Simple arithmetic expression parser
Python Shell
Latest commit dddc01d Jul 2, 2016 Stefan Urbanek Fixed binary operator compilation, which was based on grako bug; adde…
…d grako dependency


Arithmetic expression parser library. Embed customized expression evaluation into your application or library. Example uses:

  • Safely process an expression entered through a web application, for example some formula to be plotted. The library allows safe translation of such expression without exposing any application's internals
  • precompiler that checks for allowed and denied identifiers in an expression
  • have a common expression language through your application regardless of the backend languages
  • compile arithmetic expression to any other expression tree (semantic), for example SQLAlchemy expression objects

Part of the Data Brewery


Install using pip:

pip install expressions

Expressions sources are available at Github

Works with Python 2.7 and Python 3.3. Uses Grako.

Quick Start

from expressions import Compiler

compiler = Compiler()
result = compiler.compile("min(a, b) * 2")

Result from the default (non-extended) compiler will be abstract semantic graph containing nodes Literal, Variable, Function, Binary and Unary operators. Subclasses of Compiler can yield different outputs by implementing just few simple methods which represent semantic graph nodes (same as the objects).


Here is an example compiler that allows only certain variables. The list of allowed variables is provided in the compilation context:

    from expressions import Compiler, ExpressionError

    class AllowingCompiler(Compiler):
        def compile_literal(self, context, literal):
            return repr(literal)

        def compile_variable(self, context, variable):
            if context and variable not in context:
                raise ExpressionError("Variable %s is not allowed" % variable)

            return variable

        def compile_binary(self, context, operator, op1, op2):
            return "(%s %s %s)" % (op1, operator, op2)

        def compile_function(self, context, function, args):
            arglist = ", " % args
            return "%s(%s)" % (function, arglist)

Allow only a and b variables:

compiler = AllowingCompiler()

allowed_variables = ["a", "b"]

Try to compile and execute the expression:

result = compiler.compile("a + b", allowed_variables)

a = 1
b = 1

This will fail, because only a and b are allowed, c is not:

result = compiler.compile("a + c", allowed_variables)

See the examples source directory for more examples such as very simplified expression-to-SQLAlchemy compiler.


Example expressions:

    1 + 1
    (a + b) ^ 2
    sum(amount) / count()
    date.year = 2010 and amount > 10
  • Binary arithmetic operators: +, -, *, /, % (modulo), ^ (power)
  • Binary comparison operators: <, <=, =, >=, >, in, is
  • Binary bit-wise operators: | (or), & (and), << (shift left), >> (shift right)
  • Binary logical operators: and, or
  • Unary operators: +, -, ~ (bit-wise not)

  • Function call: function_name(arg1, arg2, ...)

Variable and function names are either regular identifiers or identifiers separated by .. There is no value dereference and the dot . is just namespace composition operator for variable names. Example variable names: amount, date.year,

The suggested meaning of the operators is based mostly on the PostgreSQL operators

Writing a compiler

To write a custom compiler subclass a Compiler class and implement all of some of the following methods:

  • compile_function(context, reference, args) – compile a function call. The reference is the same kind of object as passed to the compile_variable(), args is list of function arguments. Default implementation returns an object with attributes reference and args
  • compile_binary(context, operator, left, right) – compile a binary operator operator with two operands left and right. Default implementation returns an object with attributes operator, left and right
  • compile_unary(context, operator, operand) – compile a unary operator with a single operand. Default implementation returns an object with attributes operator and operand.
  • compile_variable(context, variable) – compile a variable reference variable which is an object with properties name and reference. name is the full variable name (joined with .), reference is a list of variable name components. Return value should be either evaluated variable as a constant or some other useful variable reference.
  • compile_literal(context, literal) – compile an integer, float or a string object literal. Default implementation just passes the argument. You rarely need to override this method.
  • finalize(context, object) – return the final compilation result.

When compiling function arguments or operator operands you should check whether they are literals or instances of a Variable. For example:

    def compile_function(context, reference, args):
        # Assume that the context is a dictionary with variables and functions

        values = []
        for arg in args:
            if isinstance(arg, Variable):
                value = context[]
                value = arg

        function = context[]

        return function(*args)

Example compiler: Identifier Preprocessor

The following compiler is included in the library:

    class IdentifierPreprocessor(Compiler):
        def __init__(self):
            super(IdentifierPreprocessor, self).__init__()

            self.variables = set()
            self.functions = set()

        def compile_variable(self, context, variable):
            return variable

        def compile_function(self, context, function, args):
            return function


>>> preproc = IdentifierPreprocessor()
>>> preproc.compile("a + b")
>>> preproc.compile("sum(amount)")

The preproc.variables will contain Variable objects for a, b and amount, the proproc.functions will contain one Variable object sum:

>>> print(preproc.variables)
{Variable(amount), Variable(b), Variable(a)}
>>> print(preproc.functions)

Note that the Variable object represents any named object reference – both variables and functions.


The following classes are provided by the library:

  • Compiler – core compiler class that generates default structure, compile_* methods can be overriden to generate custom results
  • IdentifierPreprocessor – a Compiler subclass with two attributes variables and functions containing list of Variable objects collected from the compiled expression. Can be used for validation or preparation of variables

What Expressions is not

  • This is not a Python expression compiler. The grammar is based on very basic SQL grammar and few other simple SQL grammar features might be added in the future. There is no SQL compatibility guaranteed though. It is not meant to be a rich expression, but a small subset of quite common expressions to allow easy translation to other languages or object structures. Main use is arithmetic expression support for a modular application with different backends

  • It is not an expression of an object-oriented language – it does not have access to object attributes – the '.' dot operator is just an attribute name concatenation. The compiler receives full object reference as a string and as a list of reference components.


Expressions framework is licensed under the MIT license.

For more information see the LICENSE file.


Stefan Urbanek,, Twitter: @Stiivi