parser for mathematical expressions

expression_parser.py

import re
from operator import add, sub, mul, floordiv, truediv
from functools import reduce
import itertools
OPERATIONS = (
    (re.compile('\+'), add),
    (re.compile('(?<=[\d\)])-'), sub), # not match the - in `(-1)`
    (re.compile('\*'), mul),
    (re.compile('//'), floordiv),
    (re.compile('/'), floordiv), # or '/': truediv,
)

PATTERN_PARENTHESES = re.compile('^(.*?)\((.*)\)(.*?)$')
PATTERN_PAREN_SIMPLE= re.compile('\((-?\d+)\)')
PAREN_OPEN = '|'
PAREN_CLOSE = '#'
def _encode(expression):
    return PATTERN_PAREN_SIMPLE.sub(rf'{PAREN_OPEN}\1{PAREN_CLOSE}', expression)
    
def _decode(expression):
    return expression.replace(PAREN_OPEN, '(').replace(PAREN_CLOSE, ')')
    
def contains_parens(expression):
    return '(' in _encode(expression)

def calculate(expression):
    expression = expression.replace(' ', '')
    while contains_parens(expression):
        expression = _extract_parens(expression)
    if PATTERN_PAREN_SIMPLE.fullmatch(expression):
        expression = expression[1:-1]
    try:
        return int(expression)
    except ValueError:
        pass
    
    operation, parts = split_expression(expression)
    parts = map(calculate, parts) # recursion
    return reduce(operation, parts)
        
def split_expression(expression):
    for pattern, operation in OPERATIONS:
        parts = pattern.split(expression)
        if len(parts) > 1:
            return operation, parts
        
def _extract_parens(expression, func=calculate):
#     print('paren: ', expression)
    expression = _encode(expression)
    begin, expression = expression.split('(', 1)
    characters = iter(expression)
    
    middle = _search_closing_paren(characters)

    middle = _decode(''.join(middle))
    middle = func(middle)
    
    end = ''.join(characters)
    result = f'{begin}({middle}){end}' if( begin or end) else str(middle)
    return _decode(result)

def _search_closing_paren(characters, close_char=')', open_char='('):
    count = 1
    for char in characters:
        if char == open_char:
            count += 1
        if char == close_char:
            count -= 1
        if not count:
            return
        else:
            yield char