{-
   Title: Examples from the first lecture
   Author: Robin Cockett
   Date: 14 Jan 2003

   Notes: some of these functions are in the standard prelude can 
          you identify them?
-}

--  Appending a pair of lists
appendpair:: ([a],[a]) -> [a]
appendpair ([],y) = y
appendpair ((x:xs),y) = x:(appendpair (xs,y))


--  Appending two lists the curried form
append:: [a] -> [a] -> [a]
append [] y = y
append (x:xs) y = x:(append xs y)

{- 
     NOTE: append is polymorphic this mean we can append lists of anything 
     with this function.  Try out the following:

     append [1,2,3] [4,5,6]
     append ["abc","def"] ["hij,"klm","nop"]
     append [[1,2],[3,4,5]],[[6,7],[8],[9,10],[11]]

-}

-- Reversing a list the naive way
nrev:: [a] -> [a]
nrev [] = []
nrev (x:xs) = append (nrev xs) [x]


-- Reversing a list the fast way
rev:: [a] -> [a]
rev xs = rev1 xs [] 
  where
  rev1 [] ys = ys
  rev1 (x:xs) ys = rev1 xs (x:ys)


-- Summing a list of integers (note the Haskell type Integer
-- has arbitary precision
sumlist:: [Integer] -> Integer
sumlist [] = 0
sumlist (x:xs) = x + (sumlist xs)


-- Mapping a function over a list
maplist:: (a -> b) -> [a] -> [b]
maplist f [] = []
maplist f (x:xs) = (f x):(maplist f xs)


-- Filtering those elements not satisfying a predicate from a list
filterlist p [] = []
filterlist p (x:xs) = if p x then x:(filterlist p xs)
                             else (filterlist p xs)