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{-# LANGUAGE BlockArguments #-}
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{-# LANGUAGE LambdaCase #-}
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{-# LANGUAGE DeriveAnyClass #-}
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{-# LANGUAGE ScopedTypeVariables #-}
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{-# LANGUAGE ViewPatterns #-}
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{-# LANGUAGE TupleSections #-}
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module Elab.Eval where
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import Control.Monad.Reader
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import Control.Exception
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import qualified Data.Map.Strict as Map
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import qualified Data.Sequence as Seq
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import qualified Data.Set as Set
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import qualified Data.Text as T
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import Data.Map.Strict (Map)
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import Data.Sequence (Seq)
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import Data.List (sortOn)
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import Data.Traversable
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import Data.Set (Set)
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import Data.Typeable
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import Data.Foldable
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import Data.IORef
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import Data.Maybe
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import Elab.Eval.Formula
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import Elab.Monad
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import GHC.Stack
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import Presyntax.Presyntax (Plicity(..))
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import Prettyprinter
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import Syntax.Pretty
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import Syntax
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import System.IO.Unsafe ( unsafePerformIO )
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import {-# SOURCE #-} Elab.WiredIn
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eval :: HasCallStack => Term -> ElabM Value
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eval t = asks (flip eval' t)
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-- everywhere force
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zonkIO :: Value -> IO Value
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zonkIO (VNe hd sp) = do
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sp' <- traverse zonkSp sp
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case hd of
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HMeta (mvCell -> cell) -> do
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solved <- liftIO $ readIORef cell
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case solved of
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Just vl -> zonkIO $ foldl applProj vl sp'
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Nothing -> pure $ VNe hd sp'
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hd -> pure $ VNe hd sp'
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zonkIO (GluedVl h sp vl) = GluedVl h <$> traverse zonkSp sp <*> zonkIO vl
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zonkIO (VLam p (Closure s k)) = pure $ VLam p (Closure s (zonk . k))
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zonkIO (VPi p d (Closure s k)) = VPi p <$> zonkIO d <*> pure (Closure s (zonk . k))
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zonkIO (VSigma d (Closure s k)) = VSigma <$> zonkIO d <*> pure (Closure s (zonk . k))
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zonkIO (VPair a b) = VPair <$> zonkIO a <*> zonkIO b
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zonkIO (VPath line x y) = VPath <$> zonkIO line <*> zonkIO x <*> zonkIO y
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zonkIO (VLine line x y f) = VLine <$> zonkIO line <*> zonkIO x <*> zonkIO y <*> zonkIO f
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-- Sorts
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zonkIO VType = pure VType
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zonkIO VTypeω = pure VTypeω
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zonkIO VI = pure VI
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zonkIO VI0 = pure VI0
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zonkIO VI1 = pure VI1
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zonkIO (VIAnd x y) = iand <$> zonkIO x <*> zonkIO y
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zonkIO (VIOr x y) = ior <$> zonkIO x <*> zonkIO y
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zonkIO (VINot x) = inot <$> zonkIO x
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zonkIO (VIsOne x) = VIsOne <$> zonkIO x
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zonkIO VItIsOne = pure VItIsOne
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zonkIO (VPartial x y) = VPartial <$> zonkIO x <*> zonkIO y
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zonkIO (VPartialP x y) = VPartialP <$> zonkIO x <*> zonkIO y
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zonkIO (VSystem fs) = do
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t <- for (Map.toList fs) $ \(a, b) -> (,) <$> zonkIO a <*> zonkIO b
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pure (mkVSystem (Map.fromList t))
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zonkIO (VSub a b c) = VSub <$> zonkIO a <*> zonkIO b <*> zonkIO c
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zonkIO (VInc a b c) = VInc <$> zonkIO a <*> zonkIO b <*> zonkIO c
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zonkIO (VComp a b c d) = comp <$> zonkIO a <*> zonkIO b <*> zonkIO c <*> zonkIO d
