[carlob]

I'm not sure I agree about the fact that notation is a pseudo-mathematisation.

For example in Mathematica there is a (mostly deprecated) package called Notation`[0] that does just this kind of stuff. I have to admit that it's not really used in production code anymore as MakeBoxes and MakeExpression are more fine-grained and robust.

Thus said I have to admit that the transformation between 2-D boxes and M-expression is not as foundational as what Tao is talking about, however the whole field of designing programming languages is deep down an exercise in defining notation, the transformation mentioned above just make this a bit more explicit.

[0] http://reference.wolfram.com/language/Notation/guide/Notatio...

[JadeNB]

> I'm not sure I agree about the fact that notation is a pseudo-mathematisation.

I definitely don't think that notation is pseudo-mathematisation; good notation is inordinately powerful in enabling good mathematics (and bad notation can make even simple mathematics hard). What I meant to describe as pseudo-mathematisation was the discussion of notation in what seemed to me in a (to me) unnecessarily formally mathematical way.