f# - Updating nested immutable data structures

Question

I want to update a nested, immutable data structure (I attached a small example of a hypothetical game.) And I wonder whether this can be done a little more elegantly.

Every time something inside the dungeon changes we need a new dungeon. So, I gave it a general update member. The best way to use this, that I could come up with for the general case, is to specify the processing functions for each nesting and than pass the combined function to the update member.

Then, for really common cases (like applying a map to all the monsters on a specific level), I provide extra members (Dungeon.MapMonstersOnLevel).

The whole thing works, I would just like to know, if anyone can think of better ways of doing it.

Thanks!

// types
type Monster(awake : bool) = 
    member this.Awake = awake

type Room(locked : bool, monsters : Monster list) = 
    member this.Locked = locked
    member this.Monsters = monsters

type Level(illumination : int, rooms : Room list) = 
    member this.Illumination = illumination
    member this.Rooms = rooms

type Dungeon(levels : Level list) = 
    member this.Levels = levels

    member this.Update levelFunc = 
        new Dungeon(this.Levels |> levelFunc)

    member this.MapMonstersOnLevel (f : Monster -> Monster) nLevel =
        let monsterFunc = List.map f
        let roomFunc = List.map (fun (room : Room) -> new Room(room.Locked, room.Monsters |> monsterFunc))
        let levelFunc = List.mapi (fun i (level : Level) -> if i = nLevel then new Level(level.Illumination, level.Rooms |> roomFunc) else level)
        new Dungeon(this.Levels |> levelFunc)

    member this.Print() = 
        this.Levels 
        |> List.iteri (fun i e -> 
            printfn "Level %d: Illumination %d" i e.Illumination
            e.Rooms |> List.iteri (fun i e ->
                let state = if e.Locked then "locked" else "unlocked"
                printfn "  Room %d is %s" i state
                e.Monsters |> List.iteri (fun i e ->
                    let state = if e.Awake then "awake" else "asleep"
                    printfn "    Monster %d is %s" i state)))

// generate test dungeon
let m1 = new Monster(true)
let m2 = new Monster(false)
let m3 = new Monster(true)
let m4 = new Monster(false)
let m5 = new Monster(true)
let m6 = new Monster(false)
let m7 = new Monster(true)
let m8 = new Monster(false)
let r1 = new Room(true, [ m1; m2 ])
let r2 = new Room(false, [ m3; m4 ])
let r3 = new Room(true, [ m5; m6 ])
let r4 = new Room(false, [ m7; m8 ])
let l1 = new Level(100, [ r1; r2 ])
let l2 = new Level(50, [ r3; r4 ])
let dungeon = new Dungeon([ l1; l2 ])
dungeon.Print()

// toggle wake status of all monsters
let dungeon1 = dungeon.MapMonstersOnLevel (fun m -> new Monster(not m.Awake)) 0
dungeon1.Print()

// remove monsters that are asleep which are in locked rooms on levels where illumination < 100 and unlock those rooms
let monsterFunc2 = List.filter (fun (monster : Monster) -> monster.Awake)
let roomFunc2 = List.map(fun (room : Room) -> if room.Locked then new Room(false, room.Monsters |> monsterFunc2) else room)
let levelFunc2 = List.map(fun (level : Level) -> if level.Illumination < 100 then new Level(level.Illumination, level.Rooms |> roomFunc2) else level)
let dungeon2 = dungeon.Update levelFunc2
dungeon2.Print()

Answer 1

Here's the same code using lenses as currently defined in FSharpx. As other answers note, it's convenient to use records here; they give you structural equality for free among other things. I also attach the corresponding lenses for the properties as static members; you can also define them in a module or as loose functions. I prefer static members here, for practical purposes it's just like a module.

open FSharpx

type Monster = {
    Awake: bool
} with 
    static member awake =
        { Get = fun (x: Monster) -> x.Awake
          Set = fun v (x: Monster) -> { x with Awake = v } }

type Room = {
    Locked: bool
    Monsters: Monster list
} with
    static member locked = 
        { Get = fun (x: Room) -> x.Locked
          Set = fun v (x: Room) -> { x with Locked = v } }
    static member monsters = 
        { Get = fun (x: Room) -> x.Monsters
          Set = fun v (x: Room) -> { x with Monsters = v } }

type Level = {
    Illumination: int
    Rooms: Room list
} with
    static member illumination = 
        { Get = fun (x: Level) -> x.Illumination
          Set = fun v (x: Level) -> { x with Illumination = v } }
    static member rooms = 
        { Get = fun (x: Level) -> x.Rooms
          Set = fun v (x: Level) -> { x with Rooms = v } }

