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。

c 复制代码

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：

解析：a+b+(c+d)*e*f+g;
进入函数时，ExprPrec为0，LHS是a。
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
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
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：【符号+数字】或【符号+(表达式)】

（外侧函数解析a）
解析+b
递归解析+(c+d)ef
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

c 复制代码

#include <cstdio>
#include <cstdlib>
#include <string>
#include <map>
#include <vector>
/*
 * 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,

  // commands
  tok_def = -2, tok_extern = -3,

  // primary
  tok_identifier = -4, tok_number = -5
};

static std::string IdentifierStr;  // Filled in if tok_identifier
static 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 ::= number
static ExprAST *ParseNumberExpr() {
  ExprAST *Result = new NumberExprAST(NumVal);
  getNextToken(); // consume the number
  return 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
///   ::= parenexpr
static 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 expression
static 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 ::= expression
static 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' prototype
static 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++14
CFLAGS = -g -O0 -I llvm/include -I llvm/build/include -I ./
LLVMFLAGS = `llvm-config --cxxflags --ldflags --system-libs --libs all`

.PHONY: main

main: main.cpp
	${CC} ${CFLAGS} ${LLVMFLAGS} $< -o $@

clean:
	rm -r main main.o

%.o: %.cpp
	${CC} ${CFLAGS} ${LLVMFLAGS} -c $< -o $@