Basic infix interpreter in Python.

infix.py

from operator import add, mul, sub, floordiv
import re

OPERATORS = {'*': mul, '+': add, '-': sub, '/': floordiv}

def parse(text, left=r'[(]', right=r'[)]', sep=r','):
    """ *** Based on https://stackoverflow.com/a/17141899/190597 (falsetru) ***
    >>> parse('1+2')
    ['1', '+', '2']
    >>> parse('(1+2)*(3-4)')
    [['1', '+', '2'], '*', ['3', '-', '4']]
    >>> parse('1000*(2+1)')
    ['1000', '*', ['2', '+', '1']]
    """
    pat = r'({}|{}|{})'.format(left, right, sep)
    tokens = re.split(pat, text)    
    stack = [[]]
    for x in tokens:
        if not x or re.match(sep, x): continue
        if re.match(left, x):
            stack[-1].append([])
            stack.append(stack[-1][-1])
        elif re.match(right, x):
            stack.pop()
            if not stack:
                raise ValueError('error: opening bracket is missing')
        else:
            stack[-1].append(x)
    if len(stack) > 1:
        print(stack)
        raise ValueError('error: closing bracket is missing')
    separate = lambda e: re.findall('[+-/*//()]|\d+', e)
    def process(e):
        if not e:
            return []
        elif isinstance(e[0], list):
            return [process(e[0])] + process(e[1:])
        else:
            return separate(e[0]) + process(e[1:])
    return process(stack.pop())

def evaluate(expr):
    """
    >>> evaluate(['2', '+', '2'])
    4
    >>> evaluate([['1', '/', '2'], '*', '3'])
    0
    """
    if isinstance(expr, str):
        return int(expr)
    elif len(expr) == 1:
        return evaluate(expr[0])
    else:
        op = expr[1]
        first = evaluate(expr[0])
        second = evaluate(expr[2])
        return OPERATORS[op](first, second)
        
def infix(expr):
    """
    >>> infix('1+2')
    3
    >>> infix('(1)+(2*3)')
    7
    >>> infix('1')
    1
    >>> infix('(1*2)-(3*(4+(3/3)))')
    -13
    >>> infix('(1000/2)*(4*((0-1)*(3-12)))')
    18000
    """
    return evaluate(parse(expr))