Un-initialized final local variable vs un-initialized final instance variable

The local variable isn't used and therefore can be left uninitialized

You will get compile error when try to use it (even if it's not final):

 System.out.println("test program" + y);

The local variable y may not have been initialized

The Java Language Specification does not state that a final variable must be assigned (emphasis mine):

A final variable may only be assigned to once.

And:

A blank final is a final variable whose declaration lacks an initializer.

So your y variable is a blank final, and since it's not referenced anywhere further in your code, it's perfectly fine to leave it unassigned.

import java.util.*;
public class test
{
 final int x = 5;
 public static void main(String[] args)
 {
     final int y;
     System.out.println("test program");
     y=6;
     y=7;   
 }
}

y=7 will give error:The final local variable y may already have been assigned. Since it is a final variable, and it has been assigned to 6.

IMHO, a final local variable means once assigned, it cannot be re-assigned. But by final int y you are only declaring a final variable without assignment(initialization), which is legal in Java.(But in order to use it you still have to initialize it, or an error occurs.)

Update:

As commented below, you have noticed the difference between a class field final variable and a local final variable.

From Java Language Specification:

1. a final field must be definely assigned in the static initializer or the constructor:

   8.3.1.2 final Fields A field can be declared final (§4.12.4). Both class and instance variables (static and non-static fields) may be declared final. A blank final class variable must be definitely assigned by a static initializer of the class in which it is declared, or a compile-time error occurs (§8.7, §16.8). A blank final instance variable must be definitely assigned at the end of every constructor of the class in which it is declared, or a compile-time error occurs (§8.8, §16.9).

(Note that a non-final field can be left un-initialized)

2.A local variable(whether final or not) must be explicitly given a value before it is used:(chapter 4.12.5,P88)

• A local variable (§14.4, §14.14) must be explicitly given a value before it is used, by either initialization (§14.4) or assignment (§15.26), in a way that can be verified using the rules for definite assignment (§16 (Definite Assignment)).

As per the definition of a final variable, they can be initialized only once. In your code, you haven't initialized 'y' and you're not using it anywhere as well.

But if you do the following,

final int y;
System.out.println(y);

you will get 'variable y might not have been initialized'

You will get an error when you try to use the declared final variable.

System.out.println(y);