amelia
/
cubical


{-# LANGUAGE BlockArguments #-}

{-# LANGUAGE LambdaCase #-}

{-# LANGUAGE DeriveAnyClass #-}

{-# LANGUAGE ScopedTypeVariables #-}

{-# LANGUAGE ViewPatterns #-}

{-# LANGUAGE TupleSections #-}

module Elab.Eval where


import Control.Monad.Reader

import Control.Exception


import qualified Data.Map.Strict as Map

import qualified Data.Sequence as Seq

import qualified Data.Set as Set

import qualified Data.Text as T

import Data.Map.Strict (Map)

import Data.Sequence (Seq)

import Data.List (sortOn)

import Data.Traversable

import Data.Set (Set)

import Data.Typeable

import Data.Foldable

import Data.IORef

import Data.Maybe


import {-# SOURCE #-} Elab.Eval.Formula

import Elab.Monad


import GHC.Stack


import Presyntax.Presyntax (Plicity(..))


import Syntax.Pretty

import Syntax


import System.IO.Unsafe ( unsafePerformIO )


import {-# SOURCE #-} Elab.WiredIn

import Debug (traceM, traceDocM)

import Prettyprinter (pretty, (<+>))


eval :: HasCallStack => Term -> ElabM Value

eval t = asks (flip eval' t)


zonkIO :: Value -> IO Value

zonkIO (VNe hd sp) = do

 sp' <- traverse zonkSp sp

 case hd of

 HMeta (mvCell -> cell) -> do

 solved <- liftIO $ readIORef cell

 case solved of

 Just vl -> zonkIO $ foldl applProj vl sp'

 Nothing -> pure $ VNe hd sp'

 hd -> pure $ VNe hd sp'


zonkIO (GluedVl h sp vl) = GluedVl h <$> traverse zonkSp sp <*> zonkIO vl


zonkIO (VLam p (Closure s k)) = pure $ VLam p (Closure s (zonk . k))

zonkIO (VPi p d (Closure s k)) = VPi p <$> zonkIO d <*> pure (Closure s (zonk . k))

zonkIO (VSigma d (Closure s k)) = VSigma <$> zonkIO d <*> pure (Closure s (zonk . k))

zonkIO (VPair a b) = VPair <$> zonkIO a <*> zonkIO b


zonkIO (VPath line x y) = VPath <$> zonkIO line <*> zonkIO x <*> zonkIO y

zonkIO (VLine line x y f) = VLine <$> zonkIO line <*> zonkIO x <*> zonkIO y <*> zonkIO f


zonkIO VType = pure VType

zonkIO VTypeω = pure VTypeω


zonkIO VI = pure VI

zonkIO VI0 = pure VI0

zonkIO VI1 = pure VI1


zonkIO (VIAnd x y) = iand <$> zonkIO x <*> zonkIO y

zonkIO (VIOr x y) = ior <$> zonkIO x <*> zonkIO y

zonkIO (VINot x) = inot <$> zonkIO x


zonkIO (VPartial x y) = VPartial <$> zonkIO x <*> zonkIO y

zonkIO (VPartialP x y) = VPartialP <$> zonkIO x <*> zonkIO y

zonkIO (VSystem fs) = do

 t <- for (Map.toList fs) $ \(a, b) -> (,) <$> zonkIO a <*> zonkIO b

 pure (mkVSystem (Map.fromList t))

zonkIO (VSub a b c) = VSub <$> zonkIO a <*> zonkIO b <*> zonkIO c

zonkIO (VInc a b c) = incS <$> zonkIO a <*> zonkIO b <*> zonkIO c

zonkIO (VComp a b c d) = pure $ VComp a b c d

zonkIO (VHComp a b c d) = pure $ VHComp a b c d


zonkIO (VGlueTy a phi ty e) = glueType <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e

zonkIO (VGlue a phi ty e t x) = glueElem <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO t <*> zonkIO x

zonkIO (VUnglue a phi ty e x) = unglue <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO x

zonkIO (VCase env t x xs) = pure $ VCase env t x xs


zonkIO (VEqStrict a x y) = VEqStrict <$> zonkIO a <*> zonkIO x <*> zonkIO y

zonkIO (VReflStrict a x) = VReflStrict <$> zonkIO a <*> zonkIO x


zonkSp :: Projection -> IO Projection

zonkSp (PApp p x) = PApp p <$> zonkIO x

zonkSp (PIElim l x y i) = PIElim <$> zonkIO l <*> zonkIO x <*> zonkIO y <*> zonkIO i

zonkSp (POuc a phi u) = POuc <$> zonkIO a <*> zonkIO phi <*> zonkIO u

zonkSp (PK a x p pr) = PK <$> zonkIO a <*> zonkIO x <*> zonkIO p <*> zonkIO pr

zonkSp (PJ a x p pr y) = PJ <$> zonkIO a <*> zonkIO x <*> zonkIO p <*> zonkIO pr <*> zonkIO y

