License

SP is available under the GNU Lesser General Public:

Simple Parser: A Python parser generator

Copyright (C) 2009-2010 Christophe Delord

Simple Parser is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published
by the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.

Simple Parser is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU Lesser General Public License for more details.

You should have received a copy of the GNU Lesser General Public License
along with Simple Parser.  If not, see <http://www.gnu.org/licenses/>.

Structure of the document

Introduction and tutorial

starts smoothly with a gentle tutorial as an introduction. I think this tutorial may be sufficent to start with SP.

SP reference

is a reference documentation. It will detail SP as much as possible.

Some examples to illustrate SP

gives the reader some examples to illustrate SP.

Getting SP

SP is freely available on its web page (http://www.cdsoft.fr/sp).

Requirements

SP is a pure Python package. It may run on any platform supported by Python. The only requirement of SP is Python 2.6, Python 3.1 or newer [2]. Python can be downloaded at http://www.python.org.

Introduction

This short tutorial presents how to make a simple calculator. The calculator will compute basic mathematical expressions (+, -, *, /) possibly nested in parenthesis. We assume the reader is familiar with regular expressions.

Defining the grammar

Expressions are defined with a grammar. For example an expression is a sum of terms and a term is a product of factors. A factor is either a number or a complete expression in parenthesis.

We describe such grammars with rules. A rule describes the composition of an item of the language. In our grammar we have 3 items (expr, term, factor). We will call these items symbols or non terminal symbols. The decomposition of a symbol is symbolized with ->.

Grammar for expressions:

We have defined here the grammar rules (i.e. the sentences of the language). We now need to describe the lexical items (i.e. the words of the language). These words - also called terminal symbols - are described using regular expressions. In the rules we have written some of these terminal symbols (+, -, *, /, (, )). We have to define number. For sake of simplicity numbers are integers composed of digits (the corresponding regular expression can be [0-9]+). To simplify the grammar and then the Python script we define two terminal symbols to group the operators (additive and multiplicative operators). We can also define a special symbol that is ignored by SP. This symbol is used as a separator. This is generaly useful for white spaces and comments.

Terminal symbol definition for expressions:

This is sufficient to define our parser with SP.

Grammar of the expression recognizer:

def Calc():

    number = R(r'[0-9]+')
    addop = R('[+-]')
    mulop = R('[*/]')

    with Separator(r'\s+'):

        expr = Rule()
        fact = Rule()
        fact |= addop & fact
        fact |= '(' & expr & ')'
        fact |= number
        term = fact & ( mulop & fact )[:]
        expr |= term & ( addop & term )[:]

    return expr

Calc is the name of the Python function that returns a parser. This function returns expr which is the axiom [3] of the grammer.

expr and fact are recursive rules. They are first declared as empty rules (expr = Rule()) and alternatives are later added (expr |= ...).

Slices are used to implement repetitions. foo[:] parses foo zero or more times, which is equivalent to foo* in a classical grammar notation.

The grammar can also be defined with the mini grammar language provided by SP:

def Calc():
    return compile("""
        number = r'[0-9]+' ;
        addop = r'[+-]' ;
        mulop = r'[*/]' ;

        separator: r'\s+' ;

        !expr = term (addop term)* ;
        term = fact (mulop fact)* ;
        fact = addop fact ;
        fact = '(' expr ')' ;
        fact = number ;
    """)

Here the axiom [3] is identified by !.

With this small grammar we can only recognize a correct expression. We will see in the next sections how to read the actual expression and to compute its value.

Reading the input and returning values

The input of the grammar is a string. To do something useful we need to read this string in order to transform it into an expected result.

This string can be read by catching the return value of terminal symbols. By default any terminal symbol returns a string containing the current token. So the token '(' always returns the string '('. For some tokens it may be useful to compute a Python object from the token. For example number should return an integer instead of a string, addop and mulop, followed by a number, should return a function corresponding to the operator. That's why we will add a function to the token and rule definitions. So we associate int to number and op1 and op2 to unary and binary operators.

int is a Python function converting objects to integers and op1 and op2 are user defined functions.

op1 and op2 functions:

op1 = lambda f,x: {'+':pos, '-':neg}[f](x)
op2 = lambda f,y: lambda x: {'+': add, '-': sub, '*': mul, '/': div}[f](x,y)

# red applyies functions to a number
def red(x, fs):
    for f in fs: x = f(x)
    return x

To associate a function to a token or a rule it must be applyed using / or * operators:

• / applyies a function to an object returned by a (sub)parser.
• * applyies a function to an tuple of objects returned by a sequence of (sub) parsers.

