Difference between method and function in Scala

Jim has got this pretty much covered in his blog post, but I'm posting a briefing here for reference.

First, let's see what the Scala Specification tell us. Chapter 3 (types) tell us about Function Types (3.2.9) and Method Types (3.3.1). Chapter 4 (basic declarations) speaks of Value Declaration and Definitions (4.1), Variable Declaration and Definitions (4.2) and Functions Declarations and Definitions (4.6). Chapter 6 (expressions) speaks of Anonymous Functions (6.23) and Method Values (6.7). Curiously, function values is spoken of one time on 3.2.9, and no where else.

A Function Type is (roughly) a type of the form (T1, ..., Tn) => U, which is a shorthand for the trait FunctionN in the standard library. Anonymous Functions and Method Values have function types, and function types can be used as part of value, variable and function declarations and definitions. In fact, it can be part of a method type.

A Method Type is a non-value type. That means there is no value - no object, no instance - with a method type. As mentioned above, a Method Value actually has a Function Type. A method type is a def declaration - everything about a def except its body.

Value Declarations and Definitions and Variable Declarations and Definitions are val and var declarations, including both type and value - which can be, respectively, Function Type and Anonymous Functions or Method Values. Note that, on the JVM, these (method values) are implemented with what Java calls "methods".

A Function Declaration is a def declaration, including type and body. The type part is the Method Type, and the body is an expression or a block. This is also implemented on the JVM with what Java calls "methods".

Finally, an Anonymous Function is an instance of a Function Type (ie, an instance of the trait FunctionN), and a Method Value is the same thing! The distinction is that a Method Value is created from methods, either by postfixing an underscore (m _ is a method value corresponding to the "function declaration" (def) m), or by a process called eta-expansion, which is like an automatic cast from method to function.

That is what the specs say, so let me put this up-front: we do not use that terminology! It leads to too much confusion between so-called "function declaration", which is a part of the program (chapter 4 -- basic declarations) and "anonymous function", which is an expression, and "function type", which is, well a type -- a trait.

The terminology below, and used by experienced Scala programmers, makes one change from the terminology of the specification: instead of saying function declaration, we say method. Or even method declaration. Furthermore, we note that value declarations and variable declarations are also methods for practical purposes.

So, given the above change in terminology, here's a practical explanation of the distinction.

A function is an object that includes one of the FunctionX traits, such as Function0, Function1, Function2, etc. It might be including PartialFunction as well, which actually extends Function1.

Let's see the type signature for one of these traits:

trait Function2[-T1, -T2, +R] extends AnyRef

This trait has one abstract method (it has a few concrete methods as well):

def apply(v1: T1, v2: T2): R

And that tell us all that there is to know about it. A function has an apply method which receives N parameters of types T1, T2, ..., TN, and returns something of type R. It is contra-variant on the parameters it receives, and co-variant on the result.

That variance means that a Function1[Seq[T], String] is a subtype of Function1[List[T], AnyRef]. Being a subtype means it can be used in place of it. One can easily see that if I'm going to call f(List(1, 2, 3)) and expect an AnyRef back, either of the two types above would work.

Now, what is the similarity of a method and a function? Well, if f is a function and m is a method local to the scope, then both can be called like this:

val o1 = f(List(1, 2, 3))
val o2 = m(List(1, 2, 3))

These calls are actually different, because the first one is just a syntactic sugar. Scala expands it to:

val o1 = f.apply(List(1, 2, 3))

Which, of course, is a method call on object f. Functions also have other syntactic sugars to its advantage: function literals (two of them, actually) and (T1, T2) => R type signatures. For example:

val f = (l: List[Int]) => l mkString ""
val g: (AnyVal) => String = {
  case i: Int => "Int"
  case d: Double => "Double"
  case o => "Other"
}

Another similarity between a method and a function is that the former can be easily converted into the latter:

val f = m _

Scala will expand that, assuming m type is (List[Int])AnyRef into (Scala 2.7):

val f = new AnyRef with Function1[List[Int], AnyRef] {
  def apply(x$1: List[Int]) = this.m(x$1)
}

On Scala 2.8, it actually uses an AbstractFunction1 class to reduce class sizes.

