Closures: Anonymous Functions that Can Capture Their Environment

Rust’s closures are anonymous functions 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 can capture values from the scope in which they’re called. We’ll demonstrate how these closure features allow for code reuse and behavior customization.

Creating an Abstraction of Behavior with Closures

Let’s work on an example of a situation in which it’s useful to store a closure to be executed later. Along the way, we’ll talk about the syntax of closures, type inference, and traits.

Consider this hypothetical situation: we work 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 factors, such as the app user’s age, body mass index, exercise preferences, 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 want to call this algorithm only when we need to and only call it once so we don’t make the user wait more than necessary.

We’ll simulate calling this hypothetical algorithm with the function simulated_expensive_calculation shown in Listing 13-1, which will print calculating slowly..., wait for two seconds, and then return whatever number we passed in.

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. use std::thread;
  4. use std::time::Duration;
  5. fn simulated_expensive_calculation(intensity: u32) -> u32 {
  6. println!("calculating slowly...");
  7. thread::sleep(Duration::from_secs(2));
  8. intensity
  9. }
  10. #}

Listing 13-1: A function to stand in for a hypothetical calculation that takes about 2 seconds to run

Next is the main function, which contains the parts of the workout app important for this example. This function represents the code that the app will 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’ll hardcode values representing inputs to our program and print the outputs.

The required inputs are these:

  • An intensity number from the user, which is specified when they request a workout to indicate whether they want a low-intensity workout or a high-intensity workout
  • A random number that will generate some variety in the workout plans

The output will be the recommended workout plan. Listing 13-2 shows the main function we’ll use.

Filename: src/main.rs

  1. fn main() {
  2. let simulated_user_specified_value = 10;
  3. let simulated_random_number = 7;
  4. generate_workout(
  5. simulated_user_specified_value,
  6. simulated_random_number
  7. );
  8. }
  9. # fn generate_workout(intensity: u32, random_number: u32) {}

Listing 13-2: A main function with hardcoded values to simulate user input and random number generation

We’ve hardcoded the variable simulated_user_specified_value as 10 and the variable simulated_random_number as 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, as we did in the Guessing Game example in Chapter 2. The main function calls a generate_workout function with the simulated input values.

Now that we have the context, let’s get to the algorithm. The function generate_workout 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

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # use std::thread;
  4. # use std::time::Duration;
  5. #
  6. # fn simulated_expensive_calculation(num: u32) -> u32 {
  7. # println!("calculating slowly...");
  8. # thread::sleep(Duration::from_secs(2));
  9. # num
  10. # }
  11. #
  12. fn generate_workout(intensity: u32, random_number: u32) {
  13. if intensity < 25 {
  14. println!(
  15. "Today, do {} pushups!",
  16. simulated_expensive_calculation(intensity)
  17. );
  18. println!(
  19. "Next, do {} situps!",
  20. simulated_expensive_calculation(intensity)
  21. );
  22. } else {
  23. if random_number == 3 {
  24. println!("Take a break today! Remember to stay hydrated!");
  25. } else {
  26. println!(
  27. "Today, run for {} minutes!",
  28. simulated_expensive_calculation(intensity)
  29. );
  30. }
  31. }
  32. }
  33. #}

Listing 13-3: The business logic 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 second else case calls it once.

The desired behavior of the generate_workout function is to first check whether the user wants a low-intensity workout (indicated by a number less than 25) or a high-intensity workout (a number of 25 or greater).

Low-intensity workout plans will recommend a number of push-ups and sit-ups based on the complex algorithm we’re simulating.

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. If not, the user will get a number of minutes of running based on the complex algorithm.

This code works the way the business wants it to now, but let’s say the data science team decides that we need to make some changes to the way we call the simulated_expensive_calculation function in the future. To simplify the update when those changes happen, we want to refactor this code so it calls the simulated_expensive_calculation function only once. We also want to cut the place where we’re currently unnecessarily calling the function twice without adding any other calls to that function in the process. That is, we don’t want to call it if the result isn’t needed, and we still want to call it only once.

Refactoring Using Functions

We could restructure the workout program in many ways. First, we’ll try extracting the duplicated call to the simulated_expensive_calculation function into a variable, as shown in Listing 13-4.

