# [Haskell-cafe] efficient and/or lazy partitions of a multiset

Greg Meredith lgreg.meredith at biosimilarity.com
Mon May 21 16:18:06 EDT 2007

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)

1. Is there a clever way to reduce the horrid complexity of the naive
approach?
2. 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

--
L.G. Meredith
Managing Partner
Biosimilarity LLC
505 N 72nd St
Seattle, WA 98103

+1 206.650.3740

http://biosimilarity.blogspot.com
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