Converting expression into string without evaluating it

Question

How can one convert a Mathematica expression into a string without the expression being evaluated first? I tried using Hold, but it returns Hold[expr], instead of expr. Is there any way to get just the expression?

For example, I have a variable var = 5, and I need to assign the name of var to another variable, so that var2 = "var". How can I do this?

My actual use case is this:

I am trying to synchronize my mathematica variables with certain fields in an external database. Every time the external database is updated, I call on a function that is supposed to update my corresponding Mathematica variables. It takes in a list of mappings like {var1 -> "field1", var2 -> "field2"}, and its role is to access the external database, look up the value in "field1", and assign it to var1, then look up the value in "field2" and assign it to var2. The number of variables in the mapping (and their names) can be arbitrary.

The problem is that I need those var1 and var2 variables to be passed as variable names, not values, so that I can assign them inside the function. I do the assignment using

Do[ i[[1]]->i[[2]]/.remoteData, {i,mappings} ]

where remoteData = {"field1"->"value of field 1", "field2" -> "value of field 2"}. I need i[[1]] to stand for var1, not for its value. I tried setting the attribute SetAttributes[fn,HoldAll] but that didn't help.

The result that I am looking for is var1 = "value of field 1", var 2 = "value of field 2".

Answer 1

It looks like I should have used HoldForm instead of Hold.

Here is my current solution that does the job:

SetAttributes[fn,HoldAll];

fn[mappings_]:= ReleaseHold[Apply[Set, HoldForm[mappings]/.remoteData, {2}]]

Answer 2

If I understand the question correctly, this is what you are asking:

You have a table with headings in a text file. You want to read this table in and assign the columns to certain variables. You want to do this based on some mapping of the form "heading-name" -> variable that your code takes as input.

First of all, personally I feel uneasy about programmatically manipulating variable names, but I know that many people disagree with this ... If I were doing this myself, I'd choose to retrieve the columns based on some name stored as a string (e.g. using replacement rules), but not actually assign to variables corresponding to this name. There are fewer things that can go wrong, e.g. variables won't accidentally get overwritten.

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That said, here's how to do what you asked for. Here's a example table stored in a string. You'll have a file instead.

table = 
 "one  two  three
   1    2    3
   4    5    6
   7    8    9"

These are the mappings. Variable names are stored as strings to prevent evaluation:

mapping = {"var1" -> "one", "var2" -> "two", "var3" -> "three"}

We'll use this function to assign to variables:

set[s_String, v_] := ToExpression[s, InputForm, Function[x, x = v, {HoldFirst}]]

The code:

data = ImportString[table, "Table"]
values = mapping[[All, 2]] /. (First[#] -> Rest[#] &) /@ Transpose[data]
MapThread[set, {mapping[[All, 1]], values}];

Now the variables are set to the values read from the table, based on the mappings we defined:

var1

(* ==> {1,4,7} *)

The key was using the third argument to ToExpression, which allows manipulating an expression converted from a string before it gets evaluated.

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However, as I said at the beginning, I would stop at creating the mapping (First[#] -> Rest[#] &) /@ Transpose[data] and using it to reference columns by their names.

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EDIT: Per the OP's request, here's how to do it without storing the variable names as strings. In this case we need to store the mapping inside Hold to prevent evaluating the variables.

mapping = Hold[var1 -> "one", var2 -> "two", var3 -> "three"]

ReleaseHold[Set @@@ (mapping /. (First[#] -> Rest[#] &) /@ Transpose[data])];

Slightly simpler with a different syntax for the mapping:

mapping = Hold[var1 = "one", var2 = "two", var3 = "three"];
ReleaseHold[ mapping /. (First[#] -> Rest[#] &) /@ Transpose[data] ];