How can I create an abstract syntax tree considering ‘|’? (Ply / Yacc)

Considering the following grammar:

expr : expr '+' term | expr '-' term | term
term : term '*' factor | term '/' factor | factor
factor : '(' expr ')' | identifier | number

This is my code using ply:

from ply import lex, yacc

tokens = [
    "identifier",
    "number",
    "plus",
    "minus",
    "mult",
    "div"
]

t_ignore = r" t"
t_identifier = r"^[a-zA-Z]+$"
t_number = r"[+-]?(d+(.d*)?|.d+)([eE][+-]?d+)?"
t_plus = r"+"
t_minus = r"-"
t_mult = r"*"
t_div = r"/"

def p_stmt(p):
    """stmt : expr"""
    p[0] = ("stmt", p[1])

def p_expr(p):
    """expr : expr plus term 
            | expr minus term 
            | term"""
    p[0] = ("expr", p[1], p[2]) # Problem here <<<

def p_term(p):
    """term : term mult factor 
            | term div factor 
            | factor"""

def p_factor(p):
    """factor : '(' expr ')' 
              | identifier 
              | number"""


if __name__ == "__main__":
    lex.lex()
    yacc.yacc()
    data = "32 + 10"
    result = yacc.parse(data)
    print(result)

How am I supposed to build an AST with the expression if I can’t access the operators? I could separate the functions like p_expr_plus, but in this case, I would eliminate operator precedence. The docs are not so helpful, since I’m a beginner and can’t solve this problem. The best material I’ve found on the subject is this, but it does not consider the complexity of operator precedence.

EDIT: I can’t access p2 or p[3], since I get an IndexError (It’s matching the term only). In the PDF I’ve linked, they explicitly put the operator inside the tuple, like: (‘+’, p1, p2), and thus, evincing my problem considering precedence (I can’t separate the functions, the expression is the expression, there should be a way to consider the pipes and access any operator).

Answer

As far as I can see, in p[0] = ("expr", p[1], p[2]), p[1] would be the left hand expression, p[2] would be the operator, and p[3] (that you aren’t using) would be the right hand term.

Just use p[2] to determine the operator, add p[3], since you will need it, and you should be good to go.

Also, you must verify how many items p has, since if the last rule, | term""" is matched, p will only have two items instead of four.

Take a look at a snippet from the GardenSnake example:

def p_comparison(p):
    """comparison : comparison PLUS comparison
                  | comparison MINUS comparison
                  | comparison MULT comparison
                  | comparison DIV comparison
                  | comparison LT comparison
                  | comparison EQ comparison
                  | comparison GT comparison
                  | PLUS comparison
                  | MINUS comparison
                  | power"""
    if len(p) == 4:
        p[0] = binary_ops[p[2]]((p[1], p[3]))
    elif len(p) == 3:
        p[0] = unary_ops[p[1]](p[2])
    else:
        p[0] = p[1]