I am looking for a Java library which can parse mathematical formulas into an AST (abstract syntax tree).

I'm open to alternatives in languages other than Java, provided that I can call these tools/libraries from Java.
For example, JavaScript can be embedded using the Rhino engine.

Essential Requirements:

  1. The ability to parse formulas in infix notation.

  2. The ability to preserve unknown variables — I am not looking for a calculator.

  3. A customizable list of operators and functions.
    It would also be excellent if one could remove already built-in functions (e.g. sin(x)).

Non-Essential Requirements:

  • The library can be open source, but it doesn't need to be. A free library suffices.
  • Note: Even though I found a more or less fitting JavaScript library in the meantime, better alternatives (preferably in Java) are still welcome!
    – ComFreek
    Commented Jun 20, 2014 at 20:00

6 Answers 6



The JavaScript part

“Math.js is an extensive math library for JavaScript and Node.js.”
Project readme

It provides a parse() function.
Example using the NodeJS environment:

var math = require('mathjs')();
var ast = math.parse('xy^(1/2)');

// Fully log the object
var util = require('util');
console.log(util.inspect(ast, {showHidden: false, depth: null}));


{ op: '^',
  fn: 'pow',
   [ { name: 'xy' },
     { op: '/',
       fn: 'divide',
        [ { valueType: 'number', value: '1' },
          { valueType: 'number', value: '2' } ] } ] }

The Java part

I use the Java Nashorn VM (only available in Java >= 8) to execute JavaScript.

Program architecture:

User ---------------> Java
      inputs formla    |----> Nashorn ----> math.js
User <-----------------|

Using the Nashorn engine is quite simple (Exception handling omitted)

ScriptEngine engine = new ScriptEngineManager().getEngineByName("nashorn");

The bridge's JavaScript code highly depends on your implementation of AST nodes. We take advantage of Nashorn's ability to create and transfer Java objects in JavaScript to Java. Example:

var math = mathjs();
function convert(formula) {
    var ast = math.parse(formula);

    var javaAst = /* build your AST with Java objects */
    return javaAst;

We can now access that function from Java and even pass arbitrary arguments:

Invocable inv = (Invocable) engine;
// Expression is my AST node type in Java
expr = (Expression) inv.invokeFunction("convert", formulaFromUser);

Note: I needed a quick way of parsing mathematical expressions. A parser (either handwritten or generated by a parser generator) is always preferable. Nonetheless, the code above shows how Java Nashorn can be easily integrated.



Few months ago, I used Esprima to parse such inputs. Actually, Esprima parses any JavaScript input (converting it into a tree), so it should work for such math expressions.

After including Esprima, you can do:


...where input is a string containing the input that should be parsed (if it's invalid, an error will be thrown).



returns the following object:

    "type": "Program",
    "body": [
            "type": "ExpressionStatement",
            "expression": {
                "type": "BinaryExpression",
                "operator": "+",
                "left": {
                    "type": "Literal",
                    "value": 1,
                    "raw": "1"
                "right": {
                    "type": "BinaryExpression",
                    "operator": "*",
                    "left": {
                        "type": "Literal",
                        "value": 2,
                        "raw": "2"
                    "right": {
                        "type": "Literal",
                        "value": 3,
                        "raw": "3"

I modified Esprima code and used it in an experimental project to define custom operators in JavaScript. The application is open source on GitHub: http://ionicabizau.net/JavaScript-custom-operators/

  • Esprima seems to be far more powerful and capable of parsing features than I actually need. Nevertheless +1 and your operators are very interesting.
    – ComFreek
    Commented Jun 20, 2014 at 20:14


It seems that JEP is a math expression parser.

JEP is a Java API for parsing and evaluating mathematical expressions. With this library you can allow your users to enter an arbitrary formula as a string, and instantly evaluate it. JEP supports user defined variables, constants, and functions. A number of common mathematical functions and constants are included.


  • Easy-to-use package for parsing mathematical expressions
  • Small size (only 56kb as jar archive)
  • Supports boolean expressions (!, &&, ||, <, >, !=, ==, >=, and <=)
  • Fast evaluation (the expression can be evaluated quickly for different variable values)
  • Includes common math functions
  • Extendable through user defined functions
  • Predefined constants such as 'pi' and 'e'
  • Support for strings, complex numbers, and vectors
  • Support for implicit multiplication (allows use of expressions such as "3x" instead of "3*x")
  • Allows choice between declared and undeclared variables
  • Java 1.1 compatible (tested with Sun Java JDK 1.1.8 and the Microsoft Java VM)
  • Supports Unicode characters (including Greek symbols)
  • Includes JavaCC grammar from which the main classes are generated

It's open source on SourceForge.

Also, there is a SO question regarding this subject: https://stackoverflow.com/q/4589951/1420197

  • The initial project seems to be discontinued. The SourceForge project page links to a new external site, which offers Jep Java as a commercial product ($550 for binaries, $950 for the source code).
    – ComFreek
    Commented Jun 24, 2014 at 14:26
  • @ComFreek You're right. Anyway, I think the initial project should cover what you need. Thank you for bounty! :-) Commented Jun 24, 2014 at 14:29

Building formula parsers/tree builders is a pretty simple exercise. You can hunt for a library, but you'll always end up modifying it to produce exactly what you want. Instead, it is likely easier to simply code what you want.

  • This StackOverflow link provides directions on how to build parsers like this easily by hand. It also provides access to a second link, that shows how to easily convert such parsers into ones that produce ASTs.
  • You can easily customize to include whatever infix operators you like, whatever function operatos ("sin") you like, scalar values and variable names.
  • You can code these kinds of parsers in virtually any language, including Java.

If you want to parse something considerably more complex than an expression, you can push this kind of parser to do it, but it is generally easier to switch to parser generator in that case.



Symja transforms a math expression into the following Symja AST .


I have used javassist to convert Java expressions to byte code (which may be what you ultimately is looking for if you want to evaluate the expression). It can even redefine existing functions.


  • Forgive me if I misunderstood you, but how does Javassist let me parse user input (string) into a tree structure (Java objects)?
    – ComFreek
    Commented Jun 24, 2014 at 14:17
  • Probably not. It allows you to compile your expression into a Java method you can then call directly to have it evaluated. This is because I was expecting that this was your final goal. If this is a part of an exercise in writing a compiler, you should do it by hand instead :) Commented Jun 24, 2014 at 14:40

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