Token and rule definitions with functions:

number = R(r'[0-9]+') / int

fact |= (addop & fact) * op1
term = (fact & ( (mulop & fact) * op2 )[:]) * red

# R(r'[0-9]+') applyed on "42" will return "42".
# R(r'[0-9]+') / int will return int("42")

# addop & fact applyied on "+ 42" will return ('+', 42)
# (addop & fact) * op1 will return op1(*('+', 42)), i.e. op1('+', 42)
# so (addop & fact) * op1 returns +42

# (addop & fact) * op2 will return op2(*('+', 42)), i.e. op2('+', 42)
# so (addop & fact) * op2 returns lambda x: add(x, 42)

# fact & ( (mulop & fact) * op2 )[:] returns a number and a list of functions
# for instance (42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# so (fact & ( (mulop & fact) * op2 )[:]) * red applyied on "42*43*44"
# will return red(42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# i.e. 42*43*44

And with the SP language:

number = r'[0-9]+' : `int` ;

addop = r'[+-]' ;
mulop = r'[*/]' ;

fact = addop fact :: `op1` ;
term = fact (mulop fact :: `op2`)* :: `red` ;

# r'[0-9]+' applyed on "42" will return "42".
# r'[0-9]+' : `int` will return int("42")

# "addop fact" applyied on "+ 42" will return ('+', 42)
# "addop fact :: `op1`" will return op1(*('+', 42)), i.e. op1('+', 42)
# so "addop fact :: `op1`" returns +42

# "addop fact :: `op2`" will return op2(*('+', 42)), i.e. op2('+', 42)
# so "addop fact :: `op2`" returns lambda x: add(x, 42)

# "fact (mulop fact :: `op2`)*" returns a number and a list of functions
# for instance (42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# so "fact (mulop fact :: `op2`)* :: `red`" applyied on "42*43*44"
# will return red(42, [(lambda x:mul(x, 43)), (lambda x:mul(x, 44))])
# i.e. 42*43*44

In the SP language, : (as /) applies a Python function (more generally a callable object) to a value returned by a sequence and :: (as *) applies a Python function to several values returned by a sequence.

Here is finally the complete parser.

Expression recognizer and evaluator:

from sp import *

def Calc():

    from operator import pos, neg, add, sub, mul, truediv as div

    op1 = lambda f,x: {'+':pos, '-':neg}[f](x)
    op2 = lambda f,y: lambda x: {'+': add, '-': sub, '*': mul, '/': div}[f](x,y)

    def red(x, fs):
        for f in fs: x = f(x)
        return x

    number = R(r'[0-9]+') / int
    addop = R('[+-]')
    mulop = R('[*/]')

    with Separator(r'\s+'):

        expr = Rule()
        fact = Rule()
        fact |= (addop & fact) * op1
        fact |= '(' & expr & ')'
        fact |= number
        term = (fact & ( (mulop & fact) * op2 )[:]) * red
        expr |= (term & ( (addop & term) * op2 )[:]) * red

    return expr

Or with SP language:

from sp import *

def Calc():

    from operator import pos, neg, add, sub, mul, truediv as div

    op1 = lambda f,x: {'+':pos, '-':neg}[f](x)
    op2 = lambda f,y: lambda x: {'+': add, '-': sub, '*': mul, '/': div}[f](x,y)

    def red(x, fs):
        for f in fs: x = f(x)
        return x

    return compile("""
        number = r'[0-9]+' : `int` ;
        addop = r'[+-]' ;
        mulop = r'[*/]' ;

        separator: r'\s+' ;

        !expr = term (addop term :: `op2`)* :: `red` ;
        term = fact (mulop fact :: `op2`)* :: `red` ;
        fact = addop fact :: `op1` ;
        fact = '(' expr ')' ;
        fact = number ;
    """)

Embeding the parser in a script

A parser is a simple Python object. This example show how to write a function that returns a parser. The parser can be applyied to strings by simply calling the parser.

