This is Part II of an essay that takes a highly informal look at two related techniques for achieving high performance when using large data structures: Structural Sharing, and Copy-on-Write Semantics.

In Part I, we used recursive functions that operate on lists to explore how we could use Structural Sharing to write code that avoids making copies of objects while still retaining the semantics of code that makes copies.

Here in Part II, we’ll consider resource ownership, starting with using copy-on-write semantics to implement safe mutation while still reserving structural sharing.


The Canonization of Blessed John XXIII and Blessed John Paul II


a brief review of structural sharing

In Part I, we created the Slice class, with its static method Slice.of(...). Instances of slice implement slices of JS arrays, but use structural sharing to keep the cost of creating a slice constant, rather than order-n.:

//
// http://raganwald.com/2019/01/14/structural-sharing-and-copy-on-write.html
//

const SliceHandler = {
  has (slice, property) {
    if (property in slice) {
      return true;
    }

    if (typeof property === 'symbol') {
      return false;
    }

    const matchInt = property.match(/^\d+$/);
    if (matchInt != null) {
      const i = parseInt(property);

      return slice.has(i);
    }

    const matchCarCdr = property.match(/^c([ad]+)r$/);
    if (matchCarCdr != null) {
      return true;
    }
  },

  get (slice, property) {
    if (property in slice) {
      return slice[property];
    }

    if (typeof property === 'symbol') {
      return;
    }

    const matchInt = property.match(/^\d+$/);
    if (matchInt != null) {
      const i = parseInt(property);
      return slice.at(i);
    }

    const matchCarCdr = property.match(/^c([ad]+)r$/);
    if (matchCarCdr != null) {
      const [, accessorString] = matchCarCdr;
      const accessors = accessorString.split('').map(ad => `c${ad}r`);
      return accessors.reduceRight(
        (value, accessor) => Slice.of(value)[accessor],
        slice);
    }
  }
};

function normalizedFrom(arrayIsh, from = 0) {
    if (from < 0) {
      from = from + arrayIsh.length;
    }
    from = Math.max(from, 0);
    from = Math.min(from, arrayIsh.length);

    return from;
}

function normalizedLength(arrayIsh, from, length = arrayIsh.length) {
    from = normalizedFrom(arrayIsh, from);

    length = Math.max(length, 0);
    length = Math.min(length, arrayIsh.length - from);

    return length;
}

function normalizedTo(arrayIsh, from, to) {
    from = normalizedFrom(arrayIsh, from);

    to = Math.max(to, 0);
    to = Math.min(arrayIsh.length, to);

    return to;
}

class Slice {
  static of(object, from = 0, to = Infinity) {
    if (object instanceof this) {
      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new Slice(object.array, object.from + from, to - from);
    }
    if (object instanceof Array) {
      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new this(object, from, to - from);
    }
    if (typeof object[Symbol.iterator] === 'function') {
      return this.of([...object], from, to);
    }
  }

  constructor(array, from, length) {
    this.array = array;
    this.from = normalizedFrom(array, from);
    this.length = normalizedLength(array, from, length);

    return new Proxy(this, SliceHandler);
  }

  * [Symbol.iterator]() {
    const { array, from, length } = this;

    for (let i = 0; i < length; i++) {
      yield array[i + from];
    }
  }

  join(separator = ",") {
    const { array, from, length } = this;

    if (length === 0) {
      return '';
    } else {
      let joined = array[from];

      for (let i = 1; i < this.length; ++i) {
        joined = joined + separator + array[from + i];
      }

      return joined;
    }
  }

  toString() {
    return this.join();
  }

  slice (from, to = Infinity) {
    from = normalizedFrom(this, from);
    to = normalizedTo(this, from, to);

    return Slice.of(this.array, this.from + from, this.from + to);
  }

  has(i) {
    const { array, from, length } = this;

    if (i >= 0 && i < length) {
      return (from + i) in array;
    } else {
      return false;
    }
  }

  at(i) {
    const { array, from, length } = this;

    if (i >= 0 && i < length) {
      return array[from + i];
    }
  }

  concat(...args) {
    const { array, from, length } = this;

    return Slice.of(array.slice(from, length).concat(...args));
  }

  get [Symbol.isConcatSpreadable]() {
    return true;
  }
}

function sum (array) {
  return sumOfSlice(Slice.of(array), 0);

  function sumOfSlice (remaining, runningTotal) {
    if (remaining.length === 0) {
      return runningTotal;
    } else {
      const first = remaining[0];
      const rest = Slice.of(remaining, 1);

      return sumOfSlice(rest, runningTotal + first);
    }
  }
}

const oneToSeven = [1, 2, 3, 4, 5, 6, 7];

sum(oneToSeven)
  //=> 28

This covers the basics, but let’s step back for a moment. In pure functional programming, data is immutable. This makes it much easier for humans and machines to reason about programs. We never have a pesky problem like passing an array to a sum function and having sum modify the array out from under us.

