.gitignore

.ipynb_checkpoints/
node_modules/

README.md

The Lambda Calculus!

Lambda calculus can be used to encode any program. Fundamentally it's the idea that everything can be build from a function of one argument. By using functions, data can be encoded.

Booleans

Start with a little bit of binary logic. Booleans are a common abstraction in programming languages which are easily expressed in lambda calculus. A boolean can be thought of as a binary construct that chooses between two values. When true, it chooses one value, and when false it chooses another.

troo = x => y => x
falz = x => y => y

Add a little helper function to display the boolean as a value.

to_bool = b => b('TRUE')('FALSE')

to_bool(troo)
// TRUE
to_bool(falz)
// FALSE

Boolean Operators

With such an encoding for booleans, you can start to develop some expressions of boolean logic. How about unary not (!), the boolean flipping operator?

not = b => b(falz)(troo)

to_bool(not(troo))
// FALSE
to_bool(not(falz))
// TRUE

Neat! Now, take a shot at a couple binary operators, and and or. Here are the truth tables for reference.

AND

b1	b2	result
true	true	true
true	false	false
false	true	false
false	false	False

OR

b1	b2	result
true	true	true
true	false	true
false	true	true
false	false	False

With that, encode their meaning.

and = b1 => b2 => b1(b2)(b1)
or = b1 => b2 => b1(b1)(b2)

to_bool(and(troo)(falz))
// FALSE
to_bool(or(troo)(falz))
// TRUE

It works! Now that we have some boolean logic, it shouldn't be too hard to implement everyone's favorite conditional operation: if/then/else.

// if(condition)(truecase)(falsecase)
iff = c => thn => els => c(thn)(els)

// cheating a bit with strings here...
iff(and(troo)(falz))('ya')('no')
// no
iff(or(troo)(falz))('ya')('no')
// ya

Not bad for a bunch of one argument functions. What else can we do?

Numbers

Another fun topic to explore is numbers and arithmetic. Like booleans (and everything for that matter), there must be an encoding for numbers as functions. This so-called "Church encoding" is based on counting function applications.

Consider zero.

zero = f => x => x

Zero applies a function, f, zero times to the value. Similarly one applies the function once, two twice, and so on.

one = f => x => f(x)
two = f => x => f(f(x))
//...

It's convenient to define a helper function that counts the function applications for visualization.

to_int = n => n(i => i+1)(0)

to_int(zero)
// 0
to_int(one)
// 1
to_int(two)
// 2

Also, if you look closely, you'll recognize that each successive number if based on its predecessor. It's just one more application of f on the result of the preceding number.

zero = f => x => x
one = f => x => f(zero(f)(x))
two = f => x => f(one(f)(x))
// ...

In fact, this routine of determining the successor of a number can be generalized. Do you see the pattern? The predecessor is hard-coded in the encoding of each number. Extract that value as an argument to another function that produces the successor.

succ = n => f => x => f(n(f)(x))
three = succ(two)
four = succ(three)

to_int(three)
// 3
to_int(four)
// 4

Basic Arithmetic

Alright, numbers are a matter of counting function applications. So it's pretty easy to imagine some basic arithmetic. Addition, for example, is m applications followed by n more applications. Multiplication would be m applications repeated n times.

add = m => n => f => x => n(f)(m(f)(x))

res = add(two)(three)
to_int(res)
// 5; whoa! that hadn't event be defined yet as a known number :mindblown:

mul = m => n => f => x => n(m(f))(x)
// Interestingly, since `x` is the last value applied, it can be dropped and the expression
// reduced to:
//   mul = m => => f => x => n(m(f))

