0;Args.push_back(Arg);if (CurTok == ')') break;if (CurTok != ',')return Error("Expected ')' or ',' in argument list");getNextToken();}}// Eat the ')'.getNextToken();return new CallExprAST(IdName, Args);}/// numberexpr ::= numberstatic ExprAST *ParseNumberExpr() {ExprAST *Result = new NumberExprAST(NumVal);getNextToken(); // consume the numberreturn Result;}/// parenexpr ::= '(' expression ')'static ExprAST *ParseParenExpr() {getNextToken();// eat (.ExprAST *V = ParseExpression();if (!V) return 0;if (CurTok != ')')return Error("expected ')'");getNextToken();// eat ).return V;}/// primary/// ::= identifierexpr/// ::= numberexpr/// ::= parenexprstatic ExprAST *ParsePrimary() {switch (CurTok) {default: return Error("unknown token when expecting an expression");case tok_identifier: return ParseIdentifierExpr();case tok_number: return ParseNumberExpr();case '(':return ParseParenExpr();}}/// binoprhs/// ::= ('+' primary)*// 函数ParseBinOpRHS用于解析有序对列表（其中RHS是Right Hand Side的缩写，表示“右侧”；与此相对应，LHS表示“左侧”——译者注）。// 它的参数包括一个整数和一个指针，其中整数代表运算符优先级，指针则指向当前已解析出来的那部分表达式。注意，单独一个“x”也是合法的表达式：// 也就是说binoprhs有可能为空；碰到这种情况时，函数将直接返回作为参数传入的表达式。在上面的例子中，传入ParseBinOpRHS的表达式是“a”，当前语元是“+”。// 传入ParseBinOpRHS的优先级表示的是该函数所能处理的最低运算符优先级。假设语元流中的下一对是“[+, x]”，且传入ParseBinOpRHS的优先级是40，// 那么该函数将直接返回（因为“+”的优先级是20）。搞清楚这一点之后，我们再来看ParseBinOpRHS的定义，函数的开头是这样的：// a+b+(c+d)*e*f+g// a[+, b]、[+, (c+d)]、[*, e]、[*, f]和[+, g]static ExprAST *ParseBinOpRHS(int ExprPrec, ExprAST *LHS) {// If this is a binop, find its precedence.while (1) {int TokPrec = GetTokPrecedence();// If this is a binop that binds at least as tightly as the current binop,// consume it, otherwise we are done.if (TokPrec < ExprPrec)return LHS;// Okay, we know this is a binop.int BinOp = CurTok;getNextToken();// eat binop// Parse the primary expression after the binary operator.ExprAST *RHS = ParsePrimary();if (!RHS) return 0;// If BinOp binds less tightly with RHS than the operator after RHS, let// the pending operator take RHS as its LHS.int NextPrec = GetTokPrecedence();if (TokPrec < NextPrec) {RHS = ParseBinOpRHS(TokPrec+1, RHS);if (RHS == 0) return 0;}// Merge LHS/RHS.LHS = new BinaryExprAST(BinOp, LHS, RHS);}}/// expression/// ::= primary binoprhs///// def foo(x y) x+y y;// 这里开始解析x+y部分：static ExprAST *ParseExpression() {ExprAST *LHS = ParsePrimary();if (!LHS) return 0;return ParseBinOpRHS(0, LHS);}/// prototype/// ::= id '(' id* ')'static PrototypeAST *ParsePrototype() {if (CurTok != tok_identifier)return ErrorP("Expected function name in prototype");std::string FnName = IdentifierStr;getNextToken();if (CurTok != '(')return ErrorP("Expected '(' in prototype");std::vector<std::string> ArgNames;while (getNextToken() == tok_identifier)ArgNames.push_back(IdentifierStr);if (CurTok != ')')return ErrorP("Expected ')' in prototype");// success.getNextToken();// eat ')'.return new PrototypeAST(FnName, ArgNames);}/// definition ::= 'def' prototype expressionstatic FunctionAST *ParseDefinition() {getNextToken();// eat def.PrototypeAST *Proto = ParsePrototype();if (Proto == 0) return 0;if (ExprAST *E = ParseExpression())return new FunctionAST(Proto, E);return 0;}/// toplevelexpr ::= expressionstatic FunctionAST *ParseTopLevelExpr() {if (ExprAST *E = ParseExpression()) {// Make an anonymous proto.PrototypeAST *Proto = new PrototypeAST("", std::vector<std::string>());return new FunctionAST(Proto, E);}return 0;}/// external ::= 'extern' prototypestatic PrototypeAST *ParseExtern() {getNextToken();// eat extern.return ParsePrototype();}//===----------------------------------------------------------------------===//// Top-Level parsing//===----------------------------------------------------------------------===//static void HandleDefinition() {if (ParseDefinition()) {fprintf(stderr, "Parsed a function definition.\n");} else {// Skip token for error recovery.getNextToken();}}static void HandleExtern() {if (ParseExtern()) {fprintf(stderr, "Parsed an extern\n");} else {// Skip token for error recovery.getNextToken();}}static void HandleTopLevelExpression() {// Evaluate a top-level expression into an anonymous function.if (ParseTopLevelExpr()) {fprintf(stderr, "Parsed a top-level expr\n");} else {// Skip token for error recovery.getNextToken();}}/// top ::= definition | external | expression | ';'static void MainLoop() {while (1) {fprintf(stderr, "ready> ");switch (CurTok) {case tok_eof:return;case ';':getNextToken(); break;// ignore top-level semicolons.case tok_def:HandleDefinition(); break;case tok_extern: HandleExtern(); break;default: HandleTopLevelExpression(); break;}}}//===----------------------------------------------------------------------===//// Main driver code.//===----------------------------------------------------------------------===//int main() {// Install standard binary operators.// 1 is lowest precedence.BinopPrecedence['<'] = 10;BinopPrecedence['+'] = 20;BinopPrecedence['-'] = 20;BinopPrecedence['*'] = 40;// highest.// Prime the first token.fprintf(stderr, "ready> ");getNextToken();// Run the main "interpreter loop" now.MainLoop();return 0;}

Makefile

CC = llvm-g++ -stdlib=libc++ -std=c++14CFLAGS = -g -O0 -I llvm/include -I llvm/build/include -I ./LLVMFLAGS = `llvm-config --cxxflags --ldflags --system-libs --libs all`.PHONY: mainmain: main.cpp${CC} ${CFLAGS} ${LLVMFLAGS} $< -o $@clean:rm -r main main.o%.o: %.cpp${CC} ${CFLAGS} ${LLVMFLAGS} -c $< -o $@