But when programming in a multi-paradigm environment, we need to accomodate code that is written around mutable data structures. In JavaScript, we can write:

const abasement = ['a', 'b', 'a', 's', 'e', 'm', 'e', 'n', 't'];

const bade = abasement.slice(1, 5);
bade[2] = 'd';

bade.join('')
  //=> "bade"

const bad = bade.slice(0, 3);

bad.join('')
  //=> "bad"

Modifying a slice of abasement does not modify the original array. But what happens with our Slice class? We haven’t done anything to handle modifying elements, so as it turns out, we can set properties but they don’t affect the underlying array that we use for things like further slices or joining:

let slice = Slice.of(abasement, 1, 5);
slice[2] = 'd';

slice.join('')
  //=> "base"

Just as we needed our proxy to mediate [...], we also need our proxy to mediate [...] =. Let’s make it so.


renovations


copy on write

In our structural sharing implementation, our slices depend upon the underlying array not mutating out from underneath them. Which seems to imply that the Slices themselves have to be immutable. But not so: The slices do not depend upon each other, but upon the underlying array.

This makes it possible for us to modify a slice without modifying any other slices that depend upon the slice’s original array… by making a copy of the slice’s array before we write to it:

const SliceHandler = {

  // ...

  set(slice, property, value) {
    if (typeof property === 'string') {
      const matchInt = property.match(/^\d+$/);
      if (matchInt != null) {
        const i = parseInt(property);
        return slice.atPut(i, value);
      }
  	}

    return slice[property] = value;
  }
}

class Slice {

  // ...

  atPut (i, value) {
    const { array, from, length } = this;

    this.array = array.slice(from, length);
    this.from = 0;
    this.length = this.array.length;

    return this.array[i] = value;
  }
}

const a1to5 = [1, 2, 3, 4, 5];
const oneToFive = Slice.of(a1to5);

oneToFive.atPut(2, 'three');
oneToFive[0] = 'uno';

a1to5
  //=> [1, 2, 3, 4, 5]
[...oneToFive]
  //=> ['uno', 2, 'three', 4, 5]

When an element of the slice is modified, the slice invokes .slice(...) on the underlying array, and switches to using the value returned as its new underlying array. It then performs the modification of the new array.

graph TD a["a1to5: [1, 2, 3, 4, 5]"] b["[1, 2, 'three', 4, 5]"] c["['uno', 2, 'three', 4, 5]"] b-. copy of .->a c-. copy of .->b d["oneToFive { from: 0, length: 5 }"] d-->|array:|c

This prevents the modification from affecting the original array, which may be shared by other slices, or by other code that expected it not to change.

This pattern is called copy on write. In effect, when we took a slice of the original array, we delayed making an actual copy until such time as we needed to make a copy to preserve the original array’s values. When do we actually need the copy? When we write to it, instead of reading from it.

And if we never write to it, we win “bigly” by never making copies. Before we go on to implement other methods like push, pop, unshift, and shift, let’s ask ourselves a question: Must we always make a fresh copy on every write?


Parts


smarter copying on write

Let’s reason about when we need to make a copy.

The first time we write something, we have to make a copy. The array that was passed to Slice in the constructor was provided by another piece of code. Given that we are emulating the protocol of Array.prototype.slice, that piece of code expects that we will not modify the array it passed to Slice.of. Absent a type system that understands mutable and immutable arrays, we must be conservative and assume that we should not modify the original.1

The first time we write to the array, we must make ourselves a copy.

What about after that? Well, after the first write, we have a new array that no other code shares (yet). So we can actually mutate it with abandon. Only when we share it with another piece of code must we revert to making a copy on writes. When do we share that array? When .slice is called, or if another object does a get on our array property.

We need to mediate other objects accessing our array with this scheme, so we’ll store it in a symbol property. That’s private enough to prevent accidental access. And if someone deliberately wants to break our encapsulation, there’s nothing we can do about a determined programmer with a commit bit anyways.

