Eliminate non-local references from closure

Question

For a code similarity detection framework I need to eliminate references to non-local variables, for example having the following closure:

{
  var a;
  var b;

  var f = function() {
    a = 5;
    b = 6;
  }

  f();
}

would be converted into something like:

{
  var a;
  var b;

  var f = function() {
    var a = 5;
    var b = 6;
    return tuple(a, b);
  }

  a, b = f();
}

Another approach would be:

{
  var world;
  var a;
  var b;

  var f = function(world) {
    world = update_world(world, "a", 5);
    world = update_world(world, "b", 6);
    return world;
  }

  world = f(world);
  a = get_world(world, "a");
  b = get_world(world, "b");
}

Basically, convert a stateful program to a purely functional one. The goal is then to transform the resulting program into the lambda calculus, normalize and look for isomorphic subtrees.

Is there a formalization of what I'm trying to do?