I didn’t realise this at the time, the previous entry wasn’t the last Objective-Swift post.

The inheritance mechanism in ObjS is prototypical, meaning that an object inherits from a single other object rather than getting its behaviour from a class. This is the same system that Self and languages that, um, inherit its approach use.

This form of inheritance gives us two capabilities: decorating an object by attaching new methods, or updating an object by shadowing existing methods. And that means that setting a variable can be mimicked by returning an object where the accessor for that variable has been overridden. So in fact the objects in this system won’t be mutable at all, but they will have mutators that return replacement values.

It sounds weird, but there are reasons to really do this. In Postscript, you can mimic variables by creating named functions that just push a value onto the stack. Rather than mutating the data, you “set” the variable by rebinding the name to a function that pushes the updated value.

Digression: updating the dispatch system

In rewriting setters to be immutable I also noticed it was possible to consolidate the “accessor” and “mutator” implementation types into a single type, using variadic arguments. I have genuinely no idea why I didn’t realise that before, when the type of an ObjC method is usually expected to be (id, SEL, id...) -> id.

enum IMP {
  case method((Selector->IMP, Selector, Selector->IMP...)->(Selector->IMP)?)
  case asInteger((Selector->IMP, Selector, Selector->IMP...)->Int?)
  case methodMissing((Selector->IMP, Selector, Selector->IMP...)->(Selector->IMP)?)
  case description((Selector->IMP, Selector, Selector->IMP...)->String?)
}

The asInteger and description types gain variadic arguments but still need to be present so you can exit the O-O type system and get back to Swift types. For the moment, methodMissing is still modelled as a separate case in the enumeration, even though it has the same type as a regular method.

Mutation as a function

Given an object, a selector to override, and the replacement value, return a new object that will return that value when messaged with that selector.

infix operator ☞ {}

func mutate(receiver: Object, selector: Selector, value:Object) -> Object {
  return { _cmd in
    switch (_cmd) {
    case selector:
      return .method({ _ in return value })
    default:
      return receiver(_cmd)
    }
  }
}

func ☞(message:(receiver: Object?, selector: Selector), value:Object) -> Object? {
  if let receiver = message.receiver {
    return mutate(receiver, message.selector, value)
  } else {
    return nil
  }
}

Taking the Point objects from the further advances post, but deleting their mutators, this can be used to make updated objects.

let p = Point(3, 4, o)
📓(p) // (3,4)
let p2 = (p,"x")☞(Integer(1,o))
📓(p2) // (1,4)

Mutation as a method

The same function can be used in the implementation of an Objective-Swift method. Here’s the setY: method on Points:

  return IMP.method({ (this, aSelector, args : Object...) in
    return (this, "y")☞args[0]
  })

Now a bit of notation to make calling mutator methods easier (I’m starting to run out of reasonable symbols):

infix operator ✍ {}

func ✍(message:(receiver:Object?, selector:Selector), value:Object) -> Object? {
  if let imp = message.receiver..message.selector {
    switch imp {
    case .method(let f):
      return f(message.receiver!, message.selector, value)
    default:
      return nil
    }
  } else {
    return nil
  }
}

Done.

let p3 = (p2, "setY:")✍(Integer(42, o))
📓(p3) // (1,42)

Fork me

I have put the current playground (which is written for the Swift 1.2 compiler, because I’m risk averseold fashioned) on GitHub.

Previously on SICPers, I defined objects as functions that return methods and built dynamic method dispatch in this object system. It’s time to tie up some loose ends.

