[SudoNhim web security SyntaxChecker](http://stackoverflow.com/questions/10661079/restricting-pythons-syntax-to-execute-user-code-safely-is-this-a-safe-approach) & [JF Sebastian Eval is Evil](http://stackoverflow.com/a/9558001/1020470)

add_a_lambda.py

tree = ast.Module()
tree.body = [ast.Expr()]
tree.body[0].value = ast.Lambda()
tree.body[0].value.args = ast.arguments()
tree.body[0].value.args.args = [ast.Name(id=a, ctx=ast.Param()) for a in args]
tree.body[0].value.args.vararg = None
tree.body[0].value.args.kwarg = None
tree.body[0].value.args.defaults = []
tree.body[0].value.body = ast.parse(expr).body[0].value

eval_expr.py

import ast
import operator as op

# supported operators
operators = {ast.Add: op.add, ast.Sub: op.sub, ast.Mult: op.mul,
             ast.Div: op.truediv, ast.Pow: op.pow, ast.BitXor: op.xor}

args = ['x', 'y', 'z_0']

def eval_expr(expr):
    """
    >>> eval_expr('2^6')
    4
    >>> eval_expr('2**6')
    64
    >>> eval_expr('1 + 2*3**(4^5) / (6 + -7)')
    -5.0
    """
    return eval_(ast.parse(expr).body[0].value) # Module(body=[Expr(value=...)])

def eval_(node):
    if isinstance(node, ast.Num): # <number>
        return node.n
    elif isinstance(node, ast.operator): # <operator>
        return operators[type(node)]
    elif isinstance(node, ast.BinOp): # <left> <operator> <right>
        return eval_(node.op)(eval_(node.left), eval_(node.right))
    elif isinstance(node, ast.Name):
        if node.id not in args:
             raise Exception('%s is not in the list of args' % node.id)
    else:
        raise TypeError(node)

# You can easily limit allowed range for each operation or any intermediate result,
# e.g., to limit input arguments for a**b:

def power(a, b):
    if any(abs(n) > 100 for n in [a, b]):
        raise ValueError((a,b))
    return op.pow(a, b)
operators[ast.Pow] = power

# Or to limit magnitude of intermediate results:

import functools

def limit(max_=None):
    """Return decorator that limits allowed returned values."""
    def decorator(func):
        functools.wraps(func)
        def wrapper(*args, **kwargs):
            ret = func(*args, **kwargs)
            try:
                mag = abs(ret)
            except TypeError:
                pass # not applicable
            else:
                if mag > max_:
                    raise ValueError(ret)
            return ret
        return wrapper
    return decorator

eval_ = limit(max_=10**100)(eval_)

SyntaxChecker1.py

import ast

allowed_functions = set([
    #math library
    'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh',
    'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'erf',
    'erfc', 'exp', 'expm1', 'fabs', 'factorial', 'floor', 'fmod',
    'frexp', 'fsum', 'gamma', 'hypot', 'isinf', 'isnan', 'ldexp',
    'lgamma', 'log', 'log10', 'log1p', 'modf', 'pi', 'pow', 'radians',
    'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'trunc',
    #builtins
    'abs', 'max', 'min', 'range', 'xrange'
    ])

allowed_node_types = set([
    #Meta
    'Module', 'Assign', 'Expr',
    #Control
    'For', 'If', 'Else',
    #Data
    'Store', 'Load', 'AugAssign', 'Subscript',
    #Datatypes
    'Num', 'Tuple', 'List',
    #Operations
    'BinOp', 'Add', 'Sub', 'Mult', 'Div', 'Mod', 'Compare'
    ])

safe_names = set([
    'True', 'False', 'None'
    ])


class SyntaxChecker(ast.NodeVisitor):

    def check(self, syntax):
        tree = ast.parse(syntax)
        self.passed=True
        self.visit(tree)

    def visit_Call(self, node):
        if node.func.id not in allowed_functions:
            raise SyntaxError("%s is not an allowed function!"%node.func.id)
        else:
            ast.NodeVisitor.generic_visit(self, node)

    def visit_Name(self, node):
        try:
            eval(node.id)
        except NameError:
            ast.NodeVisitor.generic_visit(self, node)
        else:
            if node.id not in safe_names and node.id not in allowed_functions:
                raise SyntaxError("%s is a reserved name!"%node.id)
            else:
                ast.NodeVisitor.generic_visit(self, node)

    def generic_visit(self, node):
        if type(node).__name__ not in allowed_node_types:
            raise SyntaxError("%s is not allowed!"%type(node).__name__)
        else:
            ast.NodeVisitor.generic_visit(self, node)

if __name__ == '__main__':
    x = SyntaxChecker()
    while True:
        try:
            x.check(raw_input())
        except Exception as e:
            print e

SyntaxChecker2.py

import ast

allowed_functions = set([
    #math library
    'acos', 'acosh', 'asin', 'asinh', 'atan', 'atan2', 'atanh',
    'ceil', 'copysign', 'cos', 'cosh', 'degrees', 'e', 'erf',
    'erfc', 'exp', 'expm1', 'fabs', 'factorial', 'floor', 'fmod',
    'frexp', 'fsum', 'gamma', 'hypot', 'isinf', 'isnan', 'ldexp',
    'lgamma', 'log', 'log10', 'log1p', 'modf', 'pi', 'pow', 'radians',
    'sin', 'sinh', 'sqrt', 'tan', 'tanh', 'trunc',
    #builtins
    'abs', 'max', 'min', 'range', 'xrange'
    ])

allowed_node_types = set([
    #Meta
    'Module', 'Assign', 'Expr',
    #Control
    'For', 'If', 'Else',
    #Data
    'Store', 'Load', 'AugAssign', 'Subscript',
    #Datatypes
    'Num', 'Tuple', 'List',
    #Operations
    'BinOp', 'Add', 'Sub', 'Mult', 'Div', 'Mod', 'Compare'
    ])

safe_names = set([
    'True', 'False', 'None'
    ])


class SyntaxChecker(ast.NodeVisitor):

    def check(self, syntax):
        tree = ast.parse(syntax)
        self.visit(tree)

    def visit_Call(self, node):
        if node.func.id not in allowed_functions:
            raise SyntaxError("%s is not an allowed function!"%node.func.id)
        else:
            ast.NodeVisitor.generic_visit(self, node)

    def visit_Name(self, node):
        try:
            eval(node.id)
        except NameError:
            ast.NodeVisitor.generic_visit(self, node)
        else:
            if node.id not in safe_names and node.id not in allowed_functions:
                raise SyntaxError("%s is a reserved name!"%node.id)
            else:
                ast.NodeVisitor.generic_visit(self, node)

    def generic_visit(self, node):
        if type(node).__name__ not in allowed_node_types:
            raise SyntaxError("%s is not allowed!"%type(node).__name__)
        else:
            ast.NodeVisitor.generic_visit(self, node)

if __name__ == '__main__':
    x = SyntaxChecker()
    while True:
        try:
            x.check(raw_input())
        except Exception as e:
            print e