{-# LANGUAGE BangPatterns #-}
module Check where

import Control.Monad (guard)
import Data.List ((!?))
import Debug.Trace (trace)
import Expr

type Context = [Expr]

-- λ S : * . λ P : ∏ x : S . * . ∏ x : S . P x
-- lambda S : * . lambda P : Pi x : S . * . lambda Q : Pi x : S . * . lambda H : (Pi x : S . Pi h : P x . Q x) . lambda G : (Pi x : S . P x) . lambda x : S . H x (G x)
-- lambda S : * . lambda P : (Pi x : S . *). lambda H : (Pi x : S . P x) . lambda x : S . H x
findType :: Context -> Expr -> Maybe Expr
findType g (Var k) = do
    t <- g !? fromInteger k
    kind <- findType g t
    guard $ isSort kind
    pure t
findType _ Star = Just Square
findType _ Square = Nothing
findType g (App m n) = do
    let !_ = trace ("app: " ++ show m ++ "\t" ++ show n) False
    Pi a b <- findType g m
    let !_ = trace ("Pi: " ++ show a ++ " . " ++ show b) False
    a' <- findType g n
    let !_ = trace ("a': " ++ show a' ++ "\n") False
    guard $ betaEquiv a a'
    pure $ subst n b
findType g (Abs t v) = do
    argType <- findType g t
    guard $ isSort argType
    bodyType <- findType (incIndices t : map incIndices g) v
    resType <- findType g (Pi t bodyType)
    guard $ isSort resType
    pure $ Pi t bodyType
findType g (Pi t v) = do
    let !_ = trace ("Pi rule: " ++ show t ++ "\t" ++ show v ++ "\n") False
    argType <- findType g t
    guard $ isSort argType
    bodyType <- findType (incIndices t : map incIndices g) v
    guard $ isSort bodyType
    pure bodyType