How to make an async Swift function "@synchronized"?

My original answer (in which I suggest awaiting the prior task) is below. It is a simple pattern that works well, but is unstructured concurrency (complicating cancelation workflows).

Nowadays, I would use an AsyncSequence, e.g., an AsyncStream. See WWDC 2021 video Meet AsyncSequence. Or, for queue-like behavior (where we set up the queue initially and later append items to it), more often than not, I reach for AsyncChannel from the Swift Async Algorithms package. See WWDC 2022 video Meet Swift Async Algorithms.

E.g., I can create an AsyncChannel for URLs that I want to download:

let urls = AsyncChannel<URL>()

Now that I have a channel, I can set up a task to process them serially with a for-await-in loop:

func processUrls() async {
    for await url in urls {
        await download(url)
    }
}

And, when I later want to add something to that channel to be processed, I can send to that channel:

func append(_ url: URL) async {
    await urls.send(url)
}

You can have every Task await the prior one. And you can use actor make sure that you are only running one at a time. The trick is, because of actor reentrancy, you have to put that "await prior Task" logic in a synchronous method.

E.g., you can do:

actor Experiment {
    private var previousTask: Task<Void, Error>?

    func startSomethingAsynchronous() {
        previousTask = Task { [previousTask] in
            let _ = await previousTask?.result
            try await self.doSomethingAsynchronous()
        }
    }

    private func doSomethingAsynchronous() async throws {
        let id = OSSignpostID(log: log)
        os_signpost(.begin, log: log, name: "Task", signpostID: id, "Start")
        try await Task.sleep(nanoseconds: 2 * NSEC_PER_SEC)
        os_signpost(.end, log: log, name: "Task", signpostID: id, "End")
    }
}

Now I am using os_signpost so I can watch this serial behavior from Xcode Instruments. Anyway, you could start three tasks like so:

import os.log

private let log = OSLog(subsystem: "Experiment", category: .pointsOfInterest)

class ViewController: NSViewController {

    let experiment = Experiment()

    func startExperiment() {
        for _ in 0 ..< 3 {
            Task { await experiment.startSomethingAsynchronous() }
        }
        os_signpost(.event, log: log, name: "Done starting tasks")
    }

    ... 
}

And Instruments can visually demonstrate the sequential behavior (where the ⓢ shows us where the submitting of all the tasks finished), but you can see the sequential execution of the tasks on the timeline:

I actually like to abstract this serial behavior into its own type:

actor SerialTasks<Success> {
    private var previousTask: Task<Success, Error>?

    func add(block: @Sendable @escaping () async throws -> Success) {
        previousTask = Task { [previousTask] in
            let _ = await previousTask?.result
            return try await block()
        }
    }
}

And then the asynchronous function for which you need this serial behavior would use the above, e.g.:

class Experiment {
    let serialTasks = SerialTasks<Void>()

    func startSomethingAsynchronous() async {
        await serialTasks.add {
            try await self.doSomethingAsynchronous()
        }
    }

    private func doSomethingAsynchronous() async throws {
        let id = OSSignpostID(log: log)
        os_signpost(.begin, log: log, name: "Task", signpostID: id, "Start")
        try await Task.sleep(nanoseconds: 2 * NSEC_PER_SEC)
        os_signpost(.end, log: log, name: "Task", signpostID: id, "End")
    }
}