Sort Descriptors in Swift

From Runtime Magic To Functions

Just last week, someone asked me "in what respect does Swift fall short of the dynamic features of Objective-C"?

Dynamic programming means a lot of different things to different people, and I think they meant runtime programming. In this post, we'll look at replacing Objective-C's runtime programming with Swift's functions.

This post is an excerpt from the Functions chapter in Advanced Swift, which we're currently rewriting (and making very good progress). The text below was originally written by Airspeed Velocity. I took his text and code, updated everything for Swift 3 and made some heavy edits. Thanks to Ole Begemann for reading through a draft of this.

In the chapter on collections, we talked about parametrizing behavior by passing functions as arguments. Let's look at another example of this: sorting.

If you want to sort an array in Objective-C using Foundation, you are met with a long list of different options. These provide a lot of flexibility and power, but at the cost of complexity — even the simplest probably needs a trip to the documentation to know how to use it.

Sorting collections in Swift is simple:

var myArray = [3, 1, 2]
myArray.sorted() // [1, 2, 3]

There are really four sort methods: sorted(by:) and sort(by:), times two for the overloads that default to sorting comparable things in ascending order. But the overloading means that when you want the simplest case, sorted() is all you need. If you want to sort in a different order, just supply a function:

myArray.sorted(by: >) // [3, 2, 1]

You can also supply a function if your elements don't conform to Equatable but do have a < operator, like tuples:

var numberStrings = [(2, "two"), (1, "one"), (3, "three")]
numberStrings.sort(by: <)
numberStrings // [(1, "one"), (2, "two"), (3, "three")]

Or, you can supply a more complicated function if you want to sort by some arbitrary calculated criteria:

let animals = ["elephant", "zebra", "dog"]
let sortedAnimals = animals.sorted { lhs, rhs in
    let l = lhs.characters.reversed()
    let r = rhs.characters.reversed()
    return l.lexicographicallyPrecedes(r)
sortedAnimals // ["zebra", "dog", "elephant"]

It is this last ability — the ability to use any comparison function to sort a collection — that makes the Swift sort so powerful, and makes this one function able to replicate much (if not all) of the functionality of the various different sorting methods in Foundation.

To demonstrate this, let's take a complex example inspired by the Sort Descriptor Programming Topics. The sortedArray(using:) method on NSArray is very flexible and a great example of the power of Objective-C's dynamic nature. Support for selectors and dynamic dispatch is still there in Swift, but the Swift standard library favors a more function-based approach instead. Later on, we'll show a few techniques where functions as arguments, and treating functions as data, can be used to get the same dynamic effects.

We'll start by defining a Person object. Because we want to show how Objective-C's powerful runtime system works, we'll have to make it an NSObject subclass (in pure Swift, a struct might have been a better choice):

final class Person: NSObject {
    var first: String
    var last: String
    var yearOfBirth: Int
    init(first: String, last: String, yearOfBirth: Int) {
        self.first = first
        self.last = last
        self.yearOfBirth = yearOfBirth


Let's also define an array of people, with different names and birth years:

let people = [
    Person(first: "Jo", last: "Smith", yearOfBirth: 1970),
    Person(first: "Joe", last: "Smith", yearOfBirth: 1970),
    Person(first: "Joe", last: "Smyth", yearOfBirth: 1970),
    Person(first: "Joanne", last: "smith", yearOfBirth: 1985),
    Person(first: "Joanne", last: "smith", yearOfBirth: 1970),
    Person(first: "Robert", last: "Jones", yearOfBirth: 1970),

We want to sort this array first by last name, then by first name, and finally by birth year. We want to do this case insensitively and using the user's locale. An NSSortDescriptor object describes how to order objects, and we can use them to express the individual sorting criteria.

let lastDescriptor = NSSortDescriptor(key: "last", ascending: true,
  selector: #selector(NSString.localizedCaseInsensitiveCompare(_:)))
let firstDescriptor = NSSortDescriptor(key: "first", ascending: true, 
  selector: #selector(NSString.localizedCaseInsensitiveCompare(_:)))
let yearDescriptor = NSSortDescriptor(key: "yearOfBirth", ascending: true)

To sort the array, we can use the sortedArray(using:) method on NSArray. This takes a list of sort descriptors. To determine the order of two elements, it starts by using the first sort descriptor, and uses that result. However, if two elements are equal according to the first descriptor, it uses the second descriptor, and so on.

