Understanding Immutability and Pure Functions (for OOP)

One important concept in functional programming is immutability. But also in object-oriented programming immutability and so called immutable objects getting more attention. The problem that I see especially from object-oriented programmers are really bad explanations. A lot of explanation I had see described it like this: Just create a class and make all fields readonly (final or const) and you have an immutable object.

Explanations like these are horrible. Such explanations are so simplified that I would even call them wrong. So why are they so horrible? Because they don't really explain anything at all. A programmer new to this concept will just immediately think: Uhm, but I want to change things! I want to add data to an array, I want to modify things. I want to do some kind of calculations. I don't want to have static non changing things. Immutability sounds not practical at all!

So let's see what immutability really means.

Immutability in a Nutshell

A much more useful explanation is to say that immutability is not about forbidding change at all. Instead immutability is more on how to handle change. Immutability is not about forbidding some kind of operations. You still can add an element to an array, the difference is that you just do it differently.

In an mutable world you would directly add your element to an array. In an immutable world you create a new array with your added element instead. The key concept is to understand that instead of modifying something you create something new with your change applied.

Once you understand it is more about creating new things with your changes applied, the question that arise is more: Why should that be better?

About OO

Before we go into all kinds of explanations we first have to address OO programming. At first, talking about immutability and OO at the same time is actually a bad idea. The problem is that immutability doesn't really fit in the OO world. Because of that we should first focus on immutability and how it works in a functional language. This will be several magnitudes easier. Once we understand it there, we go back to the OO world and look how everything fits in the OO world.

So why does immutability not directly fit in the OO world? Because immutability is solely about data-structures. Immutability is the core idea that data cannot be changed. Functions take immutable data and they return immutable data.

The problem is that in object-orientation you usually don't create data-structures. You encapsulate and hide data instead. Data-access is often even viewed as bad. Often you got told to create methods instead of providing access to data. This and other things are the reason why it is hard to get the concept of immutability especially as an OO programmer. We will later talk about this problem in more depth. For the moment we will put objects aside.

Immutability is about data

So Immutability really means that data itself cannot be changed. But as stated previously, instead of modifying data itself we call functions that then can return new immutable data. Let's look at some immutable data-structures.

int is immutable

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let x = 5
let y = 10
let z = x + y // 15

You actually should be familiar with this because it even feels natural that int is immutable. You have a lot of operations like +, -,*, *, and some more in the Math class. All of those operations take some number, do some kind of operation with it and return something new instead.

x stays the same, instead + takes two arguments, and produces a new result. We can actually treat + just as a function that takes two int and produces a whole new int. As a result we get z that is 15. We wouldn't expect that x or y also get modified at all.

string is immutable

Using int to get the feeling of the concept is easy, but it is sometimes hard how this concept works with more complex types. Additional int is in most languages some kind of special primitive type or a so called value type. So we threat them anyway as some kind of special.

So let's look at string. string is usually a reference type in most languages like any other class. But at least in Java or C#, they are still immutable.

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let a = "foo"
let b = "bar"
let c = a + b // "foobar"

let foo1 = "foo1"
let foo2 = foo1.Replace('1', '2')
let foo  = foo2.Remove(3,1)

In this examples we even already see a little bit of OO, because we call methods that string provides. But looking at the examples we still see that also string behaves much like int. If we add two strings together we don't modify a string. Instead we create a whole new string instead.

We can observe the same with our method calls. Calling foo1.Replace('1', '2') doesn't change foo1 instead we get a new string back with our change applied.

list is immutable

So let's look into a more advanced immutable data-type a list in F#. (This is not System.Collections.Generic.List<T>).

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let data = [1;2;3;4;5]

Usually we want operation for List, for example we want to add elements. In F# we could write something like this:

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let data2 = 0 :: data

In the same spirit like + we have :: for adding an element to the top of a list. But instead of modifying the list itself, we get a new list back. It is now important to note that now we have two lists. data now contains [1;2;3;4;5] and data2 contains [0;1;2;3;4;5].

From the examples so far we actually can see a pattern. All of our functions take some arguments. But they always return us something new with our wanted modification applied. That alone means we can often identify mutation by looking at the function signature. Functions without a return value that just return unit or similar void in C# often mutate data. This alone is not a proof, but a very high indicator.

