,3],[2]),([3],[1,2]),([1,2],[3]),([2],[1,3]),([1],[2,3]),([],[1,2,3])]
*Zoup> mSplitC [1,2,3]
[([1,2,3],[]),([2,3],[1]),([1,3],[2]),([3],[1,2])]
*Zoup>

Is there anyway to peer under the hood to see the code being generated? i notice, for example, that the original concat/zip-based implementation occasionally comes in quite a bit faster that the comprehension based example.

Best wishes,

--greg

On 5/21/07, Greg Meredith <lgreg.meredith@biosimilarity.com > wrote:

HC-er's,

Find below some simple-minded code from a naive Haskeller for generating all partitions of a multiset about which i have two questions.

mSplit :: [a] -> [([a], [a])]
mSplit [x]     = [([x],[])]
mSplit (x:xs) = (zip (map (x:) lxs) rxs)
                      ++ (zip lxs (map (x:) rxs))
                      where (lxs,rxs) = unzip (mSplit xs)
Is there a clever way to reduce the horrid complexity of the naive approach?
How lazy is this code? Is there a lazier way?
i ask this in the context of checking statements of the form \phi * \psi |= e_1 * ... * e_n where
[| \phi * \psi |] = { a \in U : a === b_1 * b_2, b_1 \in [| \phi |], b_2 \in [| \psi |] }
=== is some congruence generated from a set of relations
A nice implementation for checking such statements will iterate through the partitions, generating them as needed, checking subconditions and stopping at the first one that works (possibly saving remainder for a rainy day when the client of the check decides that wasn't the partition they meant).

Best wishes,

--greg

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