How can you form a variable from a function and its arguments?

Question

Is there a way to make the general replacement

foo[x,y,z]->fooxyz

so that I can treat the x_i as variables so that I will obtain foofgh from the following:

foo[f,g,h] /.{ foo[x,y,z]->fooxyz }

?

Answer 1

As I alluded to in my comment, this would in many cases be a bad idea: I'm fully in agreement with @Rojo when he warns not to make a mess of your data representation just because of how you want it to display. That said, perhaps there are legitimate reasons for doing this in some situations. You can accomplish it as follows:

foo[f, g, h] /. h_[args__] :> ToString[Row[{h, args}], StandardForm]
(* "foofgh" *)

It even works if you enter e.g. f^2 as an argument.

If you want a symbol rather than a string as the result, you have to be more careful about what can appear as a head or an argument. The following should perform adequately:

foo[f, g, h] /. h_Symbol[args__Symbol] :> Symbol[StringJoin @@ SymbolName /@ {h, args}]
(* foofgh *)

---

Aside: try the first of these examples, and then type any character either inside or after the resulting string. The resulting box expression is not properly formed and an internal self-test error (MathEditCells2|c|1384) appears in the messages window. This seems to be a bug in the front end, and it's been there since at least version 7.

Answer 2

Just for future users I will post my own workaround I just found (with everyones help!)

fabc := foo

f[a, b, c] /. {f[X_, Y_, Z_] -> {f, X, Y, Z}};
v = %;
{ToString[v[[1]]], ToString[v[[2]]], ToString[v[[3]]], ToString[v[[4]]]};
StringJoin[%];
ToExpression[%] 

output:= foo

Answer 3

Here we make a pattern to match all characters, except digits, for which Symbol[char] complains.

invalidCharacters = Alternatives @@ 
   Select[CharacterRange[FromCharacterCode[0], FromCharacterCode[2^16 - 1]],
     ! DigitQ[#] && Quiet@Check[Symbol[#]; False, True] &];

Presumably the function name will not start with a digit, since it cannot, so we won't worry about checking:

Symbol @ StringReplace[foo[f, g, h] // ToString, invalid -> ""]
Symbol @ StringReplace[f4d[2 + \[Angle]A, $b, 3.3] // ToString, invalidCharacters -> ""]

foofgh
f4d2\[Angle]A$b33

Caveat: This doesn't take care of all problems, but it should work for the usual sorts of things. For instance, inspecting the output of Symbol["x" <> FromCharacterCode[25]] reveals RowBox[{"x", "\.19"}]], which is interpreted as Times[\.19, x]. But Symbol[FromCharacterCode[25] <> "x"] creates a single symbol with the name "\.19x". I cannot imagine anyone wanting to use "\.19", which is nonprinting, except to make sure no one could ever figure out what the code was doing, including oneself. :)