Closure based recursive sequence for Swift

RecursiveSequence.swift

//
//  RecursiveSequence.swift
//
//  Created by John Scott on 31/03/2022.
//

///
/// To define a sequence by recursion, one needs a rule, called recurrence relation to construct each
/// element in terms of the ones before it. In addition, enough initial elements must be provided so
/// that all subsequent elements of the sequence can be computed by successive applications of
/// the recurrence relation.
///
/// For example, to get all daylight saving time transitions for a timezone:
///
///     let zone = TimeZone.current
///     let transitionDates = GeneratedSequence(initial: .distantPast) {
///         zone.nextDaylightSavingTimeTransition(after: $0)
///     }
///
///     for date in transitionDates {
///         print(date)
///     }
///
/// Or, to get the Fibonacci sequence:
///
///     let fibonacci = RecursiveSequence(initial: (1, 1)) {
///         ($0 + $1, $0)
///     }
///
///     for number in fibonacci.lazy.map({ $0.0 }) {
///         print(number)
///     }

struct RecursiveSequence<Element>: Sequence, IteratorProtocol {
    private var last: Element
    private let relation: (Element) -> Element?
    
    init(initial: Element, relation: @escaping (Element) -> Element?) {
        last = initial
        self.relation = relation
    }
    
    mutating func next() -> Element? {
        let next = relation(last)
        if let next = next {
            last = next
        }
        return next
    }
}