Proper selectors

In languages like Smalltalk and Objective-C, an object’s range isn’t a small list of selectors like count and at:. It’s the whole of the String type.

typealias Selector = String

Now an object takes a Selector (i.e. a String) and returns a method implementation. Continuing with the type-safe theme from the previous posts, I’ll define a few different types of implementation that I might want to use.

enum IMP {
  case accessor(()->((Selector)->IMP)?)
  case asInteger(()->Int?)
  case methodMissing(()->((Selector)->IMP)?)
  case mutator(((Selector->IMP))->Void)
  case description(()->String?)
}

typealias Object = Selector -> IMP

Now I can create some proper objects.

func DoesNothing()->(_cmd:Selector)->IMP {
  var _self : Object! = nil
  func myself (selector: Selector)->IMP {
    return IMP.methodMissing({assertionFailure("method missing: \(selector)"); return nil;})
  }
  _self = myself
  return _self
}

let o : Object = DoesNothing()

func Integer(x: Int, proto: Object) -> Object {
  var _self : Object! = nil
  let _x = x
  func myself(selector:Selector) -> IMP {
    switch(selector) {
    case "asInteger":
      return IMP.asInteger({ return _x })
    case "description":
      return IMP.description({ return "\(_x)" })
    default:
      return proto(selector)
    }
  }
  _self = myself
  return _self
}

let theMeaning = Integer(42, o)

A better syntax

Usually you don’t think of method lookup as a function invocation, but rather as finding a member of an object (indeed in C++ they’re called member functions). A member-like syntax could look like this:

infix operator .. {}

func .. (receiver: Object?, _cmd:Selector) -> IMP? {
  if let this = receiver {
    let method = this(_cmd)
    switch(method) {
    case .methodMissing(let f):
      return f().._cmd
    default:
      return method
    }
  }
  else {
    return nil
  }
}

This system now has the same nil behaviour as Objective-C:

nil.."asInteger" // nil

And it also has a limited form of default message forwarding:

func Proxy(target:Object)->((_cmd:Selector)->IMP) {
  var _self : Object! = nil
  var _target = target
  func myself(selector:Selector) -> IMP {
    return IMP.methodMissing({ return _target })
  }
  _self = myself
  return _self
}

let proxyMeaning = Proxy(theMeaning)
let descriptionImp = proxyMeaning.."description"
descriptionImp!.describe() // (Enum Value)

But it’s going to be pretty tedious typing all of those switch statements to unbox the correct implementation of a method. There are two ways to go here, one is to add methods to the enumeration to make it all easier. These just unbox the union and call the underlying function, so for example:

extension IMP {
  func describe() -> String? {
    switch(self) {
    case .description(let f):
      return f()
    default:
      return nil
    }
  }
}

descriptionImp!.describe() // "42"

Or if you’re really going to town, why not define more operators?

infix operator → {}

func → (receiver: Object?, _cmd:Selector) -> Object? {
  if let imp = receiver.._cmd {
    switch (imp) {
    case .accessor(let f):
      return f()
    default:
      return nil
    }
  } else {
    return nil
  }
}

func ℹ︎(receiver:Object?)->Int? {
  if let imp = receiver.."asInteger" {
    switch(imp) {
    case .asInteger(let f):
      return f()
    default:
      return nil
    }
  } else {
    return nil
  }
}

ℹ︎(theMeaning)! // 42

Mutable Objects

There’s no reason why an object couldn’t close over a var and therefore have mutable instance variables. You can’t access the variables from outside the object in any way other than through its methods[*], even from objects that inherit from it. They’re all private.

[*] Unless you were to build a trap door, e.g. declaring the var in a scope where some other function also has access to it.

Firstly, some similar notation:

infix operator ☞ {}

func ☞ (mutator:IMP?, value: Object) -> Void {
  if let mut = mutator {
    switch(mut) {
    case .mutator(let f):
      f(value)
    default:
      return
    }
  }
}

Here is, somewhat weirdly, a class of Point objects where you can redefine both the x and y coordinates after creation.

