Unbalanced Balances...

Once again, I found a challenge in a very common webpage that said the following:

You have a room-full of balances and weights. Each balance weighs ten pounds and is considered perfectly balanced when the sum of weights on its left and right sides are exactly the same. You have placed some weights on some of the balances, and you have placed some of the balances on other balances. Given a description of how the balances are arranged and how much additional weight is on each balance, determine how to add weight to the balances so that they are all perfectly balanced.

There may be more than one way to balance everything, but always choose the way that places additional weight on the lowest balances.

The input file will begin with a single integer, N, specifying how many balances there are.
Balance 0 is specified by lines 1 and 2, balance 1 is specified by lines 3 and 4, etc...
Each pair of lines is formatted as follows:

WL &lt balances &gt
WR &lt balances &gt

WL and WR indicate the weight added to the left and right sides, respectively. &lt balances &gt is a space-delimited list of the other balance that are on that side of this balance. &lt balances &gt may contain zero or more elements.

First Haskell Published Program: Arithmetic Progression

I find Haskell a challenging language, one that let you express yourself in different ways as procedural or object oriented programming allows you to do it. I knew about it quite a few months ago, but I have never had the time to concentrate to develop any example using it. As I found in the Facebook challenge example, I considered was a good opportunity to create a program with the current knowledge of Haskell (minimal) and still learn a lot using what I take for granted in other languages (C++ or Objective C).

At first, it is really a change of paradigm to start thinking about functions instead of variables that you declare at the beginning and use them as the program executes. Here those do not exist in the same way, as it does for loops (while or for) and the list are fundamental for data manipulation, you will notice my tries to force the language to behave as a procedural language, which I am aware it is not the best practice, but for the first steps I consider it is ok.

The statement of the test is the following: