michael rice nowgate at yahoo.com
Mon Jun 8 14:59:53 EDT 2009

```I wrote a Haskell solution for the Prolog problem stated below. I had written a function SQUISH before discovering that NUB does the same thing. While the solution works, I thought maybe I could apply some functions in the Data.Map module, and so wrote a second version of SERIALIZE, one no longer needing TRANSLATE. Using the Data.Map module is probably overkill for this particular problem, but wanted to familiarize myself with Map type. Suggestions welcome. Prolog code also included below for those interested.

Michael

===========

{-
From "Prolog By Example", Coelho, Cotta, Problem 42, pg. 63

Verbal statement:
Generate a list of serial numbers for the items of a given list,
the members of which are to be numbered in alphabetical order.

For example, the list [p,r,o,l,o,g] must generate [4,5,3,2,3,1]
-}

{-
Prelude> :l serialize
[1 of 1] Compiling Main             ( serialize.hs, interpreted )
*Main> serialize "prolog"
[4,5,3,2,3,1]
*Main>
-}

import Data.Char
import Data.List
import Data.Map (Map)
import qualified Data.Map as Map

{-
translate :: [Char] -> [(Char,Int)] -> [Int]
translate [] _ = []
translate (x:xs) m = (fromJust (lookup x m)) : (translate xs m )
-}

{-
serialize :: [Char] -> [Int]
serialize s = let c = nub \$ sort s
n = [1..(length c)]
in translate s (zip c n)
-}

serialize :: [Char] -> [Int]
serialize s = let c = nub \$ sort s
n = [1..(length c)]
m = Map.fromList \$ zip c n
in map (\c -> m Map.! c) s

============Prolog code============

serialize(L,R) :- pairlists(L,R,A),arrange(A,T),
numbered(T,1,N).
?  <- typo?
pairlists([X|L],[Y|R],[pair(X,Y)|A]) :- pairlist(L,R,A).
pairlists([],[],[]).

arrange([X|L],tree(T1,X,T2)) :- partition(L,X,L1,L2),
arrange(L1,T1),
arrange(L2,T2).
arrange([],_).

partition([X|L],X,L1,L2) :- partition(L,X,L1,L2).
partition([X|L],Y,[X|L1],L2) :- before(X,Y),
partition(L,Y,L1,L2).
partition([X|L],Y,L1,[X|L2]) :- before(Y,X),
partition(L,Y,L1,L2).
partition([],_,[],[]).

before(pair(X1,Y1),pair(X2,Y2)) :- X1<X2.

numbered(tree(T1,pair(X,N1),T2),N0,N) :- numbered(T1,N0,N1),
N2 is N1+1,
numbered(T2,N2,N).
numbered(void,N,N).

============Prolog examples========
Execution:

?- serialize([p,r,o,l,o,g]).
[4,5,3,2,3,1]
?- serialize ([i,n,t,.,a,r,t,i,f,i,c,i,a,l]).
[5,7,9,1,2,8,9,5,4,5,3,5,2,6]

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