res = mul(two)(three)
to_int(res)
// 6

Lambda Calculus.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# f(x)\n",
    "\n",
    "or\n",
    "\n",
    "# lambda calculus for all!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Albert Einstein:\n",
    "> If you can't explain it simply, you don't understand it well enough."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Lambda Calculus\n",
    "\n",
    "The idea is that we can describe all computation with functions of one argument."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With these fundamental building blocks, how can higher concepts be encoded?\n",
    "\n",
    "(There is a parellel to binary and CPU registers here)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Numbers (well, natural numbers)\n",
    "\n",
    "What are they? Good for counting!\n",
    "\n",
    "How might that be expressed as a function? Counting function applications."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "zero = \n",
    "one = \n",
    "two = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "to_int = n => n(i => i+1)(0) // this is NOT part of the lambda calculus!\n",
    "to_int(two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "Each successor _can_ be implementated in terms of its predecessor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "succ = \n",
    "\n",
    "three = succ(two)\n",
    "four = succ(three)\n",
    "to_int(four)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Arithmetic?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "add = \n",
    "to_int(add(three)(four))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "mul = \n",
    "to_int(mul(four)(three))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "exp = \n",
    "to_int(exp(two)(three))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Booleans\n",
    "\n",
    "What are they? A binary choice!\n",
    "\n",
    "How might that be expressed as a function? Make a choice between two inputs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "scrolled": true,
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "// use the booleans to make a choice\n",
    "troo = \n",
    "falz = "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "to_bool = b => b(true)(false)\n",
    "to_bool(troo)\n",
    "to_bool(falz)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Boolean logic?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "not = \n",
    "not(troo)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "and = \n",
    "and(troo)(falz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "or = \n",
    "or(troo)(falz)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "iff = \n",
    "iff(troo)(one)(two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Predicates"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "is_zero = \n",
    "is_zero(zero)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "is_even = \n",
    "is_even(two)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# Lists"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "pair = \n",
    "left = \n",
    "right = \n",
    "\n",
    "one_two = pair(one)(two)\n",
    "to_int(right(one_two))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "// list: (empty_flag:boolean, (head, tail))\n",
    "nil = \n",
    "is_empty = \n",
    "\n",
    "is_empty(nil)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "cons = \n",
    "head = \n",
    "tail = \n",
    "\n",
    "just_one = cons(one)(nil)\n",
    "to_int(head(just_one))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [],
   "source": [
    "map = "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "h/t Anjana Vakil! 🙌\n",
    "- https://www.youtube.com/watch?v=7BsfMMYvGaU&t=2s\n",
    "- https://gist.github.com/vakila/3d5cebaebf01c4c77b289b9a0388e3c8\n",
    "\n",
    "It me! ❤️\n",
    "- twitter/iamvery\n",
    "- tech256/jay\n",
    "- https://gist.github.com/iamvery/64735212135da5c899881f6ec234c759"
   ]
  }
 ],
 "metadata": {
  "celltoolbar": "Slideshow",
  "kernelspec": {
   "display_name": "Javascript (Node.js)",
   "language": "javascript",
   "name": "javascript"
  },
  "language_info": {
   "file_extension": ".js",
   "mimetype": "application/javascript",
   "name": "javascript",
   "version": "11.14.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

lambda.js

succ = n => f => x => f(n(f)(x))

zero = f => x => x
one = succ(zero)
two = succ(one)
three = succ(two)
four = succ(three)

add = m => n => f => x => n(f)(m(f)(x))
mul = m => n => f => n(m(f))
exp = b => e => e(b)

to_int = n => n(i => i+1)(0)

troo = x => _ => x
falz = _ => y => y

not = b => b(falz)(troo)
and = b1 => b2 => b1(b2)(b1)
or = b1 => b2 => b1(b1)(b2)
iff = c => thn => els => c(thn)(els)

to_bool = b => b('TRUE')('FALSE')

is_zero = n => n(_ => falz)(troo)
is_even = n => n(not)(troo)

pair = l => r => f => f(l)(r)
left = p => p(troo)
right = p => p(falz)
nil = pair(troo)(troo)
is_empty = left

cons = i => l => pair(falz)(pair(i)(l))
head = l => left(right(l))
tail = l => right(right(l))

double = n => add(n)(n)
one_two = cons(one)(cons(two)(nil)) // [1,2]

foldl = f => v => l =>
  iff(is_empty(l))(()=>
    v
  )(()=>
    foldl(f)(f(v)(head(l)))(tail(l))
  )()

foldr = f => v => l =>
  iff(is_empty(l))(()=>
    v
  )(()=>
    f(head(l))(foldr(f)(v)(tail(l)))
  )()

each = f => foldl(_ => i => f(i))(nil)
eachr= f => foldr(i => _ => f(i))(nil)

count = foldl(c => _ => add(c)(one))(zero)
sum = foldl(add)(zero)

map = f => foldr(i => r => cons(f(i))(r))(nil)

print_n = n => console.log(to_int(n))
print_l = each(print_n)

package.json

{
  "dependencies": {
    "global": "^4.4.0",
    "ijavascript": "^5.1.0"
  }
}

start

#!/usr/bin/env bash
yarn run ijsnotebook

yarn.lock

# THIS IS AN AUTOGENERATED FILE. DO NOT EDIT THIS FILE DIRECTLY.
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isarray@~1.0.0:
  version "1.0.0"
  resolved "https://registry.yarnpkg.com/isarray/-/isarray-1.0.0.tgz#bb935d48582cba168c06834957a54a3e07124f11"