(people as NSArray).sortedArray(using: [lastDescriptor, firstDescriptor, yearDescriptor]) 
// [Robert Jones (1970), Jo Smith (1970), Joanne smith (1970), Joanne smith (1985), Joe Smith (1970), Joe Smyth (1970)]

A sort descriptor uses two runtime features of Objective-C: the key is a key path, and key-value coding is used to lookup the value of that key at runtime. The selector parameter takes a selector (which is really just a String describing a method name). At runtime, the selector is turned into a comparison function. When comparing two objects, the values for the key are compared using that comparison function.

This is a pretty cool use of runtime programming, especially when you realize the array of sort descriptors can be built at runtime, say based on a user clicking a column heading.

How can we replicate this functionality using Swift's sort? It's simple to replicate parts of the sort, for example, if you want to sort an array using localizedCaseInsensitiveCompare:

var strings = ["Hello", "hallo", "Hallo", "hello"]
strings.sort { $0.localizedCaseInsensitiveCompare($1) == .orderedAscending}
strings // ["hallo", "Hallo", "Hello", "hello"]

If you want to sort using just a single property of an object, that's also simple.

people.sorted { $0.yearOfBirth < $1.yearOfBirth } 
// [Jo Smith (1970), Joe Smith (1970), Joe Smyth (1970), Joanne smith (1970), Robert Jones (1970), Joanne smith (1985)]

This approach doesn't work so great when optional properties are combined with methods like localizedCaseInsensitiveCompare, though — it gets ugly fast. For example, consider sorting an array of filenames by file extension (using the fileExtension property from the Optionals chapter):

var files = ["one", "file.h", "file.c", "test.h"]
files.sort { l, r in r.fileExtension.flatMap { l.fileExtension?.localizedCaseInsensitiveCompare($0) } == .orderedAscending }
files // ["one", "file.c", "file.h", "test.h"]

Later on, we'll make it easier to use optionals when sorting. However, for now, we haven't even tried sorting by multiple properties. To sort by last name, then first name, we can use the standard library's lexicographicalCompare method. This takes two sequences and performs a phonebook-style comparison by moving through each pair of elements until it finds one that isn't equal. So we can build two arrays of the elements and use lexicographicalCompare to compare them. It also takes a function to perform the comparison. We'll put our use of localizedCaseInsensitiveCompare in the function:

let sortedPeople = people.sorted { p0, p1 in
    let left =  [p0.last, p0.first]
    let right = [p1.last, p1.first]

    return left.lexicographicallyPrecedes(right) {
        $0.localizedCaseInsensitiveCompare($1) == .orderedAscending
sortedPeople // [Robert Jones (1970), Jo Smith (1970), Joanne smith (1985), Joanne smith (1970), Joe Smith (1970), Joe Smyth (1970)]

At this point, we've almost replicated the functionality of the original sort in roughly the same number of lines. But there's still a lot of room for improvement: the building of arrays on every comparison is very inefficient, the comparison is hardcoded, and we can't really sort by yearOfBirth using this approach.

Functions as Data

Rather than writing an even more complicated function that we can use to sort, let's take a step back. So far, the sort descriptors were much clearer, but they use runtime programming. The functions we wrote do not use runtime programming, but they are not so easy to write (and read).

A sort descriptor is a way of describing the ordering of objects. Instead of storing that information as a class, we can define a function to describe the ordering of objects. The simplest possible definition would take two objects, and returns true if they are ordered. This is also exactly the type that the standard library's sort(by:) and sorted(by:) methods take as an argument. It's helpful to define a generic typealias to describe sort descriptors:

typealias SortDescriptor<Value> = (Value, Value) -> Bool

As an example, we could define a sort descriptor that compares two Person objects by year of birth, or a sort descriptor that sorts by last name:

let sortByYear: SortDescriptor<Person> = { $0.yearOfBirth < $1.yearOfBirth }
let sortByLastName: SortDescriptor<Person> = { 
  $0.last.localizedCaseInsensitiveCompare($1.last) == .orderedAscending 

Rather than writing the sort descriptors by hand, we can write a function that generates them. It's not nice that we to write the same property twice: in the sortByLastName, we could have easily made a mistake and accidentally compared $0.last with $1.first. Also, it's tedious to write these sort descriptors: to sort by first name, it's probably easiest to copy and paste the sortByLastName definition and modify it.

