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- {-# LANGUAGE LambdaCase #-}
- {-# LANGUAGE DeriveAnyClass #-}
- {-# LANGUAGE ScopedTypeVariables #-}
- {-# LANGUAGE ViewPatterns #-}
- 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.Sequence (Seq)
- import Data.Traversable
- import Data.Set (Set)
- import Data.Typeable
- import Data.Foldable
- import Data.IORef
- import Data.Maybe
-
- import Elab.Eval.Formula
- import Elab.Monad
-
- import GHC.Stack
-
- import Presyntax.Presyntax (Plicity(..))
-
- import Prettyprinter
-
- import Syntax.Pretty
- import Syntax
-
- import System.IO.Unsafe
-
- import {-# SOURCE #-} Elab.WiredIn
-
- eval :: Term -> ElabM Value
- eval t = asks (flip eval' t)
-
- forceIO :: MonadIO m => Value -> m Value
- forceIO mv@(VNe (HMeta (MV _ 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 (VComp line phi u a0) = comp line <$> forceIO phi <*> pure u <*> pure a0
- forceIO x = pure x
-
- applProj :: 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 PProj1 = vProj1 fun
- applProj fun PProj2 = vProj2 fun
-
- force :: Value -> Value
- force = unsafePerformIO . forceIO
-
- -- everywhere force
- zonkIO :: Value -> IO Value
- zonkIO (VNe hd sp) = do
- sp' <- traverse zonkSp sp
- case hd of
- HMeta (MV _ 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'
- where
- 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 PProj1 = pure PProj1
- zonkSp PProj2 = pure PProj2
-
- 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 <$> zonkIO line <*> zonkIO x <*> zonkIO y <*> zonkIO f
-
- -- Sorts
- zonkIO VType = pure VType
- zonkIO VTypeω = pure VTypeω
-
- zonkIO VI = pure VI
- zonkIO VI0 = pure VI0
- zonkIO VI1 = pure VI1
-
- zonkIO (VIAnd x y) = iand <$> zonkIO x <*> zonkIO y
- zonkIO (VIOr x y) = ior <$> zonkIO x <*> zonkIO y
- zonkIO (VINot x) = inot <$> zonkIO x
-
- zonkIO (VIsOne x) = VIsOne <$> zonkIO x
- zonkIO (VIsOne1 x) = VIsOne1 <$> zonkIO x
- zonkIO (VIsOne2 x) = VIsOne2 <$> zonkIO x
- zonkIO VItIsOne = pure VItIsOne
-
- zonkIO (VPartial x y) = VPartial <$> 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) = VInc <$> zonkIO a <*> zonkIO b <*> zonkIO c
- zonkIO (VComp a b c d) = comp <$> zonkIO a <*> zonkIO b <*> zonkIO c <*> zonkIO 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 <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO x
-
- zonkIO VBool = pure VBool
- zonkIO VTt = pure VTt
- zonkIO VFf = pure VFf
- zonkIO (VIf a b c d) = elimBool <$> zonkIO a <*> zonkIO b <*> zonkIO c <*> zonkIO d
-
- mkVSystem :: Map.Map Value Value -> Value
- mkVSystem map =
- case Map.lookup VI1 map of
- Just x -> x
- Nothing -> VSystem (Map.filterWithKey (\k _ -> k /= VI0) map)
-
- zonk :: Value -> Value
- zonk = unsafePerformIO . zonkIO
-
- eval' :: ElabEnv -> Term -> Value
- eval' env (Ref x) =
- case Map.lookup x (getEnv env) of
- Just (_, vl) -> vl
- _ -> VNe (HVar 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 (error "type of abs", 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 (error "type of abs", 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 (error "type of abs", 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 (IsOne i) = VIsOne (eval' e i)