zonkSp PProj1 = pure PProj1

zonkSp PProj2 = pure PProj2


zonk :: Value -> Value

zonk = unsafePerformIO . zonkIO


eval' :: HasCallStack => ElabEnv -> Term -> Value

eval' env (Ref x) =

 case Map.lookup x (getEnv env) of

 Just (_, vl) -> vl

 _ -> VNe (HVar x) mempty


eval' env (Con x) =

 case Map.lookup x (getEnv env) of

 Just (ty, _) -> VNe (HCon ty x) mempty

 Nothing -> error $ "constructor " ++ show x ++ " has no type in scope"


eval' env (PCon sys x) =

 case Map.lookup x (getEnv env) of

 Just (ty, _) -> VNe (HPCon (eval' env sys) ty x) mempty

 Nothing -> error $ "constructor " ++ show x ++ " has no type in scope"


eval' _ (Data n x) = VNe (HData n x) mempty

eval' env (App p f x) = vApp p (eval' env f) (eval' env x)


eval' env (Lam p s t) =

 VLam p $ Closure s $ \a ->

 eval' env { getEnv = Map.insert s (idkT, a) (getEnv env) } t


eval' env (Pi p s d t) =

 VPi p (eval' env d) $ Closure s $ \a ->

 eval' env { getEnv = (Map.insert s (idkT, a) (getEnv env))} t


eval' _ (Meta m) = VNe (HMeta m) mempty


eval' env (Sigma s d t) =

 VSigma (eval' env d) $ Closure s $ \a ->

 eval' env { getEnv = Map.insert s (idkT, a) (getEnv env) } t


eval' e (Pair a b) = VPair (eval' e a) (eval' e b)


eval' e (Proj1 a) = vProj1 (eval' e a)

eval' e (Proj2 a) = vProj2 (eval' e a)


eval' _ Type = VType

eval' _ Typeω = VTypeω

eval' _ I = VI

eval' _ I0 = VI0

eval' _ I1 = VI1


eval' e (IAnd x y) = iand (eval' e x) (eval' e y)

eval' e (IOr x y) = ior (eval' e x) (eval' e y)

eval' e (INot x) = inot (eval' e x)


eval' e (PathP l a b) = VPath (eval' e l) (eval' e a) (eval' e b)

eval' e (IElim l x y f i) = ielim (eval' e l) (eval' e x) (eval' e y) (eval' e f) (eval' e i)

eval' e (PathIntro p x y f) = VLine (eval' e p) (eval' e x) (eval' e y) (eval' e f)


eval' e (Partial x y) = VPartial (eval' e x) (eval' e y)

eval' e (PartialP x y) = VPartialP (eval' e x) (eval' e y)

eval' e (System fs) = mkVSystem (Map.fromList $ map (\(x, y) -> (eval' e x, eval' e y)) $ Map.toList $ fs)


eval' e (Sub a phi u) = VSub (eval' e a) (eval' e phi) (eval' e u)

eval' e (Inc a phi u) = incS (eval' e a) (eval' e phi) (eval' e u)

eval' e (Ouc a phi u x) = outS (eval' e a) (eval' e phi) (eval' e u) (eval' e x)


eval' e (Comp a phi u a0) = comp (eval' e a) (eval' e phi) (eval' e u) (eval' e a0)

eval' e (HComp a phi u a0) = hComp (eval' e a) (eval' e phi) (eval' e u) (eval' e a0)


eval' e (GlueTy a phi tys f) = glueType (eval' e a) (eval' e phi) (eval' e tys) (eval' e f)

eval' e (Glue a phi tys eqvs t x) = glueElem (eval' e a) (eval' e phi) (eval' e tys) (eval' e eqvs) (eval' e t) (eval' e x)

eval' e (Unglue a phi tys f x) = unglue (eval' e a) (eval' e phi) (eval' e tys) (eval' e f) (eval' e x)

eval' e (Let ns x) =

 let env' = foldl (\newe (n, ty, x) ->

 let nft = eval' newe ty

 in newe { getEnv = Map.insert n (nft, evalFix' newe n nft x) (getEnv newe) })

 e

 ns

 in eval' env' x


eval' e (Case range sc xs) = evalCase e (eval' e range @@) (force (eval' e sc)) xs


eval' e (EqS a x y) = VEqStrict (eval' e a) (eval' e x) (eval' e y)

eval' e (Syntax.Refl a x) = VReflStrict (eval' e a) (eval' e x)

eval' e (Syntax.AxK a x p pr eq) = strictK (eval' e a) (eval' e x) (eval' e p) (eval' e pr) (eval' e eq)

eval' e (Syntax.AxJ a x p pr y eq) = strictJ (eval' e a) (eval' e x) (eval' e p) (eval' e pr) (eval' e y) (eval' e eq)


idkT :: NFType

idkT = VVar (Defined (T.pack "dunno") (negate 1))


isIdkT :: NFType -> Bool

isIdkT (VVar (Defined (T.unpack -> "dunno") (negate -> 1))) = True

isIdkT _ = False


evalCase :: ElabEnv -> (Value -> Value) -> Value -> [(Term, Int, Term)] -> Value

evalCase env rng sc [] = VCase (getEnv env) (fun rng) sc []


evalCase env rng (VSystem fs) cases = VSystem (fmap (flip (evalCase env rng) cases) fs)


evalCase env rng (VHComp a φ u u0) cases =

 comp (fun \i -> rng (v i))

