-- | Some small examples to introduce Haskell.
-- Functional Programming course 2016.
-- Thomas Hallgren

{-
This started out as a skeleton, the function definitions were filled in
during the first lecture.
-}

import Test.QuickCheck
       
-- * Currency conversion

exchangeRate = 9.8963  -- SEK / EUR

toEUR :: Double -> Double
toEUR sek = sek / exchangeRate

toSEK :: Double -> Double
toSEK eur = eur * exchangeRate



prop_exchange sek = toSEK (toEUR sek) ~== sek

x ~== y = abs (x-y) < 2e-10 

-- automated random testing with QuickCheck



-- * Definition by cases

{-
absolute x | x<0 = -x
absolute x | x>=0 = x
-}

absolute2 x | x<0 = -x
            | x>=0 = x

absolute1 x = if x<0 then -x else x



-- * Definition by recursion
-- The power function n^k

power :: Integer -> Integer -> Integer
power n 0       = 1
power n k | k>0 = power n (k-1) * n
--power n k | k<0 = 1 / power n (-k)

prop_power n k = k >= 0 ==> power n k == n^k


-- intersecting lines

intersect 0       = 0
intersect k | k>0 = intersect (k-1) + k - 1


-- * Tuples

examplePair :: (Bool, Double)
examplePair = (True, 3.14)

exampleTriple :: (Bool, Int, String)
exampleTriple = (False, 42, "Answer")

exampleFunction :: (Bool, Int, String) -> Int
exampleFunction (b,n,s) = if b then n else length s

-- * List

snacks = "Spam"

dinner = [snacks, "Fish", "Chips", snacks, snacks, "Pudding"]

summary :: [String] -> String
summary [] = "Nothing"
summary [x,y] = x ++ " and " ++ y
summary (x:y:xs) = x ++ " and something else, finally " ++ last xs

-- | Computing the length of a list
len [] = 0
len (x:xs) = 1 + len xs

last' [] = error "last of empty list"
last' [x] = x
last' (x:xs) = last' xs

-- * List comprehensions

ex1 = [ x | x<-[1..20], even x]

doubles xs = [ 2*x | x<-xs ]

ex2 = [[x,y] | x<-"ABC", y<-"12"]

ex3 = [[[x,y] | y<-"12"] | x<-"ABC"]


pythag n = [(a,b,c) | a <- [1..n], b<-[a..n], c<-[b..n], a^2 + b^2 == c^2]