(This is a work-in-progress, feel free to read and even submit an edit, but do not post on Reddit or Hacker News, thank you.)

Generators


author’s note

The title is, of course, a joke. Everyone cares about getting stuff done, that’s how we make the world a better place. But alongside progress and productivity, there is also room for pleasure and whimsey and light-hearted joking.

An alternate title could just as easily be, “JavaScript Generators for People Who Enjoy the Pleasure of Working Things Out.” I’m one of those people, and I enjoyed writing this post. I hope you enjoy reading it and perhaps you’ll even try a few whimsical JavaScript generators of your own.

If you do, please share them with me.


RadioShack 20-242: Hand crank for charging the battery pack. Also charges cell phones.


prerequisites

Before we get to the main bit of business, here’s what we presume we understand: In JavaScript, a generator function is a function declared with an *. Here’s the simplest possible generator function:

const Empty = function * () {};

If you invoke a generator function, you get an object back, and you don’t need to use a return keyword:

Empty()
  //=> {}

This object is a generator. Generator functions always return generators.

What can we do with a generator? We can iterate over it (even though there’s nothing to iterate over in an empty generator function):

for (const something of Empty())
  console.log(something);
  //=> nothing happens!

Generator functions can yield values. When we iterate over the resulting generator, we get that value:

const One = function * () {
  yield 1;
}

for (const something of One())
  console.log(something);
  //=> 1

If a generator function yields more than one value, the generator iterates over the values successively:

const OneTwo = function * () {
  yield 1;
  yield 2;
}

for (const something of OneTwo())
  console.log(something);
  //=> 1
       2

Yielding is dynamic. For example, we can yield three values like this:

const OneTwoThree = function * () {
  yield 1;
  yield 2;
  yield 3;
}

Or like this:

const OneTwoThree = function * () {
  for (let i = 1; i <= 3; ++i) yield i;
}

for (const something of OneTwoThree())
  console.log(something);
  //=> 1
       2
       3

Generators are iterable because they implements the [Symbol.iterator] method:

const Empty = function * () {};

const iterable = Empty();

typeof iterable[Symbol.iterator]
  //=> function

Generators are actually iterators, because they implement the .next method:

const OneTwoThree = function * () {
  for (let i = 1; i <= 3; ++i) yield i;
}

const iterator = OneTwoThree();

let { done, value } = iterator.next();

{ done, value }
  //=> {"done":false,"value":1}

({ done, value } = iterator.next());

{ done, value }
  //=> {"done":false,"value":2}

({ done, value } = iterator.next());

{ done, value }
  //=> {"done":false,"value":3}

({ done, value } = iterator.next());

{ done, value }
  //=> {"done":true}

Generator functions can flatten an iterable with yield *:

const catenate = function * (...iterables) {
  for (const iterable of iterables) {
    yield * iterable;
  }
}

const OneTwoThree = function * () {
  for (let i = 1; i <= 3; ++i) yield i;
}

const FourFive = function * () {
  yield 4;
  yield 5;
}

for (const something of catenate(OneTwoThree(), FourFive()))
  console.log(something);
  //=> 1
       2
       3
       4
       5

That’s it, we’re ready to talk about…


Generators for People Who Don’t Give a Shit About GettingStuffDone™


Plasma Generator


basic building blocks for generators

Let’s start with a simple generator function, it takes zero or more values and returns an iterator over the values (if any):

function * just (...values) {
  yield * values;
};

for (const something of just())
  console.log(something);
  //=> nothing happens!

for (const something of just('Hello'))
  console.log(something);
  //=> 'Hello'

just makes an iterable out of values. How do we get values out of an iterable? Here’s first, it’s an ordinary function that returns the first value yielded by an iterable:

function first (iterable) {
  const iterator = iterable[Symbol.iterator]();

  const { done, value } = iterator.next();
  if (!done) return value;
};

first(['Hello', 'Java', 'Script'])

We can also take multiple elements. We use a generator function so that we can iterate over the elements we take:

function * take (numberToTake, iterable) {
  const iterator = iterable[Symbol.iterator]();

  for (let i = 0; i < numberToTake; ++i) {
    const { done, value } = iterator.next();
    if (done) return;
    else yield value;
  }
}

const iterable = take(3, [1, 2, 3, 4, 5]);

for (const something of iterable)
  console.log(something);
  //=> 1
       2
       3