- eval' e (IsOne1 i) = VIsOne1 (eval' e i)
- eval' e (IsOne2 i) = VIsOne2 (eval' e i)
- eval' _ ItIsOne = VItIsOne
-
- 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) = VSystem (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) = VInc (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 (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) -> newe { getEnv = Map.insert n (eval' newe ty, eval' newe x) (getEnv newe) }) e ns
- in eval' env' x
-
- eval' e (If a b c d) = elimBool (eval' e a) (eval' e b) (eval' e c) (eval' e d)
- eval' _ Bool = VBool
- eval' _ Tt = VTt
- eval' _ Ff = VFf
-
- vApp :: HasCallStack => Plicity -> Value -> Value -> Value
- vApp p (VLam p' k) arg
- | p == p' = clCont k arg
- | otherwise = error $ "wrong plicity " ++ show p ++ " vs " ++ show p' ++ " in app " ++ show (App p (quote (VLam p' k)) (quote arg))
- vApp p (VNe h sp) arg = VNe h (sp Seq.:|> PApp p arg)
- vApp p (VSystem fs) arg = VSystem (fmap (flip (vApp p) arg) fs)
- 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 (VSystem fs) = VSystem (fmap vProj1 fs)
- vProj1 x = error $ "can't proj1 " ++ show (prettyTm (quote x))
-
- vProj2 :: HasCallStack => Value -> Value
- vProj2 (VPair _ b) = b
- vProj2 (VNe h sp) = VNe h (sp Seq.:|> PProj2)
- vProj2 (VSystem fs) = VSystem (fmap vProj2 fs)
- vProj2 x = error $ "can't proj2 " ++ show (prettyTm (quote x))
-
- data NotEqual = NotEqual Value Value
- deriving (Show, Typeable, Exception)
-
- unify' :: HasCallStack => Value -> Value -> ElabM ()
- unify' topa topb = join $ go <$> forceIO topa <*> forceIO topb where
- go (VNe (HMeta mv) sp) rhs = solveMeta mv sp rhs
- go rhs (VNe (HMeta mv) sp) = solveMeta mv sp rhs
-
- go (VNe x a) (VNe x' a')
- | x == x', length a == length a' =
- traverse_ (uncurry unify'Spine) (Seq.zip a a')
-
- go lhs@(VNe _hd (_ Seq.:|> PIElim _l x y i)) rhs =
- case force i of
- VI0 -> unify' x rhs
- VI1 -> unify' y rhs
- _ -> case rhs of
- VSystem sys -> goSystem (flip unify') sys lhs
- _ -> fail
-
- go lhs rhs@(VNe _hd (_ Seq.:|> PIElim _l x y i)) =
- case force i of
- VI0 -> unify' lhs x
- VI1 -> unify' lhs y
- _ -> case lhs of
- VSystem sys -> goSystem unify' sys rhs
- _ -> fail
-
- go (VLam p (Closure _ k)) vl = do
- t <- VVar <$> newName
- unify' (k t) (vApp p vl t)
-
- go vl (VLam p (Closure _ k)) = do
- t <- VVar <$> newName
- unify' (vApp p vl t) (k t)
-
- go (VPair a b) vl = unify' a (vProj1 vl) *> unify' b (vProj2 vl)
- go vl (VPair a b) = unify' (vProj1 vl) a *> unify' (vProj2 vl) b
-
- go (VPi p d (Closure _ k)) (VPi p' d' (Closure _ k')) | p == p' = do
- t <- VVar <$> newName
- unify' d d'
- unify' (k t) (k' t)
-
- go (VSigma d (Closure _ k)) (VSigma d' (Closure _ k')) = do
- t <- VVar <$> newName
- unify' d d'
- unify' (k t) (k' t)
-
- go VType VType = pure ()
- go VTypeω VTypeω = pure ()
-
- go VI VI = pure ()
-
- go (VPath l x y) (VPath l' x' y') = do
- unify' l l'
- unify' x x'
- unify' y y'
