module Main where

import Data.List (sort)
import UsingQuickCheck
import Test.QuickCheck

prop_half :: (Eq a, Fractional a) => a -> Bool
prop_half x = (halfIdentity x) == x

associativeGen :: (Integer -> Integer -> Integer -> Bool) -> Gen Bool
associativeGen f = do
    x <- (arbitrary :: Gen Integer)
    y <- (arbitrary :: Gen Integer)
    z <- (arbitrary :: Gen Integer)
    elements [f x y z]

commutativeGen :: (Integer -> Integer -> Bool) -> Gen Bool
commutativeGen f = do
    x <- (arbitrary :: Gen Integer)
    y <- (arbitrary :: Gen Integer)
    elements [f x y]

assocNotNegGen :: (Int -> Int -> Int -> Bool) -> Gen Bool
assocNotNegGen f = do
    x <- choose (1 :: Int, 100)
    y <- choose (1 :: Int, 100)
    z <- choose (1 :: Int, 100)
    elements [f x y z]

commutNotNegGen :: (Int -> Int -> Bool) -> Gen Bool
commutNotNegGen f = do
    x <- choose (1 :: Int, 100)
    y <- choose (1 :: Int, 100)
    elements [f x y]
    

prop_quotRem :: Property
prop_quotRem =
    forAll (prop_quotRem') (\(x ,y) -> (quot x y) * y + (rem x y) == x)
    where prop_quotRem' = do
          x <- choose (1 :: Int, 10000)
          y <- choose (1 :: Int, 10000)
          return (x, y)

prop_divMod :: Property
prop_divMod =
    forAll (prop_divMod') (\(x ,y) -> (div x y) * y + (mod x y) == x)
    where prop_divMod' = do
          x <- choose (1 :: Int, 10000)
          y <- choose (1 :: Int, 10000)
          return (x, y)

prop_reverse :: Property
prop_reverse =
    forAll prop_reverse' (\xs -> (reverse . reverse) xs == id xs)
    where prop_reverse' = do
          x <- (arbitrary :: Gen [Integer])
          return x

prop_dollar :: Property
prop_dollar =
    forAll prop_dollar' (\x -> x)
    where prop_dollar' = do
          x <- (arbitrary :: Gen Integer)
          return ((id $ x) == (id x))

prop_point :: Property
prop_point =
    forAll prop_point' (\x -> x)
    where prop_point' = do
          x <- (arbitrary :: Gen Integer)
          let pointFunc = negate . id
          let appliedFunc = \y -> negate (id y)
          return (pointFunc x == appliedFunc x)

prop_foldr1 :: Property
prop_foldr1 =
    forAll prop_foldr1' (\x -> x)
    where prop_foldr1' = do
          x <- (arbitrary :: Gen [Integer])
          y <- (arbitrary :: Gen [Integer])
          return ((foldr (:) x y) == (x ++ y))

prop_foldr2 :: Property
prop_foldr2 =
    forAll prop_foldr2' (\x -> x)
    where prop_foldr2' = do
          x <- (arbitrary :: Gen [[Integer]])
          return ((foldr (++) [] x) == (concat x))

prop_length :: Property
prop_length =
    forAll prop_length' (\x -> x)
    where prop_length' = do
          n <- (arbitrary :: Gen Int)
          xs <- (arbitrary :: Gen [Integer])
          return ((length (take n xs)) == n)

prop_readShow :: Property
prop_readShow =
    forAll prop_readShow' (\x -> x)
    where prop_readShow' = do
          x <- (arbitrary :: Gen Integer)
          return ((read (show x)) == x)

main :: IO ()
main = do
    quickCheck (prop_half :: Double -> Bool)
    quickCheck $ (listOrdered :: [Int] -> Bool) . sort
    
    quickCheck $ associativeGen plusAssociative
    quickCheck $ commutativeGen plusCommutative
    quickCheck $ associativeGen mulAssociative
    quickCheck $ commutativeGen mulCommutative

    quickCheck prop_quotRem
    quickCheck prop_divMod

    quickCheck $ assocNotNegGen (\x y z -> x ^ (y ^ z) == (x ^ y) ^ z)
    quickCheck $ commutNotNegGen (\x y -> x ^ y == y ^ x)

    quickCheck prop_reverse
    quickCheck prop_dollar
    quickCheck prop_point
    quickCheck prop_foldr1
    quickCheck prop_foldr2
    quickCheck prop_length
    quickCheck prop_readShow