Expand an expression to only built in functions

Question

This question is hard to phrase and even harder to google. Maybe it's best to explain it with a very simple example.

squareList = # # & /@ Range[10]
totalRoot = Sqrt[Total[squareList]]

Now I want to apply some kind of function to totalRoot to get the following:

Sqrt[Total[# # & /@ Range[10]]]

Hopefully you understand what I mean. I'll try to put it into words. I want a function that, given a variable or an expression, returns an expression equivalent to it, but written only using built in functions. Basically, it would substitute back any variable declaration.

In case anyone is interest in why I need this, it's because it makes it easier to share the code of very simple programs. I am still a beginner when it comes to Mathematica so I tend to write all my programs in little steps, declaring a variable for each one.

Answer 1

There are several ways to do this, but here is a simple one to get you started. One thing to fix first, though, is to use delayed assignments in your variable declarations - otherwise the variables will store already evaluated results. So:

squareList := # # & /@ Range[10]
totalRoot := Sqrt[Total[squareList]]

Here is a simple function, then. It assumes you only want to expand variables, and that all your variables live in the Global` context.

ClearAll[expandAll];
SetAttributes[expandAll, HoldAll];
expandAll[expr_] :=
   HoldComplete[expr] //. Flatten[ 
      Map[ToExpression[#, StandardForm, OwnValues] &] @ Names["Global`*"]
   ]

So that

expandAll[totalRoot]

(* HoldComplete[Sqrt[Total[(#1 #1 &) /@ Range[10]]]] *)

Note that one has to wrap the result into some wrapper that would hold the code and prevent it from evaluation, such as Hold or HoldComplete. Or, you can also use Defer:

Defer @@ expandAll[totalRoot]

(* Sqrt[Total[(#1 #1 &) /@ Range[10]]] *)