Closures - The Rust Programming Language

## Closures: Anonymous Functions that can Capture their Environment

Rust's closures are anonymous functions that you can save in a variable or pass as arguments to other functions. You can create the closure in one place, and then call the closure to evaluate it in a different context. Unlike functions, closures are allowed to capture values from the scope in which they are called. We're going to demonstrate how these features of closures allow for code reuse and customization of behavior.

### Creating an Abstraction of Behavior Using a Closure

Let's work on an example that will show a situation where storing a closure to be executed at a later time is useful. We'll talk about the syntax of closures, type inference, and traits along the way.

The hypothetical situation is this: we're working at a startup that's making an app to generate custom exercise workout plans. The backend is written in Rust, and the algorithm that generates the workout plan takes into account many different factors like the app user's age, their Body Mass Index, their preferences, their recent workouts, and an intensity number they specify. The actual algorithm used isn't important in this example; what's important is that this calculation takes a few seconds. We only want to call this algorithm if we need to, and we only want to call it once, so that we aren't making the user wait more than they need to. We're going to simulate calling this hypothetical algorithm by calling the `simulated_expensive_calculation` function shown in Listing 13-1 instead, which will print `calculating slowly...`, wait for two seconds, and then return whatever number we passed in:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    use std::thread;
    use std::time::Duration;

    fn simulated_expensive_calculation(intensity: i32) -> i32 {
        println!("calculating slowly...");
        thread::sleep(Duration::from_secs(2));
        intensity
    }

    #}

Listing 13-1: A function we'll use to stand in for a hypothetical calculation that takes about two seconds to run

Next, we have a `main` function that contains the parts of the workout app that are important for this example. This represents the code that the app would call when a user asks for a workout plan. Because the interaction with the app's frontend isn't relevant to the use of closures, we're going to hardcode values representing inputs to our program and print the outputs.

The inputs to the program are:

- An `intensity` number from the user, specified when they request a workout, so they can indicate whether they'd like a low intensity workout or a high intensity workout
- A random number that will generate some variety in the workout plans

The output the program prints will be the recommended workout plan.

Listing 13-2 shows the `main` function we're going to use. We've hardcoded the variable `simulated_user_specified_value` to 10 and the variable `simulated_random_number` to 7 for simplicity's sake; in an actual program we'd get the intensity number from the app frontend and we'd use the `rand` crate to generate a random number like we did in the Guessing Game example in Chapter 2. The `main` function calls a `generate_workout` function with the simulated input values:

Filename: src/main.rs

    fn main() {
        let simulated_user_specified_value = 10;
        let simulated_random_number = 7;

        generate_workout(simulated_user_specified_value, simulated_random_number);
    }
    # fn generate_workout(intensity: i32, random_number: i32) {}

Listing 13-2: A `main` function containing hardcoded values to simulate user input and random number generation inputs to the `generate_workout` function

That's the context of what we're working on. The `generate_workout` function in Listing 13-3 contains the business logic of the app that we're most concerned with in this example. The rest of the code changes in this example will be made to this function:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # use std::thread;
    # use std::time::Duration;
    #
    # fn simulated_expensive_calculation(num: i32) -> i32 {
    #     println!("calculating slowly...");
    #     thread::sleep(Duration::from_secs(2));
    #     num
    # }
    #
    fn generate_workout(intensity: i32, random_number: i32) {
        if intensity < 25 {
            println!(
                "Today, do {} pushups!",
                simulated_expensive_calculation(intensity)
            );
            println!(
                "Next, do {} situps!",
                simulated_expensive_calculation(intensity)
            );
        } else {
            if random_number == 3 {
                println!("Take a break today! Remember to stay hydrated!");
            } else {
                println!(
                    "Today, run for {} minutes!",
                    simulated_expensive_calculation(intensity)
                )
            }
        }
    }

    #}

Listing 13-3: The business logic of the program that prints the workout plans based on the inputs and calls to the `simulated_expensive_calculation` function

The code in Listing 13-3 has multiple calls to the slow calculation function. The first `if` block calls `simulated_expensive_calculation` twice, the `if` inside the outer `else` doesn't call it at all, and the code inside the `else` case inside the outer `else` calls it once.

