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Haskell Infinite Lists

  • Lazy Lists (Finite)
    • 
            [1 .. 10]    -- Python: range(1, 11)
            [2, 4 .. 10] -- Python: range(2, 11, 2)
  • Lazy Lists (Infinite)
    • 
            [1 ..]       -- [1, 2, 3, 4, ...]
            [1, 1 ..]    -- [1, 1, 1, 1, ...]
            [2, 4 ..]    -- [2, 4, 6, 8, ...]
            [4, 8 ..]    -- [4, 8, 12, 16, ...]
  • take - process only part of a list
    • 
            take :: Int -> [a] -> [a]
            take _ [] = []
            take 0 _ = []
            take n (h:t) = h : take (n - 1) t
            -- the below gets [3, 6, 9, 12, 15]
            take 5 [3, 6, ..]

Haskell Infinite Lists

  • Infinite Lists by Recursion
    • 
            plus2 :: Int -> [Int]
            plus2 n = n : plus (n + 2)
            
            odds :: [Int]
            odds = plus2 1
            
            evens :: [Int]
            evens = plus2 2
  • Infinite Lists by List Comprehensions
    • 
            integers = [x | x <- [1 ..]]
            odds = [x | x <- [1 ..], mod x 2 == 1]
            squares = [x^2 | x <- [1 ..]]

Haskell Infinite Lists

  • Infinite Lists of Fibonacci Sequence
    • 
            nextfib :: Int -> Int -> [Int]
            nextfib x y = (x + y) : nextfib y (x + y)
            fibs :: [Int]
            fibs = [1, 1] ++ nextfib 1 1
  • Infinite Lists by Prime Numbers
    • 
            sieve :: [Int] -> [Int]
            sieve (x:xs) = x : 
              seive [y | y <- xs, mod y x /= 0]
            primes :: [Int]
            primes = sieve [2 ..]