hs / lab3 / 6s

module Main where
import Data.List


pminone [] = []
pminone (x:xs) = ((snd x), (fst x)) : pminone xs

composition fs gs = map (mapping gs) fs where
mapping :: Eq a => [(a,a)]->(a,a)->(a,a)
mapping [] g = g
mapping (p:ps) g | (fst p) == (snd g) = ((fst g), (snd p))
| True = mapping ps g


proect1 [] = []
proect1 (p:ps) = nub ((fst p) : (proect1 ps))

proect2 [] = []
proect2 (p:ps) = nub ((snd p) : (proect1 ps))


decart _ [] = []
decart xs (y:ys) = (foo xs y) ++ (decart xs ys) where
foo [] _ = []
foo (x:xs) y = (x, y) : (foo xs y)

main = do
print $ "P"
print $ [(1,2),(2,3),(3,1),(2,2),(3,2)]
print $ "P^-1"
print $ pminone [(1,2),(2,3),(3,1),(2,2),(3,2)]
print $ "P.P"
print $ composition [(1,2),(2,3),(3,1),(2,2),(3,2)] [(1,2),(2,3),(3,1),(2,2),(3,2)]
print $ "(P^-1).P"
print $ composition (pminone [(1,2),(2,3),(3,1),(2,2),(3,2)]) [(1,2),(2,3),(3,1),(2,2),(3,2)]
print $ "pr1((P^-1).P) x pr2(P^-1).P"
print $ decart (proect1 (composition (pminone [(1,2),(2,3),(3,1),(2,2),(3,2)]) [(1,2),(2,3),(3,1),(2,2),(3,2)])) (proect1 (composition (pminone [(1,2),(2,3),(3,1),(2,2),(3,2)]) [(1,2),(2,3),(3,1),(2,2),(3,2)]))