The desired behavior of the `generate_workout` function is to first check if the user wants a low intensity workout (indicated by a number less than 25) or a high intensity workout (25 or more). Low intensity workout plans will recommend a number of pushups and situps based on the complex algorithm we're simulating with the `simulated_expensive_calculation` function, which needs the intensity number as an input.

If the user wants a high intensity workout, there's some additional logic: if the value of the random number generated by the app happens to be 3, the app will recommend a break and hydration instead. If not, the user will get a high intensity workout of a number of minutes of running that comes from the complex algorithm.

The data science team has let us know that there are going to be some changes to the way we have to call the algorithm, so we want to refactor this code to have only one place that calls the `simulated_expensive_calculation` function to update when those changes happen. We also want to get rid of the spot where we're currently calling the function twice unnecessarily, and we don't want to add any other calls to that function in the process. That is, we don't want to call it if we're in the case where the result isn't needed at all, and we still want to call it only once in the last case.

There are many ways we could restructure this program. The way we're going to try first is extracting the duplicated call to the expensive calculation function into a variable, as shown in Listing 13-4:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # use std::thread;
    # use std::time::Duration;
    #
    # fn simulated_expensive_calculation(num: i32) -> i32 {
    #     println!("calculating slowly...");
    #     thread::sleep(Duration::from_secs(2));
    #     num
    # }
    #
    fn generate_workout(intensity: i32, random_number: i32) {
        let expensive_result =
            simulated_expensive_calculation(intensity);

        if intensity < 25 {
            println!(
                "Today, do {} pushups!",
                expensive_result
            );
            println!(
                "Next, do {} situps!",
                expensive_result
            );
        } else {
            if random_number == 3 {
                println!("Take a break today! Remember to stay hydrated!");
            } else {
                println!(
                    "Today, run for {} minutes!",
                    expensive_result
                )
            }
        }
    }

    #}

Listing 13-4: Extracting the calls to `simulated_expensive_calculation` to one place before the `if` blocks and storing the result in the `expensive_result` variable

This change unifies all the calls to `simulated_expensive_calculation` and solves the problem of the first `if` block calling the function twice unnecessarily. Unfortunately, we're now calling this function and waiting for the result in all cases, which includes the inner `if` block that doesn't use the result value at all.

We want to be able to specify some code in one place in our program, but then only execute that code if we actually need the result in some other place in our program. This is a use case for closures!

### Closures Store Code to be Executed Later

Instead of always calling the `simulated_expensive_calculation` function before the `if` blocks, we can define a closure and store the closure in a variable instead of the result as shown in Listing 13-5. We can actually choose to move the whole body of `simulated_expensive_calculation` within the closure we're introducing here:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # use std::thread;
    # use std::time::Duration;
    #
    let expensive_closure = |num| {
        println!("calculating slowly...");
        thread::sleep(Duration::from_secs(2));
        num
    };
    # expensive_closure(5);

    #}

Listing 13-5: Defining a closure with the body that was in the expensive function and store the closure in the `expensive_closure` variable

The closure definition is the part after the `=` that we're assigning to the variable `expensive_closure`. To define a closure, we start with a pair of vertical pipes (`|`). Inside the pipes is where we specify the parameters to the closure; this syntax was chosen because of its similarity to closure definitions in Smalltalk and Ruby. This closure has one parameter named `num`; if we had more than one parameter, we would separate them with commas, like `|param1, param2|`.

After the parameters, we put curly braces that hold the body of the closure. The curly braces are optional if the closure body only has one line. After the curly braces, we need a semicolon to go with the `let` statement. The value returned from the last line in the closure body (`num`), since that line doesn't end in a semicolon, will be the value returned from the closure when it's called, just like in function bodies.

Note that this `let` statement means `expensive_closure` contains the definition of an anonymous function, not the resulting value of calling the anonymous function. Recall the reason we're using a closure is because we want to define the code to call at one point, store that code, and actually call it at a later point; the code we want to call is now stored in `expensive_closure`.