 φ

 (system \i is1 -> α (u @@ i @@ is1))

 (VInc (rng a) φ (α (outS a φ (u @@ VI0) u0)))

 where

 v = Elab.WiredIn.fill (fun (const a)) φ u u0

 α x = evalCase env rng x cases


evalCase env _ sc ((Ref _, _, k):_) = eval' env k @@ sc


evalCase env rng (force -> val@(VNe (HCon _ x) sp)) ((Con x', _, k):xs)

 | x == x' = foldl applProj (eval' env k) sp

 | otherwise = evalCase env rng val xs


evalCase env rng (force -> val@(VNe (HPCon _ _ x) sp)) ((Con x', _, k):xs)

 | x == x' = foldl applProj (eval' env k) sp

 | otherwise = evalCase env rng val xs


evalCase _ _ (VVar ((== trueCaseSentinel) -> True)) _ = VI1


evalCase env rng sc xs = VCase (getEnv env) (fun rng) sc xs


-- This is a great big HACK; When we see a system [ case x of ... => p

-- ], we somehow need to make the 'case x of ...' become VI1. The way we

-- do this is by substituting x/trueCaseSentinel in truthAssignments,

-- and then making case trueCaseSentinel of ... => VI1 always.

trueCaseSentinel :: Name

trueCaseSentinel = Bound (T.pack "sentinel for true cases") (-1000)


evalFix' :: HasCallStack => ElabEnv -> Name -> NFType -> Term -> Value

evalFix' env name nft term = fix $ \val -> eval' env{ getEnv = Map.insert name (nft, GluedVl (HVar name) mempty val) (getEnv env) } term


evalFix :: HasCallStack => Name -> NFType -> Term -> ElabM Value

evalFix name nft term = do

 t <- ask

 pure (evalFix' t name (GluedVl (HVar name) mempty nft) term)


data NotEqual = NotEqual Value Value

 deriving (Show, Typeable, Exception)


unify' :: HasCallStack => Bool -> Value -> Value -> ElabM ()


unify' cs topa@(GluedVl h sp a) topb@(GluedVl h' sp' b)

 | h == h', length sp == length sp' =

 traverse_ (uncurry (unify'Spine cs topa topb)) (Seq.zip sp sp')

 `catchElab` \(_ :: SomeException) -> unify' cs a b


unify' canSwitch topa topb = join $ go <$> forceIO topa <*> forceIO topb where

 go (VNe (HMeta mv) sp) rhs = solveMeta mv sp rhs

 go rhs (VNe (HMeta mv) sp) = solveMeta mv sp rhs


 go topa@(VNe (HPCon _ _ x) sp) topb@(VNe (HPCon _ _ y) sp')

 | x == y = traverse_ (uncurry (unify'Spine canSwitch topa topb)) (Seq.zip sp sp')


 go (VNe (HPCon s _ _) _) rhs | Just v <- trivialSystem s = go v rhs

 go lhs (VNe (HPCon s _ _) _) | Just v <- trivialSystem s = go lhs v


 go (VCase e _ _ b) (VCase e' _ _ b') = do

 env <- ask

 let

 go (_, _, a) (_, _, b)

 | a == b = pure ()

 | otherwise = unify' canSwitch (eval' env{getEnv=moreDefinedFrom e e' <$> e} a) (eval' env{getEnv=moreDefinedFrom e e' <$> e'} b)

 zipWithM_ go (sortOn (\(x, _, _) -> x) b) (sortOn (\(x, _, _) -> x) b')


 go (VCase e _ _ b) y = do

 env <- ask

 let

 go (_, n, a') = do

 ns <- replicateM n (VVar <$> newName)

 let a = foldl (vApp Ex) (eval' env{getEnv=e} a') ns

 unify' canSwitch a y

 traverse_ go b


 go topa@(VNe x a) topb@(VNe x' a')

 | x == x', length a == length a' =

 traverse_ (uncurry (unify'Spine canSwitch topa topb)) (Seq.zip a a')


 go (VLam p (Closure n k)) vl = do

 t <- VVar <$> newName' n

 unify' canSwitch (k t) (vApp p vl t)


 go vl (VLam p (Closure n k)) = do

 t <- VVar <$> newName' n

 unify' canSwitch (vApp p vl t) (k t)