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zonkIO (VHComp a b c d) = hComp <$> zonkIO a <*> zonkIO b <*> zonkIO c <*> zonkIO d
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zonkIO (VGlueTy a phi ty e) = glueType <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e
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zonkIO (VGlue a phi ty e t x) = glueElem <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO t <*> zonkIO x
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zonkIO (VUnglue a phi ty e x) = unglue <$> zonkIO a <*> zonkIO phi <*> zonkIO ty <*> zonkIO e <*> zonkIO x
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zonkIO (VCase env t x xs) = do
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env' <- (\x -> x {getEnv = env}) <$> emptyEnv
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let xs' = map (\(a, i, n) -> (a, i, quote (eval' env' n))) xs
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evalCase env' . (@@) <$> zonkIO t <*> zonkIO x <*> pure xs'
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zonkIO (VEqStrict a x y) = VEqStrict <$> zonkIO a <*> zonkIO x <*> zonkIO y
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zonkIO (VReflStrict a x) = VReflStrict <$> zonkIO a <*> zonkIO x
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zonkSp :: Projection -> IO Projection
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zonkSp (PApp p x) = PApp p <$> zonkIO x
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zonkSp (PIElim l x y i) = PIElim <$> zonkIO l <*> zonkIO x <*> zonkIO y <*> zonkIO i
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zonkSp (POuc a phi u) = POuc <$> zonkIO a <*> zonkIO phi <*> zonkIO u
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zonkSp (PK a x p pr) = PK <$> zonkIO a <*> zonkIO x <*> zonkIO p <*> zonkIO pr
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zonkSp (PJ a x p pr y) = PJ <$> zonkIO a <*> zonkIO x <*> zonkIO p <*> zonkIO pr <*> zonkIO y
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zonkSp PProj1 = pure PProj1
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zonkSp PProj2 = pure PProj2
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zonk :: Value -> Value
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zonk = unsafePerformIO . zonkIO
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eval' :: HasCallStack => ElabEnv -> Term -> Value
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eval' env (Ref x) =
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case Map.lookup x (getEnv env) of
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Just (_, vl) -> vl
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_ -> VNe (HVar x) mempty
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eval' env (Con x) =
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case Map.lookup x (getEnv env) of
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Just (ty, _) -> VNe (HCon ty x) mempty
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Nothing -> error $ "constructor " ++ show x ++ " has no type in scope"
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eval' env (PCon sys x) =
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case Map.lookup x (getEnv env) of
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Just (ty, _) -> VNe (HPCon (eval' env sys) ty x) mempty
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Nothing -> error $ "constructor " ++ show x ++ " has no type in scope"
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eval' _ (Data n x) = VNe (HData n x) mempty
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eval' env (App p f x) = vApp p (eval' env f) (eval' env x)
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eval' env (Lam p s t) =
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VLam p $ Closure s $ \a ->
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eval' env { getEnv = Map.insert s (error "type of abs", a) (getEnv env) } t
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eval' env (Pi p s d t) =
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VPi p (eval' env d) $ Closure s $ \a ->
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eval' env { getEnv = (Map.insert s (error "type of abs", a) (getEnv env))} t
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eval' _ (Meta m) = VNe (HMeta m) mempty
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eval' env (Sigma s d t) =
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VSigma (eval' env d) $ Closure s $ \a ->
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eval' env { getEnv = Map.insert s (error "type of abs", a) (getEnv env) } t
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eval' e (Pair a b) = VPair (eval' e a) (eval' e b)
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eval' e (Proj1 a) = vProj1 (eval' e a)
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eval' e (Proj2 a) = vProj2 (eval' e a)
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eval' _ Type = VType
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eval' _ Typeω = VTypeω
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eval' _ I = VI
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eval' _ I0 = VI0
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eval' _ I1 = VI1
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eval' e (IAnd x y) = iand (eval' e x) (eval' e y)
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eval' e (IOr x y) = ior (eval' e x) (eval' e y)
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eval' e (INot x) = inot (eval' e x)
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eval' e (PathP l a b) = VPath (eval' e l) (eval' e a) (eval' e b)
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eval' e (IElim l x y f i) = ielim (eval' e l) (eval' e x) (eval' e y) (eval' e f) (eval' e i)
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eval' e (PathIntro p x y f) = VLine (eval' e p) (eval' e x) (eval' e y) (eval' e f)
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eval' e (IsOne i) = VIsOne (eval' e i)
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eval' _ ItIsOne = VItIsOne
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eval' e (Partial x y) = VPartial (eval' e x) (eval' e y)
