Apply list to arguments in Mathematica

Question

How would I go about applying each element in a list to each argument in a function? Kind of like Map, except with a variable number of arguments.

So for example, if I have a function action[x1_,x2_,x3_]:=..., and I have a list {1,2,3}, how would I create a function to call action with action[1,2,3]?

I would like this function be able to handle me changing action to action[x1_,x2], and anything else, also, with the list now being {1,2}, and to call action now with action[1,2].

Answer 1

Based on "Kind of like Map, except with a variable number of arguments." I think you might be looking for Apply to level 1. This is done with:

Apply[function, array, {1}]

or the shorthand:

function @@@ array

Here is what it does:

array = {{1, 2, 3}, {a, b, c}, {Pi, Sin, Tan}};

action @@@ array

   {action[1, 2, 3], action[a, b, c], action[Pi, Sin, Tan]}  

---

The terminology I used above could be misleading, and limits the power of Apply. The expression to which you apply action does not need to be a rectangular array. It does not even need to be a List: {...} or have its elements be lists. Here is an example incorporating these possibilities:

args = {1, 2} | f[a, b, c] | {Pi};

action @@@ args

   action[1, 2] | action[a, b, c] | action[Pi] 

• args is not a List but a set of Alternatives
• the number of arguments passed to action varies
• one of the elements of args has head f

Observe that:

• action replaces the head of each element of args, whatever it may be.
• The head of args is preserved in the output, in this case Alternatives (short form: a | b | c)

Answer 2

Apply[action, {1,2,3}]

This also can be entered as action @@ {1,2,3}.