Recursion over a Swift Sliceable - swift

Question

I feel that I must be missing something obvious. Decomposing a list into the head and tail and then recursing over the tail is a standard functional programming technique, yet I'm struggling to do this for Sliceable types in Swift.
I have a recursive function that follows this pattern:
func recurseArray(arr: [Int]) -> [Int] {
guard let first = arr.first else {
return []
}
let rest = recurseArray(Array(dropFirst(arr)))
let next = rest.first ?? 0
return [first + next] + rest
}
Obviously the real code does a lot more than add each number to the next.
Note the call to Array(dropFirst(seq)). Converting to an Array is required since dropFirst actually returns an ArraySlice, and an ArraySlice isn't a Sliceable, so I can't pass it to my function.
I'm not sure what sort of optimization the compiler is capable of here, but it seems to me that creating a new array from a SubSlice unnecessarily won't be optimal. Is there a solution to this?
Furthermore, what I'd really like to do is create a version of this function that can take any Sliceable type:
func recurseSeq<T: Sliceable where T.Generator.Element == Int>(list: T) -> [Int] {
guard let first = list.first else {
return []
}
let rest = recurseSeq(dropFirst(list)) // <- Error - cannot invoke with argument type T.SubSlice
let next = rest.first ?? 0
return [first + next] + rest
}
This time I don't have a solution to the fact that I have a SubSlice. How can I achieve my goal?

Answer 1

It turns out that there is a generic solution. You need to add these generic requirements:
<
S : Sliceable where S.SubSlice : Sliceable,
S.SubSlice.Generator.Element == S.Generator.Element,
S.SubSlice.SubSlice == S.SubSlice
>
For the question posted, this gives:
func recurseSeq<
S : Sliceable where S.SubSlice : Sliceable,
S.SubSlice.Generator.Element == Int,
S.SubSlice.SubSlice == S.SubSlice,
S.Generator.Element == Int
>(list: S) -> [Int] {
guard let first = list.first else {
return []
}
let rest = recurseSeq(dropFirst(list))
let next = rest.first ?? 0
return [first + next] + rest
}
Here's a useful generic reduce on any sliceable:
extension Sliceable where
SubSlice : Sliceable,
SubSlice.Generator.Element == Generator.Element,
SubSlice.SubSlice == SubSlice {
func recReduce(combine: (Generator.Element, Generator.Element) -> Generator.Element) -> Generator.Element? {
return self.first.map {
head in
dropFirst(self)
.recReduce(combine)
.map {combine(head, $0)}
?? head
}
}
}
[1, 2, 3].recReduce(+) // 6
I can't take credit for this, the solution was posted on the Apple Development Forums.
It's a shame that the generic requirements are so involved for such a a basic operation - it's hardly intuitive! But I'm glad to have a solution...

Answer 2

Actually ArraySlice is Sliceable, so you can recurse on
ArraySlice<Int>:
func recurseArray(arr: ArraySlice<Int>) -> [Int] {
guard let first = arr.first else {
return []
}
let rest = recurseArray(dropFirst(arr))
let next = rest.first ?? 0
return [first + next] + rest
}
with a wrapper function which is called only once at the top level:
func recurseArray(arr: [Int]) -> [Int] {
return recurseArray(arr[arr.startIndex ..< arr.endIndex])
}
I don't have a solution for your second more general problem.
The API docs for Sliceable state that SubSlice should be
Sliceable itself (which is the case for all known Sliceable
types).
I have therefore the feeling that it should be possible by requesting
that T.SubSlice is itself sliceable with the identical SubSlice
type, however this does not compile:
func recurseSeq<T: Sliceable where T.Generator.Element == Int,
T.SubSlice : Sliceable,
T.SubSlice.SubSlice == T.SubSlice>(list: T.SubSlice) -> [Int] {
guard let first = list.first else {
return []
}
let rest = recurseSeq(dropFirst(list) as T.SubSlice)
// error: cannot invoke 'recurseSeq' with an argument list of type '(T.SubSlice)'
let next = rest.first ?? 0
return [first + next] + rest
}
The compiler accepts that dropFirst(list) can be cast to T.SubSlice,
but refuses to call recurseSeq() on that value, which I do not
understand.
Alternatively, you can recurse on a GeneratorType:
func recurseGen<G: GeneratorType where G.Element == Int>(inout gen: G) -> [Int] {
guard let first = gen.next() else {
return []
}
let rest = recurseGen(&gen)
let next = rest.first ?? 0
return [first + next] + rest
}
with a wrapper that takes a SequenceType:
func recurseSeq<T: SequenceType where T.Generator.Element == Int>(list: T) -> [Int] {
var gen = list.generate()
return recurseGen(&gen)
}
Arrays and array slices all conform to SequenceType, so that should
work in all your cases.

Answer 3

Creating an array in every iteration doesn't seem like a good idea. I don't know if the compiler optimizes it somehow, but you could probably find a different solution.
For example, in this case, you could drop de recursion and use a for loop instead that modifies the array in place.
func recurseArray2(var a: [Int]) -> [Int] {
for var i = a.count-1; i > 0; i-- {
a[i-1] += a[i]
}
return a
}