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eval' e (PartialP x y) = VPartialP (eval' e x) (eval' e y)
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eval' e (System fs) = mkVSystem (Map.fromList $ map (\(x, y) -> (eval' e x, eval' e y)) $ Map.toList $ fs)
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eval' e (Sub a phi u) = VSub (eval' e a) (eval' e phi) (eval' e u)
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eval' e (Inc a phi u) = VInc (eval' e a) (eval' e phi) (eval' e u)
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eval' e (Ouc a phi u x) = outS (eval' e a) (eval' e phi) (eval' e u) (eval' e x)
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eval' e (Comp a phi u a0) = comp (eval' e a) (eval' e phi) (eval' e u) (eval' e a0)
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eval' e (HComp a phi u a0) = hComp (eval' e a) (eval' e phi) (eval' e u) (eval' e a0)
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eval' e (GlueTy a phi tys f) = glueType (eval' e a) (eval' e phi) (eval' e tys) (eval' e f)
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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)
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eval' e (Unglue a phi tys f x) = unglue (eval' e a) (eval' e phi) (eval' e tys) (eval' e f) (eval' e x)
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eval' e (Let ns x) =
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let env' = foldl (\newe (n, ty, x) ->
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let nft = eval' newe ty
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in newe { getEnv = Map.insert n (nft, evalFix' newe n nft x) (getEnv newe) })
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e
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ns
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in eval' env' x
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eval' e (Case range sc xs) = evalCase e (eval' e range @@) (force (eval' e sc)) xs
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eval' e (EqS a x y) = VEqStrict (eval' e a) (eval' e x) (eval' e y)
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eval' e (Syntax.Refl a x) = VReflStrict (eval' e a) (eval' e x)
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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)
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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)
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evalCase :: ElabEnv -> (Value -> Value) -> Value -> [(Term, Int, Term)] -> Value
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evalCase env rng sc [] = VCase (getEnv env) (fun rng) sc []
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evalCase env rng (VSystem fs) cases = VSystem (fmap (flip (evalCase env rng) cases) fs)
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evalCase env rng (VHComp a phi u a0) cases =
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comp (fun \i -> rng (v i)) phi (system \i is1 -> evalCase env rng (u @@ i @@ is1) cases)
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(VInc (rng a) phi (evalCase env rng (outS a0 phi (u @@ VI0) a0) cases))
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where
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v = Elab.WiredIn.fill (fun (const a)) phi u a0
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evalCase env _ sc ((Ref _, _, k):_) = eval' env k @@ sc
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evalCase env rng (val@(VNe (HCon _ x) sp)) ((Con x', _, k):xs)
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| x == x' = foldl applProj (eval' env k) sp
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| otherwise = evalCase env rng val xs
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evalCase env rng (val@(VNe (HPCon _ _ x) sp)) ((Con x', _, k):xs)
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| x == x' = foldl applProj (eval' env k) sp
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| otherwise = evalCase env rng val xs
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evalCase env rng sc xs = VCase (getEnv env) (fun rng) sc xs
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evalFix' :: ElabEnv -> Name -> NFType -> Term -> Value
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evalFix' env name nft term = fix $ \val -> eval' env{ getEnv = Map.insert name (nft, val) (getEnv env) } term
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evalFix :: Name -> NFType -> Term -> ElabM Value
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evalFix name nft term = do
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t <- ask
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pure (evalFix' t name nft term)
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data NotEqual = NotEqual Value Value
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deriving (Show, Typeable, Exception)
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unify' :: HasCallStack => Value -> Value -> ElabM ()
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unify' topa topb = join $ go <$> forceIO topa <*> forceIO topb where
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go (VNe (HMeta mv) sp) rhs = solveMeta mv sp rhs
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go rhs (VNe (HMeta mv) sp) = solveMeta mv sp rhs
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go (VNe (HPCon s _ _) _) rhs = go (force s) rhs
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go lhs (VNe (HPCon s _ _) _) = go lhs (force s)
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go (VCase e _ a b) (VCase e' _ a' b') = do
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env <- ask
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unify' a a'
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let go (_, _, a) (_, _, b) = unify' (eval' env{getEnv=e} a) (eval' env{getEnv=e'} b)
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zipWithM_ go (sortOn (\(x, _, _) -> x) b) (sortOn (\(x, _, _) -> x) b')
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go (VCase e _ _ b) y = do
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env <- ask
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let
