modlist.hs

{-# LANGUAGE KindSignatures #-}
{-# LANGUAGE PolyKinds #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE DataKinds #-}

import GHC.TypeLits

import Data.Proxy

newtype ModList (mod :: Nat) a = ModList { unModList :: [a] }
    deriving Show

instance (KnownNat mod, Integral a, Num a) => Num (ModList mod a) where
    fromInteger = ModList . repeat . fromInteger . (`mod` natVal (Proxy :: Proxy mod))
    ModList as + ModList bs =
        ModList $ zipWith (\x y -> (x + y) `mod` m) as bs
      where
        m = fromInteger (natVal (Proxy :: Proxy mod))
    ModList as * ModList bs =
        error "WHat does multiplication mean here?"
    negate (ModList as) =
        error "What does negation mean?"
    abs (ModList as) = 
        error "Figure this out, too"
    signum (ModList as) =
        error "I guess this is always positive?"

fromList :: forall a mod. (Integral a, Num a, KnownNat mod) => [a] -> ModList mod a
fromList = ModList . fmap (`mod` fromInteger (natVal (Proxy :: Proxy mod)))

fromListP :: forall a mod. (Integral a, Num a, KnownNat mod) => Proxy mod -> [a] -> ModList mod a
fromListP _ = ModList . fmap (`mod` fromInteger (natVal (Proxy :: Proxy mod)))

{-
λ> :set -XDataKinds
λ> fromList [1..5] :: ModList 3 Integer
ModList {unModList = [1,2,0,1,2]}
λ> let threes = 3 :: ModList 3 Integer
λ> threes + fromList [1..7]
ModList {unModList = [1,2,0,1,2,0,1]}
λ> threes + fromList [2..100]
ModList {unModList = [2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,
0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}
λ>
-}