How to properly define this function of function

Question

I encountered real problem at first, and here is the toy example

variable argument stored some expression that is generated from other parts of the program. I suppose it's content is {xx, yy, zz}

argument = {xx, yy, zz}

and define a function test

test[argument_,t_] := {argument^2, Range[t]}

test function has only t as variable. Because when I use test, I don't need to substitute values into xx,yy,zz, I just manipulate expression stored in argument.

Now I want to define another function that has full control of xx,yy,zz,tin test function in order to get numerical results.

So I tried

f[xx_,yy_,xx_, t_] := test[t]

This won't work, because test[t] is hold. f[1,1,1,1] will give

{{xx^2, yy^2, zz^2}, {1}}

and this won't work either

f[xx_,yy_,xx_, t_] := Evaluate@test[t]

Though Evaluate unhold argument, while Range[t] can't be evaluated with letter t at the first step. So it will give errors like

Range::range: Range specification in Range[t] does not have appropriate bounds. >>

So how to do it?

ps:

For this simple case, surely I could directly define in this way.

f[xx_, yy_, zz_, t_] := test[{xx, yy, zz}, t];

But this is not what I want. As I said, the argument is dynamically generated by other parts of the program, so we cannot use its explicit form.

Answer 1

You can use Block inside body of f function to temporarily set desired symbols to those passed as arguments of f.

ClearAll[argument, f, test]
argument = {xx, yy, zz};
test[t_] := {argument^2, Range[t]}
f[kx_, ky_, kz_, t_] := Block[{xx = kx, yy = ky, zz = kz}, test[t]]

f[a, b, c, 4]
(* {{a^2, b^2, c^2}, {1, 2, 3, 4}} *)

---

Alternatively you could first define general function f and then its specialized version test as suggested by @rhermans.

We start with argument[...] function instead of argument variable:

ClearAll[argument, f, test]

Block[{xx, yy, zz},
    argument[xx_, yy_, zz_] := Evaluate[
        Print["Time consuming calculation of argument."];
        {xx, yy, zz}
    ]
]
(* Time consuming calculation of argument. *)

Now argument[...] gives you precalculated expression with proper values of xx, yy, zz inserted.

argument[a, b, c]
(* {a, b, c} *)

Now we can define f and then test:

f[xyz:PatternSequence[xx_, yy_, zz_], t_] := {argument[xyz]^2, Range[t]}
test[t_] := f[xx, yy, zz, t]

test[5]
(* {{xx^2, yy^2, zz^2}, {1, 2, 3, 4, 5}} *)
f[a, b, c, 10]
(* {{a^2, b^2, c^2}, {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}} *)