So, let's assume we want to do some more real-world stuff with our list. Let's assume we want to multiply each element in an int list. Usually in imperative languages like C# you can see something like this:

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for (int i=0; i<array.Count-1; i++) {
    array[i] = array[i] * 2
}

but in an immutable world we would create a whole new list with our change applied. Instead of direct looping we use functions instead. So for example we have List.map that does this kind of operation for us.

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let data  = [1;2;3;4;5]
let data2 = List.map (fun x -> x * 2) data

After executing we once again have two lists. data that still contains [1;2;3;4;5] and data2 that now contains [2;4;6;8;10].

Records are immutable

Let's create another more advanced example. Let's create a Person type that represents a Person in a database.

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type Person = {
    Id:       int
    Name:     string
    Birthday: DateTime
    Likes:    string list
}

We now could create a Person like this

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let me = {
    Id       = 1
    Name     = "David Raab"
    Birthday = DateTime(1983, 02, 19)
    Likes    = ["Pizza"]
}

This is a record in F#, and like all other data-types it is also immutable by default. So now let's assume we want to change some parts.I like "dark chocolate" and "tea" so let's add them. Because we cannot change our data, we have to create a new record instead.

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let me2 = {
    Id       = me.Id
    Name     = me.Name
    Birthday = me.Birthday
    Likes    = "Tea" :: "Dark Chocolate" :: me.Likes
}

What we now have are two separate variables. me still represents

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{
    Id       = 1
    Name     = "David Raab"
    Birthday = 19.02.1983 00:00:00
    Likes    = ["Pizza"]
}

while me2 represents

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{
    Id       = 1
    Name     = "David Raab"
    Birthday = 19.02.1983 00:00:00
    Likes    = ["Tea"; "Dark Chocolate"; "Pizza"]
}

Such a copy & update operation for records is quite common so F# provides a built-in language construct for it. We also could have written.

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let me2 = {me with Likes = "Tea" :: "Dark Chocolate" :: me.Likes}

So immutability is about data that cannot be changed. But when we want to change something we usually call a function that can create something new for us. Let's actually simplify our example even more. Let's create a addLike function instead of using the copy & update mechanism all over our code.

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let addLike likes person = {person with Likes = likes :: person.Likes}

What we now have is a function that takes two arguments. A string likes that we want to add and a Person record as its second argument. The function will then return a new Person record. Now we also could add our Elements by using addLike instead.

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let me2 = addLike "Dark Chocolate" me
let me3 = addLike "Tea" me2

In this example we call addLike with Dark Chocolate and me. And we get a new Person back with our change applied. Then we use addLike on me2 to create our final me3.

It can feel a little awkward to create a lot of intermediate variables, but we can get rid of them by chaining functions with |>. So we also could have written it like this.

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let me2 =
    me
    |> addLike "Dark Chocolate"
    |> addLike "Tea"

Here me is piped-into addLike "Dark Chocolate". This will result in a new Person record that then is once again piped-into addLike "Tea". In object-oriented programming we could achieve something similar if we have a Person class with a method AddLike that returns a new Person object, instead of modifying some private fields. in C# this would result into something like this

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var me2 = 
    me
    .AddLike("Dark Chocolate")
    .AddLike("Tea");

This is similar to Fluent Interfaces. But the important point is that me as an object don't get modified. AddLike would return a whole new Person object with your operation applied. Because it is once again a Person you can chain methods. You also can get a fluent-interface by just returning this after each modification. It would look the same. But in the end me and me2 would be references to the same object, and me would be changed.

Pure functions

In a functional-only language we could probably stop at this point. Data and functions are clearly separated, immutability is only about data that does not change. The big problem arises if a language also supports classes. Because a class is about hiding data and additionally contains functions, it introduces a lot of complexity. To understand the reason of this complexity, we first need to talk about pure and impure functions on its own.

Side-effects

Pure functions are only those functions that don't have any kind of side-effects. So what exactly is a side-effect? A simple explanation would be: A function only can depend on its input. Calling a function with the same input, always has to produce the same output. No matter how often, or at what time you call it. We can view + as a pure function.

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let x = 3 + 5

No matter how often or at what time we execute the above statement, x should always be 8. If at some point it is possible that it could return something different, we would have an impure function.

