-- List continued...
-- A small Introduction to Lists and List Comprehensions

-- Lists 
myLottoNumbers :: [Int] -- a list of Int
myLottoNumbers = [18,24,66,91,97]

winningLottos :: [[Int]] -- a list of lists of Int
winningLottos = [myLottoNumbers,[18,22,66,91,99],[20,30,40]]

validNumbers :: [Int]
validNumbers = [1..99] -- a built-in function to generate a list

fac :: Integer -> Integer
fac n = product [1..n] -- factorial function

-- Example standard functions
-- (++), reverse, length, sum, product, maximum, ...
-- Lots more in module Data.List 

-- The truth about String (saw that in the Kahoot)

----------------------------------------------
-- List Comprehensions

power2table :: Integer -> [Integer]
-- power2table n gives a list of powers of 2 from 0 up to n
-- power2table 7 == [1,2,4,8,16,32,64,128]
power2table n = -- undefined
   [ 2^x | x <- [0..n]]

sumsquares n = sum [x*x | x <- [1..n]]

-- Multiple Generators
example2generators = [x+y | y <- [100,200], x <- [1,2,3]  ]

-- Guards
powersUpto :: Integer -> [Integer]
-- powersUpto n  gives all powers of 2 no larger than n
powersUpto n = [p | p <- power2table n, p <= n]

--- Prime numbers
-- A prime number n has factors 1 and n and no others.

-- 1,2,5 and 10 are factors of 10 (so 10 is not a prime).

-- isFactor of n m gives True if n is a factor of m
isFactorOf :: Integer -> Integer -> Bool

n `isFactorOf` m = m `mod` n == 0
  -- using a function as an operator
  -- can be good for readability

primes :: Integer -> [Integer]
primes n = [ c |  c <- [2..n], factors c == [1,c]]
   where -- this is a local definition
    factors m = [k | k <- [1..m], k `isFactorOf` m ]