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jsverify v0.8.2

Property-based testing for JavaScript.


Property-based checking. Like QuickCheck.

Build Status NPM version Dependency Status devDependency Status Code Climate

Getting Started

Install the module with: npm install jsverify


var jsc = require("jsverify");

// forall (f : bool -> bool) (b : bool), f (f (f b)) = f(b).
var boolFnAppliedThrice =
  jsc.forall("bool -> bool", "bool", function (f, b) {
    return f(f(f(b))) === f(b);

// OK, passed 100 tests


Usage with mocha

Using jsverify with mocha is easy, just define the properties and use jsverify.assert.

Starting from version 0.4.3 you can write your specs without any boilerplate:

describe("sort", function () {"idempotent", "array nat", function (arr) {
    return _.isEqual(sort(sort(arr)), sort(arr));

Starting from version 0.8.0 you can write the specs in TypeScript. There are typings provided. The drawback is that you cannot use type DSL:

describe("basic jsverify usage", () => {"(b && b) === b", jsc.bool, b => (b && b) === b);"boolean fn thrice", jsc.fn(jsc.bool), jsc.bool, (f, b) =>
    f(f(f(b))) === f(b)

You can also provide --jsverifyRngState state command line argument, to run tests with particular random generator state.

$ mocha examples/nat.js

1) natural numbers are less than 90:
 Error: Failed after 49 tests and 1 shrinks. rngState: 074e9b5f037a8c21d6; Counterexample: 90;

$ mocha examples/nat.js --grep 'are less than' --jsverifyRngState 074e9b5f037a8c21d6

1) natural numbers are less than 90:
   Error: Failed after 1 tests and 1 shrinks. rngState: 074e9b5f037a8c21d6; Counterexample: 90;

Erroneous case is found with first try.

Usage with jasmine

Check jasmineHelpers.js and jasmineHelpers2.js for jasmine 1.3 and 2.0 respectively.

API Reference

Testing shows the presence, not the absence of bugs.

Edsger W. Dijkstra

To show that propositions hold, we need to construct proofs. There are two extremes: proof by example (unit tests) and formal (machine-checked) proof. Property-based testing is somewhere in between. We formulate propositions, invariants or other properties we believe to hold, but only test it to hold for numerous (randomly generated) values.

Types and function signatures are written in Coq/Haskell-influenced style: C# -style List<T> filter(List<T> v, Func<T, bool> predicate) is represented by filter(v: array T, predicate: T -> bool): array T in our style.

Methods and objects live in jsc object, e.g. shrink.bless method is used by

var jsc = require("jsverify");
var foo = jsc.shrink.bless(...);

Methods starting with .dot are prototype methods:

var arb = jsc.nat;
var arb2 = jsc.nat.smap(f, g);

jsverify can operate with both synchronous and asynchronous-promise properties. Generally every property can be wrapped inside functor, for now in either identity or promise functor, for synchronous and promise properties respectively.


  • forall(arbs: arbitrary a ..., userenv: (map arbitrary)?, prop : a -> property): property

    Property constructor

  • check (prop: property, opts: checkoptions?): result

    Run random checks for given prop. If prop is promise based, result is also wrapped in promise.


    • opts.tests - test count to run, default 100
    • opts.size - maximum size of generated values, default 50
    • opts.quiet - do not console.log
    • opts.rngState - state string for the rng

    The result is true if check succeeds, otherwise it's an object with various fields:

    • counterexample - an input for which property fails.
    • tests - number of tests run before failing case is found
    • shrinks - number of shrinks performed
    • exc - an optional exception thrown by property function
    • rngState - random number generator's state before execution of the property
  • assert(prop: property, opts: checkoptions?) : void

    Same as check, but throw exception if property doesn't hold.

  • property(name: string, ...)

    Assuming there is globally defined it, the same as:

    it(name, function () {

    You can use property to write facts too:"+0 === -0", function () {
      return +0 === -0;
  • compile(desc: string, env: typeEnv?): arbitrary a

    Compile the type description in provided type environment, or default one.