 go (VPair a b) vl = unify' canSwitch a (vProj1 vl) *> unify' canSwitch b (vProj2 vl)

 go vl (VPair a b) = unify' canSwitch (vProj1 vl) a *> unify' canSwitch (vProj2 vl) b


 go (VPi p d (Closure n k)) (VPi p' d' (Closure _ k')) | p == p' = do

 t <- VVar <$> newName' n

 unify' canSwitch d d'

 unify' canSwitch (k t) (k' t)


 go (VSigma d (Closure n k)) (VSigma d' (Closure _ k')) = do

 t <- VVar <$> newName' n

 unify' canSwitch d d'

 unify' canSwitch (k t) (k' t)


 go VType VType = pure ()

 go VTypeω VTypeω = pure ()


 go VI VI = pure ()


 go (VPath l x y) (VPath l' x' y') = do

 unify' canSwitch l l'

 unify' canSwitch x x'

 unify' canSwitch y y'


 go (VLine l x y p) p' = do

 n <- VVar <$> newName' (Bound (T.singleton 'i') (- 1))

 unify' canSwitch (p @@ n) (ielim l x y p' n)


 go p' (VLine l x y p) = do

 n <- VVar <$> newName

 unify' canSwitch (ielim l x y p' n) (p @@ n)


 go (VPartial phi r) (VPartial phi' r') = unify' canSwitch phi phi' *> unify' canSwitch r r'

 go (VPartialP phi r) (VPartialP phi' r') = unify' canSwitch phi phi' *> unify' canSwitch r r'


 go (VSub a phi u) (VSub a' phi' u') = traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u')]

 go (VInc a phi u) (VInc a' phi' u') = traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u')]


 go (VComp a phi u a0) (VComp a' phi' u' a0') =

 traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u'), (a0, a0')]


 go (VHComp a phi u a0) (VHComp a' phi' u' a0') =

 traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u'), (a0, a0')]


 go (VGlueTy _ (force -> VI1) u _0) rhs = unify' canSwitch (u @@ VReflStrict VI VI1) rhs

 go lhs (VGlueTy _ (force -> VI1) u _0) = unify' canSwitch lhs (u @@ VReflStrict VI VI1)


 go (VGlueTy a phi u a0) (VGlueTy a' phi' u' a0') =

 traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u'), (a0, a0')]


 go (VGlue a phi u a0 t x) (VGlue a' phi' u' a0' t' x') =

 traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u'), (a0, a0'), (t, t'), (x, x')]


 go (VUnglue a phi u a0 x) (VUnglue a' phi' u' a0' x') =

 traverse_ (uncurry (unify' canSwitch)) [(a, a'), (phi, phi'), (u, u'), (a0, a0'), (x, x')]


 go (VSystem sys) rhs = goSystem (unify' canSwitch) sys rhs

 go rhs (VSystem sys) = goSystem (flip (unify' canSwitch)) sys rhs


 go (VEqStrict a x y) (VEqStrict a' x' y') = traverse_ (uncurry (unify' canSwitch)) [(a, a'), (x, x'), (y, y')]

 go (VReflStrict a x) (VReflStrict a' x') = traverse_ (uncurry (unify' canSwitch)) [(a, a'), (x, x')]

 go _ VReflStrict{} = pure ()

 go VReflStrict{} _ = pure ()


 go (VINot x) (VINot y) = unify' canSwitch x y


 go x y =

 case (toDnf x, toDnf y) of

 (Just xs, Just ys) -> unify'Formula xs ys

 _ ->

 if canSwitch

 then goDumb x y

 else fail


 goDumb (VIOr a b) (VIOr a' b') = unify' canSwitch a a' *> goDumb b b'

 goDumb (VIAnd a b) (VIAnd a' b') = unify' canSwitch a a' *> goDumb b b'

 goDumb x y = switch $ unify' False x y


 goSystem :: (Value -> Value -> ElabM ()) -> Map.Map Value Value -> Value -> ElabM ()

 goSystem k sys rhs = do

 let rhs_q = quote rhs

 env <- ask

 for_ (Map.toList sys) $ \(f, i) -> do

 let i_q = quote i

 for (truthAssignments f (getEnv env)) $ \e -> do

 k (eval' env{getEnv = e} i_q) (eval' env{getEnv = e} rhs_q)


 fail = throwElab $ NotEqual topa topb

 unify'Formula x y

 | compareDNFs x y = pure ()

 | otherwise = fail


moreDefinedFrom :: Map Name (NFType, Value) -> Map Name (NFType, Value) -> (NFType, Value) -> (NFType, Value)

moreDefinedFrom map1 map2 ours@(_, VNe (HVar name) _) =

 case Map.lookup name map1 of

 Just (_, VNe HVar{} _) -> map2's

 Just (ty, x) -> (ty, x)