func Point(x: Int, y: Int, proto: Object)->((_cmd:Selector)->IMP) {
  var _self : Object! = nil
  var _x = Integer(x,o), _y = Integer(y,o)
  func myself (selector:Selector) -> IMP {
    switch (selector) {
    case "x":
      return IMP.accessor({
        return _x
      })
    case "y":
      return IMP.accessor({
        return _y
      })
    case "setX:":
      return IMP.mutator({ newX in
        _x = newX
      })
    case "setY:":
      return IMP.mutator({ newY in
        _y = newY
      })
    case "description":
      return IMP.description({
        let xii = ℹ︎(_self→"x")!
        let yii = ℹ︎(_self→"y")!
        return "(\(xii),\(yii))"
      })
    default:
      return proto(selector)
    }
  }
  _self = myself
  return _self
}

In use it’s much as you’d expect.

let p = Point(3, 4, o)
(p.."description")!.describe() // "(3,4)"
ℹ︎(p→"x") // 3
(p.."setX:")☞(Integer(1,o))
ℹ︎(p→"x") // 1
(p.."description")!.describe() // "(1,4)"

But there’s no need to bother

It’s possible to build mutable objects out of immutable objects. Given a Point(3,4,o), you can make an object that looks exactly like a Point at (1,4) by building an object that has replacement implementations for x and description, but otherwise forwards all methods to the original.

In this way, mutation would look a lot like the Command pattern. You have your original state, you have a linked list (via the prototype chain) of modifications to that state, and the external view is as if you only had the final state.

Further further advances

It’d be good to be able to tell a method what its self is, to make inheritance work properly. For example, if a Point‘s description knew what object was self, then replacing x on a subtype would automatically get the description right. Ben Lings shows how this might work on the previous post’s List objects.

Further thanks

Jeremy Gibbons initiated the discussion on mutable objects that led to the implementation shown above. Thanks to Lawrence Lomax for lots of feedback and discussion about how this should all work, including an alternate implementation.

In the previous episode, I said that objects are functions that map their ivars onto methods. However, the objects that I demonstrated in the post were tables, structures of functions that closed over the ivars, like this:

struct List<T> {
  let count: () -> Int
  let at: (Int) -> T?
}

Functions and tables are actually interchangeable, so this is not a problem and there’s no sleight of hand.

Here’s a simple example: imagine a function that maps Booleans (instances drawn from the set Boolean) to integers (instances drawn from the set Int):

enum Boolean {
 case False
 case True
}

func intValue(b : Boolean) -> Int
{
  switch b
  case .False:
    return 0
  case .True:
    return 1
}

This is, notation aside, identical to encoding the map in a table:

struct BooleanIntMap {
  let False = 0
  let True = 1
}

That’s the state that my objects were in at the end of the previous post. So let’s complete the story, and turn these objects from tables into functions.

Three Minute Hero

Along the way, I’ll fix a deficiency in the previous version of these objects. When you got an object, it was in the form of a table of all of its methods, but typically you only want to call one at a time. In Objective-C, you pass an object a selector and it returns the appropriate method which you then call (well, that’s how the GNU runtime works. The NeXT and Apple runtimes jump right into the returned function). See? An object really is a function that maps its variables onto the methods you want.

There are a limited (for now) number of legitimate selectors to send to an object, so they can easily be represented with an enumeration.

enum DynamicListSelectors {
  case count
  case at
}

Now it gets a bit complicated (Objective-C and Smalltalk are also this complicated, but use a different notation that hides it from you). My list object will be a function that maps these selectors onto methods, but the two methods have different signatures. I therefore need a type which can represent (function with the .count signature) OR (function with the .at signature).