  • sampler(arb: arbitrary a, genSize: nat = 10): (sampleSize: nat?) -> a

    Create a sampler for a given arbitrary with an optional size. Handy when used in a REPL:

    > jsc = require('jsverify') // or require('./lib/jsverify') w/in the project
    > jsonSampler = jsc.sampler(jsc.json, 4)
    > jsonSampler()
    > jsonSampler()
    [ [ [] ] ]
    > jsonSampler()
    > sampledJson(2)
    [-0.4199344692751765, false]
  • throws(block: () -> a, error: class?, message: string?): bool

    Executes nullary function block. Returns true if block throws. See assert.throws

  • assertForall(arbs: arbitrary a ..., userenv: (map arbitrary)?, prop : a -> property): void

    Combines 'assert' and 'forall'. Constructs a property with forall from arguments, then throws an exception if the property doesn't hold. Options for 'assert' cannot be set here - use assert(forall(...)) if you need that.

  • checkForall(arbs: arbitrary a ..., userenv: (map arbitrary)?, prop : a -> property): result

    Combines 'check' and 'forall'. Constructs a property with forall from arguments, and returns a value based on if the property holds or not. See 'check' for description of return value.

    Options for 'check' cannot be set here - use check(forall(...)) if you need that.


  • generator a is a function (size: nat) -> a.
  • show is a function a -> string.
  • shrink is a function a -> [a], returning smaller values.
  • arbitrary a is a triple of generator, shrink and show functions.
    • { generator: nat -> a, shrink : a -> array a, show: a -> string }


We chose to represent generators and shrinks by functions, yet we would like to have additional methods on them. Thus we bless objects with additional properties.

Usually you don't need to bless anything explicitly, as all combinators return blessed values.

See perldoc for bless.

DSL for input parameters

There is a small DSL to help with forall. For example the two definitions below are equivalent:

var bool_fn_applied_thrice = jsc.forall("bool -> bool", "bool", check);
var bool_fn_applied_thrice = jsc.forall(jsc.fn(jsc.bool), jsc.bool, check);

The DSL is based on a subset of language recognized by typify-parser:

  • identifiers are fetched from the predefined environment.
  • applications are applied as one could expect: "array bool" is evaluated to jsc.array(jsc.bool).
  • functions are supported: "bool -> bool" is evaluated to jsc.fn(jsc.bool).
  • square brackets are treated as a shorthand for the array type: "[nat]" is evaluated to jsc.array(jsc.nat).
  • union: "bool | nat" is evaluated to jsc.sum([jsc.bool, jsc.nat]).
    • Note oneof cannot be shrinked, because the union is untagged, we don't know which shrink to use.
  • conjunction: "bool & nat" is evaluated to jsc.tuple(jsc.bool, jsc.nat).
  • anonymous records: "{ b: bool; n: nat }" is evaluated to jsc.record({ b: jsc.bool, n: jsc.nat }).
  • EXPERIMENTAL: recursive types: "rec list -> unit | (nat & list)".

Arbitrary data

  • .smap(f: a -> b, g: b -> a, newShow: (b -> string)?): arbitrary b

    Transform arbitrary a into arbitrary b. For example:

    g should be a right inverse of f, but doesn't need to be complete inverse. i.e. i.e. f doesn't need to be invertible, only surjective.

    var positiveIntegersArb = nat.smap(
      function (x) { return x + 1; },
      function (x) { return x - 1; });
    var setNatArb =  jsc.array(jsc.nat).smap(_.uniq, _.identity);

    Right inverse means that f(g(y)) = y for all y in Y. Here Y is a type of arrays of unique natural numbers. For them

    _.uniq(_.identity(y)) = _.uniq(y) = y

    Opposite: g(f(x)) for all x in X, doesn't need to hold. X is arrays of natural numbers:

    _.identity(_uniq([0, 0])) = [0]] != [0, 0]

    We need an inverse for shrinking, and there right inverse is enough. We can always pull back smapped value, shrink the preimage, and map or push forward shrunken preimages again.

  • bless(arb: {...}): arbitrary a

    Bless almost arbitrary structure to be proper arbitrary. Note: this function mutates argument.


    var arbTokens = jsc.bless({
      generator: function () {
        switch (jsc.random(0, 2)) {
          case 0: return "foo";
          case 1: return "bar";
          case 2: return "quux";

Primitive arbitraries

  • integer: arbitrary integer

  • integer(maxsize: nat): arbitrary integer

  • integer(minsize: integer, maxsize: integer): arbitrary integer

    Integers, ℤ

  • nat: arbitrary nat

  • nat(maxsize: nat): arbitrary nat

    Natural numbers, ℕ (0, 1, 2...)

