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