Regular expressions to parse arithmetic expression

Question

Hello,
I would like to parse arithmetic expressions like the following
"5.2 + cos($PI/2) * -5"where valid expression entities are numbers, operations, variables and paranthesis. Until now I have figured out some regular expressions to match every type of entities that I need, and combine them into one big regex supplied to a pattern and matcher. I will paste some code now to see what I wrote:
public class RegexTest {
    /** A regular expression matching numeric expressions (floating point numbers) */
    private static final String REGEX_NUMERIC = "(-?[0-9]+([0-9]*|[\\.]?[0-9]+))";
    /** A regular expression matching a valid variable name */
    private static final String REGEX_VARIABLE = "(\\$[a-zA-Z][a-zA-Z0-9]*)";
    /** A regular expression matching a valid operation string */
    public static final String REGEX_OPERATION = "(([a-zA-Z][a-zA-Z0-9]+)|([\\*\\/\\+\\-\\|\\?\\:\\@\\&\\^<>'`=%#]{1,2}))";
    /** A regular expression matching a valid paranthesis */
    private static final String REGEX_PARANTHESIS = "([\\(\\)])";
    public static void main(String[] args) {
        String s = "5.2 + cos($PI/2) * -5".replaceAll(" ", "");
        Pattern p = Pattern.compile(REGEX_OPERATION + "|" + REGEX_NUMERIC + "|" + REGEX_VARIABLE + "|" + REGEX_PARANTHESIS);
        Matcher m = p.matcher(s);
        while (m.find()) {
            System.out.println(m.group());
}The output is
5
2
+
cos
$PI
2
5There are a few problems:
1. It splits "5.2" into "5" and "2" instead of keeping it together (so there might pe a problem with REGEX_NUMERIC although "5.2".matches(REGEX_NUMERIC) returns true)
2. It interprets "... * -5" as the operation " *- " and the number "5" instead of " * " and "-5".
Any solution to solve these 2 problems are greately appreciated. Thank you in advance.
Radu Cosmin.

Answer 1

cosminr wrote:
So, I've written some concludent examples and the output after parsing (separated by " , " ):
String e1 = "abs(-5) + -3";
// output now: abs , ( , - , 5 , ) , + , - , 3 ,
// should be:  abs , ( , -5 , ) , + , - , 3 , (Notice the -5)
I presume that should also be "-3" instead of ["-", "3"].
String e2 = "sqrt(abs($x=1 + -10))";
// output now: sqrt , ( , abs , ( , $x , = , 1 , + , - , 10 , ) , ) ,
// should be:  sqrt , ( , abs , ( , $x , = , 1 , + , -10 , ) , ) ,   (Notice the -10)
String e3 = "$e * -1 + (2 - sqrt(4))";
// output now: $e , * , - , 1 , + , ( , 2 , - , sqrt , ( , 4 , ) , ) ,
// should be:  $e , * , -1 , + , ( , 2 , - , sqrt , ( , 4 , ) , ) ,
String e4 = "sin($PI/4) - 3";
// output now: sin , ( , $PI , / , 4 , ) , - , 3 , (This one is correct)
String e5 = "sin($PI/4) - -3 - (-4)";
// output now: sin , ( , $PI , / , 4 , ) , - , - , 3 , - , ( , - , 4 , ) ,
// should be:  sin , ( , $PI , / , 4 , ) , - , -3 , - , ( , -4 , ) ,  (Notice -3 and -4)I hope they are relevant, If not I will supply some more.I made a small change to REGEX_NUMERIC and also put REGEX_NUMERIC at the start of the "complete pattern" when the Matcher is created:
import java.util.regex.*;
class Test {
    private static final String REGEX_NUMERIC = "(((?<=[-+*/(])|(?<=^))-)?\\d+(\\.\\d+)?";
    private static final String REGEX_VARIABLE = "\\$[a-zA-Z][a-zA-Z0-9]*";
    public static final String REGEX_OPERATION = "[a-zA-Z][a-zA-Z0-9]+|[-*/+|?:@&^<>'`=%#]";
    private static final String REGEX_PARANTHESIS = "[()]";
    public static void main(String[] args) {
        String[] tests = {
            "abs(-5) + -3",
            "sqrt(abs($x=1 + -10))",
            "$e * -1 + (2 - sqrt(4))",
            "sin($PI/4) - 3",
            "sin($PI/4) - -3 - (-4)",
            "-2-4" // minus sign at the start of the expression
        Pattern p = Pattern.compile(REGEX_NUMERIC + "|" + REGEX_OPERATION + "|" + REGEX_VARIABLE + "|" + REGEX_PARANTHESIS);
        for(String s: tests) {
            s = s.replaceAll("\\s", "");
            Matcher m = p.matcher(s);
            System.out.printf("%-21s-->", s);
            while (m.find()) {
                System.out.printf("%6s", m.group());
            System.out.println();
}Note that since Java's regex engine does not support "variable length look behinds", you will need to remove the white spaces from your expression, otherwise REGEX_NUMERIC will go wrong if a String looks like this:
"1 - - 1"Good luck!