很久以前，我制定了自己的解析算法，这在任何有关解析的书（例如《龙书》）中都找不到。查看指向Shunting Yard算法的指针，我确实看到了相似之处。
大约2年前，我在http://www.perlmonks.org/?node_id=554516上发布了有关Perl源代码的文章。。移植到其他语言很容易：我做的第一个实现是在Z80汇编器中。
它是使用数字直接计算的理想选择，但是如果需要，您可以使用它来生成解析树。
更新资料因为更多的人可以阅读（或运行）Javascript，所以在重新组织代码之后，我在Javascript中重新实现了解析器。整个解析器使用的Java代码不足5k（解析器大约100行，包装函数大约15行），包括错误报告和注释。
您可以在http://users.telenet.be/bartl/expressionParser/expressionParser.html上找到实时演示。
// operator table
var ops = {
'+' : {op: '+', precedence: 10, assoc: 'L', exec: function(l,r) { return l+r; } },
'-' : {op: '-', precedence: 10, assoc: 'L', exec: function(l,r) { return l-r; } },
'*' : {op: '*', precedence: 20, assoc: 'L', exec: function(l,r) { return l*r; } },
'/' : {op: '/', precedence: 20, assoc: 'L', exec: function(l,r) { return l/r; } },
'**' : {op: '**', precedence: 30, assoc: 'R', exec: function(l,r) { return Math.pow(l,r); } }
};
// constants or variables
var vars = { e: Math.exp(1), pi: Math.atan2(1,1)*4 };
// input for parsing
// var r = { string: '123.45+33*8', offset: 0 };
// r is passed by reference: any change in r.offset is returned to the caller
// functions return the parsed/calculated value
function parseVal(r) {
var startOffset = r.offset;
var value;
var m;
// floating point number
// example of parsing ("lexing") without aid of regular expressions
value = 0;
while("0123456789".indexOf(r.string.substr(r.offset, 1)) >= 0 && r.offset < r.string.length) r.offset++;
if(r.string.substr(r.offset, 1) == ".") {
r.offset++;
while("0123456789".indexOf(r.string.substr(r.offset, 1)) >= 0 && r.offset < r.string.length) r.offset++;
}
if(r.offset > startOffset) { // did that work?
// OK, so I'm lazy...
return parseFloat(r.string.substr(startOffset, r.offset-startOffset));
} else if(r.string.substr(r.offset, 1) == "+") { // unary plus
r.offset++;
return parseVal(r);
} else if(r.string.substr(r.offset, 1) == "-") { // unary minus
r.offset++;
return negate(parseVal(r));
} else if(r.string.substr(r.offset, 1) == "(") { // expression in parens
r.offset++; // eat "("
value = parseExpr(r);
if(r.string.substr(r.offset, 1) == ")") {
r.offset++;
return value;
}
r.error = "Parsing error: ')' expected";
throw 'parseError';
} else if(m = /^[a-z_][a-z0-9_]*/i.exec(r.string.substr(r.offset))) { // variable/constant name
// sorry for the regular expression, but I'm too lazy to manually build a varname lexer
var name = m[0]; // matched string
r.offset += name.length;
if(name in vars) return vars[name]; // I know that thing!
r.error = "Semantic error: unknown variable '" + name + "'";
throw 'unknownVar';
} else {
if(r.string.length == r.offset) {
r.error = 'Parsing error at end of string: value expected';
throw 'valueMissing';
} else {
r.error = "Parsing error: unrecognized value";
throw 'valueNotParsed';
}
}
}
function negate (value) {
return -value;
}
function parseOp(r) {
if(r.string.substr(r.offset,2) == '**') {
r.offset += 2;
return ops['**'];
}
if("+-*/".indexOf(r.string.substr(r.offset,1)) >= 0)
return ops[r.string.substr(r.offset++, 1)];
return null;
}
function parseExpr(r) {
var stack = [{precedence: 0, assoc: 'L'}];
var op;
var value = parseVal(r); // first value on the left
for(;;){
op = parseOp(r) || {precedence: 0, assoc: 'L'};
while(op.precedence < stack[stack.length-1].precedence ||
(op.precedence == stack[stack.length-1].precedence && op.assoc == 'L')) {
// precedence op is too low, calculate with what we've got on the left, first
var tos = stack.pop();
if(!tos.exec) return value; // end reached
// do the calculation ("reduce"), producing a new value
value = tos.exec(tos.value, value);
}
// store on stack and continue parsing ("shift")
stack.push({op: op.op, precedence: op.precedence, assoc: op.assoc, exec: op.exec, value: value});
value = parseVal(r); // value on the right
}
}
function parse (string) { // wrapper
var r = {string: string, offset: 0};
try {
var value = parseExpr(r);
if(r.offset < r.string.length){
r.error = 'Syntax error: junk found at offset ' + r.offset;
throw 'trailingJunk';
}
return value;
} catch(e) {
alert(r.error + ' (' + e + '):\n' + r.string.substr(0, r.offset) + '<*>' + r.string.substr(r.offset));
return;
}
}