  • number: arbitrary number

  • number(maxsize: number): arbitrary number

  • number(min: number, max: number): arbitrary number

    JavaScript numbers, "doubles", ℝ. NaN and Infinity are not included.

  • uint8: arbitrary nat

  • uint16: arbitrary nat

  • uint32: arbitrary nat

  • int8: arbitrary integer

  • int16: arbitrary integer

  • int32: arbitrary integer

  • bool: arbitrary bool

    Booleans, true or false.

  • datetime: arbitrary datetime

    Random datetime

  • elements(args: array a): arbitrary a

    Random element of args array.

  • falsy: arbitrary *

    Generates falsy values: false, null, undefined, "", 0, and NaN.

  • constant(x: a): arbitrary a

    Returns an unshrinkable arbitrary that yields the given object.

Arbitrary combinators

  • nonshrink(arb: arbitrary a): arbitrary a

    Non shrinkable version of arbitrary arb.

  • unit: arbitrary ()

  • either(arbA: arbitrary a, arbB : arbitrary b): arbitrary (either a b)

  • pair(arbA: arbitrary a, arbB : arbitrary b): arbitrary (pair a b)

    If not specified a and b are equal to value().

  • tuple(arbs: (arbitrary a, arbitrary b...)): arbitrary (a, b...)

  • sum(arbs: (arbitrary a, arbitrary b...)): arbitrary (a | b ...)

  • dict(arb: arbitrary a): arbitrary (dict a)

    Generates a JavaScript object with properties of type A.

  • array(arb: arbitrary a): arbitrary (array a)

  • nearray(arb: arbitrary a): arbitrary (array a)

  • json: arbitrary json

    JavaScript Objects: boolean, number, string, null, array of json values or object with json values.

  • oneof(gs : array (arbitrary a)...) : arbitrary a

    Randomly uses one of the given arbitraries.

  • letrec(
      (tie: key -> (arbitrary a | arbitrary b | ...))
      -> { key: arbitrary a, key: arbitrary b, ... }):
    { key: arbitrary a, key: arbitrary b, ... }

    Mutually recursive definitions. Every reference to a sibling arbitrary should go through the tie function.

    { arb1, arb2 } = jsc.letrec(function (tie) {
      return {
        arb1: jsc.tuple(, jsc.oneof(jsc.const(null), tie("arb2"))),
        arb2: jsc.tuple(jsc.bool, jsc.oneof(jsc.const(null), tie("arb1"))),

Arbitrary records

  • record(spec: { key: arbitrary a... }, userenv: env?): arbitrary { key: a... }

    Generates a javascript object with given record spec.

  • generator.record(gen: { key: generator a... }): generator { key: a... }

  • shrink.record(shrs: { key: shrink a... }): shrink { key: a... }

Arbitrary strings

  • char: arbitrary char — Single character

  • asciichar: arbitrary char — Single ascii character (0x20-0x7e inclusive, no DEL)

  • string: arbitrary string

  • nestring: arbitrary string — Generates strings which are not empty.

  • asciistring: arbitrary string

  • asciinestring: arbitrary string

Arbitrary functions

  • fn(arb: arbitrary a): arbitrary (b -> a)
  • fun(arb: arbitrary a): arbitrary (b -> a)

Small arbitraries

  • generator.small(gen: generator a): generator a
  • small(arb: arbitrary a): arbitrary a

Create a generator (abitrary) which will generate smaller values, i.e. generator's size parameter is decreased logarithmically."small array of small natural numbers", "small (array nat)", function (arr) {
  return Array.isArray(arr);
});"small array of normal natural numbers", "(small array) nat", function (arr) {
  return Array.isArray(arr);

Generator functions

A generator function, generator a, is a function (size: nat) -> a, which generates a value of given size.

Generator combinators are auto-curried:

var xs = jsc.generator.array(jsc.nat.generator, 1); // ≡
var ys = jsc.generator.array(jsc.nat.generator)(1);

In purely functional approach generator a would be explicitly stateful computation: (size: nat, rng: randomstate) -> (a, randomstate). JSVerify uses an implicit random number generator state, but the value generation is deterministic (tests are reproducible), if the primitives from random module are used.

