Scala has first-class functions.

A function is not a method in Scala: functions are a value, and may be assigned as such. Methods (created using `def`

), on the other hand, must belong to a class, trait or object.

- Functions are compiled to a class extending a trait (such as
`Function1`

) at compile-time, and are instantiated to a value at runtime. Methods, on the other hand, are members of their class, trait or object, and do not exist outside of that. - A method may be converted to a function, but a function cannot be converted to a method.
- Methods can have type parameterization, whereas functions do not.
- Methods can have parameter default values, whereas functions can not.

Anonymous functions are functions that are defined but not assigned a name.

The following is an anonymous function that takes in two integers and returns the sum.

```
(x: Int, y: Int) => x + y
```

The resultant expression can be assigned to a `val`

:

```
val sum = (x: Int, y: Int) => x + y
```

Anonymous functions are primarily used as arguments to other functions. For instance, the `map`

function on a collection expects another function as its argument:

```
// Returns Seq("FOO", "BAR", "QUX")
Seq("Foo", "Bar", "Qux").map((x: String) => x.toUpperCase)
```

The types of the arguments of the anonymous function can be omitted: the types are inferred automatically:

```
Seq("Foo", "Bar", "Qux").map((x) => x.toUpperCase)
```

If there is just one argument, the parentheses around that argument can be omitted:

```
Seq("Foo", "Bar", "Qux").map(x => x.toUpperCase)
```

There is an even shorter syntax that doesn't require names for the arguments. The above snippet can be written:

```
Seq("Foo", "Bar", "Qux").map(_.toUpperCase)
```

`_`

represents the anonymous function arguments positionally. With an anonymous function that has multiple parameters, each occurrence of `_`

will refer to a different argument. For instance, the two following expressions are equivalent:

```
// Returns "FooBarQux" in both cases
Seq("Foo", "Bar", "Qux").reduce((s1, s2) => s1 + s2)
Seq("Foo", "Bar", "Qux").reduce(_ + _)
```

When using this shorthand, any argument represented by the positional `_`

can only be referenced a single time and in the same order.

To create a value for an anonymous function that does not take parameters, leave the parameter list blank:

```
val sayHello = () => println("hello")
```

Function composition allows for two functions to operate and be viewed as a single function. Expressed in mathematical terms, given a function `f(x)`

and a function `g(x)`

, the function `h(x) = f(g(x))`

.

When a function is compiled, it is compiled to a type related to `Function1`

. Scala provides two methods in the `Function1`

implementation related to composition: `andThen`

and `compose`

. The `compose`

method fits with the above mathematical definition like so:

```
val f: B => C = ...
val g: A => B = ...
val h: A => C = f compose g
```

The `andThen`

(think `h(x) = g(f(x))`

) has a more 'DSL-like' feeling:

```
val f: A => B = ...
val g: B => C = ...
val h: A => C = f andThen g
```

A new anonymous function is allocated with that is closed over `f`

and `g`

. This function is bound to the new function `h`

in both cases.

```
def andThen(g: B => C): A => C = new (A => C){
def apply(x: A) = g(self(x))
}
```

If either `f`

or `g`

works via a side-effect, then calling `h`

will cause all side-effects of `f`

and `g`

to happen in the order. The same is true of any mutable state changes.

```
trait PartialFunction[-A, +B] extends (A => B)
```

Every single-argument `PartialFunction`

is also a `Function1`

. This is counter-intuitive in a formal mathematical sense, but better fits object oriented design. For this reason `Function1`

does not have to provide a constant `true`

`isDefinedAt`

method.

To define a partial function (which is also a function), use the following syntax:

```
{ case i: Int => i + 1 } // or equivalently { case i: Int ⇒ i + 1 }
```

For further details, take a look at PartialFunctions.

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