The inverse of first is rest, a generator function that takes an iterable and yields all but the first value:

function * rest (iterable) {
  const iterator = iterable[Symbol.iterator]();

  iterator.next()
  yield * iterator;
};

for (const something of rest(['Hello', 'Java', 'Script']))
  console.log(something);
  //=> Java
       Script

Sometimes you need both the first and the rest of an iterable, and you don’t want to call them in succession because iterables are stateful. So it’s convenient to use destructuring to get both at once:

function split (iterable) {
  const iterator = iterable[Symbol.iterator]();
  const { done, value: first } = iterator.next();

  if (done) {
    return { rest: [] };
  } else {
    return { first, rest: iterator };
  }
};

const { first, rest } = split([1, 2, 3, 4, 5]);

console.log(first);
  //=> 1
for (const something of rest)
  console.log(something);
  //=> 2
       3
       4
       5

If we already have an iterator, we don’t need split: Once you take the first value, the iterator will return the rest of the values automatically. But as we see in this example, we might have an expression that provides an iterator, so split lets us bind both values at once.

The inverse of splitting an iterable into first and rest is to join them:

function * join (first, rest) {
  yield first;
  yield * rest;
};

const iterable = join(5, [4, 3, 2, 1]);

for (const something of iterable)
  console.log(something);
  //=> 5
       4
       3
       2
       1

With these basic building blocks in place, we can look at some interesting generator functions: Generator functions that yield * themselves.


Mirror, mirror


self-referential generators

We have seen that generator functions can yield * iterators… Even those produced by other generator functions. What about themselves? Can a generator function yield itself? Consider:

function * infiniteNumberOf (something) {
  yield * join(something, infiniteNumberOf(something));
}

for (const something of infiniteNumberOf(1))
  console.log(something);
  //=> 1
       1
       1
       ...

infiniteNumberOf yields an iterator that yields something an infinite number of times. So if we want an infinite number of 1s, we can use infiniteNumberOf(1). Taking an argument for a generator function that refers to itself is interesting. For example, we could write:

function * from (first, increment = 1) {
  yield * join(first, from(first + increment, increment));
}

for (const something of from(1))
  console.log(something);
  //=> 1
       2
       3
       ...

Handy. What we have here is a sequence that calculates each element based on the element before it and an amount to increment. What if we wanted to apply some other function?

function * sequence (first, nextFn = (x) => x) {
  yield * join(first, sequence(nextFn(first), nextFn));
}

const powersOfTwo = sequence(2, (x) => x * 2);

for (const something of powersOfTwo)
  console.log(something);
  //=> 2
       4
       8
       16
       ...

Or what if we want to use a function that works on the trailing two elements, instead of the last element yielded so far?

function * sequencePairs (first, second, nextFn = (x, y) => y) {
  yield * join(first, sequencePairs(second, nextFn(first, second), nextFn));
}

const fibonacci = sequencePairs(0, 1, (x, y) => x + y);

for (const something of fibonacci)
  console.log(something);
  //=> 0
       1
       1
       2
       3
       5
       8
       13
       ...

We will come back to this sequence, but first, let’s look at generator functions that transform other generators.


Body/Frame Assembly Line


generator functions that transform other generators

Our “self-referential generator functions” yield values that are derived from the values they’ve already yielded. In a sense, these generator functions transform themselves. Generator functions can, in fact, transform other generators (or more generally, transform any iterable).

The simplest example is mapWith:

function * mapWith (fn, iterable) {
  const asSplit = split(iterable);

  if (asSplit.hasOwnProperty('first')) {
    const { first, rest } = asSplit;

    yield * join(fn(first),mapWith(fn, rest));
  }
}

const squares = mapWith((x) => x*x, from(1));

for (const something of squares)
  console.log(something);
  //=> 1
       4
       9
       16
       25
       ...

