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The Hopelessly Egocentric Blog Post

In Raymond Smullyan's delightful book on Combinatory logic, To Mock a Mockingbird, Smullyan explains combinatory logic and derives a number of important results by presenting the various combinators as songbirds in a forest.

One of his concepts is the Hopelessly Egocentric Bird:

We call a bird B hopelessly egocentric if for every bird x, Bx = B. This means that whatever bird x you call out to B is irrelevant; it only calls B back to you! Imagine that the bird's name is Bertrand. When you call out "Arthur," you get the response "Bertrand"; when you call out "Raymond," you get the response "Bertrand"; when you call out "Ann," you get the response "Bertrand." All this bird can ever think about is itself!

Some folks have proposed that by making nil hopelessly egocentric, we can avoid the need for monadic idioms like #andand. Let's examine the idea and see what consequences this has.

Mirror tunnel (c) 2007 Michael D. Dunn, some rights reserved

object-oriented egocentricity

One of the tenets of OO programming is that programs consist of objects that respond to messages they send each other. A hopelessly egocentric object is easy to imagine: No matter what message you send it, the hopelessly egocentric object responds with itself:

class HopelesslyEgocentric < BlankSlate

  def method_missing(*arguments); self; end

end

Now you can create a hopelessly egocentric object with HopelesslyEgocentric.new and no matter what message you send it, you will get it back in response. And? What good is this? What can it do? Why should we put it in our Zoo?

In Objective C, nil is hopelessly egocentric. As Learn Objective-C puts it, You usually don't need to check for nil before calling a method on an object. If you call a method on nil that returns an object, you will get nil as a return value. The idea here is that instead of getting a NoMethodError when we send a message to nil, we get nil back.

Some people like this so much they've composed the same semantics for Ruby:

class NilClass

  def method_missing(*args); nil; end

end

Now instead of writing person && person.name && person.name.upcase or person.andand.name.andand.upcase, you write person.name.upcase and either get the person's name in upper case or nil. Wonderful! Or is it? Let's take a look at what we're trying to accomplish and the limitations of this approach.

queries

Hopelessly egocentric nil works reasonably for querying properties, in other words sub-entities when an entity is constructed by composition, things like .name. I'm quite happy if person.name returns nil whether we don't have a person or if the person doesn't have a name. And we can extend this to what I would call purely functional transformations like .upcase. Just as ''.upcase is '', it is reasonable to think of nil.upcase as nil.

Now let's look at some things that aren't properties and aren't purely functional transformations. What do we do with methods that are intended to update their receiver? Consider a bank account object. Do we really want to write things like:

person.account = nil
person.account.increment_balance(100)
  => nil

This makes no sense. If we want to give them a hundred dollars, we had better have their actual account on hand! Clearly there is a huge difference between methods that are queries and methods that are updates. (Note that andand doesn't save us either, except by virtue of being explicit rather than magical so we can eschew it for update methods like #increment_balance.)

updates

Now that we are talking about methods with side-effects, let's be more specific. Our hopelessly egocentric nil does return nil to any method. But it has another property, it has no side-effects. This is sometimes what we want! Let's look at our nil account again. What about this code:

person.account.update_attribute(:primary_email, 'reg@braythwayt.com')

To decide what we think of this, we need to be specific about the meaning of nil. Generally, nil means one of two things:

  1. NONE, meaning "There isn't one of these," or;
  2. UNKNOWN, meaning "There is one of these, but we don't know what it is."

person.account.update_attribute(:primary_email, 'reg@braythwayt.com') is an example of why this difference matters. If person.account is an account, we want to update its primary email address, of course. And if person.account is NONE, we might be very happy not updating its primary email address. Perhaps our code looks like this:

class Person < ActiveRecord::Base
  belongs_to :account

  def update_email(new_email)
    self.class.transaction do
      update_attribute(:primary_email, new_email)
      account.update_attribute(:primary_email, new_email)
    end
  end

  # ...

end

Person.find(:first, :conditions => {...}).update_email('reg@braythwayt.com')

Meaning, update our person's primary email address, and if they have an account, update it too. If nil means NONE, this works. But what if nil really means UNKNOWN rather than NONE? Now it is wrong to silently fail. Let me give you a very specific way this can happen. When performing a database query, we can specify the exact columns we want returned. In Active Record, we might write something like this:

person = Person.find(:first, :conditions => {...}, :select => 'id, name')

What this means is that there is an account_id column in the people table, however we are deliberately not loading it into person. ActiveRecord will still supply us with a #account method, however it will return nil. This absolutely, positively means that person.account is UNKNOWN, not NONE. There could well be an account in our database for this person, and now if we write:

person.update_email('reg@braythwayt.com')

We do not want it to silently ignore the account email update, because we haven't loaded the account associated model. So for UNKNOWN, our two rules are:

  1. Querying UNKNOWN returns UNKNOWN;
  2. All attempts to update UNKNOWN are errors.

What about NONE? We gave two examples of updates, one of which was a really bad idea,#increment_balance, and the other of which was fine update_attribute(:primary_email, new_email). Thus we have three rules for NONE:

  1. Querying NONE returns NONE;
  2. Some updates to NONE may return NONE and have no side effects;
  3. Some updates to NONE may be errors.

