Function that counts the number of arguments of other functions

I have a newbie question: is it possible to write a function that counts the arguments (total and optionals) of a given function? Possibly it should be able to work with built-in and custom functions as well.

For example, if I define

f1[x_Integer] := x + 1;

f2[x_Integer, y_Integer: 1] := x + y;
g[x_Real, y_] := x - y;

I would like to have

countArgs[f1]
{1,0}
countArgs[f2]
{2,1}
countArgs[g]
{2,0}

and also, for example,

countArgs[Sin]
{1,0}

thank you.

@celtschk

Well, I didn't even know the use of UpValues, but basically what I am asking is the number of inputs the function needs, I don't care what the function does with those inputs. In your examples I would say

• {Infinity,0} for foo? It's more a question than an answer, sorry, but I had not thought aboute these unusual cases.



• this is nasty, I didn't think of a case like that either, I would say {3,{2}}, the {2} meaning exactly 2, to avoid bar[1,2], which is not legal.


• {2,0} but just because you wrote f[g,g], so it's practically a guess, I don't know what are UpValues and if they go against the spirit of my question by messing with the function. I hope I was clear.


• the last one I would say {3,0} as they were flattened.

Thank you, I start seeing that my question is not so obvious because there are too many complicated definitions for functions to take into account.

For now I understood that is possible with built-in functions with

SyntaxInformation[f]

(thank you Heike) but that mybe is a little too much asking for a general custom function.

Answer

Here is my attempt. The function below will work on functions with default args and options, as well as those having multiple definitions. I made the following assumptions:

• Only DownValues - based definitions are considered


• Default arguments, if present, are always to the right of mandatory arguments.


• Options, if present, are always to the right of all other arguments, and are declared either by OptionsPattern[] or opts:OptionsPattern[] pattern.

Here is the code:

ClearAll[countArgs];
SetAttributes[countArgs, {HoldAll, Listable}];
countArgs[f_Symbol] := 

   With[{dv = DownValues[f]}, countArgs[dv]];

countArgs[Verbatim[HoldPattern][HoldPattern[f_Symbol[args___]]] :> _] :=
  countArgs[f[args]];

countArgs[
   f_[Except[_Optional | _OptionsPattern | 
         Verbatim[Pattern][_, _OptionsPattern]], rest___]] :=
  {1, 0, 0} + countArgs[f[rest]];


countArgs[ f_[o__Optional, rest___]] := 
  {0, Length[HoldComplete[o]], 0} +  countArgs[f[rest]];

countArgs[f_[_OptionsPattern | Verbatim[Pattern][_, _OptionsPattern]]] := 
  {0, 0, 1};

countArgs[f_[]] := {0, 0, 0};

This function represents a mini-parser for the function's declarations. It returns a list of 3-element sublists, of the length equal to a number of DownValues. In each sublist, the first number is a number of normal arguments, the second one is a number of default arguments, and the last one (which can only be 0 or 1), tells us whether or not there are options declared.

Some examples:

ClearAll[f1, f2, f3, f4, g]
f1[x_Integer] := x + 1;
f2[x_Integer, y_Integer: 1] := x + y;
f3[x_, y_, z_: 1, q_: 2, opts : OptionsPattern[]] := x + y + z + q;
f4[x_, y_: 1] := x + y;
f4[x_, y_, z_] := x + y + z;
g[x_Real, y_] := x - y;

Now applying our function:

countArgs /@ {f1, f2, f3, f4, g}

{{{1, 0, 0}}, {{1, 1, 0}}, {{2, 2, 1}}, {{1, 1, 0}, {3, 0, 0}},{{2, 0, 0}}}