{-# LANGUAGE TupleSections #-}

module Eval where

import Control.Monad.Except (MonadError (..))
import Control.Monad.Reader
import qualified Data.Map as M
import Data.Text (Text)
import Errors
import Expr

type Env = M.Map Text Expr

-- substitute s for k *AND* decrement indices; only use after reducing a redex.
subst :: Integer -> Expr -> Expr -> Expr
subst k s (Var n x)
    | k == n = s
    | n > k = Var (n - 1) x
    | otherwise = Var n x
subst _ _ (Free s) = Free s
subst _ _ Star = Star
subst _ _ Square = Square
subst k s (App m n) = App (subst k s m) (subst k s n)
subst k s (Abs x m n) = Abs x (subst k s m) (subst (k + 1) (incIndices s) n)
subst k s (Pi x m n) = Pi x (subst k s m) (subst (k + 1) (incIndices s) n)

envLookup :: Text -> ReaderT Env Result Expr
envLookup n = asks (M.lookup n) >>= maybe (throwError $ UnboundVariable n) pure

-- reduce until β reducts are impossible in head position
whnf :: Expr -> ReaderT Env Result Expr
whnf (App (Abs _ _ v) n) = whnf $ subst 0 n v
whnf (App m n) = do
    m' <- whnf m
    if m == m'
        then pure $ App m n
        else whnf $ App m' n
whnf (Free n) = envLookup n
whnf e = pure e

betaEquiv :: Expr -> Expr -> ReaderT Env Result Bool
betaEquiv e1 e2
    | e1 == e2 = pure True
    | otherwise = do
        e1' <- whnf e1
        e2' <- whnf e2
        case (e1', e2') of
            (Var k1 _, Var k2 _) -> pure $ k1 == k2
            (Free n, Free m) -> pure $ n == m
            (Free n, e) -> envLookup n >>= betaEquiv e
            (e, Free n) -> envLookup n >>= betaEquiv e
            (Star, Star) -> pure True
            (Abs _ t1 v1, Abs _ t2 v2) -> (&&) <$> betaEquiv t1 t2 <*> betaEquiv v1 v2 -- i want idiom brackets
            (Pi _ t1 v1, Pi _ t2 v2) -> (&&) <$> betaEquiv t1 t2 <*> betaEquiv v1 v2
            _ -> pure False -- remaining cases impossible or false

checkBeta :: Env -> Expr -> Expr -> Result Bool
checkBeta env e1 e2 = runReaderT (betaEquiv e1 e2) env

isSortPure :: Expr -> Bool
isSortPure Star = True
isSortPure Square = True
isSortPure _ = False

isSort :: Expr -> ReaderT Env Result (Bool, Expr)
isSort s = (,s) . isSortPure <$> whnf s