{-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE FlexibleContexts #-} -- | -- Type class entailment -- module Language.PureScript.TypeChecker.Entailment (Context, replaceTypeClassDictionaries) where import Prelude () import Prelude.Compat import Data.Function (on) import Data.List (minimumBy, sortBy, groupBy) import Data.Maybe (maybeToList, mapMaybe) import qualified Data.Map as M import Control.Arrow (Arrow(..)) import Control.Monad.State import Control.Monad.Writer import Control.Monad.Error.Class (MonadError(..)) import Control.Monad.Supply.Class (MonadSupply(..)) import Language.PureScript.Crash import Language.PureScript.AST import Language.PureScript.Errors import Language.PureScript.Names import Language.PureScript.TypeChecker.Unify import Language.PureScript.TypeClassDictionaries import Language.PureScript.Types import qualified Language.PureScript.Constants as C -- | The 'Context' tracks those constraints which can be satisfied. type Context = M.Map (Maybe ModuleName) (M.Map (Qualified (ProperName 'ClassName)) (M.Map (Qualified Ident) TypeClassDictionaryInScope)) -- | Merge two type class contexts combineContexts :: Context -> Context -> Context combineContexts = M.unionWith (M.unionWith M.union) -- | Replace type class dictionary placeholders with inferred type class dictionaries replaceTypeClassDictionaries :: (MonadError MultipleErrors m, MonadWriter MultipleErrors m, MonadSupply m) => Bool -> ModuleName -> Expr -> m (Expr, [(Ident, Constraint)]) replaceTypeClassDictionaries shouldGeneralize mn = let (_, f, _) = everywhereOnValuesTopDownM return (WriterT . go) return in flip evalStateT M.empty . runWriterT . f where go (TypeClassDictionary constraint dicts) = entails shouldGeneralize mn dicts constraint go other = return (other, []) -- | -- Check that the current set of type class dictionaries entail the specified type class goal, and, if so, -- return a type class dictionary reference. -- entails :: forall m . (MonadError MultipleErrors m, MonadWriter MultipleErrors m, MonadSupply m) => Bool -> ModuleName -> Context -> Constraint -> StateT Context m (Expr, [(Ident, Constraint)]) entails shouldGeneralize moduleName context = solve where forClassName :: Context -> Qualified (ProperName 'ClassName) -> [Type] -> [TypeClassDictionaryInScope] forClassName ctx cn@(Qualified (Just mn) _) tys = concatMap (findDicts ctx cn) (Nothing : Just mn : map Just (mapMaybe ctorModules tys)) forClassName _ _ _ = internalError "forClassName: expected qualified class name" ctorModules :: Type -> Maybe ModuleName ctorModules (TypeConstructor (Qualified (Just mn) _)) = Just mn ctorModules (TypeConstructor (Qualified Nothing _)) = internalError "ctorModules: unqualified type name" ctorModules (TypeApp ty _) = ctorModules ty ctorModules _ = Nothing findDicts :: Context -> Qualified (ProperName 'ClassName) -> Maybe ModuleName -> [TypeClassDictionaryInScope] findDicts ctx cn = maybe [] M.elems . (>>= M.lookup cn) . flip M.lookup ctx solve :: Constraint -> StateT Context m (Expr, [(Ident, Constraint)]) solve (className, tys) = do (dict, unsolved) <- go 0 className tys return (dictionaryValueToValue dict, unsolved) where go :: Int -> Qualified (ProperName 'ClassName) -> [Type] -> StateT Context m (DictionaryValue, [(Ident, Constraint)]) go work className' tys' | work > 1000 = throwError . errorMessage $ PossiblyInfiniteInstance className' tys' go work className' tys' = do -- Get the inferred constraint context so far, and merge it with the global context inferred <- get let instances = do tcd <- forClassName (combineContexts context inferred) className' tys' -- Make sure the type unifies with the type in the type instance definition subst <- maybeToList . (>>= verifySubstitution) . fmap concat $ zipWithM (typeHeadsAreEqual moduleName) tys' (tcdInstanceTypes tcd) return (subst, tcd) solution <- lift $ unique instances case solution of Left (subst, tcd) -> do -- Solve any necessary subgoals (args, unsolved) <- solveSubgoals subst (tcdDependencies tcd) let match = foldr (\(superclassName, index) dict -> SubclassDictionaryValue dict superclassName index) (mkDictionary (tcdName tcd) args) (tcdPath tcd) return (match, unsolved) Right unsolved@(unsolvedClassName@(Qualified _ pn), unsolvedTys) -> do -- Generate a fresh name for the unsolved constraint's new dictionary ident <- freshIdent ("dict" ++ runProperName pn) let qident = Qualified Nothing ident -- Store the new dictionary in the Context so that we can solve this goal in -- future. let newDict = TypeClassDictionaryInScope qident [] unsolvedClassName unsolvedTys Nothing newContext = M.singleton Nothing (M.singleton unsolvedClassName (M.singleton qident newDict)) modify (combineContexts newContext) return (LocalDictionaryValue qident, [(ident, unsolved)]) where