In this example it seems even natural that we don't want any impure function. A 3 + 5 that sometimes could return something different sounds horrible. But the truth is, we often face impure functions and we usually also want them. Examples of impure functions are.

1. Getting a random number
2. Getting the current system time
3. Getting the user input
4. Reading data from a file
5. Reading data from a network

To deeper understand why they are impure. Which arguments would a function have that returns a random number? Usually we would say: Such a function don't need any input. And that is a problem. It means, whenever we call a function with no input. It always have to return the same output. So it just means, we cannot return random numbers, because otherwise that statement wouldn't be true. That's is also true for the other functions. We cannot for example implement a readFile "file.txt" function that returns the content of "file.txt". Because that content could change every time. And whenever the content of the file changes. readFile "file.txt" would return something different.

But currently we only only know half of the truth. Because a function still can be impure even following the above rule. There is even a second rule that a pure function have to fulfil: We always can replace a pure function call with the value it produces, without that it yields any change to the program.

That means. Whenever we see 3 + 5, we also could replace that calculations with 8. Or if we see readFile "file.txt" we could replace all calls to readFile "file.txt" by the value that the first function call would produce. This also explains better why a readFile "file.txt" would be impure. If we call readFile and some time later once again, we would assume that it returns the new current state of the file. It also could yield an error if the function in the mean time was deleted. The point is, we expect that the function can return something different every time we call it.

But this kind of description also eliminates some additional behaviour.

1. We cannot print something to a console
2. We cannot write to a file/database
3. We cannot send data over network

Let's assume we have someFunciton 5 that always will return 10 but also prints something to the console. We couldn't replace all calls to someFunction 5 just with 10 because otherwise we lose all log statements in our console.

Thinking over it, we could ask the question. Can we even write any useful program without side-effects? The answer is no. That is the reason why Erik Meijer often say: We all love side-effects. But that doesn't mean we want side-effects happens all over our code in every function. If a statement like 3 + 5 could yield 10 that would probably drive a lot of people crazy, me too. We want side-effects but we want to somehow control them. We want to minimize side-effects as much as possible.

So how do we do that? By letting pure functions return immutable data!

(Im)mutability and (im)pure functions

One interesting aspect is that both concepts are completely orthogonal. That means, we can have any combination of those. We can have pure functions that take mutable or immutable data, and return mutable or immutable data. And we can have impure functions that take and return mutable or immutable data. The thing is, mutability or immutability doesn't change whether a function is pure or not. This is important to understand that both concepts don't relate to each other. Let's for example look again at the above impure functions.

• A random number generator returns an immutable int/float
• A function returning the current time can return an immutable DateTime
• A function that returns the user input returns an immutable string
• Reading a file or from a socket can also return an immutable string
• A function that prints something to the console takes an immutable string
• Sending/Serialization of data over network can take an immutable data-structure

At this point, I cannot stress further how important it is to understand that immutability is all about data, not about functions or behaviour. We will see later why this is so important!

Pure functions with side-effects

The last important point is that we can have pure-functions even if they have some kind of side-effects. A typical example of this is a function that has internal caching with a mutable variable.

We could come to the conclusion that this is an impure function as another variable as a side-effects gets changed. But actually, such a function fulfil all rules we have above. Even the fact that it mutates some variable. It doesn't really matter, as such a function will still always return the exact same results to its input. And we always also could replace the function call with its output.

This is important because people all to often try to look at implementations, but the implementation itself shouldn't matter at all. The only thing that should matter is how a function behaves. If a function behaves like a pure function it is a pure function. The same is also true for mutability. A lot of people try hard to get rid of mutability, sometimes that can lead to bad performance or in general can make the code harder to understand. For example it is also fine to have a function with internal mutable state. As long as that function behaves like a pure function and even gets/returns immutable data, it is absolutely fine to have mutable local variables.

I would even state that this is a big advantage of F#! For example a lot of the functions from the List module turn a List into a mutable array, do some work on it, and turn it back into an immutable list. And overall we don't care that it does that. As long as we use a function and it behaves like a pure function returning immutable data, we are fine with it.

Benefits of Immutability

To shorten the example. Let's assume everything is mutable and a reference-type and it also applies to numbers. Saying that, lets look at the following code.