Notice that one can't convert the other way around -- from a function to a method.

Methods, however, have one big advantage (well, two -- they can be slightly faster): they can receive type parameters. For instance, while f above can necessarily specify the type of List it receives (List[Int] in the example), m can parameterize it:

def m[T](l: List[T]): String = l mkString ""

I think this pretty much covers everything, but I'll be happy to complement this with answers to any questions that may remain.

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One big practical difference between a method and a function is what return means. return only ever returns from a method. For example:

scala> val f = () => { return "test" }
<console>:4: error: return outside method definition
       val f = () => { return "test" }
                       ^

Returning from a function defined in a method does a non-local return:

scala> def f: String = {                 
     |    val g = () => { return "test" }
     | g()                               
     | "not this"
     | }
f: String

scala> f
res4: String = test

Whereas returning from a local method only returns from that method.

scala> def f2: String = {         
     | def g(): String = { return "test" }
     | g()
     | "is this"
     | }
f2: String

scala> f2
res5: String = is this

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function A function can be invoked with a list of arguments to produce a result. A function has a parameter list, a body, and a result type. Functions that are members of a class, trait, or singleton object are called methods. Functions defined inside other functions are called local functions. Functions with the result type of Unit are called procedures. Anonymous functions in source code are called function literals. At run time, function literals are instantiated into objects called function values.

Programming in Scala Second Edition. Martin Odersky - Lex Spoon - Bill Venners

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Let Say you have a List

scala> val x =List.range(10,20)
x: List[Int] = List(10, 11, 12, 13, 14, 15, 16, 17, 18, 19)

Define a Method

scala> def m1(i:Int)=i+2
m1: (i: Int)Int

Define a Function

scala> (i:Int)=>i+2
res0: Int => Int = <function1>

scala> x.map((x)=>x+2)
res2: List[Int] = List(12, 13, 14, 15, 16, 17, 18, 19, 20, 21)

Method Accepting Argument

scala> m1(2)
res3: Int = 4

Defining Function with val

scala> val p =(i:Int)=>i+2
p: Int => Int = <function1>

Argument to function is Optional

 scala> p(2)
    res4: Int = 4

scala> p
res5: Int => Int = <function1>

Argument to Method is Mandatory

scala> m1
<console>:9: error: missing arguments for method m1;
follow this method with `_' if you want to treat it as a partially applied function

Check the following Tutorial that explains passing other differences with examples like other example of diff with Method Vs Function, Using function as Variables, creating function that returned function

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Functions don't support parameter defaults. Methods do. Converting from a method to a function loses parameter defaults. (Scala 2.8.1)

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There is a nice article here from which most of my descriptions are taken. Just a short comparison of Functions and Methods regarding my understanding. Hope it helps:

Functions: They are basically an object. More precisely, functions are objects with an apply method; Therefore, they are a little bit slower than methods because of their overhead. It is similar to static methods in the sense that they are independent of an object to be invoked. A simple example of a function is just like bellow:

val f1 = (x: Int) => x + x
f1(2)  // 4

The line above is nothing except assigning one object to another like object1 = object2. Actually the object2 in our example is an anonymous function and the left side gets the type of an object because of that. Therefore, now f1 is an object(Function). The anonymous function is actually an instance of Function1[Int, Int] that means a function with 1 parameter of type Int and return value of type Int. Calling f1 without the arguments will give us the signature of the anonymous function (Int => Int = )

Methods: They are not objects but assigned to an instance of a class,i.e., an object. Exactly the same as method in java or member functions in c++ (as Raffi Khatchadourian pointed out in a comment to this question) and etc. A simple example of a method is just like bellow:

def m1(x: Int) = x + x
m1(2)  // 4

The line above is not a simple value assignment but a definition of a method. When you invoke this method with the value 2 like the second line, the x is substituted with 2 and the result will be calculated and you get 4 as an output. Here you will get an error if just simply write m1 because it is method and need the input value. By using _ you can assign a method to a function like bellow:

val f2 = m1 _  // Int => Int = <function1>

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Here is a great post by Rob Norris which explains the difference, here is a TL;DR

