JavaScript Expression Evaluator

Description

Parses and evaluates mathematical expressions. It's a safer and more math-oriented alternative to using JavaScript’s eval function for mathematical expressions.

It has built-in support for common math operators and functions. Additionally, you can add your own JavaScript functions. Expressions can be evaluated directly, or compiled into native JavaScript functions.

Installation

npm install expr-eval

Basic Usage

    const Parser = require('expr-eval').Parser;

    const parser = new Parser();
    let expr = parser.parse('2 * x + 1');
    console.log(expr.evaluate({ x: 3 })); // 7

    // or
    Parser.evaluate('6 * x', { x: 7 }) // 42

Documentation

• Parser
  • Parser()
  • parse(expression: string)
  • Parser.parse(expression: string)
  • Parser.evaluate(expression: string, variables?: object)
• Expression
  • evaluate(variables?: object)
  • substitute(variable: string, expression: Expression | string | number)
  • simplify(variables: object)
  • variables(options?: object)
  • symbols(options?: object)
  • toString()
  • toJSFunction(parameters: array | string, variables?: object)
• Expression Syntax
  • Operator Precedence
  • Unary operators
  • Array literals
  • Pre-defined functions
  • Custom JavaScript functions
  • Constants

Parser

Parser is the main class in the library. It has as single parse method, and "static" methods for parsing and evaluating expressions.

Parser()

Constructs a new Parser instance.

The constructor takes an optional options parameter that allows you to enable or disable operators.

For example, the following will create a Parser that does not allow comparison or logical operators, but does allow in:

    const parser = new Parser({
      operators: {
        // These default to true, but are included to be explicit
        add: true,
        concatenate: true,
        conditional: true,
        divide: true,
        factorial: true,
        multiply: true,
        power: true,
        remainder: true,
        subtract: true,

        // Disable and, or, not, <, ==, !=, etc.
        logical: false,
        comparison: false,

        // Disable 'in' and = operators
        'in': false,
        assignment: false
      }
    });

parse(expression: string)

Convert a mathematical expression into an Expression object.

Parser.parse(expression: string)

Static equivalent of new Parser().parse(expression).

Parser.evaluate(expression: string, variables?: object)

Parse and immediately evaluate an expression using the values and functions from the variables object.

Parser.evaluate(expr, vars) is equivalent to calling Parser.parse(expr).evaluate(vars).

Expression

Parser.parse(str) returns an Expression object. Expressions are similar to JavaScript functions, i.e. they can be "called" with variables bound to passed-in values. In fact, they can even be converted into JavaScript functions.

evaluate(variables?: object)

Evaluate the expression, with variables bound to the values in {variables}. Each variable in the expression is bound to the corresponding member of the variables object. If there are unbound variables, evaluate will throw an exception.

    js> expr = Parser.parse("2 ^ x");
    (2^x)
    js> expr.evaluate({ x: 3 });
    8

substitute(variable: string, expression: Expression | string | number)

Create a new Expression with the specified variable replaced with another expression. This is similar to function composition. If expression is a string or number, it will be parsed into an Expression.

    js> expr = Parser.parse("2 * x + 1");
    ((2*x)+1)
    js> expr.substitute("x", "4 * x");
    ((2*(4*x))+1)
    js> expr2.evaluate({ x: 3 });
    25

simplify(variables: object)

Simplify constant sub-expressions and replace variable references with literal values. This is basically a partial evaluation, that does as much of the calculation as it can with the provided variables. Function calls are not evaluated (except the built-in operator functions), since they may not be deterministic.

Simplify is pretty simple. For example, it doesn’t know that addition and multiplication are associative, so ((2*(4*x))+1) from the previous example cannot be simplified unless you provide a value for x. 2*4*x+1 can however, because it’s parsed as (((2*4)*x)+1), so the (2*4) sub-expression will be replaced with "8", resulting in ((8*x)+1).

    js> expr = Parser.parse("x * (y * atan(1))").simplify({ y: 4 });
    (x*3.141592653589793)
    js> expr.evaluate({ x: 2 });
    6.283185307179586

variables(options?: object)

Get an array of the unbound variables in the expression.

    js> expr = Parser.parse("x * (y * atan(1))");
    (x*(y*atan(1)))
    js> expr.variables();
    x,y
    js> expr.simplify({ y: 4 }).variables();
    x

