According to the Edsgar Dijkstra's Shunting-yard algorithm if neighboring two operators in an expressions have the same precedence level then the expression is disambiguated based on the associativity of the second operator.
- If the second operator is left associative then the operand belongs to the first operator.
- If the second operator is right associative then the operand belongs to the second operator.
Case 1: ⨂
is left associative. The expression evaluates to:
(x ⨁ y) ⨂ z
Case 2: ⨂
is right associative. The expression evaluates to:
x ⨁ (y ⨂ z)