Rather than copying and pasting, we can define a function with an interface that is much like NSSortDescriptor, but without the runtime programming. This function takes a key and a comparison method, and returns a sort descriptor (the function, not the class NSSortDescriptor). Here, key is not a string, but a function. To compare two keys, we use a function isOrderedBefore. Finally, the result type is a function as well, even though that is slightly obscured by the typealias.

func sortDescriptor<Value, Key>(
  key: @escaping (Value) -> Key,
    _ isOrderedBefore: @escaping (Key, Key) -> Bool) 
    -> SortDescriptor<Value> {
    return { isOrderedBefore(key($0), key($1)) }

This allows us to define sortByYear in a different way:

let sortByYearAlt: SortDescriptor<Person> = sortDescriptor(key: { $0.yearOfBirth }, <)
people.sorted(by: sortByYearAlt) 
// [Jo Smith (1970), Joe Smith (1970), Joe Smyth (1970), Joanne smith (1970), Robert Jones (1970), Joanne smith (1985)]

We can even define an overloaded variant that works for all Comparable types:

func sortDescriptor<Value, Key>(key: @escaping (Value) -> Key)
    -> SortDescriptor<Value> where Key: Comparable {
    return { key($0) < key($1) }
let sortByYearAlt2: SortDescriptor<Person> = sortDescriptor(key: { $0.yearOfBirth })

Both sortDescriptor above work with boolean functions. The NSSortDescriptor class has an initializer that takes a comparison function such as localizedCaseInsensitiveCompare. Adding support for this is easy as well:

func sortDescriptor<Value, Key>(
    key: @escaping (Value) -> Key,
    ascending: Bool = true,
    _ comparator: @escaping (Key) -> (Key) -> ComparisonResult
    ) -> SortDescriptor<Value> {
    return { lhs, rhs in
        let order: ComparisonResult = ascending ? .orderedAscending : .orderedDescending
        return comparator(key(lhs))(key(rhs)) == order

This allows us to write our sortByFirstName in a much shorter and clearer way:

let sortByFirstName: SortDescriptor<Person> = 
  sortDescriptor(key: { $0.first }, String.localizedCaseInsensitiveCompare)
people.sorted(by: sortByFirstName) 
// [Jo Smith (1970), Joanne smith (1985), Joanne smith (1970), Joe Smith (1970), Joe Smyth (1970), Robert Jones (1970)]

This SortDescriptor is just as expressive as its NSSortDescriptor variant, but it is typesafe, and it does not rely on runtime programming.

Currently, we can only use a single SortDescriptor function to sort arrays. If you recall, we used the NSArray.sortedArray(using:) method to sort an array with a number of comparison operators. We could easily add a similar method to Array, or even to the Sequence protocol. However, we would have to add it twice: once for the mutating variant, and once for the non-mutating variant.

We take a different approach so that we don't have to write more extensions. Instead, we write a function that combines multiple sort descriptors into a single sort descriptor. It works just like the sortedArray(using:) method: it first tries the first descriptor and uses that result. Unless the values are equal, then it uses the second descriptor, and so on.

func combine<Value>
    (sortDescriptors: [SortDescriptor<Value>]) -> SortDescriptor<Value> {
    return { lhs, rhs in
        for isOrderedBefore in sortDescriptors {
            if isOrderedBefore(lhs,rhs) { return true }
            if isOrderedBefore(rhs,lhs) { return false }
        return false

We can now finally replicate the initial example we had using sort descriptors:

let combined: SortDescriptor<Person> = combine(
  sortDescriptors: [sortByLastName,sortByFirstName,sortByYear]
people.sorted(by: combined) 
// [Robert Jones (1970), Jo Smith (1970), Joanne smith (1970), Joanne smith (1985), Joe Smith (1970), Joe Smyth (1970)]

We ended up with the same behavior as before. However, the version using functions is type-safe and does not rely on runtime programming, so it can be optimized by the compiler as well. And we can use it with structs, or non-Objective-C Objects.

