Say I have an expression as follows (where ⨁ and ⨂ are binary operators which have the same precedence level but not the same associativity):
x ⨁ y ⨂ z
Would y belong to ⨁ or ⨂, and based on what criteria?
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)
来源：https://stackoverflow.com/questions/15117457/disambiguation-of-expressions-with-neighboring-operators-of-different-associativ