How to convert from infix to postfix/prefix using AST python module?

Question

I'm trying to convert python math expressions to postfix notation using the AST python module. Here's what I got so far:

import parser
import ast
from math import sin, cos, tan

formulas = [
    "1+2",
    "1+2*3",
    "1/2",
    "(1+2)*3",
    "sin(x)*x**2",
    "cos(x)",
    "True and False",
    "sin(w*time)"
]


class v(ast.NodeVisitor):

    def __init__(self):
        self.tokens = []

    def f_continue(self, node):
        super(v, self).generic_visit(node)

    def visit_Add(self, node):
        self.tokens.append('+')
        self.f_continue(node)

    def visit_And(self, node):
        self.tokens.append('&&')
        self.f_continue(node)

    def visit_BinOp(self, node):
        # print('visit_BinOp')
        # for child in ast.iter_fields(node):
            # print('  child %s ' % str(child))

        self.f_continue(node)

    def visit_BoolOp(self, node):
        # print('visit_BoolOp')
        self.f_continue(node)

    def visit_Call(self, node):
        # print('visit_Call')
        self.f_continue(node)

    def visit_Div(self, node):
        self.tokens.append('/')
        self.f_continue(node)

    def visit_Expr(self, node):
        # print('visit_Expr')
        self.f_continue(node)

    def visit_Import(self, stmt_import):
        for alias in stmt_import.names:
            print('import name "%s"' % alias.name)
            print('import object %s' % alias)
        self.f_continue(stmt_import)

    def visit_Load(self, node):
        # print('visit_Load')
        self.f_continue(node)

    def visit_Module(self, node):
        # print('visit_Module')
        self.f_continue(node)

    def visit_Mult(self, node):
        self.tokens.append('*')
        self.f_continue(node)

    def visit_Name(self, node):
        self.tokens.append(node.id)
        self.f_continue(node)

    def visit_NameConstant(self, node):
        self.tokens.append(node.value)
        self.f_continue(node)

    def visit_Num(self, node):
        self.tokens.append(node.n)
        self.f_continue(node)

    def visit_Pow(self, node):
        self.tokens.append('pow')
        self.f_continue(node)

for index, f in enumerate(formulas):
    print('{} - {:*^76}'.format(index, f))
    visitor = v()
    visitor.visit(ast.parse(f))
    print(visitor.tokens)
    print()


# 0 - ************************************1+2*************************************
# [1, '+', 2]

# 1 - ***********************************1+2*3************************************
# [1, '+', 2, '*', 3]

# 2 - ************************************1/2*************************************
# [1, '/', 2]

# 3 - **********************************(1+2)*3***********************************
# [1, '+', 2, '*', 3]

# 4 - ********************************sin(x)*x**2*********************************
# ['sin', 'x', '*', 'x', 'pow', 2]

# 5 - ***********************************cos(x)***********************************
# ['cos', 'x']

# 6 - *******************************True and False*******************************
# ['&&', True, False]

# 7 - ********************************sin(w*time)*********************************
# ['sin', 'w', '*', 'time']

I'm trying to understand how to convert complex infix math expressions to postfix expressions to be sent to a swig c wrapper, to do that I'm trying to use the AST module.

Could anyone advice here?

Answer 1

You can use ast.dump to get more information about the the nodes and AST structure:

>>> import ast
>>> node = ast.parse("sin(x)*x**2")
>>> ast.dump(node)
"Module(body=[Expr(value=BinOp(left=Call(func=Name(id='sin', ctx=Load()), args=[Name(id='x', ctx=Load())], keywords=[]), op=Mult(), right=BinOp(left=Name(id='x', ctx=Load()), op=Pow(), right=Num(n=2))))])"

With above information you can change the visiting order of the node's children which allows you to generate postfix or prefix expression. In order to generate postfix expression change visit_BinOp, visit_BoolOp and visit_Call so that they visit arguments before visiting the operator/function:

def visit_BinOp(self, node):
    self.visit(node.left)
    self.visit(node.right)
    self.visit(node.op)

def visit_BoolOp(self, node):
    for val in node.values:
        self.visit(val)
    self.visit(node.op)

def visit_Call(self, node):
    for arg in node.args:
        self.visit(arg)
    self.visit(node.func)

With above changes you get following output:

0 - ************************************1+2*************************************

[1, 2, '+']

1 - ***********************************1+2*3************************************

[1, 2, 3, '*', '+']

2 - ************************************1/2*************************************

[1, 2, '/']

3 - **********************************(1+2)*3***********************************

[1, 2, '+', 3, '*']

4 - ********************************sin(x)*x**2*********************************

['x', 'sin', 'x', 2, 'pow', '*']

5 - ***********************************cos(x)***********************************

['x', 'cos']

6 - *******************************True and False*******************************

[True, False, '&&']

7 - ********************************sin(w*time)*********************************

['w', 'time', '*', 'sin']

If you want prefix expression instead just swap the order around so operator/function is visited first:

def visit_BinOp(self, node):
    self.visit(node.op)
    self.visit(node.left)
    self.visit(node.right)

def visit_BoolOp(self, node):
    self.visit(node.op)
    for val in node.values:
        self.visit(val)

def visit_Call(self, node):
    self.visit(node.func)
    for arg in node.args:
        self.visit(arg)

Output:

0 - ************************************1+2*************************************

['+', 1, 2]

1 - ***********************************1+2*3************************************

['+', 1, '*', 2, 3]

2 - ************************************1/2*************************************

['/', 1, 2]

3 - **********************************(1+2)*3***********************************

['*', '+', 1, 2, 3]

4 - ********************************sin(x)*x**2*********************************

['*', 'sin', 'x', 'pow', 'x', 2]

5 - ***********************************cos(x)***********************************

['cos', 'x']

6 - *******************************True and False*******************************

['&&', True, False]

7 - ********************************sin(w*time)*********************************

['sin', '*', 'w', 'time']