Now that we have the closure defined, we can change the code in the `if` blocks to call the closure in order to execute the code and get the resulting value. Calling a closure looks very similar to calling a function; we specify the variable name that holds the closure definition and follow it with parentheses containing the argument values we want to use for that call as shown in Listing 13-6:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # use std::thread;
    # use std::time::Duration;
    #
    fn generate_workout(intensity: i32, random_number: i32) {
        let expensive_closure = |num| {
            println!("calculating slowly...");
            thread::sleep(Duration::from_secs(2));
            num
        };

        if intensity < 25 {
            println!(
                "Today, do {} pushups!",
                expensive_closure(intensity)
            );
            println!(
                "Next, do {} situps!",
                expensive_closure(intensity)
            );
        } else {
            if random_number == 3 {
                println!("Take a break today! Remember to stay hydrated!");
            } else {
                println!(
                    "Today, run for {} minutes!",
                    expensive_closure(intensity)
                )
            }
        }
    }

    #}

Listing 13-6: Calling the `expensive_closure` we've defined

Now we've achieved the goal of unifying where the expensive calculation is called to one place, and we're only executing that code where we need the results. However, we've reintroduced one of the problems from Listing 13-3: we're still calling the closure twice in the first `if` block, which will call the expensive code twice and make the user wait twice as long as they need to. We could fix this problem by creating a variable local to that `if` block to hold the result of calling the closure, but there's another solution we can use since we have a closure. We'll get back to that solution in a bit; let's first talk about why there aren't type annotations in the closure definition and the traits involved with closures.

### Closure Type Inference and Annotation

Closure are different than functions defined with the `fn` keyword in a few ways. The first is that closures don't require you to annotate the types of the parameters or the return value like `fn` functions do.

Type annotations are required on functions because they're are part of an explicit interface exposed to your users. Defining this interface rigidly is important for ensuring that everyone agrees on what types of values a function uses and returns. Closures aren't used in an exposed interface like this, though: they're stored in variables and used without naming them and exposing them to be invoked by users of our library.

Additionally, closures are usually short and only relevant within a narrow context rather than in any arbitrary scenario. Within these limited contexts, the compiler is reliably able to infer the types of the parameters and return type similarly to how it's able to infer the types of most variables. Being forced to annotate the types in these small, anonymous functions would be annoying and largely redundant with the information the compiler already has available.

Like variables, we can choose to add type annotations if we want to increase explicitness and clarity in exchange for being more verbose than is strictly necessary; annotating the types for the closure we defined in Listing 13-4 would look like the definition shown here in Listing 13-7:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # use std::thread;
    # use std::time::Duration;
    #
    let expensive_closure = |num: i32| -> i32 {
        println!("calculating slowly...");
        thread::sleep(Duration::from_secs(2));
        num
    };

    #}

Listing 13-7: Adding optional type annotations of the parameter and return value types in the closure

The syntax of closures and functions looks more similar with type annotations. Here's a vertical comparison of the syntax for the definition of a function that adds one to its parameter, and a closure that has the same behavior. We've added some spaces here to line up the relevant parts). This illustrates how closure syntax is similar to function syntax except for the use of pipes rather than parentheses and the amount of syntax that is optional:

    fn  add_one_v1   (x: i32) -> i32 { x + 1 }
    let add_one_v2 = |x: i32| -> i32 { x + 1 };
    let add_one_v3 = |x|             { x + 1 };
    let add_one_v4 = |x|               x + 1  ;

The first line shows a function definition, and the second line shows a fully annotated closure definition. The third line removes the type annotations from the closure definition, and the fourth line removes the braces that are optional since the closure body only has one line. These are all valid definitions that will produce the same behavior when they're called.

Closure definitions will have one concrete type inferred for each of their parameters and for their return value. For instance, Listing 13-8 shows the definition of a short closure that just returns the value it gets as a parameter. This closure isn't very useful except for the purposes of this example. Note that we haven't added any type annotations to the definition: if we then try to call the closure twice, using a `String` as an argument the first time and an `i32` the second time, we'll get an error:

Filename: src/main.rs

    let example_closure = |x| x;

    let s = example_closure(String::from("hello"));
    let n = example_closure(5);

Listing 13-8: Attempting to call a closure whose types are inferred with two different types

The compiler gives us this error:

    error[E0308]: mismatched types
     --> src/main.rs
      |
      | let n = example_closure(5);
      |                         ^ expected struct `std::string::String`, found
      integral variable
      |
      = note: expected type `std::string::String`
                 found type `{integer}`

The first time we call `example_closure` with the `String` value, the compiler infers the type of `x` and the return type of the closure to be `String`. Those types are then locked in to the closure in `example_closure`, and we get a type error if we try to use a different type with the same closure.