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go (_, n, a') = do
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ns <- replicateM n (VVar <$> newName)
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let a = foldl (vApp Ex) (eval' env{getEnv=e} a') ns
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unify' a y
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traverse_ go b
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go (VNe x a) (VNe x' a')
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| x == x', length a == length a' =
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traverse_ (uncurry unify'Spine) (Seq.zip a a')
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go (VLam p (Closure n k)) vl = do
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t <- VVar <$> newName' n
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unify' (k t) (vApp p vl t)
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go vl (VLam p (Closure n k)) = do
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t <- VVar <$> newName' n
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unify' (vApp p vl t) (k t)
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go (VPair a b) vl = unify' a (vProj1 vl) *> unify' b (vProj2 vl)
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go vl (VPair a b) = unify' (vProj1 vl) a *> unify' (vProj2 vl) b
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go (VPi p d (Closure _ k)) (VPi p' d' (Closure _ k')) | p == p' = do
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t <- VVar <$> newName
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unify' d d'
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unify' (k t) (k' t)
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go (VSigma d (Closure _ k)) (VSigma d' (Closure _ k')) = do
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t <- VVar <$> newName
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unify' d d'
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unify' (k t) (k' t)
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go VType VType = pure ()
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go VTypeω VTypeω = pure ()
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go VI VI = pure ()
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go (VPath l x y) (VPath l' x' y') = do
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unify' l l'
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unify' x x'
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unify' y y'
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go (VLine l x y p) p' = do
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n <- VVar <$> newName
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unify' (p @@ n) (ielim l x y p' n)
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go p' (VLine l x y p) = do
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n <- VVar <$> newName
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unify' (ielim l x y p' n) (p @@ n)
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go (VIsOne x) (VIsOne y) = unify' x y
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-- IsOne is proof-irrelevant:
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go VItIsOne _ = pure ()
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go _ VItIsOne = pure ()
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go (VPartial phi r) (VPartial phi' r') = unify' phi phi' *> unify' r r'
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go (VPartialP phi r) (VPartialP phi' r') = unify' phi phi' *> unify' r r'
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go (VSub a phi u) (VSub a' phi' u') = traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u')]
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go (VInc a phi u) (VInc a' phi' u') = traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u')]
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go (VComp a phi u a0) (VComp a' phi' u' a0') =
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traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u'), (a0, a0')]
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go (VGlueTy _ (force -> VI1) u _0) rhs = unify' (u @@ VItIsOne) rhs
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go lhs (VGlueTy _ (force -> VI1) u _0) = unify' lhs (u @@ VItIsOne)
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go (VGlueTy a phi u a0) (VGlueTy a' phi' u' a0') =
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traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u'), (a0, a0')]
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go (VGlue a phi u a0 t x) (VGlue a' phi' u' a0' t' x') =
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traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u'), (a0, a0'), (t, t'), (x, x')]
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go (VSystem sys) rhs = goSystem unify' sys rhs
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go rhs (VSystem sys) = goSystem (flip unify') sys rhs
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go (VEqStrict a x y) (VEqStrict a' x' y') = traverse_ (uncurry unify') [(a, a'), (x, x'), (y, y')]
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go (VReflStrict a x) (VReflStrict a' x') = traverse_ (uncurry unify') [(a, a'), (x, x')]
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go x y
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| x == y = pure ()
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| otherwise =
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case (toDnf x, toDnf y) of
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(Just xs, Just ys) -> unify'Formula xs ys
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_ -> fail
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goSystem :: (Value -> Value -> ElabM ()) -> Map.Map Value Value -> Value -> ElabM ()
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goSystem k sys rhs = do
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let rhs_q = quote rhs
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env <- ask
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for_ (Map.toList sys) $ \(f, i) -> do
