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JavaScript Expression Evaluator

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Description

This is a fork of expr-eval 2.0.2 with some enhancements, as it appears that package is no longer being maintained. This fork adds the following enhancements.

Support for undefined

The concept of JavaScript's undefined has been added to the parser.

undefined keyword

The undefined keyword has been added to the parser allowing it to be used in expressions.

x > 3 ? undefined : x
x == undefined ? 1 : 2

setting expression variables to undefined

If you set a local variable to undefined, expr-eval would generate an error saying that your variable was unrecognized.

For example:

/* myCustomFn() returns undefined */
x = myCustomFn(); x > 3
/* Error: unrecognized variable: x */

This has been fixed, you can now set expression variables to undefined and they will resolve correctly.

operators/functions gracefully support undefined

All operators and built-in functions have been extended to gracefully support undefined. Generally speaking if one of the input values is undefined then the operator/function returns undefined. So 2 + undefined is undefined, max(0, 1, undefined) is undefined, etc.

Logical operators act just like JavaScript, so 3 > undefined is false.

coalesce operator

The coalesce operator ?? has been added; x ?? y will evaluate to y if x is

  • undefined
  • null
  • Infinity (divide by zero)
  • NaN

Examples:

var parser = new Parser();
var obj = { x: undefined, y: 10, z: 0 };
parser.evaluate('x ?? 0', obj); // 0
parser.evaluate('y ?? 0', obj); // 10
parser.evaluate('x ?? 1 * 3', obj); // (undefined ?? 1) * 3 = 3
parser.evaluate('y ?? 1 * 3', obj); // (10 ?? 1) * 3 = 30
parser.evaluate('10 / z', obj); // Infinity
parser.evaluate('10 / z ?? 0', obj); // 0
parser.evaluate('sqrt -1'); // NaN
parser.evaluate('sqrt -1 ?? 0'); // 0

array/structure references act like ?.

Structure/array property references now act like ?., meaning if the entire property chain does not exist then instead of throwing an error the value of the property is undefined.

For example:

var parser = new Parser();
var obj = { thingy: { array: [{ value: 10 }] } };
parser.evaluate('thingy.array[0].value', obj); // 10
parser.evaluate('thingy.array[1].value', obj); // undefined
parser.evaluate('thingy.doesNotExist[0].childArray[1].notHere.alsoNotHere', obj); // undefined
parser.evaluate('thingy.array[0].value.doesNotExist', obj); // undefined

This can be combined with the coalesce operator to gracefully fall back on a default value if some part of a long property reference is undefined.

var parser = new Parser();
var obj = { thingy: { array: [{ value: 10 }] } };
parser.evaluate('thingy.array[1].value ?? 0', obj); // 0

string concatenation using +

The + operator can now be used to concatenate strings.

var parser = new Parser();
var obj = { thingy: { array: [{ value: 10 }] } };
parser.evaluate('"abc" + "def" + "ghi"', obj); // 'abcdefghi'

support for promises in custom functions

Custom functions can return promises. When this happens evaluate will return a promise that when resolved contains the expression value.

const parser = new Parser();

parser.functions.doIt = value => value + value;
parser.evaluate('doIt(2) + 3'); // 7

parser.functions.doIt = value =>
    new Promise((resolve) => setTimeout(() => resolve(value + value), 100));
await parser.evaluate('doIt(2) + 3'); // 7

support for custom variable name resolution

Custom logic can be provided to resolve unrecognized variable names. The parser has a resolve callback that will be called any time a variable name is not recognized. This can return an object that either indicates that the variable name is an alias for another variable or it can return the variable value.

const parser = new Parser();
const obj = { variables
6DB6
: { a: 5, b: 1 } };
parser.resolve = token => token === '$v' ? { alias: 'variables' } : undefined;
parser.evaluate('$v.a + variables.b', obj); // 6

parser.resolve = token =>
    token.startsWith('$') ? { value: obj.variables[token.substring(1)] } : undefined;
assert.strictEqual(parser.evaluate('$a + $b'), 6);

SQL style case blocks

NOTE: toJSFunction() is not supported for expressions that use case blocks.

SQL style case blocks are now supported, for both cases which evaluate a value against other values (a switch style case) and cases which test for the first truthy when (if/else/if style cases).

const parser = new Parser();
const expr = `
    case x
        when 1 then 'one'
        when 1+1 then 'two'
        when 1+1+1 then 'three'
        else 'too-big'
    end
`;
parser.evaluate(expr, { x: 1 }); // 'one'
parser.evaluate(expr, { x: 2 }); // 'two'
parser.evaluate(expr, { x: 3 }); // 'three'
parser.evaluate(expr, { x: 4 }); // 'too-big'
const parser = new Parser();
const expr = `
    case
        when x == 1 then 'one'
        when x == 1+1 then 'two'
        when x == 1+1+1 then 'three'
        else 'too-big'
    end
`;
parser.evaluate(expr, { x: 1 }); // 'one'
parser.evaluate(expr, { x: 2 }); // 'two'
parser.evaluate(expr, { x: 3 }); // 'three'
parser.evaluate(expr, { x: 4 }); // 'too-big'

object construction

Objects can be created using JavaScript syntax. This allows for expressions that return object values and for object arguments to be passed to custom functions.

