-- !!

a = [1,2,3] !! 1

-- Lazy evaluation

fact1a :: Integer -> Integer -> Integer
fact1a 0 f = f
fact1a n f = fact1a (n-1) (n*f)

fact1b :: Integer -> Integer -> Integer
fact1b 0 f = f
fact1b n f = fact1b (n-1) $! (n*f)

-- Infinite lists

zeros = 0:zeros

powersOf2 x = x:powersOf2 (x*2)

zeros1 = repeat 0

l1 = cycle [1,2,3]

geomSeq = iterate (*2) 1

-- Fibbonacy

fibSeq :: Integer -> Integer -> [Integer]
fibSeq m n = m : (fibSeq n (m+n))
 
fib = fibSeq 1 1

-- Prime numbers

noDivisors l x = all (\n -> x `mod` n /= 0) l

isPrime x = noDivisors [2..x-1] x

primes = filter isPrime [2..]

-- Corecursion

fibC = 1:1:zipWith (+) fibC (tail fibC)

noDivisorsC l x =  all (\n -> x `mod` n /= 0) (takeWhile (<= x `div` 2) l)

primesC = 2:filter (noDivisorsC primesC) [3..]

eratosthenes (x:xs) = x:eratosthenes (filter ((/= 0).(`mod` x)) xs)

primesC2 = eratosthenes [2..]