Another simple generator function that transforms an iterator is filterWith:

function * filterWith (fn, iterable) {
  const asSplit = split(iterable);

  if (asSplit.hasOwnProperty('first')) {
    const { first, rest } = asSplit;

    if (fn(first)) {
      yield first;
    }
    yield * filterWith(fn, rest);
  }
}

const odds = filterWith((x) => x % 2 === 1, from(1));

for (const something of odds)
  console.log(something);
  //=> 1
       3
       5
       7
       9
       ...

We can use filterWith and a self-referential generator function to make an Unfaithful Sieve of Eratosthenes:

function * primes (numbers = from(2)) {
  const { first, rest } = split(numbers);

  yield * join(first, filterWith((n) => n % first !== 0, primes(rest)));
}

for (const something of primes())
  console.log(something);
  //=> 2
       3
       5
       7
       11
       13
       ...

These are great, but sometimes we want to transform more than one generator.


Zipper


generator functions that transform one or more generators

mapWith was a generator function that transformed an iterable by mapping its values with a unary function. Thus, mapWith((x) => x*3, from(1)) gives us an iterator over the multiples of three.

But what about mapping over two or more iterables? How would that work? The simplest method is to iterate over all the iterables simultaneously, taking an element from each one, and mapping the pair of elements to a value. If any of them run out of values, stop:

function * zipWith (fn, ...iterables) {
  const asSplits = iterables.map(split);

  if (asSplits.every((asSplit) => asSplit.hasOwnProperty('first'))) {
    const firsts = asSplits.map((asSplit) => asSplit.first);
    const rests = asSplits.map((asSplit) => asSplit.rest);

    yield * join(fn(...firsts), zipWith(fn, ...rests));
  }
}

const greetings = zipWith(
    (x, y) => `${x} ${y}`,
    ['hello', 'bonjour', 'hej'],
    ['frank', 'pascal', 'rognvoldr']
  );

for (const something of greetings)
  console.log(something);
  //=> "hello frank"
       "bonjour pascal"
       "hej rognvoldr"

This has an interesting possibility. We used sequencePairs to arrange things so that we could do a computation on successive elements of a self-referential sequence. What if we use zipWith self-referentially?

function * fibonacci2 () {
  yield 0;
  yield 1;
  yield * zipWith(
      (x, y) => x + y,
      fibonacci2(),
      rest(fibonacci2())
    );
};

In this case, we zip an iterator with itself, but use rest to offset it by one. Thus, each element is zipped with the element preceding it. Let’s use that trick again:

function * phi () {
  yield * rest(
    zipWith(
      (x, y) => x / y,
      rest(fibonacci2()),
      fibonacci2()
    )
  );
};

for (const something of phi())
  console.log(something);
  //=> 1
       2
       1.5
       1.6666666666666667
       1.6
       1.625
       1.6153846153846154
       1.619047619047619
       1.6176470588235294
       1.6181818181818182
       ...

We have written a generator function that converges (slowly) on the Golden Ratio, 1.6180339.... But let’s look at zipWith more closely:

function * zipWith (fn, ...iterables) {
  const asSplits = iterables.map(split);

  if (asSplits.every((asSplit) => asSplit.hasOwnProperty('first'))) {
    const firsts = asSplits.map((asSplit) => asSplit.first);
    const rests = asSplits.map((asSplit) => asSplit.rest);

    yield * join(fn(...firsts), zipWith(fn, ...rests));
  }
}

zipWith splits all of the iterables we supply. If we have a first for each iterable, it yield *’s the result of join the result of applying the fn to the firsts with the zipWith of the rests.

What happens if we only provide one iterable to zipWith?

cont reciprocals = zipWith((n) => 1/n, phi());

for (const something of reciprocals)
  console.log(something);
  //=> 1
       0.5
       0.6666666666666666
       0.6
       0.625
       0.6153846153846154
       0.6190476190476191
       0.6176470588235294
       0.6181818181818182
       0.6179775280898876
       ...

It behaves just like mapWith! Now we understand that mapWith is a special case of zipWith! So let’s consolidate our understanding, and call it mapWith:

function * mapWith (fn, ...iterables) {
  const asSplits = iterables.map(split);

  if (asSplits.every((asSplit) => asSplit.hasOwnProperty('first'))) {
    const firsts = asSplits.map((asSplit) => asSplit.first);
    const rests = asSplits.map((asSplit) => asSplit.rest);

    yield * join(fn(...firsts), zipWith(fn, ...rests));
  }
}

This is good stuff, but let’s take a moment and have a look at our programming style.