Writting SP grammars in Python:

from sp import *

def MyParser():

    parser = ...

    return parser

# You can instanciate your parser here
my_parser = MyParser()

# and use it
parsed_object = my_parser(string_to_be_parsed)

To use this parser you now just need to instanciate an object.

Complete Python script with expression parser:

from sp import *

def Calc():

    ...

calc = Calc()
while True:
    expr = input('Enter an expression: ')
    try: print(expr, '=', calc(expr))
    except Exception as e: print("%s:"%e.__class__.__name__, e)

Conclusion

This tutorial shows some of the possibilities of SP. If you have read it carefully you may be able to start with SP. The next chapters present SP more precisely. They contain more examples to illustrate all the features of SP.

Happy SP'ing!

Regular expression syntax

The lexer is based on the re [4] module. SP profits from the power of Python regular expressions. This document assumes the reader is familiar with regular expressions.

You can use the syntax of regular expressions as expected by the re [5] module.

Predefined tokens

Tokens can be explicitely defined by the R, K and Separator keywords.

A token can be defined by:

a name

which identifies the token. This name is used by the parser.

a regular expression

which describes what to match to recognize the token.

an action

which can translate the matched text into a Python object. It can be a function of one argument or a non callable object. If it is not callable, it will be returned for each token otherwise it will be applied to the text of the token and the result will be returned. This action is optional. By default the token text is returned.

Token definition examples:

integer = R(r'\d+') / int
identifier = R(r'[a-zA-Z]\w*\b')
boolean = R(r'(True|False)\b') / (lambda b: b=='True')

spaces = K(r'\s+')
comments = K(r'#.*')

with Separator(spaces|comments):
    # rules defined here will use spaces and comments as separators
    atom = '(' & expr & ')'

There are two kinds of tokens. Tokens defined by the R or K keywords are parsed by the parser and tokens defined by the Separator keyword are considered as separators (white spaces or comments for example) and are wiped out by the lexer.

The word boundary \b can be used to avoid recognizing "True" at the beginning of "Truexyz".

If the regular expression defines groups, the parser returns a tuple containing these groups:

couple = R('<(\d+)-(\d+)>')

couple("<42-43>") == ('42', '43')

If the regular expression defines only one group, the parser returns the value of this group:

first = R('<(\d+)-\d+>')

first("<42-43>") == '42'

Unwanted groups can be avoided using (?:...).

A name can be given to a token to make error messages easier to read:

couple = R('<(\d+)-(\d+)>', name="couple")

Regular expressions can be compiled using specific compilation options. Options are defined in the re module:

token = R('...', flags=re.IGNORECASE|re.DOTALL)

re defines the following flags:

I (IGNORECASE)

Perform case-insensitive matching.

L (LOCALE)

Make \w, \W, \b, \B, dependent on the current locale.

M (MULTILINE)

"^" matches the beginning of lines (after a newline) as well as the string. "$" matches the end of lines (before a newline) as well as the end of the string.

S (DOTALL)

"." matches any character at all, including the newline.

X (VERBOSE)

Ignore whitespace and comments for nicer looking RE's.

U (UNICODE)

Make \w, \W, \b, \B, dependent on the Unicode locale

Inline tokens

Tokens can also be defined on the fly. Their definition are then inlined in the grammar rules. This feature may be useful for keywords or punctuation signs.

In this case tokens can be written without the R or K keywords. They are considered as keywords (as defined by K).

Inline token definition examples:

IfThenElse = 'if' & Cond &
             'then' & Statement &
             'else' & Statement

Declaration

A parser is declared as a Python object.

Grammar rules

Rule declarations have two parts. The left side declares the symbol associated to the rule. The right side describes the decomposition of the rule. Both parts of the declaration are separated with an equal sign (=).

Rule declaration example:

SYMBOL = (A & B) * (lambda a, b: f(a, b))

Sequences

Sequences in grammar rules describe in which order symbols should appear in the input string. For example the sequence A & B recognizes an A followed by a B.

