Within a View, I'm calling a function that references some external objects and updates a chart. For the time when function is processing I would like to hide the chart and replace it with a ProgressView. Question: How to control value of the @State from inside function.

I've tried different versions, the code below returns error on line: numbers = updateNumbers()

Cannot use mutating member on immutable value: 'self' is immutable

Simplified example

Swift playground.

import SwiftUI
import Charts
import PlaygroundSupport

struct ProgressExample: View {

    @State private var isUpdating: Bool = false
    @State private var numbers: [Int] = []

    var body: some View {
        VStack {
            Button("Update data") {
                isUpdating = true // Triggered refresh, show ProgressView
                numbers = updateNumbers()
            }
            .padding()
            Spacer()
            if (isUpdating) {
                ProgressView("Updating")
            } else {
                List {
                    ForEach(numbers, id: \.self) { number in
                        Text("Number: \(number)")
                    }
                }
            }
        }
    }

    // Long running function
    mutating func updateNumbers() -> [Int] {
        var randomIntegers: [Int] = []
        for _ in 0...10 {
            randomIntegers.append(Int.random(in: 1...100))
            Thread.sleep(forTimeInterval: 0.1)
        }
        self.isUpdating = false // The method completed, hide ProgressView
        return randomIntegers
    }
}

// Present the view in the Live View window
PlaygroundPage.current.setLiveView(ProgressExample())

The function doesn't need to be mutating. State.wrappedValue has a nonmutating setter, because it actually mutates some reference type value in State, not mutating the struct value.

So just remove mutating

func updateNumbers() -> [Int] {
    var randomIntegers: [Int] = []
    for _ in 0...10 {
        randomIntegers.append(Int.random(in: 1...100))
        Thread.sleep(forTimeInterval: 0.1)
    }
    self.isUpdating = false
    return randomIntegers
}

I'd also give the view a frame when setting it as the playground live view, since the playground apparently can't figure out an appropriate size to display its live view.

PlaygroundPage.current.setLiveView(
    ProgressExample()
        .frame(width: 700, height: 700)
)

Though it doesn't work in a playground, I recommend using a Preview to play with your SwiftUI views.

#Preview {
    ProgressExample()
}

Now notice that the progress view doesn't actually show up, because Thread.sleep blocks the UI thread and stops UI updates. I hope in your real code the work is not running on the main thread.

In any case though, I strongly recommend making updateNumbers an async method and calling it in a .task modifier. For your simple example here, you can rewrite the view like this:

struct ProgressExample: View {

    @State private var isUpdating: Bool = false
    @State private var numbers: [Int] = []

    var body: some View {
        VStack {
            Button("Update data") {
                isUpdating = true
            }
            .padding()
            Spacer()
            if isUpdating {
                ProgressView("Updating")
            } else {
                List {
                    ForEach(numbers, id: \.self) { number in
                        Text("Number: \(number)")
                    }
                }
            }
        }
        .task(id: isUpdating) {
            if isUpdating {
                numbers = await updateNumbers()
            }
        }
    }

    func updateNumbers() async -> [Int] {
        var randomIntegers: [Int] = []
        for _ in 0...10 {
            // I increased the range of this so it is less likely to get duplicate numbers.
            // Since these are used in a ForEach with id being the number itself,
            // having duplicated numbers is undefined behaviour
            randomIntegers.append(Int.random(in: 1...10000))
            do {
                try await Task.sleep(for: .milliseconds(100))
            } catch {
                break // task has been cancelled
            }
        }
        self.isUpdating = false
        return randomIntegers
    }
}