Image of the front of a generator, credit www.cwcs.co.uk


writing generator functions in generator style

Let’s pause for a moment and look at the way we’ve been writing our generator functions that transform other generators. Once more, mapWith:

function * mapWith (fn, ...iterables) {
  const asSplits = iterables.map(split);

  if (asSplits.every((asSplit) => asSplit.hasOwnProperty('first'))) {
    const firsts = asSplits.map((asSplit) => asSplit.first);
    const rests = asSplits.map((asSplit) => asSplit.rest);

    yield * join(fn(...firsts), mapWith(fn, ...rests));
  }
}

Notice that we’ve written this to:

  1. Be recursive, and;
  2. To compose a new iterator with join, and;
  3. To yield * the new iterator it composes.

This is written in pure functional style. It reads as if it was a function that only has to return one value for each invocation. Furthermore, its mental model is of transforming one generator function into another:

The mapped generator consists of the function applied to the firsts of the argument iterables, joined with a mapping of the function to the rests of the iterables.

But that’s not the only way that generator functions have to work. We can just as easily write:

function * mapWith (fn, ...iterables) {
  const asSplits = iterables.map(split);

  if (asSplits.every((asSplit) => asSplit.hasOwnProperty('first'))) {
    const firsts = asSplits.map((asSplit) => asSplit.first);
    const rests = asSplits.map((asSplit) => asSplit.rest);

    yield fn(...firsts);
    yield * mapWith(fn, ...rests);
  }
}

Now we’re saying:

Yield the result of applying the function to the firsts of the argument iterables, then yield the values of mapping the function over the rests of the iterables.

Removing the join mean we’re yielding something, suspending the generator function, then yielding the remainder later. This is stateful, which is mentally the opposite of the way that functional programming works. But that doesn’t mean it’s wrong.

Let’s keep going with statefulness. Why not iterate instead of writing a recursive generator function?

function * mapWith (fn, ...iterables) {
  const iterators = iterables.map((iterable) => iterable[Symbol.iterator]());

  while (true) {
    const pairs = iterators.map((iterator) => iterator.next());
    const values = pairs.map((pair) => pair.value);
    const dones = pairs.map((pair) => pair.done);

    if (dones.find((done) => done)) {
      return;
    } else {
      yield fn(...values);
    }
  }
}

This reads in a different way:

Get iterators for all the iterables, then repeat the following: Get all the values for all the iterators. If any iterator is done, we’re done. If not, yield the result of applying the function to the values, and repeat.

This is exactly what generator functions were designed to do: To execute code while yielding values as we go. We can rewrite our other generator functions in iterative style:

function * filterWith (fn, iterable) {
  const iterator = iterable[Symbol.iterator]();

  while (true) {
    const { value, done } = iterator.next();

    if (done) {
      return;
    } else if (fn(value)) {
      yield value;
    }
  }
}

function * infiniteNumberOf (something) {
  while (true) {
    yield something;
  }
}

function * from (number, increment = 1) {
  while (true) {
    yield number;
    number = number + increment;
  }
}

function * sequence (value, nextFn = (x) => x) {
  while (true) {
    yield value;
    value = nextFn(value);
  }
}

function * primes (numbers = from(2)) {

  while (true) {
    const { first, rest } = split(numbers);

    yield first;
    numbers = filterWith((n) => n % first !== 0, rest);
  }
}

function * sequencePairs (first, second, nextFn = (x, y) => y) {
  yield first;
  while (true) {
    yield second;
    [first, second] = [second, nextFn(first, second)]
  }
}

These no longer have the mathematical “purity” of the functional-style implementations, but then again, generator functions are not really functions, aren’t really used like functions, and perhaps we shouldn’t try to write them like functions.


