module Helper where

import           Control.Monad.State
import qualified Data.BitString                as Bit
import qualified Data.ByteString               as Byte

data Error = UndeclaredFunction String | DuplicateFunction String | InvalidIndex Int | FatalError String
instance Show Error where
  show (UndeclaredFunction err) = "ERROR: undeclared function " <> show err
  show (DuplicateFunction  err) = "ERROR: duplicate function " <> show err
  show (InvalidIndex       err) = "ERROR: invalid index " <> show err
  show (FatalError         err) = show err
type Failable = Either Error

data Expression = Bruijn Int | Variable String | Abstraction Expression | Application Expression Expression
  deriving (Ord, Eq)
data Instruction = Define String Expression [Instruction] | Evaluate Expression | Comment String | Import String String | Test Expression Expression
  deriving (Show)
instance Show Expression where
  show (Bruijn      x  ) = "\ESC[31m" <> show x <> "\ESC[0m"
  show (Variable    var) = "\ESC[35m" <> var <> "\ESC[0m"
  show (Abstraction exp) = "\ESC[36m[\ESC[0m" <> show exp <> "\ESC[36m]\ESC[0m"
  show (Application exp1 exp2) =
    "\ESC[33m(\ESC[0m" <> show exp1 <> " " <> show exp2 <> "\ESC[33m)\ESC[0m"

type EnvDef = (String, Expression)
type Environment = [EnvDef]
type Program = State Environment

---

listify :: [Expression] -> Expression
listify [] = Abstraction (Abstraction (Bruijn 0))
listify (fst : rst) =
  Abstraction (Application (Application (Bruijn 0) fst) (listify rst))

encodeByte :: Bit.BitString -> Expression
encodeByte bits = listify (map encodeBit (Bit.toList bits))
 where
  encodeBit False = Abstraction (Abstraction (Bruijn 0))
  encodeBit True  = Abstraction (Abstraction (Bruijn 1))

encodeBytes :: Byte.ByteString -> Expression
encodeBytes bytes =
  listify (map (encodeByte . Bit.from01List . (: [])) (Byte.unpack bytes))

encodeStdin :: IO Expression
encodeStdin = do
  bytes <- Byte.getContents
  pure $ encodeBytes bytes

---

likeTernary :: Expression -> Bool
likeTernary (Abstraction (Abstraction (Abstraction (Abstraction _)))) = True
likeTernary _ = False

-- Dec to Bal3 in Bruijn encoding: reversed application with 0=>0; 1=>1; T=>2; end=>3
-- e.g. 0=0=[[[[3]]]]; 2=1T=[[[[2 (0 3)]]]] -5=T11=[[[[0 (0 (2 3))]]]]
decimalToTernary :: Integer -> Expression
decimalToTernary n =
  Abstraction $ Abstraction $ Abstraction $ Abstraction $ gen n
 where
  gen 0 = Bruijn 3
  gen n = Application (Bruijn $ fromIntegral $ mod n 3) (gen $ div (n + 1) 3)

ternaryToDecimal :: Expression -> Integer
ternaryToDecimal exp = sum $ zipWith (*) (resolve exp) (iterate (* 3) 1)
 where
  multiplier (Bruijn 0) = 0
  multiplier (Bruijn 1) = 1
  multiplier (Bruijn 2) = (-1)
  resolve' (Application x@(Bruijn _) (Bruijn 3)) = [multiplier x]
  resolve' (Application fst@(Bruijn _) rst@(Application _ _)) =
    (multiplier fst) : (resolve' rst)
  resolve' _ = [0]
  resolve (Abstraction (Abstraction (Abstraction (Abstraction n)))) =
    resolve' n
  resolve _ = [0]