-- Control structures as higher-order functions:

-- while loop
while :: (a -> Bool) -> (a -> a) -> a -> a
while p f x | p x       = while p f (f x)
            | otherwise = x

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-- Data structures implemented by higher-order functions:

-- Type of arrays:
type Array a = Int -> a

-- The empty array does not contain an element.
emptyArray :: Array a
emptyArray = \i -> error "No element with this index"

-- Add or set an element at some index position
putIndex :: Array a -> Int -> a -> Array a
putIndex a i x = a'
 where a' j | i==j      = x
            | otherwise = a j

-- Get an element under an index.
getIndex :: Array a -> Int -> a
getIndex a i = a i

example1 =  getIndex (putIndex (putIndex emptyArray 2 "World") 1 "Hello") 1