Points Forever


the problem with mapping generator functions with themselves

Recall fibonacci2 (now written with our new mapWith), which maps itself against itself:

function * fibonacci2 () {
  yield 0;
  yield 1;
  yield * mapWith(
      (x, y) => x + y,
      fibonacci2(),
      rest(fibonacci2())
    );
};

And phi, which uses the same technique of mapping fibonacci against itself:

function * phi () {
  yield * rest(
    mapWith(
      (x, y) => x / y,
      rest(fibonacci2()),
      fibonacci2()
    )
  );
};

These look like we’re mapping iterables against themselves, but more accurately, we are comparing generator functions against themselves, which gives us the ability to write fibonacci() and generate a brand-new generator whenever we want.

This distinction is important. If we have an iterator, we can’t restart it at the beginning whenever we like. That’s not how iterators work: They statefully progress from beginning to end, you can’t restart them or move backwards.

So the generator functions we wrote above only work because we can invoke fibonacci() and make new iterators whenever we want. If we tried to use a similar pattern with an iterable, it would break, because we can’t use an iterator twice.

One approach is to rethink the way iterators work. As supplied, they operate on one value at a time. Fine. But what if they operated on more than one element at a time, in slices of a particular length?

function * slices (length, iterable) {
  const iterator = iterable[Symbol.iterator]();
  let buffer = [...take(length, iterator)];

  if (buffer.length < length) return;

  let nextElementIndex = 0;

  while (true) {
    yield buffer;

    const { value, done } = iterator.next();

    if (done) return;

    buffer = buffer.slice(1);
    buffer.push(value);
  }
}

const numberAndNext = slices(2, from(1));

for (const something of numberAndNext)
  console.log(something);
  //=> [1,2]
       [2,3]
       [3,4]
       [4,5]
       ...

Now we can revisit our recursive fibonacci2:

function * fibonacci3 () {
  yield 0;
  yield 1;
  yield * mapWith(
      ([x, y]) => x + y,
      slices(2, fibonacci3())
    );
};

We’re still recursively calling fibonacci, but we are no longer trying to invoke it twice for each element we evaluate. Instead, we map over slices of finbonacci. We can do the same thing with phi:

function * phi2 () {
  yield * rest(
    mapWith(
      ([x, y]) => x / y,
      slices(2, fibonacci3())
    )
  );
};

How do we know when we’ve converged?

function within (tolerance) {
  return (([x, y]) => Math.abs(x - y) <= tolerance);
}

Let’s apply it:

const pairsOfPhi = slices(2, phi2());
const pairsWithinTolerance = filterWith(within(0.00000001), pairsOfPhi);
const firstPairWithinTolerance = first(pairsWithinTolerance);
const [_, estimate] = firstPairWithinTolerance;

estimate
  //=> 1.6180339901755971

But hang on, something’s not quite right.


Sanyo bottom-bracket generator


composing generator functions

Let’s look at two lines from our phi-calculating code:

const pairsWithinTolerance = filterWith(within(0.00000001), pairsOfPhi);
const firstPairWithinTolerance = first(pairsWithinTolerance);

The core logic is: first(filterWith(...)). What does it mean? “Take the first element of all the elements that pass the filter.” We can make that a function:

function firstWhen (filterFn, iterable) {
  return first(filterWith(filterFn, iterable));
}

firstWhen is useful, it’s just like Array.prototype.find. We should keep it around. But remember when we were writing everything “functionally” above? Why can’t we do the same with firstWhen? In functional programming, compose is a function that, well, composes two functions together. Thus compose(a, b)(c) === a(b(c)).

There are lots of examples around the internet, or in books like JavaScript Allongé:1

function compose(a, b) {
  return function (...args) {
    return a.call(this, b.apply(this, args));
  }
}

const a = (n) => `the result is ${n}`;
const b = (n) => n * n;
const c = compose(a, b);

c(16)
  //=> the result is 256

Looks good. Let’s use it with first and filterWith to produce firstWhen:

const firstWhen = compose(first, filterWith);

const pairsOfPhi = slices(2, phi());
const firstPairWithinTolerance = firstWhen(within(0.00000001), pairsOfPhi);
const [_, estimate] = firstPairWithinTolerance;

estimate
  //=> 1.6180339901755971

Fantastic! Let’s use compose again, we’re on a roll. If we have firstWhen, eventually we’ll want restWhen:

function * restWhen (filterFn, iterable) {
  yield * rest(filterWith(filterFn, iterable));
}

const squares = mapWith((x) => x * x, from(1));
const isOdd = (n) => n % 2 === 1;

restWhen(isOdd, squares)
  //=> 9
       25
       49
       81
       121
       169
       225
       ...