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let x = 5
someFunction x
let y = x + 3

What value is y now? The answer is, we don't know! someFunction could have changed x to some other value without that we are aware of it. So after our function did run, we cannot know what x is, so we don't know what y is. But what does that overall mean?

Usually we are told that functions, or also classes, methods should be treated as block-boxes. So we should never have to look at how something is implemented. But the thing is, as long we have mutable data, that concept cannot work. Because as long we have mutable data it means that a function could do more as documented. We actually can never be sure that x don't get changed until we look at how someFunction is implemented. Lets look at another problem.

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if value.isValid then
    someFunction x
    if value.isValid then
        ...
    ...

So what is the problem here? We are actually accessing value.isValid when it is true we enter the code. Once again we have someFunction using value. But wait, why do we now re-check value.isValid? It could probably be that the programmer in charge was drunk, but wait, can we be sure that the value.isValid is still true? In fact, as long as we have mutability the answer is no.

The problem is we don't see the scope of our variables. It could be that our someFunction also has access to our value and modifies it. This sounds like a horrible programming-style but it is not so uncommon as you think. Did you ever had an array of objects, and returned an object from this array? If yes, you are open to such kind of errors. Because you have two functions that still can access the same object used at multiple places. And in fact we don't even need an array. Looking at object-oriented languages like C# nearly everything is actually a reference-type. Objects itself never get copied, only references are copied, and the only thing you pass around are references. But hat also means that every function could hold a reference to some data and directly change it whenever it wants to!

So shortly, we cannot know if value still contains the same data. It already could have changed multiple times. This kind of possibility even raises with multi-threaded code. And I'm not talking about thread-safety or race-conditions here. value could be thread-safe and still changed in the mean time. The thing is, mutability basically makes any kind of code hard or nearly completely unpredictable.

The problem is, this kind of problem grows the bigger our program becomes. Multi-threading also increase that kind of problems by several magnitudes. And this is the overall problem. With more code we anyway face problems of designing and maintaining programs. Mutability just can create hard to track errors. It can become insanely hard to reason about some kind of code if at every blink of an eye every value can be changed at any time. Immutability overall can make code easier to read and maintain.

We also can gain other benefits out of it, like easy do/undo systems, backtracking in recursive functions for free, and a lot of other stuff.

Disadvantages of Immutability

Nothing in the world really just have only benefits. Everything in the world has its advantages and its disadvantages. So what are the disadvantages of immutability?

Mainly it is performance. Some people think that copying is the often problem or memory, but that isn't true. For example let's look at the list example. A lot of people assume that by adding an element to a list a whole list itself has to be copied. But that isn't true at all. For example adding an element to the top is an O(1) operation. It only can be made so efficient because of immutability. An immutable list is really just a data-structure that contains an element and a reference to another list.

That's why adding/removing from the top is efficient, instead of adding/removing at the end like many people knew it from types like List<T> in C#. The only reason why you could safely reference another list is because of immutability. With mutable data this wouldn't be possible as a list can change. So sharing data with immutable data is very safe. That's also the reason why you probably hear often that immutability works better with multi-threaded system. Or functional languages have advantages with multi-threaded systems. It is because immutable data are preferred and used in such languages.

But it doesn't change that there sometimes exists a problem where this is still a bottleneck or the culprit to performance problems. The problem with immutable-data is that you have to build them incrementally. A List with 1 Million elements is really build just as

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let x = 1 :: 2 :: 3 :: 4 :: ... :: []

or in other words. a lot of copy and create options. Sure a compiler or a runtime could have some optimization. F# probably have them for lists, but that overall doesn't change that immutability can sometimes lead to such problems. That is also the very reason why we have a StringBuilder.

Also a String is immutable but concatenating a lot of strings can create a lot of garbage throw-away objects. A StringBuilder can actually close that bridge. A StringBuilder uses a mutable string, and once you are done, you can get an immutable string back.

Other problems can arise that some problems or algorithms can be hard to implement with immutability. I just want to point again at what was said for pure functions. If you encounter such problems you always can convert some kind of data to some kind of mutable data. Do your operation, and convert it back to a immutable data-type.

So it is still important to understand that not everything is shiny and automatically better. Immutability can sometime have it's own problems, but there exists solutions for it.

Immutability and OO

Finally, we now have every knowledge to talk about immutability in object-oriented programming and why it is so damn hard. First, let's reconsider what an object is.