For example to say that a sum is a term plus another term you can write:

Sum = Term & '+' & Term

Alternatives

Alternatives in grammar rules describe several possible decompositions of a symbol. The infix pipe operator (|) is used to separate alternatives. A | B recognizes either an A or a B. If both A and B can be matched only the first longest match is considered. So the order of alternatives may be very important when two alternatives can match texts of the same size.

For example to say that an atom is an integer or an expression in paranthesis you can write:

Atom = integer | '(' & Expr & ')'

Repetitions

Repetitions in grammar rules describe how many times an expression should be matched.

Repetitions are greedy. Repetitions are implemented as Python loops. Thus whatever the length of the repetitions, the Python stack will not overflow.

The separator is useful to parse lists. For instance a comma separated parameter list is parameter[::','].

Precedence and grouping

The following table lists the different structures in increasing precedence order. To override the default precedence you can group expressions with parenthesis.

Precedence in SP expressions:

Actions

Grammar rules can contain actions as Python functions.

Functions are applyied to parsed objects using / or *.

* can be used to analyse the result of a sequence.

Abstract syntax trees

An abstract syntax tree (AST) is an abstract representation of the structure of the input. A node of an AST is a Python object (there is no constraint about its class). AST nodes are completely defined by the user.

AST example (parsing a couple):

class Couple:
    def __init__(self, a, b):
        self.a = a
        self.b = b

def Foo():
    couple = ('(' & item & ',' & item & ')') * Couple
    return couple

Constants

It is sometimes useful to return a constant. C defines a parser that matches an empty input and returns a constant.

Constant example:

number = (  '1' & C("one")
         |  '2' & C("two")
         |  '3' & C("three")
         )

Position in the input string

To know the current position in the input string, the At() parser returns an object containing the current index (attribute index) and the corresponding line and column numbers (attributes line and column):

position = At() / `lambda p: (p.line, p.column)`
rule = ... & pos & ...

Introduction

In the previous example, the parser computes the value of the expression on the fly, while parsing. It is also possible to build an abstract syntax tree to store an abstract representation of the input. This may be usefull when several passes are necessary.

This example shows how to parse an expression (infix, prefix or postfix) and convert it in infix, prefix and postfix notation. The expression is saved in a tree. Each node of the tree correspond to an operator in the expression. Each leaf is a number. Then to write the expression in infix, prefix or postfix notation, we just need to walk throught the tree in a particular order.

Abstract syntax trees

The AST of this converter has three types of node:

class Op

is used to store operators (+, -, *, /, ^). It has two sons associated to the sub expressions.

class Atom

is an atomic expression (a number or a symbolic name).

class Func

is used to store functions.

These classes are instanciated by the init method. The infix, prefix and postfix methods return strings containing the representation of the node in infix, prefix and postfix notation.

Grammar

ident = r'\b(?!sin|cos|tan|min|max)\w+\b' : `Atom` ;

func1 = r'sin' | r'cos' | r'tan' ;
func2 = r'min' | r'max' ;

op = op_add | op_mul | op_pow ;
op_add = r'[+-]' ;
op_mul = r'[*/]' ;
op_pow = r'\^' ;

expr = term (op_add term :: `lambda op, y: lambda x: Op(op, x, y)`)* :: `red` ;
term = fact (op_mul fact :: `lambda op, y: lambda x: Op(op, x, y)`)* :: `red` ;
fact = atom (op_pow fact :: `lambda op, y: lambda x: Op(op, x, y)`)? :: `red` ;
atom = ident ;
atom = '(' expr ')' ;
atom = func1 '(' expr ')' :: `Func` ;
atom = func2 '(' expr ',' expr ')' :: `Func` ;

def red(x, fs):
    for f in fs:
        x = f(x)
    return x

expr_pre = ident ;
expr_pre = op expr_pre expr_pre :: `Op` ;
expr_pre = func1 expr_pre :: `Func` ;
expr_pre = func2 expr_pre expr_pre :: `Func` ;