In addition to representing enumerated constants, Swift’s enums can also sum types. Remember that a type is just a set of that type’s instances: a sum type is the union of two (or more) type sets. So the list function can return something of this type:

enum DynamicList<T> {
  case count (() -> Int)
  case at ((Int) -> T?)
}

There are two things to do now. One is to define the function that maps from a selector onto an instance of this sum type: this is our message dispatch function, or more succinctly, our object.

func EmptyDynamicList<T>()(_cmd: DynamicListSelectors) -> DynamicList<T>
{
  switch _cmd {
  case .count:
    return DynamicList<T>.count({ return 0 })
  case .at:
    return DynamicList<T>.at({ (_) in return nil})
  }
}

But now we need to pull apart the enumeration in the client code to find the message implementation and invoke it. In principle, Smalltalk, Objective-C and other dynamic O-O languages have to do this too (in ObjC it works by knowing how to use function pointers of different types, and treating all the methods as function pointers), but the notation or loose type system hides it from you.

let emptyCountIMP : DynamicList<Int> = EmptyDynamicList()(_cmd: .count)
switch emptyCountIMP {
case .count(let f):
  f() // returns 0
default:
  assertionFailure("Implementation does not match selector")
}

Doing that every time you call a method would get boring quickly, averted by defining a couple of convenience functions.

func countOfList<T>(list: (DynamicListSelectors) -> DynamicList<T>) -> Int
{
  switch list(.count) {
  case .count(let f):
    return f()
  case .at(let f):
    assertionFailure("Implementation does not match selector")
    return 0 //unreached
  }
}

func elementInListAtIndex<T>(list: (DynamicListSelectors) -> DynamicList<T>, index: Int) -> T?
{
  switch list(.at) {
  case .at(let f):
    return f(index)
  case .count(let f):
    assertionFailure("Implementation does not match selector")
    return nil //unreached
  }
}

Now it should be easy enough to use a more complex implementation of the list class. Here’s a linked list, as before the tail is itself a linked list (which is now a function mapping a selector to an implemetation).

func DynamicLinkedList<T>(head: T,
                          tail: (DynamicListSelectors) -> DynamicList<T>)
                         (_cmd: DynamicListSelectors) -> DynamicList<T>
{
  switch _cmd {
  case .count:
    return DynamicList<T>.count({
      return 1 + countOfList(tail)
    })
  case .at:
    return DynamicList<T>.at({ (i) in
      if i < 0 {
        return nil
      }
      if i == 0 {
        return head
      }
      else {
        return elementInListAtIndex(tail, i - 1)
      }
    })
  }
}

let unitList = DynamicLinkedList("Wow", EmptyDynamicList()) //(Function)
countOfList(unitList) // 1
elementInListAtIndex(unitList, 0) // "Wow"
elementInListAtIndex(unitList, 1) // nil

Draw the rest of the owl

Going from here to Smalltalk is a small matter of types. The object defined above is a total function of a small number of list message selectors to a small number list method implementations: every selector resolves to a method.

A Smalltalk object is also a function from selectors to methods, but from the range of all possible selectors (which are strings) to the domain of all possible function types. [Aside: as C doesn’t have closures, Objective-C’s message lookup domain is all possible function types that receive an object and selector as the first two arguments.] You probably didn’t write implementations for every possible selector, so most of these messages will be resolved to the doesNotRecognize: implementation which is where Smalltalk does its forwarding and dynamic method resolution, similar to Objective-C’s forwardInvocation: and Ruby’s method_missing.

The awesome power of the runtime. Now available in Swift.

The maths behind functional programming predates computers. Once people had some experience with both of these things, they stripped them down and created object-oriented programming. It’s still possible to jettison a lot of the features of functional programming and work with the object-oriented core, and in this post I’ll do so using a subset of the Swift programming language.

Step One: Useing you’re type’s good

I’ll use this particular definition of a type: it’s a set. I could define a type completely as a set of constants:

Boolean :: {True, False}

or using constructors:

Natural :: {Zero, Successor(N : Natural)}

An element drawn from the set is an instance of the type. So True is an instance of Boolean, and Successor(Successor(Zero)) is an instance of Natural.

A particular, um, type of type is the “product” type, which represents a combination of other types. A tuple is product type: a tuple of type (Boolean, Natural) represents an instance of Boolean and an instance of Natural. The set (Boolean, Natural) or Boolean x Natural is the set of all possible combinations of Boolean and Natural.