jmp@1:
  version "1.1.0"
  resolved "https://registry.yarnpkg.com/jmp/-/jmp-1.1.0.tgz#fed82c8ad74ed8380239cfbc1e60d1df102e6fce"
  dependencies:
    uuid "3"
    zeromq "4"

jp-kernel@1:
  version "1.2.0"
  resolved "https://registry.yarnpkg.com/jp-kernel/-/jp-kernel-1.2.0.tgz#a695536b67db4882b8d4e99ed0cce3d5a43bb421"
  dependencies:
    jmp "1"
    nel "^1.1.0"
    uuid "3"

mimic-response@^1.0.0:
  version "1.0.1"
  resolved "https://registry.yarnpkg.com/mimic-response/-/mimic-response-1.0.1.tgz#4923538878eef42063cb8a3e3b0798781487ab1b"

min-document@^2.19.0:
  version "2.19.0"
  resolved "https://registry.yarnpkg.com/min-document/-/min-document-2.19.0.tgz#7bd282e3f5842ed295bb748cdd9f1ffa2c824685"
  dependencies:
    dom-walk "^0.1.0"

[email protected]:
  version "0.0.8"
  resolved "https://registry.yarnpkg.com/minimist/-/minimist-0.0.8.tgz#857fcabfc3397d2625b8228262e86aa7a011b05d"

minimist@^1.2.0:
  version "1.2.0"
  resolved "https://registry.yarnpkg.com/minimist/-/minimist-1.2.0.tgz#a35008b20f41383eec1fb914f4cd5df79a264284"

mkdirp@^0.5.1:
  version "0.5.1"
  resolved "https://registry.yarnpkg.com/mkdirp/-/mkdirp-0.5.1.tgz#30057438eac6cf7f8c4767f38648d6697d75c903"
  dependencies:
    minimist "0.0.8"

nan@^2.6.2:
  version "2.14.0"
  resolved "https://registry.yarnpkg.com/nan/-/nan-2.14.0.tgz#7818f722027b2459a86f0295d434d1fc2336c52c"

nel@^1.1.0:
  version "1.1.0"
  resolved "https://registry.yarnpkg.com/nel/-/nel-1.1.0.tgz#b5be807c7901b2c7690df560cbb517b74a52b9be"

node-abi@^2.2.0:
  version "2.9.0"
  resolved "https://registry.yarnpkg.com/node-abi/-/node-abi-2.9.0.tgz#ae4075b298dab2d92dd1e22c48ccc7ffd7f06200"
  dependencies:
    semver "^5.4.1"

noop-logger@^0.1.1:
  version "0.1.1"
  resolved "https://registry.yarnpkg.com/noop-logger/-/noop-logger-0.1.1.tgz#94a2b1633c4f1317553007d8966fd0e841b6a4c2"

npmlog@^4.0.1:
  version "4.1.2"
  resolved "https://registry.yarnpkg.com/npmlog/-/npmlog-4.1.2.tgz#08a7f2a8bf734604779a9efa4ad5cc717abb954b"
  dependencies:
    are-we-there-yet "~1.1.2"
    console-control-strings "~1.1.0"
    gauge "~2.7.3"
    set-blocking "~2.0.0"

number-is-nan@^1.0.0:
  version "1.0.1"
  resolved "https://registry.yarnpkg.com/number-is-nan/-/number-is-nan-1.0.1.tgz#097b602b53422a522c1afb8790318336941a011d"

object-assign@^4.1.0:
  version "4.1.1"
  resolved "https://registry.yarnpkg.com/object-assign/-/object-assign-4.1.1.tgz#2109adc7965887cfc05cbbd442cac8bfbb360863"

once@^1.3.1, once@^1.4.0:
  version "1.4.0"
  resolved "https://registry.yarnpkg.com/once/-/once-1.4.0.tgz#583b1aa775961d4b113ac17d9c50baef9dd76bd1"
  dependencies:
    wrappy "1"

os-homedir@^1.0.1:
  version "1.0.2"
  resolved "https://registry.yarnpkg.com/os-homedir/-/os-homedir-1.0.2.tgz#ffbc4988336e0e833de0c168c7ef152121aa7fb3"

prebuild-install@^2.2.2:
  version "2.5.3"
  resolved "https://registry.yarnpkg.com/prebuild-install/-/prebuild-install-2.5.3.tgz#9f65f242782d370296353710e9bc843490c19f69"
  dependencies:
    detect-libc "^1.0.3"
    expand-template "^1.0.2"
    github-from-package "0.0.0"
    minimist "^1.2.0"
    mkdirp "^0.5.1"
    node-abi "^2.2.0"
    noop-logger "^0.1.1"
    npmlog "^4.0.1"
    os-homedir "^1.0.1"
    pump "^2.0.1"
    rc "^1.1.6"
    simple-get "^2.7.0"
    tar-fs "^1.13.0"
    tunnel-agent "^0.6.0"
    which-pm-runs "^1.0.0"