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # use std::thread;
  4. # use std::time::Duration;
  5. #
  6. # fn simulated_expensive_calculation(num: u32) -> u32 {
  7. # println!("calculating slowly...");
  8. # thread::sleep(Duration::from_secs(2));
  9. # num
  10. # }
  11. #
  12. fn generate_workout(intensity: u32, random_number: u32) {
  13. let expensive_result =
  14. simulated_expensive_calculation(intensity);
  15. if intensity < 25 {
  16. println!(
  17. "Today, do {} pushups!",
  18. expensive_result
  19. );
  20. println!(
  21. "Next, do {} situps!",
  22. expensive_result
  23. );
  24. } else {
  25. if random_number == 3 {
  26. println!("Take a break today! Remember to stay hydrated!");
  27. } else {
  28. println!(
  29. "Today, run for {} minutes!",
  30. expensive_result
  31. );
  32. }
  33. }
  34. }
  35. #}

Listing 13-4: Extracting the calls to simulated_expensive_calculation to one place 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 unnecessarily calling the function twice. 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 define code in one place in our program, but only execute that code where we actually need the result. This is a use case for closures!

Refactoring with Closures to Store Code

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 rather than storing the result of the function call, as shown in Listing 13-5. We can actually move the whole body of simulated_expensive_calculation within the closure we’re introducing here.

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # use std::thread;
  4. # use std::time::Duration;
  5. #
  6. let expensive_closure = |num| {
  7. println!("calculating slowly...");
  8. thread::sleep(Duration::from_secs(2));
  9. num
  10. };
  11. # expensive_closure(5);
  12. #}

Listing 13-5: Defining a closure and storing it in the expensive_closure variable

The closure definition comes after the = to assign it to the variable expensive_closure. To define a closure, we start with a pair of vertical pipes (|), inside which 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 place curly brackets that hold the body of the closure—these are optional if the closure body is a single expression. The end of the closure, after the curly brackets, needs a semicolon to complete the let statement. The value returned from the last line in the closure body (num) will be the value returned from the closure when it’s called, because that line doesn’t end in a semicolon; just as 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 that we’re using a closure because we want to define the code to call at one point, store that code, and call it at a later point; the code we want to call is now stored in expensive_closure.

With the closure defined, we can change the code in the if blocks to call the closure to execute the code and get the resulting value. We call a closure like we do 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, as shown in Listing 13-6.

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # use std::thread;
  4. # use std::time::Duration;
  5. #
  6. fn generate_workout(intensity: u32, random_number: u32) {
  7. let expensive_closure = |num| {
  8. println!("calculating slowly...");
  9. thread::sleep(Duration::from_secs(2));
  10. num
  11. };
  12. if intensity < 25 {
  13. println!(
  14. "Today, do {} pushups!",
  15. expensive_closure(intensity)
  16. );
  17. println!(
  18. "Next, do {} situps!",
  19. expensive_closure(intensity)
  20. );
  21. } else {
  22. if random_number == 3 {
  23. println!("Take a break today! Remember to stay hydrated!");
  24. } else {
  25. println!(
  26. "Today, run for {} minutes!",
  27. expensive_closure(intensity)
  28. );
  29. }
  30. }
  31. }
  32. #}

Listing 13-6: Calling the expensive_closure we’ve defined

Now the expensive calculation is called in only 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 closures provide us with another solution. We’ll talk about that solution in a bit. But first let’s talk about why there aren’t type annotations in the closure definition and the traits involved with closures.

Closure Type Inference and Annotation

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 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. But closures aren’t used in an exposed interface like this: they’re stored in variables and used without naming them and exposing them to users of our library.

Closures are usually short and relevant only 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 the return type, similar to how it’s able to infer the types of most variables.

Making programmers annotate the types in these small, anonymous functions would be annoying and largely redundant with the information the compiler already has available.

As with variables, we can add type annotations if we want to increase explicitness and clarity at the cost of being more verbose than is strictly necessary. Annotating the types for the closure we defined in Listing 13-5 would look like the definition shown in Listing 13-7.

