我怎样才能有一个“隐式乘法"?野牛统治?

问题描述

我正在为数学表达式解析器开发Bison文件.到目前为止，基本上都还可以，但是我面临着隐式乘法的问题.

I'm working on a Bison file for a mathematical expression parser. Up to now it's mostly fine, but I'm facing a problem with implicit multiplications.

您知道，我想支持2x sin(4x) cos(4x)之类的表达式.它应该像2 * x * sin(4 * x) * cos(4 * x)一样进行解析.这里没什么不好的，但是请考虑以下规则:

You see, I'd like to support expressions like 2x sin(4x) cos(4x). It should parse like 2 * x * sin(4 * x) * cos(4 * x). Nothing too bad here, but consider the following set of rules:

expr
    : /* snip */
    | '-' expr      { /* negate expression */ }
    | expr '-' expr { /* subtract expressions */ }
    | expr expr     { /* multiply expressions */ }

具有该隐式乘法规则会与减法规则产生歧义:x - log(x)是log(x)减去x还是x乘-log(x)?

Having that implicit multiplication rule creates an ambiguity with the subtraction rule: is x - log(x) the subtraction of log(x) to x or the multiplication of x by -log(x)?

我愿意准备一个简单的解决方案，例如除非减去，否则就是乘法"，但我不知道该如何告诉野牛.

I'd be ready to settle for an easy solution, like "it's a multiplication unless it's subtracting", but I don't know how to tell that to Bison.

推荐答案

甚至是x - l * o * g * x?或者只是x - log * x?

所以不是一个简单的问题.假设您仅通过查看log就能知道它是一个函数.然后，您可以在词法分析器中消除歧义，然后剩下如果有疑问，看起来像中缀运算符的运算符就是中缀运算符".这是一个快速的解决方案:

So not quite a simple problem. Suppose you can tell just by looking at log that it is a function. Then you can disambiguate in your lexer, and you're left with "in case of doubt, an operator that looks like an infix operator is an infix operator". Here's a quick solution:

term   : ID
       | NUMBER
       | '(' expr ')'      { $$ = $2; }
       | FUNC '(' expr ')' { $$ = new_expr($1, 'c', $3); }
       ;

factor : term
       | term factor       { $$ = new_expr($1, '*', $2); }
       ;

prefix : factor
       | '-' factor        { $$ = new_expr(0, '-', $2); }
       ;

muldiv : prefix
       | muldiv '/' prefix { $$ = new_expr($1, '/', $3); }
       | muldiv '*' prefix { $$ = new_expr($1, '*', $3); }
       ;

expr   : muldiv
       | expr '+' muldiv { $$ = new_expr($1, '+', $3); }
       | expr '-' muldiv { $$ = new_expr($1, '-', $3); }
       ;

这个特殊的语法不允许--x，尽管它对y--x非常满意，这意味着y-(-x).如果您要接受--x，则可以将第二个prefix生产更改为'-' prefix.

This particular grammar disallows --x, although it's perfectly happy with y--x, which means y-(-x). If you want to accept --x, you could change the second prefix production to '-' prefix.

就我个人而言，我更希望能够键入sin 2x和log 3n，但这开始变得有些棘手. sin 2x cos 2x是什么意思?大概是(sin(2*x))*(cos(2*x)).但是log nlog n并不意味着log(n*log(n))吗?这一切都可以实现；它只需要考虑所有可能性.

Personally, I'd prefer to be able to type sin 2x and log 3n but that starts to get a bit tricky. What does sin 2x cos 2x mean? Presumably, it means (sin(2*x))*(cos(2*x)). But does log nlog n not mean log(n*log(n)) ? This can all be achieved; it just requires thinking through all the possibilities.

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