-
- go (VLine l x y p) p' = do
- n <- VVar <$> newName
- unify' (p @@ n) (ielim l x y p' n)
-
- go p' (VLine l x y p) = do
- n <- VVar <$> newName
- unify' (ielim l x y p' n) (p @@ n)
-
- go (VIsOne x) (VIsOne y) = unify' x y
-
- -- IsOne is proof-irrelevant:
- go VItIsOne _ = pure ()
- go _ VItIsOne = pure ()
- go VIsOne1{} _ = pure ()
- go _ VIsOne1{} = pure ()
- go VIsOne2{} _ = pure ()
- go _ VIsOne2{} = pure ()
-
- go (VPartial phi r) (VPartial phi' r') = unify' phi phi' *> unify' r r'
- go (VPartialP phi r) (VPartialP phi' r') = unify' phi phi' *> unify' r r'
-
- go (VSub a phi u) (VSub a' phi' u') = traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u')]
- go (VInc a phi u) (VInc a' phi' u') = traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u')]
-
- go (VComp a phi u a0) (VComp a' phi' u' a0') =
- traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u'), (a0, a0')]
-
- go (VGlueTy _ VI1 u _0) rhs = unify' (u @@ VItIsOne) rhs
- go lhs (VGlueTy _ VI1 u _0) = unify' lhs (u @@ VItIsOne)
-
- go (VGlueTy a phi u a0) (VGlueTy a' phi' u' a0') =
- traverse_ (uncurry unify') [(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') [(a, a'), (phi, phi'), (u, u'), (a0, a0'), (t, t'), (x, x')]
-
- go (VSystem sys) rhs = goSystem unify' sys rhs
- go rhs (VSystem sys) = goSystem (flip unify') sys rhs
-
- go VTt VTt = pure ()
- go VFf VFf = pure ()
- go VBool VBool = pure ()
-
- go x y
- | x == y = pure ()
- | otherwise =
- case (toDnf x, toDnf y) of
- (Just xs, Just ys) -> unify'Formula xs ys
- _ -> fail
-
- 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 ->
- k (eval' env{getEnv = e} i_q) (eval' env{getEnv = e} rhs_q)
-
- fail = throwElab $ NotEqual topa topb
-
- unify'Spine (PApp a v) (PApp a' v')
- | a == a' = unify' v v'
-
- unify'Spine PProj1 PProj1 = pure ()
- unify'Spine PProj2 PProj2 = pure ()
-
- unify'Spine (PIElim _ _ _ i) (PIElim _ _ _ j) = unify' i j
- unify'Spine (POuc a phi u) (POuc a' phi' u') =
- traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u')]
-
- unify'Spine _ _ = fail
-
- unify'Formula x y
- | compareDNFs x y = pure ()
- | otherwise = fail
-
- unify :: HasCallStack => Value -> Value -> ElabM ()
- unify a b = unify' a b `catchElab` \(_ :: NotEqual) -> 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)))))
-
- isConvertibleTo a b = do
- unify' a b
- pure id
-
- newMeta :: Value -> ElabM Value
- newMeta _dom = do
- n <- newName
- c <- liftIO $ newIORef Nothing
- let m = MV (getNameText n) c
-
- env <- asks getEnv
-
- t <- for (Map.toList env) $ \(n, _) -> pure $
- case n of
- Bound{} -> Just (PApp Ex (VVar n))
- _ -> Nothing
-
- pure (VNe (HMeta m) (Seq.fromList (catMaybes t)))
-
- newName :: MonadIO m => m Name
- newName = liftIO $ do
- x <- atomicModifyIORef _nameCounter $ \x -> (x + 1, x + 1)
- pure (Bound (T.pack (show x)) x)
-
- _nameCounter :: IORef Int
- _nameCounter = unsafePerformIO $ newIORef 0
- {-# NOINLINE _nameCounter #-}
-
- solveMeta :: MV -> Seq Projection -> Value -> ElabM ()
- solveMeta m@(MV _ cell) sp rhs = do
- env <- ask
