As it happens, I can still remember being confused the first few times I saw this notation: not to put too fine a point on it, but there is something syntactically new going on there beyond the usual function / arrow notation.

In my opinion this is not notation at all but rather shorthand. In other words, it is something that you can use in your own handwritten notes and something that you can write on the board if you are confident that your listeners will understand you. (I suppose if I start telling stories about all the talks I witnessed as a Harvard graduate student that sailed over my head whether the speaker intended them to or not, I will not get enough "Oh, you poor dear" responses to justify the effort. But it happened quite a lot!) It's nice to have an agreed upon shorthand. For instance, in the commutative algebra class I just taught, when things were hot and heavy I didn't want to keep writing out "$I$ is an ideal of $R$", so I used a shorthand for it and explained it the first 20 times I used it. (The students used it too when presenting solutions to problems.) But in my lecture notes it appears nowhere: if I have the time to tex up lecture notes at all, then I certainly have the time to write out "$I$ is an ideal of $R$".

Thus I would not recommend that anyone include this notation in their formal mathematical writings. Note that Dick Palais has said essentially the same thing above, so: don't listen to me, but listen to him!