const parser = new Parser();
const expr = `{
    a: x * 3,
    b: {
        /*this x is a property and not the x on the input object*/
        x: "first" + "_" + "second",
        y: min(x, 0),
    },
    c: [0, 1, 2, x],
}`;
parser.evaluate(expr, { x: 3 });
/*
{
    a: 15,
    b: {
        x: 'first_second',
        z: 0
    },
    c: [0, 1, 2, 3]
}
*/

as operator

An as operator has been added to support type conversion. This operator is disabled by default and must be explicitly enabled by setting operators.conversion to true in the options. It can be used to perform value conversion. By default is of limited value; it only supports converting values to numbers, int/integer (by rounding the number), and boolean. The intent is to allow integration of more sophisticated value conversion packages such as numeral.js and moment for conversion of other values.

const parser = new Parser({ operators: { conversion: true } });
parser.evaluate('"1.6" as "number"'); // 1.6
parser.evaluate('"1.6" as "int"'); // 2
parser.evaluate('"1.6" as "integer"'); // 2
parser.evaluate('"1.6" as "boolean"'); // true

The default as implementation can be overridden by replacing parser.binaryOps.as.

const parser = new Parser({ operators: { conversion: true } });
parser.binaryOps.as = (a, _b) => a + '_suffix';
parser.evaluate('"abc" as "suffix"'); // 'abc_suffix'

Original expr-eval readme below:

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 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

Operator Associativity Description
(...) None Grouping
f(), x.y, a[i] Left Function call, property access, array indexing
! Left Factorial
^ Right Exponentiation
+, -, not, sqrt, etc. Right Unary prefix operators (see below for the full list)
*, /, % Left Multiplication, division, remainder
+, -, || Left Addition, subtraction, array/list concatenation
==, !=, >=, <=, >, <, in Left Equals, not equals, etc. "in" means "is the left operand included in the right array operand?"
and Left Logical AND
or Left Logical OR
x ? y : z Right Ternary conditional (if x then y else z)
= Right Variable assignment
; Left Expression separator 
    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.

Operator Description
-x Negation
+x Unary plus. This converts it's operand to a number, but has no other effect.
x! Factorial (x * (x-1) * (x-2) * … * 2 * 1). gamma(x + 1) for non-integers.
abs x Absolute value (magnitude) of x
acos x Arc cosine of x (in radians)
acosh x Hyperbolic arc cosine of x (in radians)
asin x Arc sine of x (in radians)
asinh x Hyperbolic arc sine of x (in radians)
atan x Arc tangent of x (in radians)
atanh x Hyperbolic arc tangent of x (in radians)
cbrt x Cube root of x
ceil x Ceiling of x — the smallest integer that’s >= x
cos x Cosine of x (x is in radians)
cosh x Hyperbolic cosine of x (x is in radians)
exp x e^x (exponential/antilogarithm function with base e)
expm1 x e^x - 1
floor x Floor of x — the largest integer that’s <= x
length x String or array length of x
ln x Natural logarithm of x
log x Natural logarithm of x (synonym for ln, not base-10)
log10 x Base-10 logarithm of x
log2 x Base-2 logarithm of x
log1p x Natural logarithm of (1 + x)
not x Logical NOT operator
round x X, rounded to the nearest integer, using "grade-school rounding"
sign x Sign of x (-1, 0, or 1 for negative, zero, or positive respectively)
sin x Sine of x (x is in radians)
sinh x Hyperbolic sine of x (x is in radians)
sqrt x Square root of x. Result is NaN (Not a Number) if x is negative.
tan x Tangent of x (x is in radians)
tanh x Hyperbolic tangent of x (x is in radians)
trunc x Integral part of a X, looks like floor(x) unless for negative number

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.

Function Description
random(n) Get a random number in the range [0, n). If n is zero, or not provided, it defaults to 1.
fac(n) n! (factorial of n: "n * (n-1) * (n-2) * … * 2 * 1") Deprecated. Use the ! operator instead.
min(a,b,…) Get the smallest (minimum) number in the list.
max(a,b,…) Get the largest (maximum) number in the list.
hypot(a,b) Hypotenuse, i.e. the square root of the sum of squares of its arguments.
pyt(a, b) Alias for hypot.
pow(x, y) Equivalent to x^y. For consistency with JavaScript's Math object.
atan2(y, x) Arc tangent of x/y. i.e. the angle between (0, 0) and (x, y) in radians.
roundTo(x, n) Rounds x to n places after the decimal point.
map(f, a) Array map: Pass each element of a the function f, and return an array of the results.
fold(f, y, a) Array fold: Fold/reduce array a into a single value, y by sett 8733 ing y = f(y, x, index) for each element x of the array.
filter(f, a) Array filter: Return an array containing only the values from a where f(x, index) is true.
indexOf(x, a) Return the first index of string or array a matching the value x, or -1 if not found.
join(sep, a) Concatenate the elements of a, separated by sep.
if(c, a, b) Function form of c ? a : b. Note: This always evaluates both a and b, regardless of whether c is true or not. Use c ? a : b instead if there are side effects, or if evaluating the branches could be expensive.

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:

Constant Description
E The value of Math.E from your JavaScript runtime
PI The value of Math.PI from your JavaScript runtime
true Logical true value
false Logical false value

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

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Mathematical expression evaluator in JavaScript

silentmatt.com/javascript-expression-evaluator/

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