- names <- checkSpine Set.empty sp
- checkScope (Set.fromList names) rhs
- `withNote` hsep [prettyTm (quote (VNe (HMeta m) sp)), pretty '≡', prettyTm (quote rhs)]
- let tm = quote rhs
- lam = eval' env $ foldr (Lam Ex) tm names
- liftIO . atomicModifyIORef' cell $ \case
- Just _ -> error "filled cell in solvedMeta"
- Nothing -> (Just lam, ())
-
- checkScope :: Set Name -> Value -> ElabM ()
- checkScope scope (VNe h sp) =
- do
- case h of
- HVar v@Bound{} ->
- unless (v `Set.member` scope) . throwElab $
- NotInScope v
- HVar{} -> pure ()
- HMeta{} -> pure ()
- traverse_ checkProj sp
- where
- checkProj (PApp _ t) = checkScope scope t
- checkProj (PIElim l x y i) = traverse_ (checkScope scope) [l, x, y, i]
- checkProj (POuc a phi u) = traverse_ (checkScope scope) [a, phi, u]
- checkProj PProj1 = pure ()
- checkProj PProj2 = pure ()
-
- checkScope scope (VLam _ (Closure n k)) =
- checkScope (Set.insert n scope) (k (VVar n))
-
- checkScope scope (VPi _ d (Closure n k)) = do
- checkScope scope d
- checkScope (Set.insert n scope) (k (VVar n))
-
- checkScope scope (VSigma d (Closure n k)) = do
- checkScope scope d
- checkScope (Set.insert n scope) (k (VVar n))
-
- checkScope s (VPair a b) = traverse_ (checkScope s) [a, b]
-
- checkScope _ VType = pure ()
- checkScope _ VTypeω = pure ()
-
- checkScope _ VI = pure ()
- checkScope _ VI0 = pure ()
- checkScope _ VI1 = pure ()
-
- checkScope s (VIAnd x y) = traverse_ (checkScope s) [x, y]
- checkScope s (VIOr x y) = traverse_ (checkScope s) [x, y]
- checkScope s (VINot x) = checkScope s x
-
- checkScope s (VPath line a b) = traverse_ (checkScope s) [line, a, b]
- checkScope s (VLine _ _ _ line) = checkScope s line
-
- checkScope s (VIsOne x) = checkScope s x
- checkScope s (VIsOne1 x) = checkScope s x
- checkScope s (VIsOne2 x) = checkScope s x
- checkScope _ VItIsOne = pure ()
-
- checkScope s (VPartial x y) = traverse_ (checkScope s) [x, y]
- checkScope s (VPartialP x y) = traverse_ (checkScope s) [x, y]
- checkScope s (VSystem fs) =
- for_ (Map.toList fs) $ \(x, y) -> traverse_ (checkScope s) [x, y]
-
- checkScope s (VSub a b c) = traverse_ (checkScope s) [a, b, c]
- checkScope s (VInc a b c) = traverse_ (checkScope s) [a, b, c]
- checkScope s (VComp a phi u a0) = traverse_ (checkScope s) [a, phi, u, a0]
-
- checkScope s (VGlueTy a phi ty eq) = traverse_ (checkScope s) [a, phi, ty, eq]
- checkScope s (VGlue a phi ty eq inv x) = traverse_ (checkScope s) [a, phi, ty, eq, inv, x]
- checkScope s (VUnglue a phi ty eq vl) = traverse_ (checkScope s) [a, phi, ty, eq, vl]
-
- checkScope s (VIf a b c d) = traverse_ (checkScope s) [a, b, c, d]
- checkScope _ VBool = pure ()
- checkScope _ VTt = pure ()
- checkScope _ VFf = pure ()
-
- 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 []
-
- newtype NonLinearSpine = NonLinearSpine { getDupeName :: Name }
- deriving (Show, Typeable, Exception)
-
- newtype SpineProjection = SpineProj { getSpineProjection :: Projection }
- deriving (Show, Typeable, Exception)
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