Arrow (->) operator precedence/priority is lowest, or priority of assignment/combined assignment is lowest?

Question

JLS:

The lowest precedence operator is the arrow of a lambda expression (->), followed by the assignment operators.

Answer 1

First, let's explain the practical issue here.

Assuming you have a definition like

IntUnaryOperator op;

The following is syntactically accepted, and works as expected:

op = x -> x;

That is, we have an identity function on int assigned to the op variable. But if = had a higher priority, we'd expect Java to interpret this as

(op = x) -> x;

Which is not syntactically valid, thus should be a compile error. Hence, assignment does not, in practice, have higher precedence than the arrow.

But the following is also OK (assume t is a class/instance variable of type int):

op = x -> t = x;

This compiles, and the function, if applied, assigns the value of the operand to t and also returns it.

This means that the arrow doesn't have higher precedence than the assignment t = x. Otherwise it would have been interpreted as

op = ( x -> t ) = x

and clearly, this is not what happens.

So it seems that the operations have equal precedence. What's more, that they are right-associative. This is implied from the grammar at JLS chapter 19:

Expression:
  LambdaExpression
  AssignmentExpression

LambdaExpression:
  LambdaParameters -> LambdaBody

...

LambdaBody:
  Expression
  Block

So the right side of the lambda body gets us back to Expression, which means we can either have a (higher priority) lambda inside it, or a (higher priority) assignment in it. What I mean by "higher priority" is that the deeper you go through the production rules, the earlier the expression will be evaluated.

The same is true for the assignment operator:

AssignmentExpression:
  ConditionalExpression
  Assignment

Assignment:
  LeftHandSide AssignmentOperator Expression

Once again, the right side of the assignment throws us back to Expression, so we can have a lambda expression or an assignment there.

So rather than relying on the JLS text, the grammar gives us a well defined description of the situation.