  • generator.bless(f: nat -> a): generator a

    Bless function with .map and .flatmap properties.

  • .map(f: a -> b): generator b

    Map generator a into generator b. For example:

    positiveIntegersGenerator =
      function (x) { return x + 1; });
  • .flatmap(f: a -> generator b): generator b

    Monadic bind for generators. Also flatMap version is supported.

  • generator.constant(x: a): generator a

  • generator.combine(gen: generator a..., f: a... -> b): generator b

  • generator.oneof(gens: list (generator a)): generator a

  • generator.recursive(genZ: generator a, genS: generator a -> generator a): generator a

  • generator.pair(genA: generator a, genB: generator b): generator (a, b)

  • generator.either(genA: generator a, genB: generator b): generator (either a b)

  • generator.unit: generator ()

    unit is an empty tuple, i.e. empty array in JavaScript representation. This is useful as a building block.

  • generator.tuple(gens: (generator a, generator b...)): generator (a, b...)

  • generator.sum(gens: (generator a, generator b...)): generator (a | b...)

  • generator.array(gen: generator a): generator (array a)

  • generator.nearray(gen: generator a): generator (array a)

  • generator.dict(gen: generator a): generator (dict a)

Shrink functions

A shrink function, shrink a, is a function a -> [a], returning an array of smaller values.

Shrink combinators are auto-curried:

var xs = jsc.shrink.array(jsc.nat.shrink, [1]); // ≡
var ys = jsc.shrink.array(jsc.nat.shrink)([1]);
  • shrink.bless(f: a -> [a]): shrink a

    Bless function with .smap property.

  • .smap(f: a -> b, g: b -> a): shrink b

    Transform shrink a into shrink b. For example:

    positiveIntegersShrink = nat.shrink.smap(
      function (x) { return x + 1; },
      function (x) { return x - 1; });
  • shrink.noop: shrink a

  • shrink.pair(shrA: shrink a, shrB: shrink b): shrink (a, b)

  • shrink.either(shrA: shrink a, shrB: shrink b): shrink (either a b)

  • shrink.tuple(shrs: (shrink a, shrink b...)): shrink (a, b...)

  • shrink.sum(shrs: (shrink a, shrink b...)): shrink (a | b...)

  • shrink.array(shr: shrink a): shrink (array a)

  • shrink.nearray(shr: shrink a): shrink (nearray a)

Show functions

  • show.def(x : a): string

    Currently implemented as JSON.stringify.

  • show.pair(showA: a -> string, showB: b -> string, x: (a, b)): string

  • show.either(showA: a -> string, showB: b -> string, e: either a b): string

  • show.tuple(shrinks: (a -> string, b -> string...), x: (a, b...)): string

  • show.sum(shrinks: (a -> string, b -> string...), x: (a | b ...)): string

  • show.array(shrink: a -> string, x: array a): string

Random functions

  • random(min: int, max: int): int

    Returns random int from [min, max] range inclusively.

    getRandomInt(2, 3) // either 2 or 3
  • random.number(min: number, max: number): number

    Returns random number from [min, max) range.


  • either.left(value: a): either a b

  • either.right(value: b): either a b

  • either.either(l: a -> x, r: b -> x): x

  • either.isEqual(other: either a b): bool

    TODO: add eq optional parameter

  • either.bimap(f: a -> c, g: b -> d): either c d

    either.bimap(compose(f, g), compose(h, i)) ≡ either.bimap(g, i).bimap(f, h);
  • either.first(f: a -> c): either c b

    either.first(f) ≡ either.bimap(f, utils.identity)
  • either.second(g: b -> d): either a d

    either.second(g) === either.bimap(utils.identity, g)

Utility functions

Utility functions are exposed (and documented) only to make contributions to jsverify more easy. The changes here don't follow semver, i.e. there might be backward-incompatible changes even in patch releases.

Use underscore.js, lodash, ramda, lazy.js or some other utility belt.

  • utils.isEqual(x: json, y: json): bool

    Equality test for json objects.

  • utils.isApproxEqual(x: a, y: b, opts: obj): bool

    Tests whether two objects are approximately and optimistically equal. Returns false only if they are distinguishable not equal. Returns true when x and y are NaN. This function works with cyclic data.