The fundamental thing of object-oriented programming is to hide data and instead provide methods that do some stuff. We even have rules like Law-of-Demeter or Tell don't ask that express it. An object is not about asking it form some data, we usually just call a method to tell it that it should do something.

Or in other words. Objects are just collection of functions. And here starts the problem. We actually learned that immutability has nothing to-do with functions at all! Immutability is about data not functions! Functions sure can be pure or impure but once again, we also learned that it doesn't matter at all for immutability. In fact we even consider it as good if we have side-effects that returns immutable data. That is how to solve the problem of side-effects. But just having data is usually discouraged in OO. OO has even it's own term for it. It is named the Anemic Domain Model to express if we have classes that just contains data.

So, if object-oriented programming don't try to use data explicitly, if we only have objects that provides us functions (methods) to call. How on earth can we even talk about immutable objects? What should that thing even be? Does it even makes sense to talk about immutable objects? If we only provide methods, doesn't it make more sense to talk about pure and impure objects instead?

To better see the problem, let's look at at the Random class.

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let rng    = System.Random()
let random = rng.Next();

Do we consider rng to be immutable or not? Let's look what we have. Besides the usual method inherited from object we only have three additional methods. Next, NextDouble and NextBytes. rng don't have any data or additional properties. We can call Next and we get an immutable int back. Besides that we cannot see any difference at all that rng itself changed at all! From the outside it looks like an immutable object!

Sure we have knowledge on how a random class works. Usually we have an internal private field that holds the last generated number, with this the next number will be created when we call Next. But the point is, we cannot see that. Theoretically the implementation could also use no mutable field at all. It could just use the current time to generate a random number instead. So that Next is impure, but don't have any mutable field.

From the outside the only thing we could say is that Random has three impure functions. And the object itself looks like immutable. We cannot see that any changes at all happens!

So do we consider Random immutable or not? Actually if you really expect an answer, there isn't really one. Sure we could look at the implementation of it, but that is really bad, we shouldn't needed to look at some kind of implementation to determine if something is immutable or not. And as already explained above, it is anyway not a good idea. We should view something as immutable or pure by looking at how it behaves, not how it is implemented.

So, now we are in a dilemma, how do we solve it? One thing we could do is to broaden the view of what an immutable object is. So we only consider something as immutable only if it has pure functions. As soon as we have one impure function on an object, we have to think that there exists a possibility that a private property could be modified.

Let's look at another example that I saw some time ago. Someone provided a class like this

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type MutableSite(url:string) =
    member val Url  = url
    member val Text = ""  with get,set
    member this.Download() =
        use wc      = new System.Net.WebClient()
        let content = wc.DownloadString(this.Url)
        this.Text <- content

So, we have obviously a mutable object, right? We have an mutable Text. To fetch the current site we call Download that mutates Text. So let's look how that person made it immutable.

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type ImmutableSite(url:string) =
    member val Url = url
    member this.Text() =
        use wc      = new System.Net.WebClient()
        let content = wc.DownloadString(this.Url)
        content

So, he just eliminated the Text field. Instead he created a Text method that would directly download the site and return the content. Obviously he thought that now he had an immutable class. And actually that things is just silly. Both version don't differ at all!

What is the difference between a Text field that always can return another string after we called Download, or a Text method that directly return a new string whenever we call the method? There is no difference at all between both version. The problem is that Text always can return something different. If it is either a mutable field or an impure method doesn't matter at all! Actually it even could also just be a property that could do this kind of stuff, so it doesn't even look any different to a normal mutable field instead of a method call.

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type SiteWithProperty(url:string) =
    member this.Url  = url
    member this.Text
        with get() =
            use wc      = new System.Net.WebClient()
            let content = wc.DownloadString(this.Url)
            content

The thing is, he thought he made any improvement just because he eliminated a mutable field, but actually that change don't matter at all. Whether you have a Text field that can change, a Text property that changes, or a Text method, in the end, Text always can return something different if you try to access it. So it improves nothing at all. We don't get any benefits at all that we should get by imposing immutability.

This example just shows how hard it is to reason about immutable objects. The problem is the combination of functions and data in one container like a class. And there is even another problem. Actually it is just fine to have impure functions that return immutable data. But how do we do that if we consider impure functions on an object as bad?