### Using Closures with Generic Parameters and the `Fn` Traits

Returning to our workout generation app, in Listing 13-6 we left our code still calling the expensive calculation closure more times than it needs to. In each place throughout our code, if we need the results of the expensive closure more than once, we could save the result in a variable for reuse and use the variable instead of calling the closure again. This could be a lot of repeated code saving the results in a variety of places.

However, because we have a closure for the expensive calculation, we have another solution available to us. We can create a struct that will hold the closure and the resulting value of calling the closure. The struct will only execute the closure if we need the resulting value, and it will cache the resulting value so that the rest of our code doesn't have to be responsible for saving and reusing the result. You may know this pattern as memoization or lazy evaluation.

In order to make a struct that holds a closure, we need to be able to specify the type of the closure. Each closure instance has its own unique anonymous type: that is, even if two closures have the same signature, their types are still considered to be different. In order to define structs, enums, or function parameters that use closures, we use generics and trait bounds like we discussed in Chapter 10.

The `Fn` traits are provided by the standard library. All closures implement one of the traits `Fn`, `FnMut`, or `FnOnce`. We'll discuss the difference between these traits in the next section on capturing the environment; in this example, we can use the `Fn` trait.

We add types to the `Fn` trait bound to represent the types of the parameters and return values that the closures must have in order to match this trait bound. In this case, our closure has a parameter of type `i32` and returns an `i32`, so the trait bound we specify is `Fn(i32) -> i32`.

Listing 13-9 shows the definition of the `Cacher` struct that holds a closure and an optional result value:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    struct Cacher<T>
        where T: Fn(i32) -> i32
    {
        calculation: T,
        value: Option<i32>,
    }

    #}

Listing 13-9: Defining a `Cacher` struct that holds a closure in `calculation` and an optional result in `value`

The `Cacher` struct has a `calculation` field of the generic type `T`. The trait bounds on `T` specify that `T` is a closure by using the `Fn` trait. Any closure we want to store in the `calculation` field of a `Cacher` instance must have one `i32` parameter (specified within the parentheses after `Fn`) and must return an `i32` (specified after the `->`).

The `value` field is of type `Option<i32>`. Before we execute the closure, `value` will be `None`. If the code using a `Cacher` asks for the result of the closure, we'll execute the closure at that time and store the result within a `Some` variant in the `value` field. Then if the code asks for the result of the closure again, instead of executing the closure again, we'll return the result that we're holding in the `Some` variant.

The logic around the `value` field that we've just described is defined in Listing 13-10:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # struct Cacher<T>
    #     where T: Fn(i32) -> i32
    # {
    #     calculation: T,
    #     value: Option<i32>,
    # }
    #
    impl<T> Cacher<T>
        where T: Fn(i32) -> i32
    {
        fn new(calculation: T) -> Cacher<T> {
            Cacher {
                calculation,
                value: None,
            }
        }

        fn value(&mut self, arg: i32) -> i32 {
            match self.value {
                Some(v) => v,
                None => {
                    let v = (self.calculation)(arg);
                    self.value = Some(v);
                    v
                },
            }
        }
    }

    #}

Listing 13-10: Implementations on `Cacher` of an associated function named `new` and a method named `value` that manage the caching logic

The fields on the `Cacher` struct are private since we want `Cacher` to manage their values rather than letting the calling code potentially change the values in these fields directly. The `Cacher::new` function takes a generic parameter `T`, which we've defined in the context of the `impl` block to have the same trait bound as the `Cacher` struct. `Cacher::new` returns a `Cacher` instance that holds the closure specified in the `calculation` field and a `None` value in the `value` field, since we haven't executed the closure yet.

When the calling code wants the result of evaluating the closure, instead of calling the closure directly, it will call the `value` method. This method checks to see if we already have a resulting value in `self.value` in a `Some`; if we do, it returns the value within the `Some` without executing the closure again.