 Nothing -> map2's

 where

 map2's = case Map.lookup name map2 of

 Just (_, VNe HVar{} _) -> ours

 Just (ty, x) -> (ty, x)

 Nothing -> ours

moreDefinedFrom _ _ ours = ours


trivialSystem :: Value -> Maybe Value

trivialSystem = go . force where

 go VSystem{} = Nothing

 go x = Just x


unify'Spine :: Bool -> Value -> Value -> Projection -> Projection -> ElabM ()

unify'Spine cs _ _ (PApp a v) (PApp a' v')

 | a == a' = unify' cs v v'


unify'Spine _ _ _ PProj1 PProj1 = pure ()

unify'Spine _ _ _ PProj2 PProj2 = pure ()


unify'Spine cs _ _ (PIElim _ _ _ i) (PIElim _ _ _ j) = unify' cs i j

unify'Spine cs _ _ (POuc a phi u) (POuc a' phi' u') =

 traverse_ (uncurry (unify' cs)) [(a, a'), (phi, phi'), (u, u')]


unify'Spine cs _ _ (PK a x p pr) (PK a' x' p' pr') =

 traverse_ (uncurry (unify' cs)) [(a, a'), (x, x'), (p, p'), (pr, pr')]


unify'Spine cs _ _ (PJ a x p pr y) (PJ a' x' p' pr' y') =

 traverse_ (uncurry (unify' cs)) [(a, a'), (x, x'), (p, p'), (pr, pr'), (y, y')]


unify'Spine _ x y _ _ = throwElab (NotEqual x y)


unify :: HasCallStack => Value -> Value -> ElabM ()

unify x y = shallowly $ go x y where

 go topa@(GluedVl h sp a) topb@(GluedVl h' sp' b)

 | h == h', length sp == length sp' =

 traverse_ (uncurry (unify'Spine True topa topb)) (Seq.zip sp sp')

 `catchElab` \(_ :: SomeException) -> unify' True a b

 go a b = unify' True a b `catchElab` \(_ :: SomeException) -> liftIO $ throwIO (NotEqual a b)


isConvertibleTo :: Value -> Value -> ElabM (Term -> Term)

isConvertibleTo a b = isConvertibleTo (force a) (force b) where

 VPi Im d (Closure _v k) `isConvertibleTo` ty = do

 meta <- newMeta d

 cont <- k meta `isConvertibleTo` ty

 pure (\f -> cont (App Im f (quote meta)))

 VType `isConvertibleTo` VTypeω = pure id


 VPi p d (Closure _ k) `isConvertibleTo` VPi p' d' (Closure _ k') | p == p' = do

 wp <- d' `isConvertibleTo` d

 n <- newName

 wp_n <- eval (Lam Ex n (wp (Ref n)))


 wp' <- k (VVar n) `isConvertibleTo` k' (wp_n @@ VVar n)

 pure (\f -> Lam p n (wp' (App p f (wp (Ref n)))))


 VPath a x y `isConvertibleTo` VPi Ex d (Closure _ k') = do

 unify d VI

 nm <- newName

 wp <- isConvertibleTo (a @@ VVar nm) (k' (VVar nm))

 pure (\f -> Lam Ex nm (wp (IElim (quote a) (quote x) (quote y) f (Ref nm))))


 isConvertibleTo a b = do

 unify' True a b

 pure id


newMeta' :: Bool -> Value -> ElabM Value

newMeta' int dom = do

 loc <- liftM2 (,) <$> asks currentFile <*> asks currentSpan

 n <- newName

 c <- liftIO $ newIORef Nothing

 let m = MV (getNameText n) c dom (flatten <$> loc) int

 flatten (x, (y, z)) = (x, y, z)


 env <- asks getEnv


 t <- fmap catMaybes . for (Map.toList env) $ \(n, t) -> pure $

 case n of

 Bound{} -> Just (PApp Ex (VVar n), n, t)

 _ -> Nothing


 let

 ts = Map.fromList $ fmap (\(_, n, (t, _)) -> (n, t)) t

 t' = fmap (\(x, _, _) -> x) t


 um <- asks unsolvedMetas

 liftIO . atomicModifyIORef um $ \um -> (Map.insert (m ts) [] um, ())


 pure (VNe (HMeta (m ts)) (Seq.fromList t'))


newMeta :: Value -> ElabM Value

newMeta = newMeta' False


newName :: MonadIO m => m Name

newName = liftIO $ do

 x <- atomicModifyIORef _nameCounter $ \x -> (x + 1, x + 1)

 pure (Bound (T.pack (show x)) x)


newName' :: Name -> ElabM Name

newName' n = do

 ~(Bound _ x) <- newName

 pure (Bound (getNameText n) x)


