Mathematica Notation and syntax mods

Question

I am experimenting with syntax mods in Mathematica, using the Notation package.

I am not interested in mathematical notation for a specific field, but general purpos

Answer 1

Not a full answer, but just to show a trick I learned here (more related to symbol redefinition than to Notation, I reckon):

Unprotect[Fold];
Fold[f_, x_] :=
  Block[{$inMsg = True, result},
    result = Fold[f, First@x, Rest@x];
    result] /; ! TrueQ[$inMsg];
Protect[Fold];

Fold[f, {a, b, c, d}]
(*
--> f[f[f[a, b], c], d]
*)

Edit

Thanks to @rcollyer for the following (see comments below).

You can switch the definition on or off as you please by using the $inMsg variable:

$inMsg = False;
Fold[f, {a, b, c, d}]
(*
->f[f[f[a,b],c],d]
*)

$inMsg = True;
Fold[f, {a, b, c, d}]
(*
->Fold::argrx: (Fold called with 2 arguments; 3 arguments are expected. 
*)

Fold[f, {a, b, c, d}]

That's invaluable while testing