[Haskell-cafe] data structures question

[Tamas K Papp]

Hi,

Having read some tutorials, I would like to start using Haskell "for
real", but I have some questions about data structures.

The mathematical description of the problem is the following: assume
there is a function V(a,b,theta), where a and b can have two values,
High or Low, and theta is a number between zero and n (n is given).
The range of V is the real numbers.

Then there is an algorithm (called value iteration, but that's not
important) that takes V and produces a function of the same type,
called V'.  The algorithm uses a mapping that is not elementwise, ie
more than the corresponding values of V are needed to compute a
particular V'(a,b,theta) -- things like V(other a,b,theta) and
V(a,b,theta+1), where

data State = Low | High
other :: State -> State
other High = Low
other Low = High

Question 1: V can be represented as a 3-dimensional array, where the
first two indices are of type State, the third is Int (<= n).  What
data structure do you suggest in Haskell to store V?  Is there a
multidimensional array or something like this?

Let's call this structure TypeV.

Question 2: I would like to write

valueit :: TypeV -> TypeV
valueit V = mapondescartesproduct [Low,High] [Low,High] [0..n] mapV where
	    -- mapV would calculate the new V' using V
	    -- mapV :: State -> State -> Int -> Double

to fill the new data structure.  How to do this sensibly?

Thanks,

Tamas