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Zij gegeven:
init :: [a] -> [a]
init [x] = [] (1)
init [x:xs] = [x:init xs] (2)
take :: Int [a] -> [a]
take 0 xs = [] (3)
take n [] = [] (4)
take n [x:xs] = [x : take (n-1) xs] (5)
length :: [a] -> Int
length [] = 0 (6)
length [x:xs] = 1 + length xs (7)
(f o g) x = f (g x) (8)
Bewijs de volgende stelling voor alle eindige, niet-lege lijsten xs:
init xs = take (length xs - 1) xs
Je mag aannemen dat het Int-bereik onbeperkt is.
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