    Takes optional 'opts' parameter with properties:

    • fnEqual - whether all functions are considered equal (default: yes)
    • depth - how deep to recurse until treating as equal (default: 5)
  • utils.force(x: a | () -> a) : a

    Evaluate x as nullary function, if it is one.

  • utils.merge(x... : obj): obj

    Merge two objects, a bit like _.extend({}, x, y).


Why do all the examples import the library as jsc instead of jsv?

Does JSC originate with JSCheck?

A: Yes

smap requires an inverse function, which isn't always practical. Is this complexity related to shrinking?

A: Yes. We don't want to give an easy-to-use interface which forgets shrinking altogether. Note, that right inverse is enough, which is most likely easy to write, even complete inverse doesn't exist.


  • is generated from the source with ljs, say make literate.
  • jsverify.standalone.js is also generated by the build process
  • Before creating a pull request run make test, yet travis will do it for you.

Release History

  • 0.8.22017-04-01 — Typescript updates

    • Typings fixes
    • Sources are tslinted
  • 0.8.12017-03-31 — Typescript updates

  • 0.8.02017-03-12 — TypeScript typings

  • 0.7.52017-03-08 — International Women's Day

    • Add letrec combinator #193
    • Add null to json arbitrary #201
    • Fix typos and outdated links in documentation
  • 0.7.42016-09-07 — Bless suchthat

    • Fix "arbitraries created with suchthat are missing .smap" #184
  • 0.7.32016-08-26 — Remove lodash

    • Fixed accidental use of lodash. We have our own isNaN now.
  • 0.7.22016-08-25 — One year since the last release

    • jsc.utils.isEqual returns true if both arguments are NaN.
    • Add jsc.assertForall and jsc.checkForall
  • 0.7.12015-08-24 — jsc.throws

    • Add jsc.throws #133
  • 0.7.02015-08-23 — More experiments

    • jsc.sum - generate arbitrary sum types (generalisation of either) #125
      • BREAKING CHANGE: bar (|) in DSL generates jsc.sum
    • experimental support of recursive types in DSL (especially no shrinking yet) #109 #126
    • fail early when jsc.forall is given zero generators #128
    • jsc.json has shrink #122
    • non-true non-function results from properties are treated as exceptions #127
  • 0.6.32015-07-27 — Bug fixes

    • jsc.utils.isEqual doesn't care about key ordering #123
    • tuple's shrink is blessed #124
  • 0.6.22015-07-13 — Trampolines

  • 0.6.12015-07-13 — Bug fixes

    • Print stacktrace of catched exceptions
    • maxsize = 0 for numeric generators works
    • Issue with non-parametric returning property.
  • 0.6.02015-06-19 — Minor but major release!

    • added jsc.utils.isApproxEqual
  • 0.6.0-beta.22015-05-31 — Beta!

    • Fix issue #113 - Shrink of tuple with arrays failed.
  • 0.6.0-beta.12015-05-04 — Beta!

    • FAQ section
    • Improved smap documentation
    • flatmap is also flatMap
    • Fix function arbitrary
    • small arbitraries
    • jsc.generator.record
    • Thanks to @peterjoel for reporting issues
  • 0.6.0-alpha.62015-04-25 — Fix issues #98

    • Documentation improvements
    • Fix issue #98 - error while generating int32 values
  • 0.6.0-alpha.52015-04-23 — Fix issue #99

    • Documentation improvements
    • Fix issue #99 (suchthat shrink)
  • 0.6.0-alpha.42015-04-26 — Fix issue #87

    • didn't fail with asynchronous properties
    • thanks @Ezku for reporting
  • 0.6.0-alpha.32015-04-24 — promise shrink fixed

  • 0.6.0-alpha.22015-04-24 — jsc.bless

    • Added jsc.bless
  • 0.6.0-alpha.12015-04-22 — Preview

    • Using lazy sequences for shrink results
    • Breaking changes:
      • renamed to jsc.dict
      • jsc.value removed, use jsc.json
      • jsc.string() removed, use jsc.string
      • shrink.isomap renamed to shrink.smap
  • 0.5.32015-04-21 — More algebra

    • unit and either arbitraries
    • arbitrary.smap to help creating compound data
  • 0.5.22015-04-10show.def -change

  • 0.5.12015-02-19 — Dependencies bump

    • We also work on 0.12 and iojs!
  • 0.5.02014-12-24 — Merry Chrismas 2014!

