Why does Java require an explicit cast on a final variable if it was copied from an array?

The JLS (§5.2) has special rules for assignment conversion with constant expressions:

In addition, if the expression is a constant expression (§15.28) of type byte, short, char, or int:

• A narrowing primitive conversion may be used if the type of the variable is byte, short, or char, and the value of the constant expression is representable in the type of the variable.

If we follow the link above, we see these in the definition of constant expression:

• Literals of primitive type and literals of type String
• The additive operators + and -
• Simple names (§6.5.6.1) that refer to constant variables (§4.12.4).

If we follow the second link above, we see that

A variable of primitive type or type String, that is final and initialized with a compile-time constant expression (§15.28), is called a constant variable.

It follows that foo + foo can only be assigned to fooFoo if foo is a constant variable. To apply that to your cases:

• byte foo = 1; does not define a constant variable because it's not final.

• final byte foo = 1; does define a constant variable, because it's final and initialized with a constant expression (a primitive literal).

• final byte foo = fooArray[0]; does not define a constant variable because it's not initialized with a constant expression.

Note that whether fooFoo is itself final doesn't matter.

The value 1 fits nicely into a byte; so does 1+1; and when the variable is final, the compiler can do constant folding. (in other words: the compiler doesn't use foo when doing that + operation; but the "raw" 1 values)

But when the variable is not final, then all the interesting rules about conversions and promotions kick in (see here; you want to read section 5.12 about widening primitive conversions).

For the second part: making an array final still allows you to change any of its fields; so again; no constant folding possible; so that "widening" operation is kicking in again.

It is indeed what compiler do in constant folding when used with final, as we can see from byte code:

    byte f = 1;
    // because compiler still use variable 'f', so `f + f` will 
    // be promoted to int, so we need cast
    byte ff = (byte) (f + f);
    final byte s = 3;
    // here compiler will directly compute the result and it know
    // 3 + 3 = 6 is a byte, so no need cast
    byte ss = s + s;
    //----------------------
    L0
    LINENUMBER 12 L0
    ICONST_1 // set variable to 1
    ISTORE 1 // store variable 'f'
    L1
    LINENUMBER 13 L1
    ILOAD 1 // use variable 'f'
    ILOAD 1
    IADD
    I2B        
    ISTORE 2 // store 'ff'
    L2

    LINENUMBER 14 L2
    ICONST_3 // set variable to 3
    ISTORE 3 // store 's'
    L3
    LINENUMBER 15 L3
    BIPUSH 6 // compiler just compute the result '6' and set directly
    ISTORE 4 // store 'ss'

And if you change your final byte to 127, it will also complain:

    final byte s = 127;
    byte ss = s + s;

in which cases, the compiler compute the result and know it out of limit, so it will still complain they are incompatible.

More:

And here is another question about constant folding with string: