Граматика

expression = term  { ("+" | "-") term} .
term       = factor  { ("*"|"/") factor} .
factor     = constant | variable | "("  expression  ")" .
variable   = "x" | "y" | "z" .
constant   = digit {digit} .
digit      = "0" | "1" | " ... " | "9" .

LL(2)

Вихідний код
"1 + 4 * 3 - ( 5 + 7 )"

Лексичний аналіз

("1", "+", "4", "*", "3", "-", "(", "5", "+", "7", ")" )


Таблиця переходів
            expression  term  factor  variable   constant  digit "(" ")" $
expression                      +
term            +
factor					 +
variable  						+
constant						+
digit												+					+
"("                             +										+
")"                             +										+

$
 +
   1
   ( 4 * 3 - ( 5 + 7 ))

$
 +
   1
   -
     4 * 3 
     5 + 7



$
|__+
   |__1
   |__-
      |__*
      |  |__ 4
      |  |__ 3 
      |__+
         |__ 5
         |__ 7

(+, 1, (-, (*, 4, 5), (+,5,7)))

Рекурсивний нисхідний аналізатор

	expression = term  { ("+" | "-") term} .  => is_applicable(), apply()
	term       = factor  { ("*"|"/") factor} .  => is_applicable(), apply()
	factor     = constant | variable | "("  expression  ")" .   => is_applicable(), apply()
	variable   = "x" | "y" | "z" .   => is_applicable(), apply()
	constant   = digit {digit} .    => is_applicable(), apply()
	digit      = "0" | "1" | " ... " | "9" .   => is_applicable(), apply()



digit_is_applicable(s):
   return re.match("/[0-9]/", s)

constant__is_applicable(s):
   return re.match("/[0-9]+/", s)

term_is_applicable(s):
   x = re.split(r"/\*|\//", s)
   return factor_is_applicable(x[0])

expression_apply(s):
   x = re.split(r"/\+|-/", s, 1)
   return (+, term_apply(x[0]), term_apply(x[1]))

digit_apply(s):
	($, s)

print(expression_apply("1 + 4 * 3 - ( 5 + 7 )"))
	(+, 1, (-, (*, 4, 5), (+,5,7)))