_nameCounter :: IORef Int

_nameCounter = unsafePerformIO $ newIORef 0

{-# NOINLINE _nameCounter #-}


solveMeta :: MV -> Seq Projection -> Value -> ElabM ()

solveMeta m Seq.Empty (VNe (HMeta m') Seq.Empty) | m == m' = pure ()

solveMeta m@(mvCell -> cell) sp rhs = do

 when (mvName m == T.pack "2801") do

 traceM (VNe (HMeta m) sp)

 traceM rhs


 env <- ask

 names <- tryElab $ checkSpine Set.empty sp

 case names of

 Right names -> do

 scope <- tryElab $ checkScope m (Set.fromList names) rhs

 case scope of

 Right () -> do

 let tm = quote rhs

 lam = eval' env $ foldr (Lam Ex) tm names

 liftIO . atomicModifyIORef (unsolvedMetas env) $ \mp -> (Map.delete m mp, ())

 liftIO . atomicModifyIORef' cell $ \case

 Just _ -> error "filled cell in solvedMeta"

 Nothing -> (Just lam, ())

 Left (_ :: MetaException) -> abort env

 Left (_ :: MetaException) -> abort env

 where

 abort env =

 liftIO . atomicModifyIORef' (unsolvedMetas env) $ \x -> (, ()) $

 case Map.lookup m x of

 Just qs -> Map.insert m ((sp, rhs):qs) x

 Nothing -> Map.insert m [(sp, rhs)] x


checkScope :: MV -> Set Name -> Value -> ElabM ()

checkScope mv scope (VNe h sp) =

 do

 case h of

 HVar v@Bound{} ->

 unless (v `Set.member` scope) . throwElab $

 ScopeCheckingFail v

 HVar{} -> pure ()

 HCon{} -> pure ()

 HPCon{} -> pure ()

 HMeta m' -> when (mv == m') $ throwElab $ CircularSolution mv

 HData{} -> pure ()

 traverse_ checkProj sp

 where

 checkProj (PApp _ t) = checkScope mv scope t

 checkProj (PIElim l x y i) = traverse_ (checkScope mv scope) [l, x, y, i]

 checkProj (PK l x y i) = traverse_ (checkScope mv scope) [l, x, y, i]

 checkProj (PJ l x y i j) = traverse_ (checkScope mv scope) [l, x, y, i, j]

 checkProj (POuc a phi u) = traverse_ (checkScope mv scope) [a, phi, u]

 checkProj PProj1 = pure ()

 checkProj PProj2 = pure ()


checkScope mv scope (GluedVl _ _p vl) = checkScope mv scope vl


checkScope mv scope (VLam _ (Closure n k)) =

 checkScope mv (Set.insert n scope) (k (VVar n))


checkScope mv scope (VPi _ d (Closure n k)) = do

 checkScope mv scope d

 checkScope mv (Set.insert n scope) (k (VVar n))


checkScope mv scope (VSigma d (Closure n k)) = do

 checkScope mv scope d

 checkScope mv (Set.insert n scope) (k (VVar n))


checkScope mv s (VPair a b) = traverse_ (checkScope mv s) [a, b]


checkScope _ _ VType = pure ()

checkScope _ _ VTypeω = pure ()


checkScope _ _ VI = pure ()

checkScope _ _ VI0 = pure ()

checkScope _ _ VI1 = pure ()


checkScope mv s (VIAnd x y) = traverse_ (checkScope mv s) [x, y]

checkScope mv s (VIOr x y) = traverse_ (checkScope mv s) [x, y]

checkScope mv s (VINot x) = checkScope mv s x


checkScope mv s (VPath line a b) = traverse_ (checkScope mv s) [line, a, b]

checkScope mv s (VLine _ _ _ line) = checkScope mv s line


checkScope mv s (VPartial x y) = traverse_ (checkScope mv s) [x, y]

checkScope mv s (VPartialP x y) = traverse_ (checkScope mv s) [x, y]

checkScope mv s (VSystem fs) =

 for_ (Map.toList fs) $ \(x, y) -> traverse_ (checkScope mv s) [x, y]


checkScope mv s (VSub a b c) = traverse_ (checkScope mv s) [a, b, c]

checkScope mv s (VInc a b c) = traverse_ (checkScope mv s) [a, b, c]

checkScope mv s (VComp a phi u a0) = traverse_ (checkScope mv s) [a, phi, u, a0]

checkScope mv s (VHComp a phi u a0) = traverse_ (checkScope mv s) [a, phi, u, a0]


checkScope mv s (VGlueTy a phi ty eq) = traverse_ (checkScope mv s) [a, phi, ty, eq]

checkScope mv s (VGlue a phi ty eq inv x) = traverse_ (checkScope mv s) [a, phi, ty, eq, inv, x]

checkScope mv s (VUnglue a phi ty eq vl) = traverse_ (checkScope mv s) [a, phi, ty, eq, vl]


checkScope mv s (VCase _ _ v _) = checkScope mv s v


checkScope mv s (VEqStrict a x y) = traverse_ (checkScope mv s) [a, x, y]

checkScope mv s (VReflStrict a x) = traverse_ (checkScope mv s) [a, x]