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # use std::thread;
  4. # use std::time::Duration;
  5. #
  6. let expensive_closure = |num: u32| -> u32 {
  7. println!("calculating slowly...");
  8. thread::sleep(Duration::from_secs(2));
  9. num
  10. };
  11. #}

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

With type annotations added, the syntax of closures looks more similar to the syntax of functions. The following is a vertical comparison of the syntax for the definition of a function that adds 1 to its parameter and a closure that has the same behavior. We’ve added some spaces to line up the relevant parts. This illustrates how closure syntax is similar to function syntax except for the use of pipes and the amount of syntax that is optional:

fn add_one_v1 (x: u32) -> u32 { x + 1 } let add_one_v2 = |x: u32| -> u32 { 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 brackets, which are optional because the closure body has only one expression. 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 receives 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 a u32 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.

Storing Closures Using Generic Parameters and the Fn Traits

Let’s return to our workout generation app. In Listing 13-6, our code was still calling the expensive calculation closure more times than it needed to. One option to solve this issue is to save the result of the expensive closure in a variable for reuse and use the variable in each place we need the result, instead of calling the closure again. However, this method could result in a lot of repeated code.

Fortunately, another solution is available to us. We can create a struct that will hold the closure and the resulting value of calling the closure. The struct will execute the closure only if we need the resulting value, and it will cache the resulting value so 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.

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

The Fn traits are provided by the standard library. All closures implement at least one of the traits: Fn, FnMut, or FnOnce. We’ll discuss the difference between these traits in the “Capturing the Environment with Closures” section; 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 the closures must have to match this trait bound. In this case, our closure has a parameter of type u32 and returns a u32, so the trait bound we specify is Fn(u32) -> u32.

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

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. struct Cacher<T>
  4. where T: Fn(u32) -> u32
  5. {
  6. calculation: T,
  7. value: Option<u32>,
  8. }
  9. #}

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 it’s a closure by using the Fn trait. Any closure we want to store in the calculation field must have one u32 parameter (specified within the parentheses after Fn) and must return a u32 (specified after the ->).

Note: Functions implement all three of the Fn traits too. If what we want to do doesn’t require capturing a value from the environment, we can use a function rather than a closure where we need something that implements an Fn trait.

The value field is of type Option<u32>. Before we execute the closure, value will be None. When code using a Cacher asks for the result of the closure, the Cacher will 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, the Cacher will return the result held in the Some variant.

The logic around the value field we’ve just described is defined in Listing 13-10.

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # struct Cacher<T>
  4. # where T: Fn(u32) -> u32
  5. # {
  6. # calculation: T,
  7. # value: Option<u32>,
  8. # }
  9. #
  10. impl<T> Cacher<T>
  11. where T: Fn(u32) -> u32
  12. {
  13. fn new(calculation: T) -> Cacher<T> {
  14. Cacher {
  15. calculation,
  16. value: None,
  17. }
  18. }
  19. fn value(&mut self, arg: u32) -> u32 {
  20. match self.value {
  21. Some(v) => v,
  22. None => {
  23. let v = (self.calculation)(arg);
  24. self.value = Some(v);
  25. v
  26. },
  27. }
  28. }
  29. }
  30. #}

Listing 13-10: The caching logic of Cacher

We want Cacher to manage the struct fields’ values rather than letting the calling code potentially change the values in these fields directly, so these fields are private.

The Cacher::new function takes a generic parameter T, which we’ve defined as having the same trait bound as the Cacher struct. Then Cacher::new returns a Cacher instance that holds the closure specified in the calculation field and a None value in the value field, because we haven’t executed the closure yet.

When the calling code needs the result of evaluating the closure, instead of calling the closure directly, it will call the value method. This method checks whether 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, the code calls the closure stored in self.calculation, saves the result in self.value for future use, and returns the value as well.