unique :: [(a, TypeClassDictionaryInScope)] -> m (Either (a, TypeClassDictionaryInScope) Constraint) unique [] | shouldGeneralize && all canBeGeneralized tys' = return $ Right (className, tys) | otherwise = throwError . errorMessage $ NoInstanceFound className' tys' unique [a] = return $ Left a unique tcds | pairwise overlapping (map snd tcds) = do tell . errorMessage $ OverlappingInstances className' tys' (map (tcdName . snd) tcds) return $ Left (head tcds) | otherwise = return $ Left (minimumBy (compare `on` length . tcdPath . snd) tcds) canBeGeneralized :: Type -> Bool canBeGeneralized TUnknown{} = True canBeGeneralized Skolem{} = True canBeGeneralized _ = False -- | -- Check if two dictionaries are overlapping -- -- Dictionaries which are subclass dictionaries cannot overlap, since otherwise the overlap would have -- been caught when constructing superclass dictionaries. overlapping :: TypeClassDictionaryInScope -> TypeClassDictionaryInScope -> Bool overlapping TypeClassDictionaryInScope{ tcdPath = _ : _ } _ = False overlapping _ TypeClassDictionaryInScope{ tcdPath = _ : _ } = False overlapping TypeClassDictionaryInScope{ tcdDependencies = Nothing } _ = False overlapping _ TypeClassDictionaryInScope{ tcdDependencies = Nothing } = False overlapping tcd1 tcd2 = tcdName tcd1 /= tcdName tcd2 -- Create dictionaries for subgoals which still need to be solved by calling go recursively -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively. solveSubgoals :: [(String, Type)] -> Maybe [Constraint] -> StateT Context m (Maybe [DictionaryValue], [(Ident, Constraint)]) solveSubgoals _ Nothing = return (Nothing, []) solveSubgoals subst (Just subgoals) = do zipped <- traverse (uncurry (go (work + 1)) . second (map (replaceAllTypeVars subst))) subgoals let (dicts, unsolved) = unzip zipped return (Just dicts, concat unsolved) -- Make a dictionary from subgoal dictionaries by applying the correct function mkDictionary :: Qualified Ident -> Maybe [DictionaryValue] -> DictionaryValue mkDictionary fnName Nothing = LocalDictionaryValue fnName mkDictionary fnName (Just []) = GlobalDictionaryValue fnName mkDictionary fnName (Just dicts) = DependentDictionaryValue fnName dicts -- Turn a DictionaryValue into a Expr dictionaryValueToValue :: DictionaryValue -> Expr dictionaryValueToValue (LocalDictionaryValue fnName) = Var fnName dictionaryValueToValue (GlobalDictionaryValue fnName) = Var fnName dictionaryValueToValue (DependentDictionaryValue fnName dicts) = foldl App (Var fnName) (map dictionaryValueToValue dicts) dictionaryValueToValue (SubclassDictionaryValue dict superclassName index) = App (Accessor (C.__superclass_ ++ showQualified runProperName superclassName ++ "_" ++ show index) (dictionaryValueToValue dict)) valUndefined -- Ensure that a substitution is valid verifySubstitution :: [(String, Type)] -> Maybe [(String, Type)] verifySubstitution subst = do let grps = groupBy ((==) `on` fst) . sortBy (compare `on` fst) $ subst guard (all (pairwise unifiesWith . map snd) grps) return $ map head grps valUndefined :: Expr valUndefined = Var (Qualified (Just (ModuleName [ProperName C.prim])) (Ident C.undefined)) -- | -- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup), -- and return a substitution from type variables to types which makes the type heads unify. -- typeHeadsAreEqual :: ModuleName -> Type -> Type -> Maybe [(String, Type)] typeHeadsAreEqual _ (TUnknown u1) (TUnknown u2) | u1 == u2 = Just [] typeHeadsAreEqual _ (Skolem _ s1 _ _) (Skolem _ s2 _ _) | s1 == s2 = Just [] typeHeadsAreEqual _ t (TypeVar v) = Just [(v, t)] typeHeadsAreEqual _ (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = Just [] typeHeadsAreEqual m (TypeApp h1 t1) (TypeApp h2 t2) = (++) <$> typeHeadsAreEqual m h1 h2 <*> typeHeadsAreEqual m t1 t2 typeHeadsAreEqual _ REmpty REmpty = Just [] typeHeadsAreEqual m r1@RCons{} r2@RCons{} = let (s1, r1') = rowToList r1 (s2, r2') = rowToList r2 int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ] sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ] sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ] in (++) <$> foldMap (uncurry (typeHeadsAreEqual m)) int <*> go sd1 r1' sd2 r2' where go :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> Maybe [(String, Type)] go [] REmpty [] REmpty = Just [] go [] (TUnknown _) _ _ = Just [] go [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = Just [] go [] (Skolem _ s1 _ _) [] (Skolem _ s2 _ _) | s1 == s2 = Just [] go sd r [] (TypeVar v) = Just [(v, rowFromList (sd, r))] go _ _ _ _ = Nothing typeHeadsAreEqual _ _ _ = Nothing -- | -- Check all values in a list pairwise match a predicate -- pairwise :: (a -> a -> Bool) -> [a] -> Bool pairwise _ [] = True pairwise _ [_] = True pairwise p (x : xs) = all (p x) xs && pairwise p xs