Define Tilde as a postfix operator

Question

I have read a lot of posts in this forum on defining infix symbols like CircleDot and Tilde. The Help pages say Tilde is often used either as an infix or postfix operator, but I can find no example in the Mathematica documentation nor in this forum of how to define it as a postfix operator. I have several such operators I would like to define but I am unable to define even a very simple one.

It is straight-forward to define Tilde as an infix operator. For example, input:

Foo[expr_] := -expr
expr1_∼expr2_ := Foo[expr1]
x=.;
100∼x

Answer:

-100

However, the operation I wish to define would be

expr1_∼:=Foo[expr1]
100∼

also with an answer of -100, but this is not accepted by Mathematica. I don't wish to invoke the Notations package. Is this possible to do? I hope the answer is trivial and, if so, I apologize for asking.

Answer 1

It is not possible to make \[Tilde] postfix. It is not possible to define new operators with new parsing rules in Mathematica in such a way that they work generally. It is only possible to do it with the Notation package, but it will only work in the notebook interface, not in plain text source files or in terminal mode. Perhaps someone else will write an answer about that topic, as I don't use the Notation package. Instead I'll talk about how Mathematica parses plain text input.

a \[Tilde] b is hard-wired to parse to Tilde[a, b]. You can assign any definition to the symbol Tilde, but you cannot change how a \[Tilde] b is parsed. You cannot change the fact that it is infix, you cannot change its precedence, and you cannot change the fact that it parses directly to Tilde[a, b].

Note 1: Parsing means converting a textual representation of an expression into an in-memory data structure. It is separate from evaluation. Example: f@x doesn't evaluate to f[x]. It directly parses to the same in-memory data structure as f[x]. f@x and f[x] are indistinguishable by the evaluator, as it never even sees their textual form, only their internal representation.

Note 2: Perhaps it is unlucky to work with \[Tilde] because it looks very similar to ~, which has a completely different meaning: x ~f~ y is the same as f[x, y].