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.

Answer 1

I asked a similar question, but about haskell: Is there a Haskell idiom for updating a nested data structure?

The excellent answers mentioned a concept known as functional lenses.

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Unfortunately, I don't know what the package is, or if it even exists, for F#.

Update: two knowledgeable F#-ists (F#-ers? F#as?) left useful links about this in comments, so I'll post them here:

• @TomasPetricek suggested FSharpX and this website describing it

• @RyanRiley gave the link for the package

It's awesome that these two guys took the time to read my answer, comment and improve it, as they're both developers of FSharpX!

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More extraneous information: I was motivated to figure out how to do this by Clojure's assoc-in and update-in functions, which proved to me that it is possible in functional languages! Of course, Clojure's dynamic typing makes it simpler than in Haskell/F#. Haskell's solution involves templating, I believe.

Answer 2

I don't know why you want to use classes here. I think you can leverage the power of pattern matching if you use records for holding data and keeping them minimal:

// Types
type Monster = {
    Awake: bool
    }
    with override x.ToString() =
            if x.Awake then "awake" else "asleep"
type Room = {
    Locked: bool;
    Monsters: Monster list
    }
    with override x.ToString() =
            let state = if x.Locked then "locked" else "unlocked"
            state + "\n" + (x.Monsters |> List.mapi (fun i m -> sprintf "    Monster %d is %s" i (string m)) |> String.concat "\n")

type Level = {
    Illumination : int;
    Rooms : Room list
    }
    with override x.ToString() =
              (string x.Illumination) + "\n" + (x.Rooms |> List.mapi (fun i r -> sprintf "  Room %d is %s" i (string r)) |> String.concat "\n")

type Dungeon = {
    Levels: Level list;
    }
    with override x.ToString() =
            x.Levels |> List.mapi (fun i l -> sprintf "Level %d: Illumination %s" i (string l)) |> String.concat "\n"

To me, putting functions for manipulating Dungeon inside the class is unnatural. The code looks better if you put them in a module and make use of above declarations:

/// Utility functions
let updateMonster (m: Monster) a =
    {m with Awake = a}

let updateRoom (r: Room) l monstersFunc =
    {   Locked = l; 
        Monsters = r.Monsters |> monstersFunc}    

let updateLevel (l: Level) il roomsFunc = 
    {Illumination = il; Rooms = l.Rooms |> roomsFunc}

let updateDungeon (d: Dungeon) levelsFunc =
    {d with Levels = d.Levels |> levelsFunc}


/// Update functions
let mapMonstersOnLevel (d: Dungeon) nLevel =
    let monstersFunc = List.map (fun m -> updateMonster m (not m.Awake))
    let roomsFunc = List.map (fun r -> updateRoom r r.Locked monstersFunc)
    let levelsFunc = List.mapi (fun i l -> if i = nLevel then updateLevel l l.Illumination roomsFunc else l)
    updateDungeon d levelsFunc

let removeSleptMonsters (d: Dungeon) =
    let monstersFunc = List.filter (fun m -> m.Awake)
    let roomsFunc = List.map (fun r -> if r.Locked then updateRoom r false monstersFunc else r)
    let levelsFunc = List.map (fun l -> if l.Illumination < 100 then updateLevel l l.Illumination roomsFunc else l)
    updateDungeon d levelsFunc

Then you can see manipulating these nested data structures is much easier. However, above functions still have redundancy. You can refactor more if you use lenses which come very natural with records. Check out the insightful article by Mauricio Scheffer, which is really close to this formulation.

Answer 3

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

Answer 4

I posted a similar question about Scala about a year back. The answers mention three concepts as a solution to this problem: Zippers, Tree rewriting, and Lenses.

Answer 5

I've implemented a lens library in C# via reflection. The core of the library is this function

/// <summary>
/// Perform an immutable persistent set on a sub
/// property of the object. The object is not
/// mutated rather a copy of the object with
/// the required change is returned.
/// </summary>
/// <typeparam name="ConvertedTo">type of the target object</typeparam>
/// <typeparam name="V">type of the value to be set</typeparam>
/// <param name="This">the target object</param>
/// <param name="names">the list of property names composing the property path</param>
/// <param name="value">the value to assign to the property</param>
/// <returns>A new object with the required change implemented</returns>
private static T Set<T, V>
    (this T This, List<string> names, V value)
    where T : class, Immutable
{
    var name = names.First();
    var rest = names.Skip(1).ToList();
    if (names.Count == 1)
    {
        var copy = This.ShallowClone();
        copy.SetPrivatePropertyValue(names.First(), value);
        return copy as T;
    }
    else
    {
        var copy = This.ShallowClone();
        var subtree = copy
            .GetPrivatePropertyValue<Immutable>(name)
            .Set(rest, value);

        copy.SetPrivatePropertyValue(names.First(), subtree);
        return copy as T;
    }
}

The above function is composed using helper library into various utilities, one of which is an undo stack based on immutable persistent records. There is an overload of this function

public static Maybe<T> MaybeSet<T,V>
    (this T This, Expression<Func<T, V>> prop, V value)
    where T : class, Immutable
{
    if (!EqualityComparer<V>.Default.Equals(This.Get(prop.Compile()),value))
    {
        var names = ReactiveUI.Reflection.ExpressionToPropertyNames(prop).ToList();
        return This.Set(names, value).ToMaybe();
    }
    else
    {
        return None<T>.Default;
    }
}

which allows more natural type safe notation using LINQ expressions.

foo = foo.Set(f=>f.A.B.C, 10);

There is a lot of reflection going on in the library but the reduction in boilerplate is worth the performance hit. See the spec. I only need to tag the record as Immutable to get it to work. I don't have to provide getters and settors.

class A : Immutable
{
    public int P { get; private set; }
    public B B { get; private set; }
    public A(int p, B b)
    {
        P = p;
        B = b;
    }
}

class B : Immutable
{
    public int P { get; private set; }
    public C C { get; private set; }
    public B(int p, C c)
    {
        P = p;
        C = c;
    }
}

class C : Immutable
{
    public int P { get; private set; }
    public C(int p)
    {
        P = p;
    }
}


namespace Utils.Spec
{
    public class ImmutableObjectPatternSpec : IEnableLogger
    {
        [Fact]
        public void SetterSpec()
        {
            var a = new A
                ( p:10
                , b: new B
                    ( p: 20
                    , c : new C(30)));

            var a_ = a.Set(p => p.B.C.P, 10);

            a.Should().NotBe(a_);
            a.B.C.P.Should().Be(30);
            a_.B.C.P.Should().Be(10);
        }

        [Fact]
        public void StringListGettersShouldWork()
        {
            var a = new A
                ( p:10
                , b: new B
                    ( p: 20
                    , c : new C(30)));

            var a_ = a.Set(p => p.B.C.P, 10);

            a_.Get(p=>p.B.C.P).Should().Be(10);

        }




    }
}

Perhaps reflection based lenses would reduce boiler plate in F#. Maybe performance could be improved with caching of the accessors or maybe IL generation.