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

Filename: src/main.rs

  1. # #![allow(unused_variables)]
  2. #fn main() {
  3. # use std::thread;
  4. # use std::time::Duration;
  5. #
  6. # struct Cacher<T>
  7. # where T: Fn(u32) -> u32
  8. # {
  9. # calculation: T,
  10. # value: Option<u32>,
  11. # }
  12. #
  13. # impl<T> Cacher<T>
  14. # where T: Fn(u32) -> u32
  15. # {
  16. # fn new(calculation: T) -> Cacher<T> {
  17. # Cacher {
  18. # calculation,
  19. # value: None,
  20. # }
  21. # }
  22. #
  23. # fn value(&mut self, arg: u32) -> u32 {
  24. # match self.value {
  25. # Some(v) => v,
  26. # None => {
  27. # let v = (self.calculation)(arg);
  28. # self.value = Some(v);
  29. # v
  30. # },
  31. # }
  32. # }
  33. # }
  34. #
  35. fn generate_workout(intensity: u32, random_number: u32) {
  36. let mut expensive_result = Cacher::new(|num| {
  37. println!("calculating slowly...");
  38. thread::sleep(Duration::from_secs(2));
  39. num
  40. });
  41. if intensity < 25 {
  42. println!(
  43. "Today, do {} pushups!",
  44. expensive_result.value(intensity)
  45. );
  46. println!(
  47. "Next, do {} situps!",
  48. expensive_result.value(intensity)
  49. );
  50. } else {
  51. if random_number == 3 {
  52. println!("Take a break today! Remember to stay hydrated!");
  53. } else {
  54. println!(
  55. "Today, run for {} minutes!",
  56. expensive_result.value(intensity)
  57. );
  58. }
  59. }
  60. }
  61. #}

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. Change the values in the simulated_user_specified_value and simulated_random_number variables to verify that in all the cases in the various if and else blocks, calculating slowly... appears only 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 so generate_workout can focus on the business logic.

Limitations of the Cacher Implementation

Caching values is a generally useful behavior that we might want to use in other parts of our code with different closures. However, there are two problems with the current implementation of Cacher that would make reusing it in different contexts difficult.

The first problem is that 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 the call to value with the arg value of 2 to return 2.

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

thread 'call_with_different_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. Thereafter, 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.

The second problem with the current Cacher implementation is that it only accepts closures that take one parameter of type u32 and return a u32. We might want to cache the results of closures that take a string slice and return usize values, for example. To fix this issue, try introducing more generic parameters to increase the flexibility of the Cacher functionality.

Capturing the Environment with Closures

In the workout generator example, we only used closures as inline anonymous functions. However, closures have an additional capability that functions don’t have: 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 equal_to_x variable that uses the x variable from the closure’s surrounding environment.

Filename: src/main.rs

  1. fn main() {
  2. let x = 4;
  3. let equal_to_x = |z| z == x;
  4. let y = 4;
  5. assert!(equal_to_x(y));
  6. }

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; if we try with the following example, our code won’t compile:

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 --> src/main.rs | 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, it uses memory to store the values for use in the closure body. This use of memory is overhead that we don’t want to pay in more common cases 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 mutably, and borrowing immutably. These are encoded in the three Fn traits as follows:

  • FnOnce consumes the variables it captures from its enclosing scope, known as the closure’s environment. To consume the captured variables, the closure must take ownership of these variables and move them into the closure when it is defined. The Once part of the name represents the fact that the closure can’t take ownership of the same variables more than once, so it can be called only once.
  • FnMut can change the environment because it mutably borrows values.
  • Fn borrows values from the environment immutably.

When you create a closure, Rust infers which trait to use based on how the closure uses the values from the environment. All closures implement FnOnce because they can all be called at least once. Closures that don’t move the captured variables also implement FnMut, and closures that don’t need mutable access to the captured variables also implement Fn. In Listing 13-12, the equal_to_x closure borrows x immutably (so equal_to_x has the Fn trait) because the body of the closure only needs to read the value in x.

If you want to force the closure to take ownership of the values it uses in the environment, you can use the move keyword before the parameter list. This technique is mostly useful when passing a closure to a new thread to move the data so it’s owned by the new thread.

We’ll have more examples of move closures in Chapter 16 when we talk about concurrency. 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, because integers can be copied rather than moved; note that this code will not yet compile.

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)); }

We receive the following error:

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 we added the move keyword. The closure then has ownership of x, and main isn’t allowed to use x anymore in the println! statement. Removing 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.