Methods in Scala are not values, but functions are. You can construct a function that delegates to a method via η-expansion (triggered by the trailing underscore thingy).

with the following definition:

a method is something defined with def and a value is something you can assign to a val

In a nutshell (extract from the blog):

When we define a method we see that we cannot assign it to a val.

scala> def add1(n: Int): Int = n + 1
add1: (n: Int)Int

scala> val f = add1
<console>:8: error: missing arguments for method add1;
follow this method with `_' if you want to treat it as a partially applied function
       val f = add1

Note also the type of add1, which doesn’t look normal; you can’t declare a variable of type (n: Int)Int. Methods are not values.

However, by adding the η-expansion postfix operator (η is pronounced “eta”), we can turn the method into a function value. Note the type of f.

scala> val f = add1 _
f: Int => Int = <function1>

scala> f(3)
res0: Int = 4

The effect of _ is to perform the equivalent of the following: we construct a Function1 instance that delegates to our method.

scala> val g = new Function1[Int, Int] { def apply(n: Int): Int = add1(n) }
g: Int => Int = <function1>

scala> g(3)
res18: Int = 4

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Practically, a Scala programmer only needs to know the following three rules to use functions and methods properly:

Methods defined by def and function literals defined by => are functions. It is defined in page 143, Chapter 8 in the book of Programming in Scala, 4th edition.

Function values are objects that can be passed around as any values. Function literals and partially applied functions are function values.

You can leave off the underscore of a partially applied function if a function value is required at a point in the code. For example: someNumber.foreach(println)

After four editions of Programming in Scala, it is still an issue for people to differentiate the two important concepts: function and function value because all editions don't give a clear explanation. The language specification is too complicated. I found the above rules are simple and accurate.

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In Scala 2.13, unlike functions, methods can take/return

type parameters (polymorphic methods)

implicit parameters

dependent types

However, these restrictions are lifted in dotty (Scala 3) by Polymorphic function types #4672, for example, dotty version 0.23.0-RC1 enables the following syntax

Type parameters

def fmet[T](x: List[T]) = x.map(e => (e, e))
val ffun = [T] => (x: List[T]) => x.map(e => (e, e))

Implicit parameters (context parameters)

def gmet[T](implicit num: Numeric[T]): T = num.zero
val gfun: [T] => Numeric[T] ?=> T = [T] => (using num: Numeric[T]) => num.zero

Dependent types

class A { class B }
def hmet(a: A): a.B = new a.B
val hfun: (a: A) => a.B = hmet

For more examples, see tests/run/polymorphic-functions.scala

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The most important difference between them is that a method is a definition that belongs to an object (usually the class, trait or object in which you define it), whereas a function is by itself a value, and because in Scala every value is an object, therefore, a function is an object.

For example, here's a method:

def timesTwoMethod(x :Int): Int = x * 2

And here's a function:

def timesTwoFunction = (x: Int) => x * 2

What is the real difference between the two?

The real difference is that the second one is an object. Its type is Int => Int, or more specifically Function1[Int, Int].

Why Scala treats functions as objects?

They do that so that you can pass around functions to other functions as arguments, because functions in Scala are first-class citizens.

However, in some situations, Scala can treat methods more or less like functions via an important mechanism.

For example, the higher-order function map defined on type List, receives another function f as its only parameter in its definition, of type f: A => B. The next two lines both compile, run and output the same result:

List(1, 2, 3).map(timesTwoMethod)
List(1, 2, 3).map(timesTwoFunction)

Why does this work?

This works because of the existence of a mechanism called Eta Expansion implemented in the Scala compiler. What it does is to convert an expression of a method type to an equivalent expression of a function type, and it does so seamlessly and quietly.

This is why the two lines above are equivalent.

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A method operates on an object but a function doesn't.

Scala and C++ has Fuction but in JAVA, you have to imitate them with static methods.

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