• The function type A => B is just an abbreviation for the class scala. Function1[A, B], which is defined as follows. 

package scala;

trait Function1[A, B] {

 def apply(x: A): B

}

• An anonymous function such as 

(x: Int) => x * x

is expanded to: 

new Function1[Int, Int] {

 def apply(x: Int) = x * x

}

• A function call, such as f(a), where f is a value of some class type, is expanded to f.apply(a) 

val f = (x: Int) => x * x;

f(7)

would be 

val f = new Function1[Int, Int] {

 def apply(x: Int) = x * x

}

f.apply(7)

• A method such as 

def f(x: Int): Boolean = ...

is not itself a function value. 

But if f is used in a place where a Function type is expected, it is converted automatically to the function value

(x: Int) => f(x)