Haskell Vector learnings

Vector.hs

data Vec = Vec [Int]
  deriving (Show, Eq)

instance Monoid Vec where
  mempty = (Vec mempty)
  mappend = vecAdd

vecAdd (Vec a) (Vec b) = Vec $ zipWith (+) a b
vecSubtract (Vec a) (Vec b) = Vec $ zipWith (-) a b

scalarMultiply :: Int -> Vec -> Vec
scalarMultiply s (Vec v) = Vec $ map (s*) v

vecFold :: Vec -> Int
vecFold (Vec v) = foldr (+) 0 v

dotProduct :: Vec -> Vec -> Int
dotProduct (Vec a) (Vec b) = foldr (+) 0 zipped
  where
    zipped = zipWith (*) a b

-- Produces a matrix as*bs instead of a zip
-- dotProduct' :: Vec -> Vec -> Int
-- dotProduct' (Vec as) (Vec bs) = sum [ a*b | a <- as, b <- bs] 

--using let instead of where
dotProduct' :: Vec -> Vec -> Int
dotProduct' (Vec a) (Vec b) = 
  let zipped = zipWith (*) a b
  in foldr (+) 0 zipped

vecSquare :: Int -> Vec -> Vec
vecSquare n v = foldr mappend v vs
  where
    vs = replicate (n -1) v

  
vecLength :: Floating a => Vec -> a
vecLength v = sqrt $ fromIntegral $ vecFold $ (vecSquare 2 v)

fromTuple :: (Int, Int, Int) -> Vec
fromTuple (a,b,c) = Vec [a,b,c]

crossProduct :: (Int, Int, Int) -> (Int, Int, Int) -> (Int, Int, Int)
crossProduct (a1, a2, a3) (b1, b2, b3) = (c1, c2, c3)
  where
    c1 = (a2*b3) - (a3*b2)
    c2 = (a3*b1) - (a1*b3)
    c3 = (a1*b2) - (a2*b1)

a = Vec [1,2,3]
b = Vec [1,5,7]
c = (1,2,3)
d = (1,5,7)
cIsOrthoganal = (fromTuple $ crossProduct c d) `dotProduct` (fromTuple c) == 0
dIsOrthoganal = (fromTuple $ crossProduct c d) `dotProduct` (fromTuple d) == 0

main = do
  putStrLn $ "Addition: " ++ (show $ vecAdd a b)
  putStrLn $ "Subtraction: " ++ (show $ vecSubtract a b)
  putStrLn $ "Scalar Multiply: " ++ (show $ scalarMultiply 3 a)
  putStrLn $ "Dot Product: " ++ (show $ dotProduct a b)
  putStrLn $ "Dot Product List comp: " ++ (show $ dotProduct' a b)
  putStrLn $ "Length: " ++ (show $ vecLength a)
  putStrLn $ "Cross Product: " ++ (show $ crossProduct c d)
  putStrLn $ "Cross Product is orthoganal: " ++ (show cIsOrthoganal) ++ " & " ++ (show dIsOrthoganal)