The document discusses the concepts of object-oriented programming and functional programming in the context of Swift. It explores the definition of sets, functions, and lists, illustrating these with code examples and type aliases. The conclusion emphasizes that objects in this paradigm are essentially functions that encapsulate properties and map selectors to method implementations.

1. Object-Oriented
Programming

2. …in Functional
Programming
Object-Oriented Programming

3. …in SwiftObject-Oriented Programming
…in Functional Programming

4. –Randall Munroe
“I’m being quoted to introduce something, but I have
no idea what it is and certainly don’t endorse it.”

5. First, an assertion
U
A ⇔ f == ∀𝑥: 𝕌•𝑥∈A
⇔ isDuck(𝑥)

6. …
⇔ isDuck(𝑥)

7. Some sets
let emptySet = {(_) in return false}
let universe = {(_) in return true}

8. All sets
typealias MySet<T> = (T) -> Bool

9. Parameterising sets
func RangeSet(from lower: Int, to upper: Int) -> MySet<Int>
{
return { (x) in (x >= lower) && (x <= upper)}
}
func UnionSet<T>(of left: @escaping MySet<T>,
and right: @escaping MySet<T>) -> MySet<T>
{
return { (x) in (left(x) || right(x))}
}

10. Digression: 2 > 1
⇔
Count: ℕ
At: ℕ→T?
<T>
struct List<T> {
let count: () -> Int
let at: (Int) -> T?
}
protocol List {
associatedtype T
func count() -> Int
func at(index: Int) -> T?
}
⇔

11. struct List<T> {
let count: () -> Int
let at: (Int) -> T?
}
protocol List {
associatedtype T
func count() -> Int
func at(index: Int) -> T?
}
⇔
count f(𝑥)
at g(𝑥)

12. count f()
at g(𝑥)

13. enum ListSelectors {
case count
case at
}
enum ListIMPs<T> {
case count (() -> Int)
case at ((Int) -> T?)
}
typealias List<T> = (ListSelectors) -> ListIMPs<T>

14. If 2>1, then ∞>2
typealias Selector = String
typealias Object = (Selector) -> IMP
enum IMP {
case accessor(()->(Object?)
case mutator((Object)->Void)
…
}
func swift_msgSend(this: Object, _cmd: Selector) -> IMP
{
return this(_cmd)
}

15. TL;DR
• Objects are functions
• …that close over their ivars (constructors are HOFs)
• …that map method selectors to method implementations
• …they’re just ways to pick functions at runtime
Sample code with more discussion: https://github.com/iamleeg/OOPInFPInSwift