How to stop a single function to be evaluated?

Question

See this example:

AA = {x} \[Function] Normalize[x]
BB = {x} \[Function] Evaluate[AA[x]*5]

I need BB to be Normalize[x]*5.

Some context:I call evaluate because I'm using CForm later to do some optimizations, so my functions need not to call other user-defined functions which would translate into something that is not really valid C code.

Normalize though just evaluates to a version which makes some sense only for complex numbers, this is not what the definition of Normalize does... Also, afaik Evaluate doesn't take assumptions, so I don't know how to "hint" it not to incorrectly expand Normalize...

I've tried various hold/replace/single step evaluate tricks, all not working. Any ideas?

Answer 1

Try this:

AA[x_] := Normalize[x];
Hold[BB[x_] := 5 AA[x]] /. DownValues[AA] // ReleaseHold

??BB

Answer 2

Using the function ExpandCode defined here, you can expand any code that you want, for example expand all functions which name consist in upper case letters.

AA[x_] := Normalize[x];  
ExpandCode@Hold[Bb[x_] := 5 AA[x]] // ReleaseHold
Bb // DownValues

Answer 3

If you need BB to be Normalize[x]*5 explicitly, then use

AA[x_] := Normalize[x]

BBtemp[x_] := 5*AA[x]

BB[x_] = Hold[BBtemp[x]] /. DownValues[BBtemp] /. DownValues[AA]

(*Hold[5 Normalize[x]]*)

Unfortunately, when you act by ReleaseHold on it, it becomes 5 x/Norm[x].