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let i_q = quote i
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for (truthAssignments f (getEnv env)) $ \e ->
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k (eval' env{getEnv = e} i_q) (eval' env{getEnv = e} rhs_q)
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fail = throwElab $ NotEqual topa topb
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unify'Spine (PApp a v) (PApp a' v')
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| a == a' = unify' v v'
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unify'Spine PProj1 PProj1 = pure ()
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unify'Spine PProj2 PProj2 = pure ()
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unify'Spine (PIElim _ _ _ i) (PIElim _ _ _ j) = unify' i j
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unify'Spine (POuc a phi u) (POuc a' phi' u') =
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traverse_ (uncurry unify') [(a, a'), (phi, phi'), (u, u')]
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unify'Spine (PK a x p pr) (PK a' x' p' pr') =
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traverse_ (uncurry unify') [(a, a'), (x, x'), (p, p'), (pr, pr')]
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unify'Spine (PJ a x p pr y) (PJ a' x' p' pr' y') =
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traverse_ (uncurry unify') [(a, a'), (x, x'), (p, p'), (pr, pr'), (y, y')]
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unify'Spine _ _ = fail
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unify'Formula x y
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| compareDNFs x y = pure ()
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| otherwise = fail
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unify :: HasCallStack => Value -> Value -> ElabM ()
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unify a b = unify' a b `catchElab` \(_ :: SomeException) -> liftIO $ throwIO (NotEqual a b)
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isConvertibleTo :: Value -> Value -> ElabM (Term -> Term)
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isConvertibleTo a b = isConvertibleTo (force a) (force b) where
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VPi Im d (Closure _v k) `isConvertibleTo` ty = do
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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
|
|
loc <- liftM2 (,) <$> asks currentFile <*> asks currentSpan
|
|
n <- newName
|
|
c <- liftIO $ newIORef Nothing
|
|
let m = MV (getNameText n) c dom (flatten <$> loc)
|
|
flatten (x, (y, z)) = (x, y, z)
|
|
|
|
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)
|
|
|
|
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@(mvCell -> cell) sp rhs = do
|
|
env <- ask
|
|
names <- tryElab $ checkSpine Set.empty sp
|
|
case names of
|
|
Right names -> do
|
|
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, ())
|
|
Left (_ :: SpineProjection) -> do
|
|
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 :: 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 ()
|
|
HCon{} -> pure ()
|
|
HPCon{} -> pure ()
|
|
HMeta{} -> pure ()
|
|
HData{} -> 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 (PK l x y i) = traverse_ (checkScope scope) [l, x, y, i]
|
|
checkProj (PJ l x y i j) = traverse_ (checkScope scope) [l, x, y, i, j]
|
|
checkProj (POuc a phi u) = traverse_ (checkScope scope) [a, phi, u]
|
|
checkProj PProj1 = pure ()
|
|
checkProj PProj2 = pure ()
|
|
|
|
checkScope scope (GluedVl _ _p vl) = checkScope scope vl
|
|
|
|
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 _ 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 (VHComp 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 (VCase _ _ v _) = checkScope s v
|
|
|
|
checkScope s (VEqStrict a x y) = traverse_ (checkScope s) [a, x, y]
|
|
checkScope s (VReflStrict a x) = traverse_ (checkScope 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 []
|
|
|
|
newtype NonLinearSpine = NonLinearSpine { getDupeName :: Name }
|
|
deriving (Show, Typeable, Exception)
|
|
|
|
newtype SpineProjection = SpineProj { getSpineProjection :: Projection }
|
|
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
|
|
HMeta (mvCell -> cell) -> do
|
|
solved <- liftIO $ readIORef cell
|
|
case solved of
|
|
Just vl -> substituteIO $ foldl applProj vl sp'
|
|
Nothing -> pure $ VNe hd sp'
|
|
HVar v ->
|
|
case Map.lookup v sub of
|
|
Just vl -> substituteIO $ foldl applProj vl sp'
|
|
Nothing -> pure $ VNe hd 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 <$> substituteIO line <*> substituteIO x <*> substituteIO y <*> substituteIO f
|
|
|
|
-- Sorts
|
|
substituteIO VType = pure VType
|
|
substituteIO VTypeω = pure VTypeω
|
|
|
|
substituteIO VI = pure VI
|
|
substituteIO VI0 = pure VI0
|
|
substituteIO VI1 = pure VI1
|
|
|
|
substituteIO (VIAnd x y) = iand <$> substituteIO x <*> substituteIO y
|
|
substituteIO (VIOr x y) = ior <$> substituteIO x <*> substituteIO y
|
|
substituteIO (VINot x) = inot <$> substituteIO x
|
|
|
|
substituteIO (VIsOne x) = VIsOne <$> substituteIO x
|
|
substituteIO VItIsOne = pure VItIsOne
|
|
|
|
substituteIO (VPartial x y) = VPartial <$> 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) = VInc <$> substituteIO a <*> substituteIO b <*> substituteIO c
|
|
substituteIO (VComp a b c d) = comp <$> 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 <$> substituteIO t <*> substituteIO x <*> pure xs
|
|
substituteIO (VEqStrict a x y) = VEqStrict <$> zonkIO a <*> zonkIO x <*> zonkIO y
|
|
substituteIO (VReflStrict a x) = VReflStrict <$> zonkIO a <*> zonkIO x
|
|
|
|
substitute :: Map Name Value -> Value -> Value
|
|
substitute sub = unsafePerformIO . substituteIO sub
|
|
|
|
substituteSp :: Map Name Value -> Projection -> IO Projection
|
|
substituteSp sub (PApp p x) = PApp p <$> 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 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 _ 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) = VInc 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 (prettyTm (quote 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) = VInc (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))
|