{-# LANGUAGE DerivingVia, StandaloneDeriving #-}

  Comparison(..),
  Debatable(..),
  Front,
  singleton,
  getFront

import Data.Foldable
import Data.List (transpose)
import Data.Ord (Down(..))

class Debatable a where
  weigh :: a -> a -> Comparison
newtype OrdDebatable a = OrdDebatable a deriving (Ord, Eq)
instance Ord a => Debatable (OrdDebatable a) where
  weigh (OrdDebatable a) (OrdDebatable b) = case compare a b of
    LT -> Dominates
    GT -> Dominated
    EQ -> WeakTie
deriving via OrdDebatable Int instance Debatable Int
deriving via OrdDebatable Integer instance Debatable Integer
deriving via OrdDebatable Double instance Debatable Double
deriving via OrdDebatable Float instance Debatable Float
instance Debatable a => Debatable (Down a) where
  weigh (Down a) (Down b) = case weigh a b of
    Dominates -> Dominated
    Dominated -> Dominates
    r -> r
instance (Debatable a, Debatable b) => Debatable (a,b) where
  weigh ~(a1,a2) ~(b1,b2) = weigh a1 b1 <> weigh a2 b2
newtype Front a = Front [a] deriving (Show)
singleton :: a -> Front a
singleton a = Front [a]
instance Debatable a => Semigroup (Front a) where
  Front a <> Front b = let
    m = map (flip map b . weigh) a
    m' = transpose m
    s = map (not . any (== Dominated)) m
    s' = map (not . any (== Dominates)) m'
    in Front $ map fst $ filter snd $ zip a s ++ zip b s'
instance Debatable a => Monoid (Front a) where
  mempty = Front []
getFront :: Front a -> [a]
getFront (Front l) = l