So let’s use compose to do the same thing:

const restWhen = compose(rest, filterWith);

restWhen(isOdd, squares)
  //=> 9
       25
       49
       81
       121
       169
       225
       ...

It is handy to be able to compose generator functions, but using compose to create generator functions teaches us something: We can make generators with ordinary functions that invoke generator functions.

But not always! Recall our recursive generator functions, like infiniteNumberOf:

function * infiniteNumberOf (something) {
  yield * join(something, infiniteNumberOf(something));
}

[...take(10, infiniteNumberOf('spam'))]
  //=> ["spam","spam","spam","spam","spam","spam","spam","spam","spam","spam"]

We know we can also rewrite it as an ordinary function that returns a generator. Or can we?

function infiniteNumberOf2 (something) {
  return join(something, infiniteNumberOf2(something));
}

[...take(10, infiniteNumberOf2('spam'))]
  //=> Maximum call stack size exceeded.

When invoked, a generator function immediately returns a generator. When we ask for the first value with with .next, it executes until it reaches a yield, then suspends its execution until we ask for another value with .next.

Thus, our infiniteNumberOf generator function returns a generator immediately. When we invoke .next on it, it invokes .join, and the yield * invokes .next on that generator. Which executes until it reaches a yield and yields 'spam'. When we invoke .next again, it starts to evaluate he nested infiniteNumberOf(something).

But when we invoke infiniteNumberOf2, an ordinary function, things are very different. Right away, it evaluates join(something, infiniteNumberOf2(something)). To do that, it evaluates the variable reference something, and the function invocation infiniteNumberOf2(something). Which starts the cycle all over again and continues to infinity, or until we un out of stack.

The lesson is that we can write functions that return generators, but we must be careful lest the eager evaluation of ordinary functions destroys the lazy evaluation semantics we expect from generator functions.


Generalizing Generators


Oware


invocations

Let’s back up a bit. Consider this ridiculously simple generator, written in generator style:

function * infiniteNumberOf (something) {
  while (true) {
    yield something;
  }
}

When we invoke it, we get back an iterator:

const iterator = infiniteNumberOf('JavaScript Allongé');

From that point on, whenever we invoke .next() on the iterator, we get a “Plain Old JavaScript Object” back, with a value property:

iterator.next();
  //=> {"value":"JavaScript Allongé", "done":false}

iterator.next();
  //=> {"value":"JavaScript Allongé", "done":false}

iterator.next();
  //=> {"value":"JavaScript Allongé", "done":false}

We can do the semantically same thing with plain-old-functions:

function plentyOf (something) {
  return () => something;
}

const fn = plentyOf('JavaScript Allongé');

fn()
  //=> "JavaScript Allongé"

fn()
  //=> "JavaScript Allongé"

fn()
  //=> "JavaScript Allongé"

A generator makes a thingummy that when invoked, returns a value, and you can invoke it more than once, and you get a value each time. And we can make a function-making-function that returns a function, and you can invoke that function more than once, and you get a value each time.

Of course, you don’t need to get the same value each time. Here’s a generator and an equivalent function-making-function that produce squares of two:

function * exponentsOfTwo () {
  let exponent = 0;

  while (true) {
    yield Math.pow(2, exponent++);
  }
}

const exponents = exponentsOfTwo();

exponents.next()
  //=> {"value":1,"done":false}

exponents.next()
  //=> {"value":2,"done":false}

exponents.next()
  //=> {"value":4,"done":false}

exponents.next()
  //=> {"value":8,"done":false}


function powersOfTwo () {
  let exponent = 0;

  return () => Math.pow(2, exponent++);
}

const fn = powersOfTwo();

fn()
  //=> 1

fn()
  //=> 2

fn()
  //=> 4

fn()
  //=> 8

We can see that internally, the fundamental difference between invoking a generator with .next() and invoking a function with (), is that if we want the function to maintain state, we do it by storing the state as bindings in an enclosing scope.

