#!perl -w
use strict;
use re 'eval';

# Validation of arithmetic expressions like +1*(2-3/(4*5))
# Author: Serge Melnikov (www.cronc.com)
 
my @testexpr=(
# Valid arithmetic expressions:
'+3',
'-(3/4+(-2-3)/3)',
'(-((3)))',
'-(+1+2)*(3/(1-2))/((-3))',
# Invalid (from the point of view of a human or mathematical notation) arithmetic expressions:
'2*-3',           # in math we must write 2*(-3)
'-(3/4+(-2-3)/3',
'(-((3)+))');
 
my $number=qr/\d+/; # the regex for a term (number/variable/function call)
my $arithm;
# The x modifier used only to split the long regex to publish it
$arithm=qr#[+-]?(?:$number|\((??{$arithm})\))(?:[*/](?:$number|\((??{$arithm})\)))*
   (?:[+-](?:$number|\((??{$arithm})\))(?:[*/](?:$number|\((??{$arithm})\)))*)*#x;
 
print /^$arithm$/ ? "Valid: $_\n" : "Invalid: $_\n" for (@testexpr);