    • Documentation cleanup
  • 0.5.0-beta.22014-12-21 — Beta 2!

    • Pair & tuple related code cleanup
    • Update
    • Small documentation type fixes
    • Bless jsc.elements shrink
  • 0.5.0-beta.12014-12-20 — Beta!

    • bless don't close over (uses this)
    • Cleanup generator module
    • Other code cleanup here and there
  • 0.4.62014-11-30 — better shrinks & recursive

    • Implemented shrinks: #51
    • jsc.generator.recursive: #37
    • array, nearray & map generators return a bit smaller results (log2 of size)
  • 0.4.52014-11-22 — stuff

    • generator.combine & .flatmap
    • nat, integer, number & and string act as objects too
  • 0.4.42014-11-22 — new generators

    • New generators: nearray, nestring
    • generator.constant
    • zero-ary (it ∘ assert)
    • jsc.sampler
  • 0.4.32014-11-08 —

    • Now you can write your bdd specs without any boilerplate
    • support for nat-litearls in dsl #36
      describe("Math.abs", function () {"result is non-negative", "integer 100", function (x) {
          return Math.abs(x) >= 0;
    • Falsy generator #42
  • 0.4.22014-11-03 — User environments for DSL

    • User environments for DSL
    • Generator prototype map, and shrink prototype isomap
    • JSON generator works with larger sizes
  • 0.4.1 Move to own organization in GitHub

  • 0.4.02014-10-27 — typify-dsl & more arbitraries. Changes from 0.3.6:

    • DSL for forall and suchthat
    • new primitive arbitraries
    • oneof behaves as in QuickCheck (BREAKING CHANGE)
    • elements is new name of old oneof
    • Other smaller stuff under the hood
  • 0.4.0-beta.4 generator.oneof

  • 0.4.0-beta.3 Expose shrink and show modules

  • 0.4.0-beta.2 Move everything around

    • Better looking!
  • 0.4.0-beta.1 Beta!

    • Dev Dependencies update
  • 0.4.0-alpha8 oneof & record -dsl support

    • also jsc.compile
    • record is shrinkable!
  • 0.4.0-alpha7 oneof & record

    • oneof and record generator combinators (@fson)
    • Fixed uint* generators
    • Default test size increased to 10
    • Numeric generators with size specified are independent of test size (#20)
  • 0.4.0-alpha6 more primitives

    • int8, int16, int32, uint8, uint16, uint32
    • char, asciichar and asciistring
    • value → json
    • use eslint
  • 0.4.0-alpha5 move david to be devDependency

  • 0.4.0-alpha4 more typify

    • suchchat supports typify dsl
    • oneofelements to be in line with QuickCheck
    • Added versions of examples using typify dsl
  • 0.4.0-alpha3 David, npm-freeze and jscs

  • 0.4.0-alpha2 Fix typo in readme

  • 0.4.0-alpha1 typify

    • DSL for forall

      var bool_fn_applied_thrice = jsc.forall("bool -> bool", "bool", check);
    • generator arguments, which are functions are evaluated. One can now write:

      jsc.forall(jsc.nat, check) // previously had to be jsc.nat()
  • 0.3.6 map generator

  • 0.3.5 Fix forgotten rngState in console output

  • 0.3.4 Dependencies update

  • 0.3.3 Dependencies update

  • 0.3.2 funfn

  • 0.3.1 Documentation typo fixes

  • 0.3.0 Major changes

    • random generate state handling
    • --jsverifyRngState parameter value used when run on node
    • karma tests
    • use make
    • dependencies update
  • 0.2.0 Use browserify

  • 0.1.4 Mocha test suite

    • major cleanup
  • 0.1.3 and exception catching

  • 0.1.2 Added jsc.assert

  • 0.1.1 Use grunt-literate

  • 0.1.0 Usable library

  • 0.0.2 Documented preview

  • 0.0.1 Initial preview

Related work



The MIT License (MIT)

Copyright (c) 2013-2015 Oleg Grenrus

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.



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