Matching math expression with regular expression?

Question

For example, these are valid math expressions:

a * b + c
-a * (b / 1.50)
(apple + (-0.5)) * (boy - 1)

And these are invalid math expression

Answer 1

This is tricky with one single regular expression, but quite easy using mixed regexp/procedural approach. The idea is to construct a regexp for the simple expression (without parenthesis) and then repeatedly replace ( simple-expression ) with some atomic string (e.g. identifier). If the final reduced expression matches the same `simple' pattern, the original expression is considered valid.

Illustration (in php).

function check_syntax($str) {

    // define the grammar
    $number = "\d+(\.\d+)?";
    $ident  = "[a-z]\w*";
    $atom   = "[+-]?($number|$ident)";
    $op     = "[+*/-]";
    $sexpr  = "$atom($op$atom)*"; // simple expression

    // step1. remove whitespace
    $str = preg_replace('~\s+~', '', $str);

    // step2. repeatedly replace parenthetic expressions with 'x'
    $par = "~\($sexpr\)~";
    while(preg_match($par, $str))
        $str = preg_replace($par, 'x', $str);

    // step3. no more parens, the string must be simple expression
    return preg_match("~^$sexpr$~", $str);
}


$tests = array(
    "a * b + c",
    "-a * (b / 1.50)",
    "(apple + (-0.5)) * (boy - 1)",
    "--a *+ b @ 1.5.0",
    "-a * b + 1)",
    "a) * (b + c) / (d",
);

foreach($tests as $t)
    echo $t, "=", check_syntax($t) ? "ok" : "nope", "\n";

The above only validates the syntax, but the same technique can be also used to construct a real parser.