If `self.value` is `None`, we call the closure stored in `self.calculation`, save the result in `self.value` for future use, and return the value as well.

Listing 13-11 shows how we can use this `Cacher` struct in the `generate_workout` function from Listing 13-6:

Filename: src/main.rs

    # #![allow(unused_variables)]
    #fn main() {
    # use std::thread;
    # use std::time::Duration;
    #
    # struct Cacher<T>
    #     where T: Fn(i32) -> i32
    # {
    #     calculation: T,
    #     value: Option<i32>,
    # }
    #
    # impl<T> Cacher<T>
    #     where T: Fn(i32) -> i32
    # {
    #     fn new(calculation: T) -> Cacher<T> {
    #         Cacher {
    #             calculation,
    #             value: None,
    #         }
    #     }
    #
    #     fn value(&mut self, arg: i32) -> i32 {
    #         match self.value {
    #             Some(v) => v,
    #             None => {
    #                 let v = (self.calculation)(arg);
    #                 self.value = Some(v);
    #                 v
    #             },
    #         }
    #     }
    # }
    #
    fn generate_workout(intensity: i32, random_number: i32) {
        let mut expensive_result = Cacher::new(|num| {
            println!("calculating slowly...");
            thread::sleep(Duration::from_secs(2));
            num
        });

        if intensity < 25 {
            println!(
                "Today, do {} pushups!",
                expensive_result.value(intensity)
            );
            println!(
                "Next, do {} situps!",
                expensive_result.value(intensity)
            );
        } else {
            if random_number == 3 {
                println!("Take a break today! Remember to stay hydrated!");
            } else {
                println!(
                    "Today, run for {} minutes!",
                    expensive_result.value(intensity)
                )
            }
        }
    }

    #}

Listing 13-11: Using `Cacher` in the `generate_workout` function to abstract away the caching logic

Instead of saving the closure in a variable directly, we save a new instance of `Cacher` that holds the closure. Then, in each place we want the result, we call the `value` method on the `Cacher` instance. We can call the `value` method as many times as we want, or not call it at all, and the expensive calculation will be run a maximum of once. Try running this program with the `main` function from Listing 13-2, and change the values in the `simulated_user_specified_value` and `simulated_random_number` variables to verify that in all of the cases in the various `if` and `else` blocks, `calculating slowly...` printed by the closure only shows up once and only when needed.

The `Cacher` takes care of the logic necessary to ensure we aren't calling the expensive calculation more than we need to be so that `generate_workout` can focus on the business logic. Caching values is a more generally useful behavior that we might want to use in other parts of our code with other closures as well. However, there are a few problems with the current implementation of `Cacher` that would make reusing it in different contexts difficult.

The first problem is a `Cacher` instance assumes it will always get the same value for the parameter `arg` to the `value` method. That is, this test of `Cacher` will fail:

    #[test]
    fn call_with_different_values() {
        let mut c = Cacher::new(|a| a);

        let v1 = c.value(1);
        let v2 = c.value(2);

        assert_eq!(v2, 2);
    }

This test creates a new `Cacher` instance with a closure that returns the value passed into it. We call the `value` method on this `Cacher` instance with an `arg` value of 1 and then an `arg` value of 2, and we expect that the call to `value` with the `arg` value of 2 returns 2.

Run this with the `Cacher` implementation from Listing 13-9 and Listing 13-10 and the test will fail on the `assert_eq!` with this message:

    thread 'call_with_different_arg_values' panicked at 'assertion failed:
    `(left == right)` (left: `1`, right: `2`)', src/main.rs

The problem is that the first time we called `c.value` with 1, the `Cacher` instance saved `Some(1)` in `self.value`. After that, no matter what we pass in to the `value` method, it will always return 1.

Try modifying `Cacher` to hold a hash map rather than a single value. The keys of the hash map will be the `arg` values that are passed in, and the values of the hash map will be the result of calling the closure on that key. Instead of looking at whether `self.value` directly has a `Some` or a `None` value, the `value` function will look up the `arg` in the hash map and return the value if it's present. If it's not present, the `Cacher` will call the closure and save the resulting value in the hash map associated with its `arg` value.

