How to make a function work on symbols in a specific context

Question

Let us say we have two sets of symbols $(x, y, z)$ with the same names that live in two different contexts:

{context1`x,context1`y,context1`z} = {1, 10, 100}

{context2`x,context2`y,context2`z} = {2, 20, 200}

How can we define a function which takes as an argument a context name, adds $x$ and $y$ that live in the specified context and assigns the result to $z$ in the same context?

Example:

f["context1`"]

would result in

{context1`x, context1`y, context1`z} = {1 ,10, 11}

{context2`x, context2`y, context2`z} = {2, 20, 200}

Answer 1

{context1`x, context1`y, context1`z} = {1, 10, 100}
f[input_String] := (
  input <> "z" <> "=" <> 
    ToString[
      ToExpression[input <> "x"] + ToExpression[input <> "y"]
    ]
  ) //ToExpression
f["context1`"]
context1`z

EDIT: now that we've established that we are trying to define methods on structures, let's create general get and set functions. Then the methods that operate on those parameters can be written in terms of get and set directly or in Modules.

set[context_String, var_String, val_] :=
  ToExpression[context <> var <> "=" <> ToString[val]];

get[context_String, var_String] := 
  ToExpression[context <> var]

f[input_String] := Module[{
   x = get[input, "x"],
   y = get[input, "y"],
   z
   },
   z = x + y;
   set[input, "z", z]
]
g[input_String]:=set[input,"z",get[input,"x"]+get[input,"y"]]

Answer 2

How can we define a function which takes as an argument a context name, adds x and y that live in the specified context and assigns the result to z in the same context?

Keep the body of your function as a String (or Boxes, if necessary), and then:

f[context_String] := (Begin[context]; ToExpression["z=x+y"]; End[])

f["foo`"];

Definition[foo`z]

foo`z = foo`x + foo`y

Edit: this assumes no global ($ContextPath) definitions for x, y, or z, which I now realize isn't too good. No time to fix it however.