checkSpine :: Set Name -> Seq Projection -> ElabM [Name]

checkSpine scope (PApp Ex (VVar n@Bound{}) Seq.:<| xs)

 | n `Set.member` scope = throwElab $ NonLinearSpine n

 | otherwise = (n:) <$> checkSpine scope xs

checkSpine _ (p Seq.:<| _) = throwElab $ SpineProj p

checkSpine _ Seq.Empty = pure []


data MetaException = NonLinearSpine { getDupeName :: Name }

 | SpineProj { getSpineProjection :: Projection }

 | CircularSolution { getCycle :: MV }

 | ScopeCheckingFail { outOfScope :: Name }

 deriving (Show, Typeable, Exception)


substituteIO :: Map.Map Name Value -> Value -> IO Value

substituteIO sub = substituteIO . force where

 substituteIO (VNe hd sp) = do

 sp' <- traverse (substituteSp sub) sp

 case hd of

 HVar v ->

 case Map.lookup v sub of

 Just vl -> substituteIO $ foldl applProj vl sp'

 Nothing -> pure $ foldl applProj (VNe hd mempty) sp'

 hd -> pure $ VNe hd sp'


 substituteIO (GluedVl h sp vl) = GluedVl h <$> traverse (substituteSp sub) sp <*> substituteIO vl


 substituteIO (VLam p (Closure s k)) = pure $ VLam p (Closure s (substitute (Map.delete s sub) . k))

 substituteIO (VPi p d (Closure s k)) = VPi p <$> substituteIO d <*> pure (Closure s (substitute (Map.delete s sub) . k))

 substituteIO (VSigma d (Closure s k)) = VSigma <$> substituteIO d <*> pure (Closure s (substitute (Map.delete s sub) . k))

 substituteIO (VPair a b) = VPair <$> substituteIO a <*> substituteIO b


 substituteIO (VPath line x y) = VPath <$> substituteIO line <*> substituteIO x <*> substituteIO y

 substituteIO (VLine line x y f) = VLine <$> substituteIO line <*> substituteIO x <*> substituteIO y <*> substituteIO f


 substituteIO VType = pure VType

 substituteIO VTypeω = pure VTypeω


 substituteIO VI = pure VI

 substituteIO VI0 = pure VI0

 substituteIO VI1 = pure VI1


 substituteIO (VIAnd x y) = iand <$> substituteIO x <*> substituteIO y

 substituteIO (VIOr x y) = ior <$> substituteIO x <*> substituteIO y

 substituteIO (VINot x) = inot <$> substituteIO x


 substituteIO (VPartial x y) = VPartial <$> substituteIO x <*> substituteIO y

 substituteIO (VPartialP x y) = VPartialP <$> substituteIO x <*> substituteIO y

 substituteIO (VSystem fs) = do

 t <- for (Map.toList fs) $ \(a, b) -> (,) <$> substituteIO a <*> substituteIO b

 pure (mkVSystem (Map.fromList t))

 substituteIO (VSub a b c) = VSub <$> substituteIO a <*> substituteIO b <*> substituteIO c

 substituteIO (VInc a b c) = incS <$> substituteIO a <*> substituteIO b <*> substituteIO c

 substituteIO (VComp a b c d) = comp <$> substituteIO a <*> substituteIO b <*> substituteIO c <*> substituteIO d

 substituteIO (VHComp a b c d) = hComp <$> substituteIO a <*> substituteIO b <*> substituteIO c <*> substituteIO d


 substituteIO (VGlueTy a phi ty e) = glueType <$> substituteIO a <*> substituteIO phi <*> substituteIO ty <*> substituteIO e

 substituteIO (VGlue a phi ty e t x) = glueElem <$> substituteIO a <*> substituteIO phi <*> substituteIO ty <*> substituteIO e <*> substituteIO t <*> substituteIO x

 substituteIO (VUnglue a phi ty e x) = unglue <$> substituteIO a <*> substituteIO phi <*> substituteIO ty <*> substituteIO e <*> substituteIO x

 substituteIO (VCase env t x xs) = VCase env <$> substituteIO t <*> substituteIO x <*> pure xs

 substituteIO (VEqStrict a x y) = VEqStrict <$> substituteIO a <*> substituteIO x <*> substituteIO y

 substituteIO (VReflStrict a x) = VReflStrict <$> substituteIO a <*> substituteIO x


substitute :: Map Name Value -> Value -> Value

substitute sub = unsafePerformIO . substituteIO sub


substituteSp :: Map Name Value -> Projection -> IO Projection

substituteSp sub (PApp p x) = PApp p <$> substituteIO sub x

substituteSp sub (PIElim l x y i) = PIElim <$> substituteIO sub l <*> substituteIO sub x <*> substituteIO sub y <*> substituteIO sub i

