```-- --------------------------------------------------------------------------
--  \$Revision: 262 \$ \$Date: 2007-04-12 12:19:50 +0200 (Thu, 12 Apr 2007) \$
-- --------------------------------------------------------------------------

-- |
--
-- Module      :  PureFP.OrdSet
-- Copyright   :  Peter Ljunglof 2002
-- License     :  GPL
--
-- Maintainer  :  otakar.smrz mff.cuni.cz
-- Stability   :  provisional
-- Portability :  portable
--
-- Chapter 1 and Appendix A of /Pure Functional Parsing &#150; an advanced
-- tutorial/ by Peter Ljungl&#246;f
--
-- <http://www.ling.gu.se/~peb/pubs/p02-lic-thesis.pdf>

--------------------------------------------------
-- The class of ordered sets
-- as described in section 2.2.1

-- and an example implementation,
-- derived from the implementation in appendix A.1

module PureFP.OrdSet (OrdSet(..), Set) where

import Data.List (intersperse)

--------------------------------------------------
-- the class of ordered sets

class OrdSet m where
emptySet  :: Ord a => m a
unitSet   :: Ord a => a -> m a
isEmpty   :: Ord a => m a -> Bool
elemSet   :: Ord a => a -> m a -> Bool
(<++>)    :: Ord a => m a -> m a -> m a
(<\\>)    :: Ord a => m a -> m a -> m a
plusMinus :: Ord a => m a -> m a -> (m a, m a)
union     :: Ord a => [m a] -> m a
makeSet   :: Ord a => [a] -> m a
elems     :: Ord a => m a -> [a]
ordSet    :: Ord a => [a] -> m a
limit     :: Ord a => (a -> m a) -> m a -> m a

xs <++> ys      = fst (plusMinus xs ys)
xs <\\> ys      = snd (plusMinus xs ys)
plusMinus xs ys = (xs <++> ys, xs <\\> ys)

union []   = emptySet
union [xs] = xs
union xyss = union xss <++> union yss
where (xss, yss)       = split xyss
split (x:y:xyss) = let (xs, ys) = split xyss in (x:xs, y:ys)
split xs         = (xs, [])

makeSet xs = union (map unitSet xs)

limit more start = limit' (start, start)
where limit' (old, new)
| isEmpty new' = old
| otherwise    = limit' (plusMinus new' old)
where new'       = union (map more (elems new))

--------------------------------------------------
-- sets as ordered lists,
-- paired with a binary tree

data Set a = Set [a] (TreeSet a)

instance Eq a => Eq (Set a) where
Set xs _ == Set ys _ = xs == ys

instance Ord a => Ord (Set a) where
compare (Set xs _) (Set ys _) = compare xs ys

instance Show a => Show (Set a) where
show (Set xs _) = "{" ++ concat (intersperse "," (map show xs)) ++ "}"

instance OrdSet Set where
emptySet  = Set []  (makeTree [])
unitSet a = Set [a] (makeTree [a])

isEmpty   (Set xs _) = null xs
elemSet a (Set _ xt) = elemTree a xt

plusMinus (Set xs _) (Set ys _) = (Set ps (makeTree ps), Set ms (makeTree ms))
where (ps, ms) = plm xs ys
plm [] ys = (ys, [])
plm xs [] = (xs, xs)
plm xs@(x:xs') ys@(y:ys') = case compare x y of
LT -> let (ps, ms) = plm xs' ys  in (x:ps, x:ms)
GT -> let (ps, ms) = plm xs  ys' in (y:ps,   ms)
EQ -> let (ps, ms) = plm xs' ys' in (x:ps,   ms)

elems (Set xs _) = xs
ordSet xs        = Set xs (makeTree xs)

--------------------------------------------------
-- binary search trees
-- for logarithmic lookup time

data TreeSet a = Nil | Node (TreeSet a) a (TreeSet a)

makeTree xs = tree
where (tree,[])       = sl2bst (length xs) xs
sl2bst 0 xs     = (Nil, xs)
sl2bst 1 (a:xs) = (Node Nil a Nil, xs)
sl2bst n xs     = (Node ltree a rtree, zs)
where llen    = (n-1) `div` 2
rlen    = n - 1 - llen
(ltree, a:ys) = sl2bst llen xs
(rtree, zs)   = sl2bst rlen ys

elemTree a Nil = False
elemTree a (Node ltree x rtree)
= case compare a x of
LT -> elemTree a ltree
GT -> elemTree a rtree
EQ -> True

```