-- $Id: Aufgabe9.hs,v 1.2 2004/01/14 06:33:03 fp010 Exp $
module Aufgabe9(listFilt,fOne,fTwo,fThree,
		extractSet,
		union,inters,diff,
		isSet,isEqual,isElem)
where
import Prelude
import qualified List
import qualified Char
----------------------------------------------------------------------------
listFilt :: (a->Bool) -> [[a]] -> [[a]]
listFilt = map . filter

fOne :: String -> Bool
fOne (c:_) | Char.isUpper c = False
fOne s = even $ length s

fTwo :: Integer -> Bool
fTwo n = isFib n 0 1
    where isFib n f f' | n > f     = isFib n f' (f+f')
                       | otherwise = n == f

{- caching variant -- might run into GC-issues

fTwo = isFib allFibs
  where allFibs = 0 : 1 : [ x+y | (x,y) <- (zip allFibs (tail allFibs)) ]
	isFib (f:fs) n | n < f = False
		       | n ==f = True
		       | n > f = isFib fs n
-}

fThree :: String -> Bool
fThree = isPal
  where isPal s = reverse s == s

----------------------------------------------------------------------------
extractSet :: Eq a => [a] -> [a]
extractSet = List.nub

--------------------------------
union,diff,inters :: Eq a => [a] -> [a] -> [a]
union = List.union
diff = (List.\\)
inters = List.intersect

--------------------------------
isSet :: Eq a => [a] -> Bool
isSet s = s == extractSet s

isEqual :: Eq a => [a] -> [a] -> Bool
isEqual a b = null (a `diff` b) && null (b `diff` a)

isElem :: Eq a => a -> [a] -> Bool
isElem = elem

----------------------------------------------------------------------------
-- $Log: Aufgabe9.hs,v $
-- Revision 1.2  2004/01/14 06:33:03  fp010
-- fixed [100..(-100)]; added some testcases with [String];
--
-- Revision 1.1  2004/01/07 12:59:19  fp010
-- first draft
--