An updated version that only makes copies when necessary:

const arraySymbol = Symbol('array');

class Slice {

  // ...

  constructor(array, from, length) {
    this[arraySymbol] = array;
    this.from = normalizedFrom(array, from);
    this.length = normalizedLength(array, from, length);
    this.makeUnsafe();

    return new Proxy(this, SliceHandler);
  }

  get array() {
    this.makeUnsafe();

    return this[arraySymbol];
  }

  makeUnsafe () {
    this.safe = false;
  }

  makeSafe () {
    const { [arraySymbol]: array, from, length, [safeSymbol]: safe } = this;

    if (!safe) {
      this[arraySymbol] = array.slice(from, length);
      this.from = 0;
      this.length = this[arraySymbol].length;
      this.safe = true;
    }
  }

  atPut (i, value) {
    this.makeSafe();

    const { [arraySymbol]: array, from, length } = this;

    this[arraySymbol] = array.slice(from, length);
    this.from = 0;
    this.length = this[arraySymbol].length;

    return this[arraySymbol][i] = value;
  }

  slice (from, to = Infinity) {
    this.makeUnsafe();

    from = normalizedFrom(this, from);
    to = normalizedTo(this, from, to);

    return Slice.of(this.array, this.from + from, this.from + to);
  }
}

const oneToFive = Slice.of([1, 2, 3, 4, 5]);

oneToFive[0] = 'uno';
oneToFive[1] = "zwei";
oneToFive[2] = 'three';

const fourAndFive = oneToFive.slice(3);

oneToFive[3] = 'for';
oneToFive[4] = 'marun';

[...oneToFive]
  //=> ['uno', "zwei", 'three', 'for', 'marun']
[...fourAndFive]
  //=> [4, 5]

If we trace the code, we see that we made a copy when we invoked oneToFive[0] = 'uno', because we can’t make assumptions about the array provided to the constructor. We did not make a copy after oneToFive[1] = "zwei" or oneToFive[2] = 'three', because we knew that we had our copy all to ourselves.

We then invoked oneToFive.slice(3). We didn’t make a copy, but we noted that we were no longer safe, so then when we called oneToFive[3] = 'for', we made another copy. We then were safe again, so invoking oneToFive[4] = 'marun' did not make a third copy.

graph TD a["[1, 2, 3, 4, 5]"] b["['uno', 'zwei', 'three', 4, 5]"] c["['uno', 'zwei', 'three', 'for', 'marun']"] b-. copy of .->a c-. copy of .->b d["oneToFive: { from: 0, length: 5 }"] e["fourAndFive: { from: 3, length: 2 }"] d-->|array:|c e-->|array:|b

The result is identical to the behaviour of making a copy every time we slice, or every time we write, but we’re stingier about making copies when we don’t need them.

And now, emulating other Array.prototype methods that modify the underlying array is easy. For example:

class Slice {

  // ...

  push(element) {
    this.makeSafe();

    const value = this[arraySymbol].push(element);
    this.length = this[arraySymbol].length;

    return value;
  }

  pop() {
    this.makeSafe();

    const value = this[arraySymbol].pop();
    this.length = this[arraySymbol].length;

    return value;
  }

  unshift(element) {
    this.makeSafe();

    const value = this[arraySymbol].unshift(element);
    this.length = this[arraySymbol].length;

    return value;
  }

  shift() {
    this.makeSafe();

    const value = this[arraySymbol].shift();
    this.length = this[arraySymbol].length;

    return value;
  }
}

We could go on implementing other array-ish methods for our Slice class, but let’s reëxamine what we have been doing.


Arenberg Mine


resource ownership

Our implementation of copy-on-write semantics is written as if the primary issue is whether it is safe for an instance of Slice to mutate its underlying array. Which is the case. But how do we decide?

  • The slice’s underlying array is safe to mutate if The current slice is the only piece of code that could possibly own a reference to that array.
  • The slice’s underlying array is not safe to mutate if Other pieces of code that could share references to that array with the current slice.

Another way to look at this is to ask whether the current slice owns the underlying array:

  • If the slice doesn’t share references to the underlying array, the slice owns the underlying array.
  • If the slice might share references to the underlying array, the slice does not own the underlying array.

We don’t have to rename all of our methods, but let’s keep this concept in mind. In a structural sharing environment:

A piece of code is safe to mutate a data structure if that piece of code owns the data structure.

Our code follows this thinking with respect to modifying the slice’s underlying array after the slice has been constructed. But hang on! Recall that when we construct a new slice, we always begin with it being unsafe, meaning that we may share a reference to the array being passed in.

