Non-Determinism Monad for Level-Wise Search

This Haskell library provides an implementation of the MonadPlus type class that enumerates the levels of the search space using breadth-first search or iterativ deepening.

A search space is formed by calls to return and mplus yielding a search tree with solutions in its leaves. For example, in the monadic action

return 1 `mplus` ((return 2 `mplus` return 3) `mplus` return 4)

the result 1 is in the second level, 4 in the third, and the results 2 and 3 are in the forth level. This is apparent from the following representation of this monadic action:

           `mplus`
         /         \
   return 1          `mplus`
                   /         \
               `mplus`      return 4
             /         \
         return 2    return 3

However, the implementation does not build this tree structure as a data term but constructs its levels directly.

The library provides an operation to get the list of levels from a non-deterministic computation. The nth element in this list contains the results of the computation that are found on the nth level of the computation.