Q205.hs

module Main where

import qualified Data.Set as S

-- hasMorph p m and hasMorph p n
isValid :: (a -> a -> Bool) -> (a -> a -> a) -> a -> a -> Bool
isValid f op x y = f p x && f p y
  where p = x `op` y


-- (a)
divides :: Int -> Int -> Bool
divides m n = n `mod` m ==  0
prodA = gcd 42 27

-- (b)
s1 = S.fromList "abc"
s2 = S.fromList "bdc"

prodB = S.intersection s1 s2

-- (c)
prodC = True && False
implies True True = True
implies True False = False
implies False True = True
implies False False = True

main = do
  putStr "The product of 42 and 27 is "
  print prodA 
  putStr "Is there a morphism from (a,b) -> a and (a,b) -> b? "
  print $ isValid divides gcd 42 27

  putStr "The product of abc and bcd is "
  print prodB
  putStr "Is there a morphism from (a,b) -> a and (a,b) -> b? "
  print $ isValid S.isSubsetOf S.intersection s1 s2

  putStr "The product of True and False is "
  print prodC
  putStr "Is there a morphism from (a,b) -> a and (a,b) -> b? "
  print $ isValid implies (&&) True False