expr_post = ident expr_post_rest :: `lambda x, f: f(x)` ;
expr_post_rest =
    (   expr_post op    :: `lambda y, op: lambda x: Op(op, x, y)`
    |   expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
    |   func1           : `lambda f: lambda x: Func(f, x)`
    )   expr_post_rest  :: `lambda f, g: lambda x: g(f(x))` ;
expr_post_rest = `lambda x: x` ;

expr_post = ident expr_post_rest* :: `red` ;
expr_post_rest =
    (   expr_post op    :: `lambda y, op: lambda x: Op(op, x, y)`
    |   expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
    |   func1           : `lambda f: lambda x: Func(f, x)`
    ) ;

expr_post = ident
    (   expr_post op    :: `lambda y, op: lambda x: Op(op, x, y)`
    |   expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
    |   func1           : `lambda f: lambda x: Func(f, x)`
    )* :: `red` ;

Source code

Here is the complete source code (notation.py):

#!/usr/bin/env python
#coding: UTF-8

# Simple Parser
# Copyright (C) 2009-2010 Christophe Delord
# http://www.cdsoft.fr/sp

# This file is part of Simple Parser.
# 
# Simple Parser is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# 
# Simple Parser is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
# 
# You should have received a copy of the GNU Lesser General Public License
# along with Simple Parser.  If not, see <http://www.gnu.org/licenses/>.

# Infix/prefix/postfix expression conversion

import sp

try:
    import readline
except ImportError:
    pass

class Op:
    """ Binary operator """
    precedence = {'+':1, '-':1, '*':2, '/':2, '^':3}
    def __init__(self, op, a, b):
        self.op = op                    # operator ("+", "-", "*", "/", "^")
        self.prec = Op.precedence[op]   # precedence of the operator
        self.a, self.b = a, b           # operands
    def infix(self):
        a = self.a.infix()
        if self.a.prec < self.prec: a = "(%s)"%a
        b = self.b.infix()
        if self.b.prec <= self.prec: b = "(%s)"%b
        return "%s %s %s"%(a, self.op, b)
    def prefix(self):
        a = self.a.prefix()
        b = self.b.prefix()
        return "%s %s %s"%(self.op, a, b)
    def postfix(self):
        a = self.a.postfix()
        b = self.b.postfix()
        return "%s %s %s"%(a, b, self.op)

class Atom:
    """ Atomic expression """
    def __init__(self, s):
        self.a = s
        self.prec = 99
    def infix(self): return self.a
    def prefix(self): return self.a
    def postfix(self): return self.a

class Func:
    """ Function expression """
    def __init__(self, name, *args):
        self.name = name
        self.args = args
        self.prec = 99
    def infix(self):
        args = [a.infix() for a in self.args]
        return "%s(%s)"%(self.name, ",".join(args))
    def prefix(self):
        args = [a.prefix() for a in self.args]
        return "%s %s"%(self.name, " ".join(args))
    def postfix(self):
        args = [a.postfix() for a in self.args]
        return "%s %s"%(" ".join(args), self.name)

# Grammar for arithmetic expressions

def red(x, fs):
    for f in fs:
        x = f(x)
    return x

parser = sp.compile(r"""

    ident = ident.r'\b(?!sin|cos|tan|min|max)\w+\b' : `Atom` ;

    func1 = r'sin' | r'cos' | r'tan' ;
    func2 = r'min' | r'max' ;

    op = op_add | op_mul | op_pow ;
    op_add = r'[+-]' ;
    op_mul = r'[*/]' ;
    op_pow = r'\^' ;

    separator: r'\s+' ;

    !axiom = expr      `"infix"`
           | expr_pre  `"prefix"`
           | expr_post `"postfix"`
           ;

    # Infix expressions

    expr = term (op_add term :: `lambda op, y: lambda x: Op(op, x, y)`)* :: `red` ;
    term = fact (op_mul fact :: `lambda op, y: lambda x: Op(op, x, y)`)* :: `red` ;
    fact = atom (op_pow fact :: `lambda op, y: lambda x: Op(op, x, y)`)? :: `red` ;
    atom = ident ;
    atom = '(' expr ')' ;
    atom = func1 '(' expr ')' :: `Func` ;
    atom = func2 '(' expr ',' expr ')' :: `Func` ;