With a little forethought and design, you may be able to construct one or more classes if your application for which all updates to NONE return NONE and have no side effects. But for all others, methods like #increment_balance represent a semantic problem with using a hopelessly egocentric nil to represent NONE. We also see a problem with writing a hopelessly egocentric nil to handle UNKNOWN: How does it know which methods are queries and which methods are updates?

If we work really hard and eliminate all possibility of an update to NONE being an error, are there any other issues with using a hopelessly egocentric nil? Let's return to our initial case:

person.name
  => nil

person.name.upcase
  => nil

Makes sense. And then we write:

person.name + ", esq."
  => nil

Dubious, but let's go with it. If this makes sense, we ought to be able to write this as well:

"Mister " + person.name
  => TypeError: can't convert nil into String

Why is this an error? Things don't get any better using a hopelessly egocentric nil to handle UNKNOWN. Even if we can get past the issue of update methods, we have another problem that is much more difficult to resolve. UNKNOWN introduces tri-value logic:

UNKNOWN == Object.new
  => UNKNOWN
UNKNOWN != Object.new
  => UNKNOWN
UNKNOWN == UNKNOWN
  => UNKNOWN
UNKNOWN != UNKNOWN
  => UNKNOWN
Object.new == UNKNOWN
  => UNKNOWN
Object.new != UNKNOWN
  => UNKNOWN

When you don't know something's value, it is neither equal to nor not equal to any other value, including another unknown value. And our fifth and sixth examples suffer from the same problem as nil + ", esq." vs. "Mister " + nil. We would need to patch all sorts of other objects to make equality testing many many other methods work. (What is 42 < UNKNOWN?) But things get worse:

How does truthiness work? In Ruby, you cannot override the way and, or, if, unless, &&, and || work. What are the semantics of if UNKNOWN? What do true && UNKNOWN or UNKNOWN or true return? Before implementing a true UNKNOWN in any language, I would want those questions answered.

Finally, there is actually a fifth and sixth rule that we are ignoring because these examples are in Ruby rather than a language with an expressive type system. Consider:

'Reg Braithwaite'.wealthy?
  => NoMethodError: undefined method `wealthy?' for "Reg Braithwaite":String

And now we write:

person.name.wealthy?         # or...
person.name.andand.wealthy?

What happens if person.name is NONE? What happens if person.name is UNKNOWN? Our problem here is that #wealthy? is never a valid message to send to something returned by person.name. Our behaviour ought to be:

  • Sending an invalid message to NONE raises a NoMethodError;
  • Sending an invalid message to UNKNOWN raises a NoMethodError.

There is no easy way to do this in Ruby, of course. Not only do we have trouble disambiguating queries from updates, we have trouble disambiguating valid from invalid messages.

For all of these reasons, I am loathe to implement a hopelessly egocentric nil and prefer to use an explicit idiom like #andand or #try. With explicit idioms, I can deal with the ambiguity between nil meaning NONE and nil meaning UNKNOWN and make sure my code does not violate the rules given here. But what I like about the idea of a hopelessly egocentric nil is that thinking the consequences provokes me to really think about the semantics of my data schemas.

Representing NONE and UNKNOWN values is a subtle problem requiring a deep and pervasive approach to typing similar to C++'s const keyword and/or writing custom null objects that understand which methods are safe to respond egocentrically and which are errors.

More on combinators: Kestrels, The Thrush, Songs of the Cardinal, Quirky Birds and Meta-Syntactic Programming, Aspect-Oriented Programming in Ruby using Combinator Birds, The Enchaining and Obdurate Kestrels, Finding Joy in Combinators, Refactoring Methods with Recursive Combinators, Practical Recursive Combinators, The Hopelessly Egocentric Blog Post, Wrapping Combinators, and Mockingbirds and Simple Recursive Combinators in Ruby.


My recent work:

JavaScript AllongéCoffeeScript RistrettoKestrels, Quirky Birds, and Hopeless Egocentricity


(Spot a bug or a spelling mistake? This is a Github repo, fork it and send me a pull request!)

Reg Braithwaite | @raganwald

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