The notation for avoiding parentheses is interesting, and I've thought that it might be useful in programming languages.

To illustrate, suppose you have a non-associative operator $. Rather than write a$(b$c), you can write a$.b$c - the . makes the $ before it be lower precedence on the right side. More dots make things be even lower precedence.

So, for example,

    a$b .$: x$y .$. p$q

means

    (a$b) $ ((x$y) $ (p$q))

At least, that's my recollection. It's been over fifty years since I read (significant parts of) it...