    # Prefix expressions

    expr_pre = ident ;
    expr_pre = op expr_pre expr_pre :: `Op` ;
    expr_pre = func1 expr_pre :: `Func` ;
    expr_pre = func2 expr_pre expr_pre :: `Func` ;

    # Postfix expressions

    expr_post = ident
        (   expr_post op    :: `lambda y, op: lambda x: Op(op, x, y)`
        |   expr_post func2 :: `lambda y, f: lambda x: Func(f, x, y)`
        |   func1           : `lambda f: lambda x: Func(f, x)`
        )* :: `red` ;

""")

try: raw_input
except NameError: raw_input = input

while 1:
    e = raw_input(":")
    if e == "": break
    try:
        expr, t = parser(e)
    except Exception as e:
        print(e)
    else:
        print("« %s » is a %s expression"%(e, t))
        print("\tinfix   : %s"%expr.infix())
        print("\tprefix  : %s"%expr.prefix())
        print("\tpostfix : %s"%expr.postfix())

New functions

The calculator has memories. A memory cell is identified by a name. For example, if the user types pi = 3.14, the memory cell named pi will contain the value of pi and 2*pi will return 6.28.

Source code

Here is the complete source code (calc.py):

#!/usr/bin/env python

# Simple Parser
# Copyright (C) 2009-2010 Christophe Delord
# http://www.cdsoft.fr/sp

# This file is part of Simple Parser.
# 
# Simple Parser is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
# 
# Simple Parser is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
# GNU Lesser General Public License for more details.
# 
# You should have received a copy of the GNU Lesser General Public License
# along with Simple Parser.  If not, see <http://www.gnu.org/licenses/>.

from __future__ import division

import sys
import sp

try:
    import readline
except ImportError:
    pass

class Calc(dict):

    def __init__(self):
        dict.__init__(self)
        _fy = lambda f, y: lambda x: f(x, y)
        fx = lambda f, x: f(x)
        def reduce(x, fs):
            for f in fs: x = f(x)
            return x
        self.parser = sp.compile(r"""

            ident = r'[a-zA-Z_]\w*' ;

            real = r'(?:\d+\.\d*|\d*\.\d+)(?:[eE][-+]?\d+)?|\d+[eE][-+]?\d+' : `float` ;
            int = r'\d+' : `int` ;
            var = ident : `self.__getitem__`;

            add_op = '+'    `lambda x, y: x + y` ;
            add_op = '-'    `lambda x, y: x - y` ;
            add_op = '|'    `lambda x, y: x | y` ;
            add_op = '^'    `lambda x, y: x ^ y` ;

            mul_op = '*'    `lambda x, y: x * y` ;
            mul_op = '/'    `lambda x, y: x / y` ;
            mul_op = '%'    `lambda x, y: x % y` ;
            mul_op = '&'    `lambda x, y: x & y` ;
            mul_op = '>>'   `lambda x, y: x << y` ;
            mul_op = '<<'   `lambda x, y: x >> y` ;

            pow_op = '**'   `lambda x, y: x ** y` ;

            un_op = '+'     `lambda x: +x` ;
            un_op = '-'     `lambda x: -x` ;
            un_op = '~'     `lambda x: ~x` ;

            separator: r'\s+';

            !S = ident '=' expr :: `self.__setitem__`
               | expr
               ;

            expr = term (add_op term :: `_fy`)* :: `reduce` ;
            term = fact (mul_op fact :: `_fy`)* :: `reduce` ;
            fact = un_op fact :: `fx` | pow ;
            pow = atom (pow_op fact :: `_fy`)? :: `reduce` ;

            atom = '(' expr ')' ;
            atom = real | int ;
            atom = var ;

        """)

    def __call__(self, input):
        return self.parser(input)

def exc():
    e = getattr(sys, 'exc_value', None)
    if e is None:
        info = getattr(sys, 'exc_info', None)
        if info is not None: e = info()[1]
    return e

try: raw_input
except NameError: raw_input = input

calc = Calc()

while True:
    expr = raw_input(": ")
    sp.clean()
    try:
        val = calc(expr)
        if val is not None:
            print("= %s"%calc(expr))
    except:
        print("! %s"%exc())
    print("")