But what if we knew that we were the only ones with a reference to the array? This is extremely difficult to guarantee mechanically, but if we rely on the code that creates an instance of Slice to tell us whether the array being passed is ours to own, we take that into account when creating a new instance.

So our new version of the constructor will take a parameter, safe, indicating whether the slice is safe. Our first pass at our existing of static method will always indicate that the array being passed is unsafe, just as we do now.

class Slice {
  static of(object, from = 0, to = Infinity) {
    if (object instanceof this) {
      const safe = false;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new Slice(object.array, object.from + from, to - from, safe);
    }
    if (object instanceof Array) {
      const safe = false;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new this(object, from, to - from, safe);
    }
    if (typeof object[Symbol.iterator] === 'function') {
      return this.of([...object], from, to);
    }
  }

  constructor(array, from, length, safe = false) {
    this[arraySymbol] = array;
    this.from = normalizedFrom(array, from);
    this.length = normalizedLength(array, from, length);
    this.safe = safe;

    return new Proxy(this, SliceHandler);
  }
}

Wait, what happens when we call Slice.of with an object that is not an array and not another instance of slice? If it’s iterable, we make a new array using [...object], and then pass that to the constructor to make a new slice.

Well, if we’re making an array with [...object], and we don’t do anything else with the array, the new array we’re passing to Slice.of is one that won’t be used anywhere else, so it is safe:

class Slice {
  static of(object, from = 0, to = Infinity) {
    if (object instanceof this) {
      const safe = false;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new Slice(object.array, object.from + from, to - from, safe);
    }
    if (object instanceof Array) {
      const safe = false;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new this(object, from, to - from, safe);
    }
    if (typeof object[Symbol.iterator] === 'function') {
      const safe = true;
      const array = [...object];

      from = normalizedFrom(array, from);
      to = normalizedTo(array, from, to);

      return new Slice(array, from, to, safe);
    }
  }

  // ...

}

function * countTo (n) {
  let i = 1;
  while (i <= n) {
    yield i++;
  }
}

const arrayToTen = Slice.of([...countTo(10)]);
const oneToTen = Slice.of(countTo(10));

arrayToTen.safe
  //=> false

oneToTen.safe
  //=> true

There will be other times that a piece of code will want to create a slice of an object, but know that the object is no longer owned. In effect, and object is being given to the Slice glass. To represent this, we’ll create a new static method. .given:

class Slice {
  static given(object, from = 0, to = Infinity) {
    if (object instanceof this) {
      const safe = object.safe;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new Slice(object[arraySymbol], object.from + from, to - from, safe);
    }
    if (object instanceof Array) {
      const safe = true;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new this(object, from, to - from, safe);
    }
    if (typeof object[Symbol.iterator] === 'function') {
      return this.given([...object], from, to);
    }
  }

  // ...

}

const unsafeTen = Slice.of([...countTo(10)]);
const safeTen = Slice.given([...countTo(10)]);

unsafeTen.safe
  //=> false

safeTen.safe
  //=> true

const givenUnsafeTen = Slice.of(unsafeTen);
const givenSafeTen = Slice.given(safeTen]);

givenUnsafeTen.safe
  //=> false

givenSafeTen.safe
  //=> true

givenUnsafeTen === unsafeTen
  //=> false

givenSafeTen === safeTen
  //=> false

When Slice.given is passed another slice, the slice it returns is safe if the object passed was safe. If that object owned its array, and that object will not be accessed again, then the array is safe for the newly created slice. In effect, we are given the slice, but necessarily the array backing it.

Hmmmm… If that slice is no longer needed, why are we creating another instance of Slice? We can reuse the one that already exists:

class Slice {
  static given(object, from = 0, to = Infinity) {
    if (object instanceof this) {
      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      object.from = object.from + from;
      object.length = to - from;

      return object;
    }
    if (object instanceof Array) {
      const safe = true;

      from = normalizedFrom(object, from);
      to = normalizedTo(object, from, to);

      return new this(object, from, to - from, safe);
    }
    if (typeof object[Symbol.iterator] === 'function') {
      return this.given([...object], from, to);
    }
  }

  // ...

