# Operator precedence — Precedence and associativity

> Consider an expression describable by the representation below, where both OP1 and OP2 are fill-in-the-blanks for OPerators.

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## Knowledge

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Consider an expression describable by the representation below, where both OP1 and OP2 are fill-in-the-blanks for OPerators.

The combination above has two possible interpretations

Which one the language decides to adopt depends on the identity of OP1 and OP2.

If OP1 and OP2 have different precedence levels (see the table below), the operator with the higher _precedence_ goes first and associativity does not matter. Observe how multiplication has higher precedence than addition and executed first, even though addition is written first in the code.

Within operators of the same precedence, the language groups them by _associativity_. _Left-associativity_ (left-to-right) means that it is interpreted as (a OP1 b) OP2 c, while _right-associativity_ (right-to-left) means it is interpreted as a OP1 (b OP2 c). Assignment operators are right-associative, so you can write

with the expected result that a and b get the value 5. This is because the assignment operator returns the value that is assigned. First, b is set to 5. Then the a is also set to 5 — the return value of b = 5, a.k.a. right operand of the assignment.

As another example, the unique exponentiation operator has right-associativity, whereas other arithmetic operators have left-associativity.

Operators are first grouped by precedence, and then, for adjacent operators that have the same precedence, by associativity. So, when mixing division and exponentiation, the exponentiation always comes before the division. For example, 2 3 / 3 2 results in 0.8888888888888888 because it is the same as (2 3) / (3 2).

For prefix unary operators, suppose we have the following pattern

where OP1 is a prefix unary operator and OP2 is a binary operator. If OP1 has higher precedence than OP2, then it would be grouped as (OP1 a) OP2 b; otherwise, it would be OP1 (a OP2 b).

If the unary operator is on the second operand

Then the binary operator OP2 must have lower precedence than the unary operator OP1 for it to be grouped as a OP2 (OP1 b). For example, the following is invalid

Because + has higher precedence than yield, this would become (a + yield) 1 — but because yield is a reserved word in generator functions, this would be a syntax error. Luckily, most unary operators have higher precedence than binary operators and do not suffer from this pitfall.

If we have two prefix unary operators …

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