Safe way to parse user-supplied mathematical formula in Python

Check out Paul McGuire’s pyparsing. He has written both the general parser and a grammar for arithmetic expressions:

from __future__ import division
import pyparsing as pyp
import math
import operator

class NumericStringParser(object):
    '''
    Most of this code comes from the fourFn.py pyparsing example
    http://pyparsing.wikispaces.com/file/view/fourFn.py
    http://pyparsing.wikispaces.com/message/view/home/15549426
    __author__='Paul McGuire'

    All I've done is rewrap Paul McGuire's fourFn.py as a class, so I can use it
    more easily in other places.
    '''
    def pushFirst(self, strg, loc, toks ):
        self.exprStack.append( toks[0] )
    def pushUMinus(self, strg, loc, toks ):
        if toks and toks[0] == '-':
            self.exprStack.append( 'unary -' )
    def __init__(self):
        """
        expop   :: '^'
        multop  :: '*' | "https://stackoverflow.com/"
        addop   :: '+' | '-'
        integer :: ['+' | '-'] '0'..'9'+
        atom    :: PI | E | real | fn '(' expr ')' | '(' expr ')'
        factor  :: atom [ expop factor ]*
        term    :: factor [ multop factor ]*
        expr    :: term [ addop term ]*
        """
        point = pyp.Literal( "." )
        e     = pyp.CaselessLiteral( "E" )
        fnumber = pyp.Combine( pyp.Word( "+-"+pyp.nums, pyp.nums ) + 
                           pyp.Optional( point + pyp.Optional( pyp.Word( pyp.nums ) ) ) +
                           pyp.Optional( e + pyp.Word( "+-"+pyp.nums, pyp.nums ) ) )
        ident = pyp.Word(pyp.alphas, pyp.alphas+pyp.nums+"_$")       
        plus  = pyp.Literal( "+" )
        minus = pyp.Literal( "-" )
        mult  = pyp.Literal( "*" )
        div   = pyp.Literal( "https://stackoverflow.com/" )
        lpar  = pyp.Literal( "(" ).suppress()
        rpar  = pyp.Literal( ")" ).suppress()
        addop  = plus | minus
        multop = mult | div
        expop = pyp.Literal( "^" )
        pi    = pyp.CaselessLiteral( "PI" )
        expr = pyp.Forward()
        atom = ((pyp.Optional(pyp.oneOf("- +")) +
                 (pi|e|fnumber|ident+lpar+expr+rpar).setParseAction(self.pushFirst))
                | pyp.Optional(pyp.oneOf("- +")) + pyp.Group(lpar+expr+rpar)
                ).setParseAction(self.pushUMinus)       
        # by defining exponentiation as "atom [ ^ factor ]..." instead of 
        # "atom [ ^ atom ]...", we get right-to-left exponents, instead of left-to-right
        # that is, 2^3^2 = 2^(3^2), not (2^3)^2.
        factor = pyp.Forward()
        factor << atom + pyp.ZeroOrMore( ( expop + factor ).setParseAction(
            self.pushFirst ) )
        term = factor + pyp.ZeroOrMore( ( multop + factor ).setParseAction(
            self.pushFirst ) )
        expr << term + pyp.ZeroOrMore( ( addop + term ).setParseAction( self.pushFirst ) )
        self.bnf = expr
        # map operator symbols to corresponding arithmetic operations
        epsilon = 1e-12
        self.opn = { "+" : operator.add,
                "-" : operator.sub,
                "*" : operator.mul,
                "https://stackoverflow.com/" : operator.truediv,
                "^" : operator.pow }
        self.fn  = { "sin" : math.sin,
                "cos" : math.cos,
                "tan" : math.tan,
                "abs" : abs,
                "trunc" : lambda a: int(a),
                "round" : round,
                # For Python3 compatibility, cmp replaced by ((a > 0) - (a < 0)). See
                # https://docs.python.org/3.0/whatsnew/3.0.html#ordering-comparisons
                "sgn" : lambda a: abs(a)>epsilon and ((a > 0) - (a < 0)) or 0}
        self.exprStack = []
    def evaluateStack(self, s ):
        op = s.pop()
        if op == 'unary -':
            return -self.evaluateStack( s )
        if op in "+-*/^":
            op2 = self.evaluateStack( s )
            op1 = self.evaluateStack( s )
            return self.opn[op]( op1, op2 )
        elif op == "PI":
            return math.pi # 3.1415926535
        elif op == "E":
            return math.e  # 2.718281828
        elif op in self.fn:
            return self.fn[op]( self.evaluateStack( s ) )
        elif op[0].isalpha():
            return 0
        else:
            return float( op )
    def eval(self, num_string, parseAll = True):
        self.exprStack = []
        results = self.bnf.parseString(num_string, parseAll)
        val = self.evaluateStack( self.exprStack[:] )
        return val

nsp = NumericStringParser()
print(nsp.eval('1+2'))
# 3.0

print(nsp.eval('2*3-5'))
# 1.0