substituteSp sub (PK l x y i) = PK <$> substituteIO sub l <*> substituteIO sub x <*> substituteIO sub y <*> substituteIO sub i

substituteSp sub (PJ l x y i j) = PJ <$> substituteIO sub l <*> substituteIO sub x <*> substituteIO sub y <*> substituteIO sub i <*> substituteIO sub j

substituteSp sub (POuc a phi u) = POuc <$> substituteIO sub a <*> substituteIO sub phi <*> substituteIO sub u

substituteSp _ PProj1 = pure PProj1

substituteSp _ PProj2 = pure PProj2


mkVSystem :: Map.Map Value Value -> Value

mkVSystem vals =

 let map' = Map.fromList (Map.toList vals >>= go)

 go (x, y) =

 case (force x, y) of

 (VI0, _) -> []

 (VIOr _ _, VSystem y) -> Map.toList y >>= go

 (a, b) -> [(a, b)]

 in case Map.lookup VI1 map' of

 Just x -> x

 Nothing -> VSystem map'


forceIO :: MonadIO m => Value -> m Value

forceIO mv@(VNe (HMeta (mvCell -> cell)) args) = do

 solved <- liftIO $ readIORef cell

 case solved of

 Just vl -> forceIO (foldl applProj vl args)

 Nothing -> pure mv

forceIO vl@(VSystem fs) =

 case Map.lookup VI1 fs of

 Just x -> forceIO x

 Nothing -> pure vl

forceIO (GluedVl _ _ vl) = forceIO vl

forceIO (VComp line phi u a0) = comp <$> forceIO line <*> forceIO phi <*> pure u <*> pure a0

forceIO (VHComp line phi u a0) = hComp <$> forceIO line <*> forceIO phi <*> pure u <*> pure a0

forceIO (VCase env rng v vs) = do

 env' <- liftIO emptyEnv

 r <- forceIO rng

 evalCase env'{getEnv=env} (r @@) <$> forceIO v <*> pure vs

forceIO x = pure x


force :: Value -> Value

force = unsafePerformIO . forceIO


applProj :: HasCallStack => Value -> Projection -> Value

applProj fun (PApp p arg) = vApp p fun arg

applProj fun (PIElim l x y i) = ielim l x y fun i

applProj fun (POuc a phi u) = outS a phi u fun

applProj fun (PK a x p pr) = strictK a x p pr fun

applProj fun (PJ a x p pr y) = strictJ a x p pr y fun

applProj fun PProj1 = vProj1 fun

applProj fun PProj2 = vProj2 fun


vApp :: HasCallStack => Plicity -> Value -> Value -> Value

vApp _ (VLam _ k) arg = clCont k arg

vApp p (VNe (HData True n) _) _ | T.unpack (getNameText n) == "S1" = undefined

vApp p (VNe h sp) arg = VNe h (sp Seq.:|> PApp p arg)

vApp p (GluedVl h sp vl) arg = GluedVl h (sp Seq.:|> PApp p arg) (vApp p vl arg)

vApp p (VSystem fs) arg = mkVSystem (fmap (flip (vApp p) arg) fs)

vApp p (VCase env rng sc branches) arg =

 VCase env (fun \x -> let VPi _ _ (Closure _ r) = rng @@ x in r arg) sc

 (map (projIntoCase (flip (App p) (quote arg))) branches)

-- vApp _ (VLine _ _ _ (VLam _ k)) arg = clCont k arg

vApp _ x _ = error $ "can't apply " ++ show (prettyTm (quote x))


(@@) :: HasCallStack => Value -> Value -> Value

(@@) = vApp Ex

infixl 9 @@


vProj1 :: HasCallStack => Value -> Value

vProj1 (VPair a _) = a

vProj1 (VNe h sp) = VNe h (sp Seq.:|> PProj1)

vProj1 (GluedVl h sp vl) = GluedVl h (sp Seq.:|> PProj1) (vProj1 vl)

vProj1 (VSystem fs) = VSystem (fmap vProj1 fs)

vProj1 (VInc (VSigma a _) b c) = incS a b (vProj1 c)

vProj1 (VCase env rng sc branches) =

 VCase env rng sc (map (projIntoCase Proj1) branches)

vProj1 x = error $ "can't proj1 " ++ show x


vProj2 :: HasCallStack => Value -> Value

vProj2 (VPair _ b) = b

vProj2 (VNe h sp) = VNe h (sp Seq.:|> PProj2)

vProj2 (GluedVl h sp vl) = GluedVl h (sp Seq.:|> PProj2) (vProj2 vl)

vProj2 (VSystem fs) = VSystem (fmap vProj2 fs)

vProj2 (VInc (VSigma _ (Closure _ r)) b c) = incS (r (vProj1 c)) b (vProj2 c)

vProj2 (VCase env rng sc branches) =

 VCase env rng sc (map (projIntoCase Proj2) branches)

vProj2 x = error $ "can't proj2 " ++ show (prettyTm (quote x))