{-# LANGUAGE TypeFamilies #-}

class ProjResult a where
  projection :: Int -> a
  constant :: Int -> a

instance ProjResult Int where
  projection _ = error "index too large"
  constant x = x

instance (ProjResult a, arg ~ Int) => ProjResult (arg -> a) where
  projection 0 x = constant x
  projection n _ = projection (n-1)
  constant j _ = constant j

p :: Int -> Int -> Int -> Int -> Int
p = projection

main = do
  print $ p 2 1 2 3
  print (projection 2 1 2 3 :: Int) -- 型注釈はこれだけでいい