michael rice nowgate at yahoo.com
Mon Jan 31 18:29:59 CET 2011

```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#Statistic

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)

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