}

const unsafeTen = Slice.of([...countTo(10)]);
const safeTen = Slice.given([...countTo(10)]);

unsafeTen.safe
  //=> false

safeTen.safe
  //=> true

const givenUnsafeTen = Slice.of(unsafeTen);
const givenSafeTen = Slice.given(safeTen]);

givenUnsafeTen.safe
  //=> false

givenSafeTen.safe
  //=> true

givenUnsafeTen === unsafeTen
  //=> true

givenSafeTen === safeTen
  //=> true

Now when we call Slice.given and pass in another slice, Slice.given mutates the slice that was provided, much as our existing copy-on-write code can mutate the slice’s array when it knows that it does not share it with any other code.


Connex Labyrinth


given in action

The recursive function sum was provided above. It looks like this:

function sum (array) {
  return sumOfSlice(Slice.of(array), 0);

  function sumOfSlice (remaining, runningTotal) {
    if (remaining.length === 0) {
      return runningTotal;
    } else {
      const first = remaining[0];
      const rest = Slice.of(remaining, 1);

      return sumOfSlice(rest, runningTotal + first);
    }
  }
}

When we invoke sum([1, 2, 3, 4, 5, 6, 7]), the outer function creates a new slice out of the original array, and then it calls someOfSlice, which calls itself 7 times, each time invoking Slice.of and creating a new instance of Slice. The net result is that eight slices are created. This may be much less memory than copying slices out of a long array, but it’s unnecessary.

Here’s how we can stop making all those temporary slices:

function sum (array) {
  return sumOfSlice(Slice.of(array), 0);

  function sumOfSlice (remaining, runningTotal) {
    if (remaining.length === 0) {
      return runningTotal;
    } else {
      const first = remaining[0];
      const rest = Slice.given(remaining, 1);

      return sumOfSlice(rest, runningTotal + first);
    }
  }
}

In this formulation, sumOfSlice invokes Slice.given instead of Slice.of. The only objects passed to sumOfSlice are slices created for this function. And having created a slice, it is not used again after being passed to sumOfSlice. Therefore, we can use .given, and the code recycles the same slice over and over again.

Now when we invoke sum([1, 2, 3, 4, 5, 6, 7]), the outer function creates a new slice out of the original array as before, and then it calls someOfSlice, which calls itself 7 times as before. But now, each time it is called, it invokes Slice.given. That reuses the existing slice. The net result is that only one slice is created.


caution


caution

We now have two different mechanisms that manage the mutability of a Slice. The original copy-on-write code is extremely conservative. In conjunction with Slice.of, it assumes that its array is shared with other code, and makes a copy the moment we try to mutate the slice with [...] = or one of the mutating methods like .pop(). Once it makes a copy, it knows that it owns the copy until we share the underlying array with other code via get array() or .slice(...), at which point it becomes conservative again.

Although it’s possible to deliberately circumvent this copy-on-write protocol, for almost all purposes it can be trusted to “just work.” No knowledge of the protocol is needed to understand how to use the Slice class, it is a full-encapsulated implementation detail.

This is not the situation with our other mechanism, Slice.given. Using Slice.given requires that clients of the Slice class understand about resource ownership and the consequences of “aliasing” an array passed to Slice.given. In days of distant yore, programmers managed their own memory with malloc and free. A lot of debugging was devoted to finding places where memory was allocated, but not freed, or freed incorrectly when it was still in use.

The Slice.given mechanism is a return to those days, when programmers would have to manage the ownership of data structures by hand. In general, it is a win that we no longer have to do this. There can be some times when the optimization offered by explicitly managing resource ownership is valuable.

In this code, we have only considered the cost of creating and recycling objects. But sometimes there are other resources attached to an object, like an open web socket or file handle. Under such circumstances, protocols such as distinguishing between a resource being shared with an object, and a resource being given to an object can be useful.2

In sum, we have seen that we can create abstractions for data structures that use structural sharing to reduce copying. This is ridiculously easy when all data is immutable, but nevertheless, we can still write code that saves us from making copies, or even entire objects, until we need to.

the end.


The Complete Code


End Notes

  1. JavaScript has the notion of a frozen object, so if we’re passed a frozen array, we certainly don’t need to worry about anyone else modifying the array ot from under us. but likewise, we can’t modify a frozen array ourselves, so it doesn’t help us know whether the array that is used to construct the slice is safe to modify or not. So we’ll be paranoid and assume that it is not safe to modify. 

  2. If you scratch the surface of JavaScript’s Iterator protocols, you get deep into the weeds of .return() and .throw() methods that exist to allow resource-backed iterators (like an iterator that iterates over lines in an open text file) perform resource cleanup (like closing the file). Abstractions like .given could be used to help keep track of which piece of code is responsible for telling the iterator to dispose of its resources when it’s done.