A script to demonstrate how to use property-based testing to test str_to_int function. Not all tests are required.

test_str_to_int.py

# Python -- v3.6
# https://docs.pytest.org/en/latest/ -- v3.2.1
# http://hypothesis.readthedocs.io/en/latest/ -- v3.7

from hypothesis import assume, given
from hypothesis.strategies import text
import pytest

rep2int = {
        '1':1, 
        '2':2, 
        '3':3, 
        '4':4, 
        '5':5, 
        '6':6, 
        '7':7, 
        '8':8, 
        '9':9, 
        '0':0 
}

def str_to_int(s):
    '''
    Return X if s represents a valid integer X
    Raise ValueError if s does not represent a valid integer
    '''
    tmp1 = list(s)
    tmp1.reverse()
    val = 0
    pos = 0
    signSeen = False
    numSeen = False
    for i in tmp1:
        if i in rep2int:
            val += rep2int[i] * (10 ** pos)
            numSeen = True
        elif i == '-' or i == '+':
            if signSeen:
                raise ValueError("Invalid repr")
            val *= -1 if i == '-' else 1
            signSeen = True
        else:
            raise ValueError("Invalid repr")
        pos += 1

    if not numSeen:
        raise ValueError("Invalid repr")

    return val


@given(text(min_size=1, max_size=15))
def test_invalid_repr(s):
    # assume clause can be simplified by using regex
    assume(
        not(
            all(i in list('1234567890-+') for i in s) and 
            s.count('-') + s.count('+') < 2 and 
            (s.count('-') == 0 or s.index('-') == 0 and len(s) > 1) and 
            (s.count('+') == 0 or s.index('+') == 0 and len(s) > 1)
        )
    )
    with pytest.raises(ValueError):
        str_to_int(s)


@given(text(alphabet='+1234567890', min_size=1, max_size=15))
def test_positive_int_repr(s):
    assume(
        s.count('+') < 2 and 
        (s.count('+') == 0 or s.index('+') == 0 and len(s) > 1)
    )
    if all(i in ['0', '+'] for i in s):
        assert str_to_int(s) == 0
    else:
        assert str_to_int(s) > 0
 

@given(text(alphabet='-1234567890', min_size=1, max_size=15))
def test_negative_int_repr(s):
    assume(s.count('-') == 1 and s.index('-') == 0 and len(s) > 1)
    # assuming we deem -0 as valid repr
    if all(i in ['0', '-'] for i in s): 
        assert str_to_int(s) == 0
    else:
        assert str_to_int(s) < 0


@given(text(alphabet='1234567890', min_size=1, max_size=1))
def test_single_digit_int_repr(s):
    assert str_to_int(s) == rep2int[s]


@given(text(alphabet='-+1234567890', min_size=1, max_size=15))
def test_multi_digit_int_repr(s):
    assume(
        s.count('-') + s.count('+') < 2 and 
        (s.count('-') == 0 or s.index('-') == 0 and len(s) > 1) and
        (s.count('+') == 0 or s.index('+') == 0 and len(s) > 1)
    )
    val = str_to_int(s)
    revS = list(s)
    sgn = 1
    if revS[0] == '+':
        del revS[0]
    if revS[0] == '-':
        del revS[0]
        sgn = -1
    revS.reverse()
    for i in range(0, len(revS)):
        tmp1 = str_to_int(revS[i])
        tmp2 = val * sgn // (10 ** i)
        tmp3 = tmp2 - (tmp2 // 10) * 10
        assert tmp1 == tmp3


@given(text(alphabet='+-1234567890', min_size=1, max_size=15))
def test_convert_back(s):
    assume(
        s.count('-') + s.count('+') < 2 and 
        (s.count('-') == 0 or s.index('-') == 0 and len(s) > 1) and
        (s.count('+') == 0 or s.index('+') == 0 and len(s) > 1)
    )
    # this would be the simplest test for all valid repr
    tmp1 = ""
    sgn = ''
    nonZeroSeen = False
    for i in s:
        if i == '-':
            sgn = '-'
        elif i == '+':
            pass
        elif i != '0':
            nonZeroSeen = True
        if nonZeroSeen:
            tmp1 += i
    tmp1 = sgn + tmp1 if tmp1 else '0'
    assert str(str_to_int(s)) == tmp1