This approach of using functions as data — storing them in array and building those arrays at runtime — opens up a new level of dynamic behavior, and it is one way in which a statically typed compile-time-oriented language like Swift can still replicate some of the dynamic behavior of languages like Objective-C or Ruby.

Also, it is possible to write functions that combine other functions. For example, our combine(sortDescriptors:) function took an array of sort descriptors, and combined them into a single sort descriptor. Alternatively, we could have written an operator to combine two sort functions:

infix operator <||> : LogicalDisjunctionPrecedence
func <||><A>(lhs: @escaping (A,A) -> Bool, rhs: @escaping (A,A) -> Bool) -> (A,A) -> Bool {
    return { x,y in
        if lhs(x,y) { return true }
        if lhs(y,x) { return false }
        // Otherwise, they're the same, so we check for the second condition
        if rhs(x,y) { return true }
        return false

Most of the time, writing a custom operator is a bad idea. Custom operators are often harder to read than functions, because the name isn't explicit. However, they can be very powerful when used sparingly. The operator above allows us to rewrite our combined sort example like so:

let combinedAlt = sortByLastName <||> sortByFirstName <||> sortByYear
people.sorted(by: combinedAlt) 
// [Robert Jones (1970), Jo Smith (1970), Joanne smith (1970), Joanne smith (1985), Joe Smith (1970), Joe Smyth (1970)]

That said, we prefer the combine(sortDescriptors:) function over the custom operator. It is clearer at the call-site, which makes for more readable code. Unless you are writing highly domain-specific code, a custom operator is probably overkill.

The Foundation version still has one functional advantage over our version. It can deal with optionals without having to write any more code. For example, if we would make the last property on Person an optional string, we wouldn't have to change anything in our sorting code that uses NSSortDescriptor.

However, all is not lost. You can feel it coming: once again, we write a function which takes a function and returns a function. We can take a regular comparing function such as localizedCaseInsensitiveCompare, which works on two Strings, and turn it into a function that takes two optional Strings. If both values are nil, they are equal. If the left-hand side is nil, but the right-hand isn't they're ascending, and the other way around. Finally, if they are both non-nil, we can use the compare function to compare them.

func lift<A>(_ compare: @escaping (A) -> (A) -> ComparisonResult) -> (A?) -> (A?) -> ComparisonResult {
    return { lhs in { rhs in
        switch (lhs, rhs) {
        case (nil, nil): return .orderedSame
        case (nil, _): return .orderedAscending
        case (_, nil): return .orderedDescending
        case let (l?, r?): return compare(l)(r)
        default: fatalError() // Impossible case
    } }

This allows us to "lift" a regular comparison function into the domain of optionals, and it can be used together with our sortDescriptor function. If you recall the files array from before, sorting them by fileExtension got really ugly because we had to deal with optionals. However, with our new lift function, it's very clean again:

let lcic = lift(String.localizedCaseInsensitiveCompare)
let result = files.sorted(by: sortDescriptor(key: { $0.fileExtension }, lcic))
result // ["one", "file.c", "file.h", "test.h"]

We can write a similar version of lift for functions that return a Bool. Before Swift 3, operators like > were defined on optionals. They were removed because they can lead to accidental bugs. However, with a boolean lift you can easily take an existing operator and make it work for optionals.

One drawback of the function-based approach is that functions are opaque. We can take an NSSortDescriptor, print it to the console, and we get some information about the sort descriptor: the key path, the selector name and whether it's ascending. Our function-based approach cannot do this. For sort descriptors, this is not a problem in practice. If it's important to have that information, we could wrap the functions in a struct or class, and store additional debug information.

This approach has also given us a clean separation between the sorting method and the comparison method. The algorithm that Swift's sort uses is a hybrid of multiple sorting algorithms — as of writing, it is an introsort (which is itself a hybrid of a quicksort and a heapsort), but it switches to an insertion sort for small collections to avoid the upfront startup cost of the more complex sort algorithms.

Introsort is not a "stable" sort. That is, it does not necessarily maintain relative ordering of values that are otherwise equal according to the comparison function.

But if you implemented a stable sort, the separation of the sort method from the comparison would allow you to swap it in easily:

people.stableSorted(by: combine(
  sortDescriptors: [sortByLastName,sortByFirstName,sortByYear]