Day 12 part 1

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diff --git a/2020/12.hs b/2020/12.hs
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+module Main where
+
+import Data.List (foldl')
+
+import Input
+
+
+data V2 a = V2 a a deriving (Show)
+
+data M2 a = M2 a a a a deriving (Show)
+
+class LinMappable v where
+    vfmap :: (a -> b) -> v a -> v b
+    vzip :: (a -> b -> c) -> v a -> v b -> v c
+    vzero :: Num a => v a
+instance LinMappable V2 where
+    vfmap f (V2 a b) = V2 (f a) (f b)
+    vzip f (V2 a b) (V2 a' b') = V2 (f a a') (f b b')
+    vzero = V2 0 0
+instance LinMappable M2 where
+    vfmap f (M2 a b c d) = M2 (f a) (f b) (f c) (f d)
+    vzip f (M2 a b c d) (M2 a' b' c' d') = M2 (f a a') (f b b') (f c c') (f d d')
+    vzero = M2 0 0 0 0
+
+(!+!) :: (LinMappable v, Num a) => v a -> v a -> v a
+(!+!) = vzip (+)
+
+dot :: Num a => V2 a -> V2 a -> a
+dot (V2 a b) (V2 c d) = a * c + b * d
+
+(*$) :: (LinMappable v, Num a) => v a -> a -> v a
+v *$ s = vfmap (* s) v
+
+(*!) :: Num a => M2 a -> V2 a -> V2 a
+M2 a b c d *! v = V2 (V2 a b `dot` v) (V2 c d `dot` v)
+
+-- mathematical axes: X faces east, Y faces north
+-- Shift v: pos = pos + v
+-- Sail v m1 m2: direction' = m1 *! direction; pos = pos + v + m2 *! direction'
+data Instr = Sail (V2 Int) (M2 Int) (M2 Int)
+  deriving (Show)
+
+parseInstr :: String -> Instr
+parseInstr (c : ns) = case (c, read ns :: Int) of
+    ('N', n) -> Sail (V2 0 1 *$ n) idMat vzero
+    ('S', n) -> Sail (V2 0 (-1) *$ n) idMat vzero
+    ('E', n) -> Sail (V2 1 0 *$ n) idMat vzero
+    ('W', n) -> Sail (V2 (-1) 0 *$ n) idMat vzero
+    ('F', n) -> Sail vzero idMat (M2 1 0 0 1 *$ n)
+    ('R', 90) -> Sail vzero rotRightMat vzero
+    ('R', 180) -> Sail vzero mirrorMat vzero
+    ('R', 270) -> Sail vzero rotLeftMat vzero
+    ('L', 90) -> Sail vzero rotLeftMat vzero
+    ('L', 180) -> Sail vzero mirrorMat vzero
+    ('L', 270) -> Sail vzero rotRightMat vzero
+    _ -> error "Cannot parse instr"
+  where
+    idMat = M2 1 0 0 1
+    rotRightMat = M2 0 1 (-1) 0
+    rotLeftMat = rotRightMat *$ (-1)
+    mirrorMat = idMat *$ (-1)
+parseInstr _ = error "Cannot parse empty instr"
+
+data State = State { sPos :: V2 Int, sDir :: V2 Int }
+  deriving (Show)
+
+sail :: Instr -> State -> State
+sail (Sail offset dirm posm) (State pos dir) =
+    let dir' = dirm *! dir
+    in State (pos !+! offset !+! (posm *! dir')) dir'
+
+manhattan :: Num a => V2 a -> a
+manhattan (V2 a b) = abs a + abs b
+
+main :: IO ()
+main = do
+    input <- map parseInstr <$> getInput 12
+    print (manhattan . sPos $ foldl' (flip sail) (State (V2 0 0) (V2 1 0)) input)
diff --git a/2020/12.in b/2020/12.in
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