I'm mapping a function over a list of data, where the mapping function is determined from the data. g f l = map (g l) l So g serialize "prolog" -> [4,5,3,2,3,1] But I'm having typing problems trying to do a similar thing with a function that statistically normalizes data. See: http://people.revoledu.com/kardi/tutorial/Similarity/Normalization.html#Stat... So g normalize [2,5,3,2] -> [-0.7071067811865475,1.414213562373095,0.0,-0.7071067811865475] Is my typing for normalize too loose. Should I be using Floating rather than Num? Michael =======Code============== {- See Problem 42, pg. 63, Prolog by Example, Coelho & Cotta Generate a list of serial numbers for the items of a given list, the members of which are to be numbered in alphabetical order. *Main> serialize "prolog" [4,5,3,2,3,1] *Main> serialize "int.artificial" [5,7,9,1,2,8,9,5,4,5,3,5,2,6] *Main> ["prolog"] >>= serialize [4,5,3,2,3,1] *Main> ["int.artificial"] >>= serialize [5,7,9,1,2,8,9,5,4,5,3,5,2,6] -} import Data.Map hiding (map) import Data.List {- serialize :: [Char] -> [Int] serialize l = map (f l) l where f = ((!) . fromList . ((flip zip) [1..]) . (sort . nub)) -} serialize :: (Ord a, Integral b) => [a] -> a -> b serialize = ((!) . fromList . ((flip zip) [1..]) . (sort . nub)) g f l = map (f l) l normalize :: (Num a, Num b) => [a] -> a -> b normalize l = let (total,len) = sumlen l avg = total/len stdev = sqrt $ ((/) (len-1)) $ sum $ map ((** 2.0) . (subtract avg)) l in ((/) stdev) . (subtract avg) sumlen :: (Num a, Integral b) => [a] -> (a,b) sumlen l = sumlen' l 0 0 where sumlen' [] sum len = (sum,len) sumlen' (h:t) sum len = sumlen' t (sum+h) (len+1) ========================= Prelude> :r [1 of 1] Compiling Main ( serialize2.hs, interpreted ) serialize2.hs:34:32: Could not deduce (Integral a) from the context (Num a, Num b) arising from a use of `sumlen' at serialize2.hs:34:32-39 Possible fix: add (Integral a) to the context of the type signature for `normalize' In the expression: sumlen l In a pattern binding: (total, len) = sumlen l In the expression: let (total, len) = sumlen l avg = total / len stdev = sqrt $ ((/) (len - 1)) $ sum $ map ((** 2.0) . (subtract avg)) l in (/ stdev) . (subtract avg) serialize2.hs:36:61: Could not deduce (Floating a) from the context (Num a, Num b) arising from a use of `**' at serialize2.hs:36:61-66 Possible fix: add (Floating a) to the context of the type signature for `normalize' In the first argument of `(.)', namely `(** 2.0)' In the first argument of `map', namely `((** 2.0) . (subtract avg))' In the second argument of `($)', namely `map ((** 2.0) . (subtract avg)) l' serialize2.hs:37:18: Couldn't match expected type `b' against inferred type `a' `b' is a rigid type variable bound by the type signature for `normalize' at serialize2.hs:33:25 `a' is a rigid type variable bound by the type signature for `normalize' at serialize2.hs:33:18 In the expression: (/ stdev) . (subtract avg) In the expression: let (total, len) = sumlen l avg = total / len stdev = sqrt $ ((/) (len - 1)) $ sum $ map ((** 2.0) . (subtract avg)) l in (/ stdev) . (subtract avg) In the definition of `normalize': normalize l = let (total, len) = sumlen l avg = total / len .... in (/ stdev) . (subtract avg) Failed, modules loaded: none.