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Non-Determinism Monad for Level-Wise Search http://github.com/sebfisch/level-monad
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README

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 and allows to
implement breadth-first search.

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. Hence, using `concat` to merge the levels, yields
breadth-first search, but different combination function
(e.g. diagonalisation) can be applied too.

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