type Dungeon = {
    Levels: Level list
} with
    static member levels =
        { Get = fun (x: Dungeon) -> x.Levels 
          Set = fun v (x: Dungeon) -> { x with Levels = v } }
    static member print (d: Dungeon) = 
        d.Levels 
        |> List.iteri (fun i e -> 
            printfn "Level %d: Illumination %d" i e.Illumination
            e.Rooms |> List.iteri (fun i e ->
                let state = if e.Locked then "locked" else "unlocked"
                printfn "  Room %d is %s" i state
                e.Monsters |> List.iteri (fun i e ->
                    let state = if e.Awake then "awake" else "asleep"
                    printfn "    Monster %d is %s" i state)))

I also define print as a static member; again it's like a function in a module, and it's more composable than an instance method (though I won't compose it here).

Now to generate the sample data. I think { Monster.Awake = true } is more desciptive than new Monster(true). If you wanted to use classes I'd name the parameter explicitly, e.g. Monster(awake: true)

// generate test dungeon
let m1 = { Monster.Awake = true }
let m2 = { Monster.Awake = false }
let m3 = { Monster.Awake = true }
let m4 = { Monster.Awake = false }
let m5 = { Monster.Awake = true }
let m6 = { Monster.Awake = false }
let m7 = { Monster.Awake = true }
let m8 = { Monster.Awake = false }

let r1 = { Room.Locked = true;  Monsters = [m1; m2] }
let r2 = { Room.Locked = false; Monsters = [m3; m4] }
let r3 = { Room.Locked = true;  Monsters = [m5; m6] }
let r4 = { Room.Locked = false; Monsters = [m7; m8] }

let l1 = { Level.Illumination = 100; Rooms = [r1; r2] }
let l2 = { Level.Illumination = 50;  Rooms = [r3; r4] }

let dungeon = { Dungeon.Levels = [l1; l2] }
Dungeon.print dungeon

Now comes the fun part: composing lenses to update the monsters for all rooms for a particular level in a dungeon:

open FSharpx.Lens.Operators

let mapMonstersOnLevel nLevel f =
    Dungeon.levels >>| Lens.forList nLevel >>| Level.rooms >>| Lens.listMap Room.monsters
    |> Lens.update (f |> List.map |> List.map)

// toggle wake status of all monsters
let dungeon1 = dungeon |> mapMonstersOnLevel 0 (Monster.awake.Update not)
Dungeon.print dungeon1

For the second dungeon I also use lenses but without lens composition. It's sort of a DSL defined by small composed functions (some of the functions are from lenses). Maybe there are lenses to express this more concisely, but I haven't figured it out.

// remove monsters that are asleep 
// which are in locked rooms on levels where illumination < 100 
// and unlock those rooms

let unlock = Room.locked.Set false
let removeAsleepMonsters = Room.monsters.Update (List.filter Monster.awake.Get)

let removeAsleepMonsters_unlock_rooms = List.mapIf Room.locked.Get (unlock >> removeAsleepMonsters)

let isLowIllumination = Level.illumination.Get >> ((>)100)
let removeAsleepMonsters_unlock_level = Level.rooms.Update removeAsleepMonsters_unlock_rooms
let removeAsleepMonsters_unlock_levels = List.mapIf isLowIllumination removeAsleepMonsters_unlock_level

let dungeon2 = dungeon |> Dungeon.levels.Update removeAsleepMonsters_unlock_levels
Dungeon.print dungeon2

I overused lenses and pointfree a bit here, partially on purpose, just to show what it could look like. Some won't like it, claiming it's not idiomatic or clear. Maybe so, but it's another tool that you can choose to use or not, depending on your context.

But more importantly, because Update is a Get followed by a function followed by a Set, this isn't as efficient as your code when it comes to processing lists: an Update in Lens.forList first gets the nth element in the list, which is an O(n) operation.

To summarize:

Pros:

• Very concise.
• Enables pointfree style.
• Code involving lenses is generally oblivious of the source type representation (it can be a class, a record, a single-case DU, a dictionary, it doesn't matter).

Cons:

• May be inefficient for some cases in current implementation.
• Due to lack of macros, requires some boilerplate.

Thanks for this example, as a result I'll be revising the current design of lenses in FSharpx and see if it can be optimized.

I committed this code to the FSharpx repository: https://github.com/fsharp/fsharpx/commit/136c763e3529abbf91ad52b8127ce11cbb3dff28