Crucially, for the following argument, a struct is also a product type. Has been since before C was created, will be forever.

A function is a map from an input type to an output type. Really there’s more nuance in the world than that, particularly around whether the function works for all instances of the input type and whether there’s a one-to-one mapping between input and output instances, but that’s not relevant right now. All we need to know is that given an instance of the input type, applying a function to it will always result in a particular instance of the output type.

f :: InputType -> OutputType

You may think that you’ve seen functions with more than one input argument: that’s the same (roughly) as a function that takes a single tuple argument.

Step Two: Know what an object is

Defining instance variables as the values “known” inside an object, and methods as functions attached to an object that have access to its instance variables, I could say this:

An object is a collection of instance variables and methods that act on those instance variables.

But I want to put this a different way.

Given a collection of values, an object gives you a collection of methods that yield particular results based on those values.

But I want to put this a different way.

Given the input of a product type drawn from possible instance variables, an object will return a particular member of the product type drawn from possible methods.

But I want to put this a different way.

An object is a function that maps from instance variables to methods.

Step Three: Build an object

As the output of an object is a collection of methods, you can define an object entirely by its methods. In object-oriented programming, this is called “data hiding” or “encapsulation” and means that you can’t see what went into making the objects work this way, only that they do.

Starting small, think about the set data type. You only ever want to do one thing with a set: discover whether a particular element is contained in the set. That means that, for example, the type of a set of integers is equivalent to this type of function (in Swift syntax):

typealias Set = (Int) -> Bool

Now it’s possible to build trivial sets. Here’s one that contains no integers, and one that contains all the integers:

let emptySet : Set = { (_) in return false }
let universe : Set = { (_) in return true }

It’s easy to use the one method that these objects define: just call the objects as functions.

emptySet(12) //false
universe(12) //true

Step Four: Add some instance variables

I want to keep my Set method signature, because I want the objects I create to all be compatible (I really want them to all be of the same class). But I also want to be able to store and use instance variables from within the Set‘s method, so I can build some more interesting sets.

I’ll build a Set constructor, a function that returns properly-configured instances of Set. That constructor can close over the instance variables, therefore making them available from within the method. Here’s a constructor for Sets that represent contiguous ranges of Ints.

func RangeSet(lowerBound:Int, upperBound:Int)->Set
{
  return { (x) in (x >= lowerBound) && (x <= upperBound) }
}

Now it’s possible to create these Sets and use their method:

RangeSet(3, 7)(2) //false

let mySet = RangeSet(0, 2) //(Function)
mySet(1) //true
mySet(3) //false

Of course, the instance variables don’t have to be Ints. They could be anything else, including other Sets.

func UnionSet(setOne:Set, setTwo:Set) -> Set
{
  return { (x) in (setOne(x) || setTwo(x)) }
}

UnionSet(RangeSet(0, 2), RangeSet(3, 5))(4) //true

func IntersectSet(setOne:Set, setTwo:Set) -> Set
{
  return { (x) in (setOne(x) && setTwo(x)) }
}

IntersectSet(RangeSet(0, 5), RangeSet(3, 7))(5) //true

Even when a Set has another Set as an instance variable, it cannot see how that Set was constructed or what instance variables it has. It can only see the Set‘s method, because the encapsulation is working.

Step Five: Add more methods

Not all things that we might want to use as objects can be expressed as one method. A list has two methods: a count of the number of items it holds and a method to get the item at a given index. A list object therefore needs to represent the product of (count method, at method) and to let clients select which method they want to use from that product. This product could be expressed as a tuple:

typealias ListSelectors = (count:() -> Int, at:Int->AnyObject?)