Another problem with the current `Cacher` implementation that restricts its use is that it only accepts closures that take one parameter of type `i32` and return an `i32`. We might want to be able to cache the results of closures that take a string slice as an argument and return `usize` values, for example. Try introducing more generic parameters to increase the flexibility of the `Cacher` functionality.

### Closures Can Capture Their Environment

In the workout generator example, we only used closures as inline anonymous functions. Closures have an additional ability we can use that functions don't have, however: they can capture their environment and access variables from the scope in which they're defined.

Listing 13-12 has an example of a closure stored in the variable `equal_to_x` that uses the variable `x` from the closure's surrounding environment:

Filename: src/main.rs

    fn main() {
        let x = 4;

        let equal_to_x = |z| z == x;

        let y = 4;

        assert!(equal_to_x(y));
    }

Listing 13-12: Example of a closure that refers to a variable in its enclosing scope

Here, even though `x` is not one of the parameters of `equal_to_x`, the `equal_to_x` closure is allowed to use the `x` variable that's defined in the same scope that `equal_to_x` is defined in.

We can't do the same with functions; let's see what happens if we try:

Filename: src/main.rs

    fn main() {
        let x = 4;

        fn equal_to_x(z: i32) -> bool { z == x }

        let y = 4;

        assert!(equal_to_x(y));
    }

We get an error:

    error[E0434]: can't capture dynamic environment in a fn item; use the || { ... }
    closure form instead
     -->
      |
    4 |     fn equal_to_x(z: i32) -> bool { z == x }
      |                                          ^

The compiler even reminds us that this only works with closures!

When a closure captures a value from its environment, the closure uses memory to store the values for use in the closure body. This use of memory is overhead that we don't want pay for in the more common case where we want to execute code that doesn't capture its environment. Because functions are never allowed to capture their environment, defining and using functions will never incur this overhead.

Closures can capture values from their environment in three ways, which directly map to the three ways a function can take a parameter: taking ownership, borrowing immutably, and borrowing mutably. These ways of capturing values are encoded in the three `Fn` traits as follows:

- `FnOnce` takes ownership of the variables it captures from the environment and moves those variables into the closure when the closure is defined. Therefore, a `FnOnce` closure cannot be called more than once in the same context.
- `Fn` borrows values from the environment immutably.
- `FnMut` can change the environment since it mutably borrows values.

When we create a closure, Rust infers how we want to reference the environment based on how the closure uses the values from the environment. In Listing 13-12, the `equal_to_x` closure borrows `x` immutably (so `equal_to_x` has the `Fn` trait) since the body of the closure only needs to read the value in `x`.

If we want to force the closure to take ownership of the values it uses in the environment, we can use the `move` keyword before the parameter list. This is mostly useful when passing a closure to a new thread in order to move the data to be owned by the new thread. We'll have more examples of `move` closures in Chapter 16 when we talk about concurrency, but for now here's the code from Listing 13-12 with the `move` keyword added to the closure definition and using vectors instead of integers, since integers can be copied rather than moved:

Filename: src/main.rs

    fn main() {
        let x = vec![1, 2, 3];

        let equal_to_x = move |z| z == x;

        println!("can't use x here: {:?}", x);

        let y = vec![1, 2, 3];

        assert!(equal_to_x(y));
    }

This example doesn't compile:

    error[E0382]: use of moved value: `x`
     --> src/main.rs:6:40
      |
    4 |     let equal_to_x = move |z| z == x;
      |                      -------- value moved (into closure) here
    5 |
    6 |     println!("can't use x here: {:?}", x);
      |                                        ^ value used here after move
      |
      = note: move occurs because `x` has type `std::vec::Vec<i32>`, which does not
        implement the `Copy` trait

The `x` value is moved into the closure when the closure is defined because of the `move` keyword. The closure then has ownership of `x`, and `main` isn't allowed to use `x` anymore. Removing the `println!` will fix this example.

Most of the time when specifying one of the `Fn` trait bounds, you can start with `Fn` and the compiler will tell you if you need `FnMut` or `FnOnce` based on what happens in the closure body.

To illustrate situations where closures that can capture their environment are useful as function parameters, let's move on to our next topic: iterators.