{-# LANGUAGE DeriveGeneric #-}
{-# LANGUAGE NamedFieldPuns #-}
module Infer.Treat where

import Data.Aeson (ToJSON, FromJSON, eitherDecode)
import Data.ByteString.Lazy.UTF8 (fromString)
import GHC.Generics (Generic)
import qualified Data.Set as S

data Rule = Rule {
  premises :: S.Set String,
  conclusion :: String
}
  deriving (Eq, Ord, Show, Generic)

instance ToJSON Rule
instance FromJSON Rule

run :: String -> [String] -> Either String [String]
run input pre = fmap f (eitherDecode $ fromString input)
  where f = S.toList . infer (S.fromList pre)

infer :: S.Set String -> [Rule] -> S.Set String
infer pre env =
  let (found, nenv) = find
  in if S.isSubsetOf found pre
     then pre
     else infer (S.union found pre) nenv
  where find = foldr mlook (S.empty, []) env
        mlook r@Rule{premises, conclusion} (f, e) =
          if S.isSubsetOf premises pre
          then (S.insert conclusion f, e)
          else (f, r:e)