process-nextick-args@~2.0.0:
  version "2.0.1"
  resolved "https://registry.yarnpkg.com/process-nextick-args/-/process-nextick-args-2.0.1.tgz#7820d9b16120cc55ca9ae7792680ae7dba6d7fe2"

process@^0.11.10:
  version "0.11.10"
  resolved "https://registry.yarnpkg.com/process/-/process-0.11.10.tgz#7332300e840161bda3e69a1d1d91a7d4bc16f182"

pump@^1.0.0:
  version "1.0.3"
  resolved "https://registry.yarnpkg.com/pump/-/pump-1.0.3.tgz#5dfe8311c33bbf6fc18261f9f34702c47c08a954"
  dependencies:
    end-of-stream "^1.1.0"
    once "^1.3.1"

pump@^2.0.1:
  version "2.0.1"
  resolved "https://registry.yarnpkg.com/pump/-/pump-2.0.1.tgz#12399add6e4cf7526d973cbc8b5ce2e2908b3909"
  dependencies:
    end-of-stream "^1.1.0"
    once "^1.3.1"

rc@^1.1.6:
  version "1.2.8"
  resolved "https://registry.yarnpkg.com/rc/-/rc-1.2.8.tgz#cd924bf5200a075b83c188cd6b9e211b7fc0d3ed"
  dependencies:
    deep-extend "^0.6.0"
    ini "~1.3.0"
    minimist "^1.2.0"
    strip-json-comments "~2.0.1"

readable-stream@^2.0.6, readable-stream@^2.3.0, readable-stream@^2.3.5:
  version "2.3.6"
  resolved "https://registry.yarnpkg.com/readable-stream/-/readable-stream-2.3.6.tgz#b11c27d88b8ff1fbe070643cf94b0c79ae1b0aaf"
  dependencies:
    core-util-is "~1.0.0"
    inherits "~2.0.3"
    isarray "~1.0.0"
    process-nextick-args "~2.0.0"
    safe-buffer "~5.1.1"
    string_decoder "~1.1.1"
    util-deprecate "~1.0.1"

safe-buffer@^5.0.1, safe-buffer@^5.1.1:
  version "5.2.0"
  resolved "https://registry.yarnpkg.com/safe-buffer/-/safe-buffer-5.2.0.tgz#b74daec49b1148f88c64b68d49b1e815c1f2f519"

safe-buffer@~5.1.0, safe-buffer@~5.1.1:
  version "5.1.2"
  resolved "https://registry.yarnpkg.com/safe-buffer/-/safe-buffer-5.1.2.tgz#991ec69d296e0313747d59bdfd2b745c35f8828d"

semver@^5.4.1:
  version "5.7.0"
  resolved "https://registry.yarnpkg.com/semver/-/semver-5.7.0.tgz#790a7cf6fea5459bac96110b29b60412dc8ff96b"

set-blocking@~2.0.0:
  version "2.0.0"
  resolved "https://registry.yarnpkg.com/set-blocking/-/set-blocking-2.0.0.tgz#045f9782d011ae9a6803ddd382b24392b3d890f7"

signal-exit@^3.0.0:
  version "3.0.2"
  resolved "https://registry.yarnpkg.com/signal-exit/-/signal-exit-3.0.2.tgz#b5fdc08f1287ea1178628e415e25132b73646c6d"

simple-concat@^1.0.0:
  version "1.0.0"
  resolved "https://registry.yarnpkg.com/simple-concat/-/simple-concat-1.0.0.tgz#7344cbb8b6e26fb27d66b2fc86f9f6d5997521c6"

simple-get@^2.7.0:
  version "2.8.1"
  resolved "https://registry.yarnpkg.com/simple-get/-/simple-get-2.8.1.tgz#0e22e91d4575d87620620bc91308d57a77f44b5d"
  dependencies:
    decompress-response "^3.3.0"
    once "^1.3.1"
    simple-concat "^1.0.0"

string-width@^1.0.1:
  version "1.0.2"
  resolved "https://registry.yarnpkg.com/string-width/-/string-width-1.0.2.tgz#118bdf5b8cdc51a2a7e70d211e07e2b0b9b107d3"
  dependencies:
    code-point-at "^1.0.0"
    is-fullwidth-code-point "^1.0.0"
    strip-ansi "^3.0.0"

