将表达式与具有不同关联性和相同优先级的相邻运算符进行歧义消除 [英] Disambiguation of expressions with neighboring operators of different associativity and same precedence

问题描述

说我有一个表达式如下(其中⨁和⨂是具有相同优先级但不具有相同关联性的二进制运算符):

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

y是否属于⨁或⨂，并且基于什么条件?

Would y belong to ⨁ or ⨂, and based on what criteria?

推荐答案

根据Edsgar Dijkstra的

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.

1. 如果第二个运算符保持关联，则该操作数属于第一个运算符.
2. 如果第二个运算符是右关联的，则该操作数属于第二个运算符.

情况1: ⨂处于关联状态.该表达式的计算结果为:

Case 1: ⨂ is left associative. The expression evaluates to:

(x ⨁ y) ⨂ z

情况2: ⨂是正确的关联.该表达式的计算结果为:

Case 2: ⨂ is right associative. The expression evaluates to:

x ⨁ (y ⨂ z)

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