front end - Usage of [InvisibleApplication] and other related invisible characters

From the front end, \[InvisibleApplication] can be entered as Esc @ Esc, and is an invisible operator for @!. By an unfortunate combination of key-presses (there may have been a cat involved), this crept up in my code and I spent a great deal of time trying to figure out why in the world f x was being interpreted as f[x]. Example:

enter image description here

Now there is no way I could've spotted this visually. The *Forms weren't of much help either. If you're careful enough, you can see an invisible character between f and x if you move your cursor across the expression. Eventually, I found this out only by looking at the contents of the cell.

There's also \[InvisibleSpace], \[InvisibleComma] and \[ImplicitPlus], which are analogous to the above. There must be some use for these (perhaps internally), which is why it has been implemented in the first place. I can see the use for invisible space (lets you place superscripts/subscripts without needing anything visible to latch on to), and invisible comma (lets you use indexing like in math). It's the invisible apply that has me wondering...

The only advantage I can see is to sort of visually obfuscate the code. Where (or how) is this used (perhaps internally?), and can I disable it? If it's possible to disable, will there be any side effects?

Answer

It is used in TraditionalForm output, e.g. here:

TraditionalForm[ Hypergeometric2F1[a,b,c,x] ]

Without \[InvisibleApplication] it would probably be hard for Mathematica to parse it back to InputForm. Probably it is used in more places internally.

In order to get rid of it:

Locate the file UnicodeCharacters.tr in /usr/local/Wolfram/Mathematica/8.0/SystemFiles/FrontEnd/TextResources (or the equivalent under Windows or MacOSX), make a backup of the file, open it and delete the line

0xF76D         \[InvisibleApplication]         ($@$ ...

Then your cat can jump on the keyboard again.

Comments

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