Parsing integers with LPEG in Lua

integer.parse.lua

local lpeg = require"lpeg"  
local P, R, S = lpeg.P, lpeg.R, lpeg.S
-- Any non-zero digit: (R stands for Range)
local nonzero = R"19"
-- Only zero: (P stands for Pattern)
local zero = P"0"
-- Any digit:
local digit = R"09"

-- Match a sqeuence of one or more numbers not starting with zero (aka positive numbers)
local positive = nonzero * (zero + nonzero)^0
-- Match the natural numbers (positive numbers including zero)
local natural = zero + positive
-- Match all integers (including negative numbers)
local integer = P"-"^-1 * natural * P(-1)

print(integer:match"1")  --> '2', match successful
print(integer:match"0")  --> '2', match successful
print(integer:match"109234")  --> '7', match successful
print(integer:match"-10")  --> '4', match successful
print(integer:match"-0")  --> '3', match successful
print(integer:match"012")  --> 'nil', match unsuccessful
print(integer:match"2a12")  --> 'nil', match unsuccessful