-- Name: Zhang Xiaomenghan
-- Exercise 2.1, 2.2, 2.3

-- Exercise 2.1
-- sumf (sumf square) [[1,2],[3,4]]
-- sumf square [1,2] + sumf (sumf square) [[3,4]]
-- square 1 + sumf square [2] + sumf (sumf square) [[3,4]]
-- 1 + sumf square [2] + sumf (sumf square) [[3,4]]
-- 1 + square 2 + sumf square [] + sumf (sumf square) [[3,4]]
-- 1 + 4 + sumf square [] + sumf (sumf square) [[3,4]]
-- 1 + 4 + 0 + sumf (sumf square) [[3,4]]
-- 1 + 4 + 0 + sumf square [3,4] + sumf (sumf square) []
-- 1 + 4 + 0 + square 3 + sumf square [4] + sumf (sumf square) []
-- 1 + 4 + 0 + 9 + sumf square [4] + sumf (sumf square) []
-- 1 + 4 + 0 + 9 + square 4 + sumf square [] + sumf (sumf square) []
-- 1 + 4 + 0 + 9 + 16 + sumf square [] + sumf (sumf square) []
-- 1 + 4 + 0 + 9 + 16 + 0 + sumf (sumf square) []
-- 1 + 4 + 0 + 9 + 16 + 0 + 0
-- 30

-- Exercise 2.2
module Product where
import Prelude hiding (product)

square :: Num n => n -> n
square x = x ^ 2

-- Implementation of product function
product :: Num a => [a] -> a
product [] = 1
product (x:xs) = x * product xs

-- Determining the product of the squares of the first numbers 1 through 10.
answer :: Num a => a
answer = product $ map square [1,2,3,4,5,6,7,8,9,10]

-- END OF CODE

-- GHCI run for answer
-- *Product> answer
-- 13168189440000

-- SAMPLE GHCI RUNS
-- *Product> product [12,4,5]
-- 240
-- *Product> product [1,1,1,5]
-- 5

-- Exercise 2.3

module Results where

divisibleBy :: Integer -> Integer -> Bool
divisibleBy a b
    | b > a = divisibleBy a (b - a)
    | b == a = True
    | otherwise = False

allp :: [a -> Bool] -> a -> Bool
allp [] a = True
allp (x:xs) a
    | null xs = x a
    | x a = allp xs a
    | otherwise = False

filterAll :: [a -> Bool] -> [a] -> [a]
filterAll = filter . allp

result :: Integer
result = sum
    . take 100
    . filter (divisibleBy 2)
    . filter (divisibleBy 3)
    . filter (not . divisibleBy 4)
    . filter (not . divisibleBy 9)
    $ [0..]

result2 :: Integer
result2 = sum
    . take 100
    . filter (allp [ divisibleBy 2
                    , divisibleBy 3
                    , not . divisibleBy 4
                    , not . divisibleBy 9
                    ])
    $ [0..]

result3 :: Integer
result3 = sum
    . take 100
    . filterAll [ divisibleBy 2
                , divisibleBy 3
                , not . divisibleBy 4
                , not . divisibleBy 9
                ]
    $ [0..]

-- END OF CODE

-- SAMPLE GHCI RUNS
-- *Results> result
-- 90000
-- *Results> result2
-- 90000
-- *Results> result3
-- 90000