Or (perhaps more usefully because the compiler for Swift allows generics in this case) as a struct:

struct List<T> {
  let count: () -> Int
  let at: (Int) -> T?
}

Now it’s possible to rely on the old trick of making constructor functions that return Lists:

func EmptyList<T>() -> List<T>
{
  return List(count: {return 0}, at: {(_) in return nil})
}

including the use of instance variables captured by closing over them:

func LinkedList<T>(head:T, tail:List<T>) -> List<T>
{
  return List(count: {return 1 + tail.count()},
    at: { index in return (index == 0) ? head : tail.at(index - 1)})
}

Step Six: Inherit from objects

The List is cool, but it’d be nice to be able to describe lists. I could create a function:

func describeList(list:List<SomeType>) -> String

but wouldn’t it be better to add description as a method on Lists? That would make the List type look like this:

struct ListWithDescription<T> {
  let count: () -> Int
  let at: (Int) -> T?
  let describe: () -> String
}

OK, but I don’t want to go back to all of my previous List implementations and add describe methods to them. What I really want to do is to add this method as an extension to Lists. I’ll define a type that includes a describe method and optionally implementations of the other methods too.

struct ListWithDescriptionSelectors<T> {
  let count: (() -> Int)?
  let at: ((Int) -> T?)?
  let describe: () -> String
}

Given a List and some ListWithDescriptionSelectors, it’s possible to build a ListWithDescription that knows how to describe itself and either inherits count and at from its List or overrides them itself.

func SubtypeListByAddingDescription<T>(prototype: List<T>,
  overrides: ListWithDescriptionSelectors<T>) ->
  ListWithDescription<T>
{
  let countImplementation : () -> Int
  if let count = overrides.count {
    countImplementation = count
  } else {
    countImplementation = prototype.count
  }
  let atImplementation : (Int)->T?
  if let at = overrides.at {
    atImplementation = at
  } else {
    atImplementation = prototype.at
  }
  return ListWithDescription<T>(count: countImplementation, at:     atImplementation, describe: overrides.describe)
}

(The slight complication with all the if lets is because the Swift compiler at time of writing wasn’t happy with using the ?? operator in their place.)

It’s now possible to put this into practice. In order to work with the elements in a List I need to know more about what type of thing they are, so here’s a specialisation of ListWithDescription that can describe a List of Strings. As ever, it has no special access to the instance variables of the List it extends and can only work with it through the published methods.

func ListOfStringsWithDescription(strings: List<String>) ->
  ListWithDescription<String>
{
  let describe: () -> String = {
    var output = ""
    for i in 0..<strings.count() {
      output = output.stringByAppendingString(strings.at(i)!)
      output = output.stringByAppendingString(" ")
    }
    return
      output.stringByTrimmingCharactersInSet(
        NSCharacterSet.whitespaceCharacterSet()
      )
  }
  return SubtypeListByAddingDescription(strings,
    ListWithDescriptionSelectors<String>(count: nil,
      at: nil,
      describe: describe))
}

let awesomeGreeting =
  ListOfStringsWithDescription(LinkedList("Hello,",
    LinkedList("World",
      EmptyList())))

awesomeGreeting.at(1) //"World"
awesomeGreeting.describe() //"Hello, World"

Next Step: Draw some conclusions

Object-Oriented Programming is a simple, easy to use subset of Functional Programming.

Open Step: Cite references

The objects in this article (like the objects in Microsoft COM or my earlier BlockObject) are Procedural Data Types, which I discovered in Object-Oriented Programming Versus Abstract Data Types and User-defined types and procedural data structures as complementary approaches to data abstraction. The idea of objects as closures first appeared, to my knowledge, in Objects as Closures: Abstract Semantics of Object Oriented Languages. The last two of these articles were brought to my attention by my colleague Peter O’Hearn after a discussion on the topic of functional/O-O duality. I am indebted to him for his help in drawing this article out of me.

After Step: Finish this idea

This journey, as we say at Facebook, is 1% complete. There’s plenty more to explore here, and I’m not sure the explanation is as clear as it could be. It is, however, written down, which is a start.