haskell - 关联和交换之间的区别

Question

我试图理解幺半群中的关联。

从书中，它说:

Associativity simply says that you can associate the arguments of your operation differently and the result will be the same.

例如:

Prelude> (1 + 9001) + 9001
18003
Prelude> 1 + (9001 + 9001)
18003

关于交换:

This is not as strong a property as an operation that commutes or is commutative. Commutative means you can reorder the arguments and still get the same result. Addition and multiplication are commutative, but (++) for the list type is only associative.

上面的例子是关联的和可交换的，但有什么区别呢？
我看不出有什么区别。

Answer 1

以字符串连接为例。假设您使用的语言使用 +用于字符串连接。这自然是关联的，因为分组无关紧要:

("a" + "b") + "c" == "abc"
"a" + ("b" + "c") == "abc"

但操作数顺序绝对重要:

"a" + "b" = "ab"
"b" + "a" = "ba"