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