This is because every time we invoke the function, we start with a fresh invocation of the function, whereas with the iterator we have the same invocation, its just that when it yields a value, we suspend its invocation until we call .next() again.


Play


suspension and resumption

Let’s look at suspending and resuming again. Here’s a generator that gratuitously makes this explicit:

function * numbers () {
  let tens = 0;

  while (true) {
    yield tens + 0;
    yield tens + 1;
    yield tens + 2;
    yield tens + 3;
    yield tens + 4;
    yield tens + 5;
    yield tens + 6;
    yield tens + 7;
    yield tens + 8;
    yield tens + 9;
    ++tens;
  }
}

As we can see, it suspends and resumes its execution, moving on to the next yield statement each time. This is not the same thing as a function: Functions start a new invocation each time, with execution beginning at the top and moving to the end or to a return statement, which ends the invocation.

In fact, when a compiler translates ECMAScript 2015 code into ECMAScript 5, it has to translate the generators into functions. Since functions cannot suspend and resume their operation, the compiler has to transform generators into objects that act as state machines.

Here’s how Babel translates our function (as of June, 2016):

function numbers() {
  var tens;
  return regeneratorRuntime.wrap(function numbers$(_context10) {
    while (1) {
      switch (_context10.prev = _context10.next) {
        case 0:
          tens = 0;

        case 1:
          if (!true) {
            _context10.next = 25;
            break;
          }

          _context10.next = 4;
          return tens + 0;

        case 4:
          _context10.next = 6;
          return tens + 1;

        case 6:
          _context10.next = 8;
          return tens + 2;

        case 8:
          _context10.next = 10;
          return tens + 3;

        case 10:
          _context10.next = 12;
          return tens + 4;

        case 12:
          _context10.next = 14;
          return tens + 5;

        case 14:
          _context10.next = 16;
          return tens + 6;

        case 16:
          _context10.next = 18;
          return tens + 7;

        case 18:
          _context10.next = 20;
          return tens + 8;

        case 20:
          _context10.next = 22;
          return tens + 9;

        case 22:
          ++tens;
          _context10.next = 1;
          break;

        case 25:
        case "end":
          return _context10.stop();
      }
    }
  }, _marked[9], this);

There are a lot of moving parts we cannot see, but fundamentally what has happened is that the generator function that proceeds form yield to yield has been turned into a state machine. Each time it is invoked, it executes some code, then changes to another state. We can no longer see the linear execution.

If we write a more complex generator with if statements and other control flow constructs, it will likewise be transformed into a state machine, with more complex rules for transitioning from state to state.

Although this is not a particularly stellar example, it does illustrate the idea that sometimes, if we want a stateful function that can be called multiple times, a generator that suspends and resumes can provide a clearer way to express the statefulness versus a function or object that stores state in properties or variables outside of the function.


Controllers


interactive functions and generators

So far, our generators and functions have not been interactive. We have initialized some of them, but thereafter, whenever we have invoked them, we have called .next() or () and obtained a value in return.

We have seen that generators and functions do similar things when invoked without arguments. But functions can also be invoked with arguments. For example:

function accumulator () {
  let sum = 0;

  return (n) => (sum = sum + n);
}

const acc = accumulator();

acc(1)
  //=> 1

acc(2)
  //=> 3

acc(3)
  //=> 6

acc(4)
  //=> 10

If generators really were equivalent to functions, we could call them with .next(...) and get a similar behaviour. And as it happens, we can do that:

function * accumulator () {
  let sum = 0;
  while (true) {
    const n = yield(sum);
    sum += n;
  }
}

const acc = accumulator();

acc.next();

acc.next(1)
  //=> {"value":1,"done":false}

acc.next(2)
  //=> {"value":3,"done":false}

acc.next(3)
  //=> {"value":6,"done":false}

acc.next(4)
  //=> {"value":10,"done":false}

Now let’s analyze what happens. When we first call .next(), the iterator runs up to the first yield it encounters. We don’t pass a value in, but if we did, it would be ignored. So our iterator runs right up to const n = yield(sum);. At that point, sum is zero, and the expression yield(sum) yields {"value":0,"done":false}. We ignore that in our code. The iterator then suspends execution until we invoke .next(1).