By default, variables will return "top-level" objects, so for example, Parser.parse(x.y.z).variables() returns ['x']. If you want to get the whole chain of object members, you can call it with { withMembers: true }. So Parser.parse(x.y.z).variables({ withMembers: true }) would return ['x.y.z'].

symbols(options?: object)

Get an array of variables, including any built-in functions used in the expression.

    js> expr = Parser.parse("min(x, y, z)");
    (min(x, y, z))
    js> expr.symbols();
    min,x,y,z
    js> expr.simplify({ y: 4, z: 5 }).symbols();
    min,x

Like variables, symbols accepts an option argument { withMembers: true } to include object members.

toString()

Convert the expression to a string. toString() surrounds every sub-expression with parentheses (except literal values, variables, and function calls), so it’s useful for debugging precedence errors.

toJSFunction(parameters: array | string, variables?: object)

Convert an Expression object into a callable JavaScript function. parameters is an array of parameter names, or a string, with the names separated by commas.

If the optional variables argument is provided, the expression will be simplified with variables bound to the supplied values.

    js> expr = Parser.parse("x + y + z");
    ((x + y) + z)
    js> f = expr.toJSFunction("x,y,z");
    [Function] // function (x, y, z) { return x + y + z; };
    js> f(1, 2, 3)
    6
    js> f = expr.toJSFunction("y,z", { x: 100 });
    [Function] // function (y, z) { return 100 + y + z; };
    js> f(2, 3)
    105

Expression Syntax

The parser accepts a pretty basic grammar. It's similar to normal JavaScript expressions, but is more math-oriented. For example, the ^ operator is exponentiation, not xor.

Operator Precedence

    const parser = new Parser({
      operators: {
        'in': true,
        'assignment': true
      }
    });
    // Now parser supports 'x in array' and 'y = 2*x' expressions

Unary operators

The parser has several built-in "functions" that are actually unary operators. The primary difference between these and functions are that they can only accept exactly one argument, and parentheses are optional. With parentheses, they have the same precedence as function calls, but without parentheses, they keep their normal precedence (just below ^). For example, sin(x)^2 is equivalent to (sin x)^2, and sin x^2 is equivalent to sin(x^2).

The unary + and - operators are an exception, and always have their normal precedence.

Pre-defined functions

Besides the "operator" functions, there are several pre-defined functions. You can provide your own, by binding variables to normal JavaScript functions. These are not evaluated by simplify.

Array literals

Arrays can be created by including the elements inside square [] brackets, separated by commas. For example:

[ 1, 2, 3, 2+2, 10/2, 3! ]

Function definitions

You can define functions using the syntax name(params) = expression. When it's evaluated, the name will be added to the passed in scope as a function. You can call it later in the expression, or make it available to other expressions by re-using the same scope object. Functions can support multiple parameters, separated by commas.

Examples:

    square(x) = x*x
    add(a, b) = a + b
    factorial(x) = x < 2 ? 1 : x * factorial(x - 1)

Custom JavaScript functions

If you need additional functions that aren't supported out of the box, you can easily add them in your own code. Instances of the Parser class have a property called functions that's simply an object with all the functions that are in scope. You can add, replace, or delete any of the properties to customize what's available in the expressions. For example:

    const parser = new Parser();

    // Add a new function
    parser.functions.customAddFunction = function (arg1, arg2) {
      return arg1 + arg2;
    };

    // Remove the factorial function
    delete parser.functions.fac;

    parser.evaluate('customAddFunction(2, 4) == 6'); // true
    //parser.evaluate('fac(3)'); // This will fail

Constants

The parser also includes a number of pre-defined constants that can be used in expressions. These are shown in the table below:

Pre-defined constants are stored in parser.consts. You can make changes to this property to customise the constants available to your expressions. For example:

    const parser = new Parser();
    parser.consts.R = 1.234;

    console.log(parser.parse('A+B/R').toString());  // ((A + B) / 1.234)

To disable the pre-defined constants, you can replace or delete parser.consts:

    const parser = new Parser();
    parser.consts = {};

Tests

1. cd to the project directory
2. Install development dependencies: npm install
3. Run the tests: npm test