"string-width@^1.0.2 || 2":
  version "2.1.1"
  resolved "https://registry.yarnpkg.com/string-width/-/string-width-2.1.1.tgz#ab93f27a8dc13d28cac815c462143a6d9012ae9e"
  dependencies:
    is-fullwidth-code-point "^2.0.0"
    strip-ansi "^4.0.0"

string_decoder@~1.1.1:
  version "1.1.1"
  resolved "https://registry.yarnpkg.com/string_decoder/-/string_decoder-1.1.1.tgz#9cf1611ba62685d7030ae9e4ba34149c3af03fc8"
  dependencies:
    safe-buffer "~5.1.0"

strip-ansi@^3.0.0, strip-ansi@^3.0.1:
  version "3.0.1"
  resolved "https://registry.yarnpkg.com/strip-ansi/-/strip-ansi-3.0.1.tgz#6a385fb8853d952d5ff05d0e8aaf94278dc63dcf"
  dependencies:
    ansi-regex "^2.0.0"

strip-ansi@^4.0.0:
  version "4.0.0"
  resolved "https://registry.yarnpkg.com/strip-ansi/-/strip-ansi-4.0.0.tgz#a8479022eb1ac368a871389b635262c505ee368f"
  dependencies:
    ansi-regex "^3.0.0"

strip-json-comments@~2.0.1:
  version "2.0.1"
  resolved "https://registry.yarnpkg.com/strip-json-comments/-/strip-json-comments-2.0.1.tgz#3c531942e908c2697c0ec344858c286c7ca0a60a"

tar-fs@^1.13.0:
  version "1.16.3"
  resolved "https://registry.yarnpkg.com/tar-fs/-/tar-fs-1.16.3.tgz#966a628841da2c4010406a82167cbd5e0c72d509"
  dependencies:
    chownr "^1.0.1"
    mkdirp "^0.5.1"
    pump "^1.0.0"
    tar-stream "^1.1.2"

tar-stream@^1.1.2:
  version "1.6.2"
  resolved "https://registry.yarnpkg.com/tar-stream/-/tar-stream-1.6.2.tgz#8ea55dab37972253d9a9af90fdcd559ae435c555"
  dependencies:
    bl "^1.0.0"
    buffer-alloc "^1.2.0"
    end-of-stream "^1.0.0"
    fs-constants "^1.0.0"
    readable-stream "^2.3.0"
    to-buffer "^1.1.1"
    xtend "^4.0.0"

to-buffer@^1.1.1:
  version "1.1.1"
  resolved "https://registry.yarnpkg.com/to-buffer/-/to-buffer-1.1.1.tgz#493bd48f62d7c43fcded313a03dcadb2e1213a80"

tunnel-agent@^0.6.0:
  version "0.6.0"
  resolved "https://registry.yarnpkg.com/tunnel-agent/-/tunnel-agent-0.6.0.tgz#27a5dea06b36b04a0a9966774b290868f0fc40fd"
  dependencies:
    safe-buffer "^5.0.1"

util-deprecate@~1.0.1:
  version "1.0.2"
  resolved "https://registry.yarnpkg.com/util-deprecate/-/util-deprecate-1.0.2.tgz#450d4dc9fa70de732762fbd2d4a28981419a0ccf"

uuid@3:
  version "3.3.2"
  resolved "https://registry.yarnpkg.com/uuid/-/uuid-3.3.2.tgz#1b4af4955eb3077c501c23872fc6513811587131"

which-pm-runs@^1.0.0:
  version "1.0.0"
  resolved "https://registry.yarnpkg.com/which-pm-runs/-/which-pm-runs-1.0.0.tgz#670b3afbc552e0b55df6b7780ca74615f23ad1cb"

wide-align@^1.1.0:
  version "1.1.3"
  resolved "https://registry.yarnpkg.com/wide-align/-/wide-align-1.1.3.tgz#ae074e6bdc0c14a431e804e624549c633b000457"
  dependencies:
    string-width "^1.0.2 || 2"

wrappy@1:
  version "1.0.2"
  resolved "https://registry.yarnpkg.com/wrappy/-/wrappy-1.0.2.tgz#b5243d8f3ec1aa35f1364605bc0d1036e30ab69f"

xtend@^4.0.0:
  version "4.0.2"
  resolved "https://registry.yarnpkg.com/xtend/-/xtend-4.0.2.tgz#bb72779f5fa465186b1f438f674fa347fdb5db54"

zeromq@4:
  version "4.6.0"
  resolved "https://registry.yarnpkg.com/zeromq/-/zeromq-4.6.0.tgz#7b1ca19cf740f484abfb9358430728f1339f03db"
  dependencies:
    nan "^2.6.2"
    prebuild-install "^2.2.2"