Note that at this point, the iterator is in the middle of const n = yield(sum). It yielded the value, but is waiting for a value to come back so it can be assigned to n. yield is aptly named: It yields the flow of control to another piece of code.

Now we invoke acc.next(1). This passes 1 to the iterator, which resumes execution. 1 is now the value of yield(sum) within the iterator, so const n = yield(sum) at that point is equivalent to const n = 1, and on the next line, sum += n means that sum becomes 1.

The iterator continues to run, and loops around to const n = yield(sum) again. Now it yields {"value":1,"done":false} and suspends execution again, waiting for the code to call .next(2). And so it goes until we stop calling .next(…).

Thus, interactive generators are not exactly like interactive functions: We always need to call .next() to advance an interactive generator to the point where it can accept a value from .next(…). This is a crucial difference from interactive functions: With an interactive function, you don’t need to call it once before passing values in.

Interactive generators are crucially different in another respect: When you write something like let foo = yield(bar), the sequence of events is that bar is yielded, and then the iterator suspends its execution until the code that is calling the iterator invokes it again with .next().

That is different from an ordinary function, because in an ordinary function, the caller suspends its execution when it calls a function or invokes a method. The invoked function calls return and, well, returns a value and resumes the caller’s execution.

Thus, in ordinary functions, the act of invoking another function or method suspends execution and waits for a value, and the return statement resumes the caller’s execution. Whereas in an iterator, calling .next(…) suspends execution and waits for the iterator to yield a value, but within the iterator, yield acts just like a function call as well: It suspends execution and waits for a value.

This is very interesting! Ordinary functions suspend execution and wait for values, but there is no easy way for two functions to suspend execution and wait for each other. But with an iterator, we can have this piece of code:

const acc = accumulator();
acc.next();

let n = 1;

while (true) {
  acc.next(n++);
}

And it will suspend execution and wait for this piece of code:

function * accumulator () {
  let sum = 0;
  while (true) {
    const n = yield(sum);
    sum += n;
  }
}

Which also suspends execution and waits for the first piece of code. We have pieces of code that interleave their execution instead of neatly invoking functions in a hierarchal manner.


Generators inside the Hoover Dam


coroutines

Functions and methods are units of execution that can suspend themselves, allow other units to run, then resume where they left off. But strictly speaking, functions only do so in a very rigid, hierarchal way. There is no way for two functions to interleave their execution as we saw is possible with an iterator created by a generator.

Functions can suspend themselves and resume, but they cannot “yield” to another suspended function, they can only invoke another function from its beginning, and that function attempts to run to its end. Even when we have recursive functions that invoke themselves, they are always creating new invocations of themselves, they never yield to a suspended function, they can only return to a function that invoked them.

Not all languages have this restriction. Some languages have units of execution that can yield to any arbitrary suspended unit of execution. The general term for a unit of execution that can suspend itself and yield to another suspended unit of execution is a coroutine.

JavaScript’s generators are more like coroutines than functions. They can suspend themselves and resume execution, but they cannot arbitrarily choose which unit of execution to invoke. Let’s look at an example problem to be solved with coroutines: The Prisoner’s Dilemma.

Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge. They hope to get both sentenced to a year in prison on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to: betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent.

The offer is: If A and B each betray the other, each of them serves 2 years in prison; If A betrays B but B remains silent, A will be set free and B will serve 3 years in prison (and vice versa); If A and B both remain silent, both of them will only serve 1 year in prison (on the lesser charge).

In game theory parlance, remaining silent is called “coöperating,” and betraying the other player is called “defecting.” The payoff matrix for the game (presuming that a lower score is better) is:

  B coöperates B defects
A coöperates A: 1, B: 1 A: 3, B: 0
A defects A: 0, B: 3 A: 2, B: 2

miscellanea


Vulcan Airborne Auxiliary Power Unit


source code


Important Message


important message

(This is a work-in-progress, feel free to read and even submit an edit, but do not post on Reddit or Hacker News, thank you.)

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notes