Actually in functional programming we don't have that problem at all. As every function stands on its own. Sure we group them in Modules, but it doesn't mean a function is part of some kind of structure. We can reason about every function separately. We can have pure and impure functions. And none of those changes the fact that we have immutable data. But in a class you combine functions with some kind of data in one container, the result is that we have to view an object as mutable as soon as it provides an impure method. The reason is that it behaves exactly like a mutable field would do.

So how do we create our impure functions in object-oriented programming? As we learned, we just need them to do anything useful. Just eliminating all kind of impure functions doesn't help us to solve any problems. The only way out of it is if you write static methods for impure functions. In this way you can separate impure functions from pure functions and an object could be considered as pure/immutable as long it only has pure methods. So let's consider how a good immutable object should look like.

How to Design immutable objects

1. An immutable class don't have hidden (private) fields. private in the sense of hidden fields not exposed to the user. Sure a class can have private fields for its data. But a class always have to provide access to the data through a readonly getter. If you have hidden fields not exposed to the user, we cannot be sure that an object is immutable at all.
2. A class should only contain pure functions (methods). We don't knew if an impure function modifies probably some hidden field or not. And it also doesn't matter. As soon we have a method that can return something different on every call we also cannot view it as immutable. If a field got changed alongside it or not doesn't matter at all. We judge immutability on how it behaves, not in how it is implemented. Because functions and data are mixed together in a class. We have to view every impure method as a violation against immutability.
3. All impure functions should be static methods on a class, or extracted into it's own class. Let's look at DateTime as an example. For example we have DateTime.Now or DateTime.Today. Those are impure properties as they always return a different DateTime whenever we call it. But once we have a DateTime object we only have pure methods operating on it. All data are accessible through getters. All methods are pure.
4. As we learned at the beginning, immutability is not about forbidding change, so an immutable objects should have a lot of methods that gives us easy ways to create new objects with our needed modification. If you don't provide them, it will probably painful to work with your objects. You can look again at DateTime. We have rich ways like Add, AddDays, AddHours, AddMinutes to create new DateTime objects. All of those methods return a new DateTime instead of mutating a field.

So let's reconsider the Site class above. How should an immutable Site class looks like?

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type SiteImmutable(url:string, content:string, size:int) =
    member val Url     = url
    member val Content = content
    member val Size    = size
    static member Download(url:string) =
        use wc      = new System.Net.WebClient()
        let content = wc.DownloadString(url)
        SiteImmutable(url, content, content.Length)

So what we really have is a class with our immutable fields. Our member fields cannot be changed later as they are immutable. Our class constructor has to be pure, the same as all methods. The creation of our immutable object is handled by a static impure method let site = SiteImmutable.Download("http://example.org")

Let's for example consider we later want an Update method, so we can re-fetch the content of a site. Instead of providing an impure Update method we have to provide an impure static method that does this for us.

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type SiteImmutable(url:string, content:string, size:int) =
    member val Url     = url
    member val Content = content
    member val Size    = size
    static member Download(url:string) =
        use wc      = new System.Net.WebClient()
        let content = wc.DownloadString(url)
        SiteImmutable(url, content, content.Length)
    static member Update(site:SiteImmutable) =
        use wc      = new System.Net.WebClient()
        let content = wc.DownloadString(site.Url)
        SiteImmutable(site.Url, content, content.Length)

So if a user wants to update the content of an object he can do something like this

1: 
2: 
3: 

let site = SiteImmutable.Download("http://example.org");
// Later...
let updatedSite = SiteImmutable.Update(site)

Conclusion

Immutability itself is actually an easy concept. The problem starts when we don't separate data and functions clearly from each other like OO programming does it. To really embrace immutability in OOP you have to forget a lot of stuff you were taught that should be good. Create pure data-objects as much as possible. Don't implement impure methods on such data-objects. Instead create impure static methods. Those should be as small as possible with as little logic possible. They should return an immutable data-objects as soon as possible.

A good place for impure functions are static methods or either create special impure/mutable objects instead. But don't try to implement a lot of logic for them, provide methods to convert an mutable object to an immutable object. StringBuilder is a good example for an mutable object that fixes the performance problems for creating complex strings. Once you are done you convert a StringBuilder instance to an immutable string.