@@ -0,0 +1,465 @@
1+-----------------------------------------------------------------------------
3+-- Module : PureScript.TypeChecker.Types
4+-- Copyright : (c) Phil Freeman 2013
7+-- Maintainer : Phil Freeman <paf31@cantab.net>
8+-- Stability : experimental
13+-----------------------------------------------------------------------------
15+module PureScript.TypeChecker.Types (
24+import PureScript.Values
25+import PureScript.Types
26+import PureScript.TypeChecker.Monad
28+import Control.Monad.State
29+import Control.Monad.Error
31+import Control.Applicative
32+import Control.Arrow (Kleisli(..), (***), (&&&))
33+import qualified Control.Category as C
35+import qualified Data.Map as M
38+ = TypeConstraint Int Type
39+ | RowConstraint Int Row deriving Show
41+newtype TypeSolution = TypeSolution { runTypeSolution :: (Int -> Type, Int -> Row) }
43+emptyTypeSolution :: TypeSolution
44+emptyTypeSolution = TypeSolution (TUnknown, RUnknown)
46+typeOf :: String -> Value -> Check Type
49+ (cs, n) <- typeConstraints (M.singleton name me) val
50+ solution <- solveTypeConstraints ((TypeConstraint me (TUnknown n)) : cs) emptyTypeSolution
51+ return $ varIfUnknown $ fst (runTypeSolution solution) n
53+varIfUnknown :: Type -> Type
54+varIfUnknown = flip evalState M.empty . varIfUnknown'
56+ varIfUnknown' :: Type -> State (M.Map Int String) Type
57+ varIfUnknown' (TUnknown n) = do
61+ let name = "t" ++ show (M.size m)
62+ put $ M.insert n name m
63+ return $ TypeVar name
64+ Just name -> return $ TypeVar name
65+ varIfUnknown' (Array t) = Array <$> varIfUnknown' t
66+ varIfUnknown' (Object row) = Object <$> varIfUnknown'' row
67+ varIfUnknown' (Function args ret) = Function <$> mapM varIfUnknown' args <*> varIfUnknown' ret
68+ varIfUnknown' (TypeApp t1 t2) = TypeApp <$> varIfUnknown' t1 <*> varIfUnknown' t2
69+ varIfUnknown' t = return t
70+ varIfUnknown'' :: Row -> State (M.Map Int String) Row
71+ varIfUnknown'' (RUnknown n) = do
75+ let name = "r" ++ show (M.size m)
76+ put $ M.insert n name m
78+ Just name -> return $ RowVar name
79+ varIfUnknown'' (RCons name ty row) = RCons name ty <$> varIfUnknown'' row
80+ varIfUnknown'' r = return r
82+replaceVarsWithUnknowns :: Type -> Check Type
83+replaceVarsWithUnknowns = flip evalStateT M.empty . replaceVarsWithUnknowns'
85+ replaceVarsWithUnknowns' :: Type -> StateT (M.Map String Int) Check Type
86+ replaceVarsWithUnknowns' (Array t) = Array <$> replaceVarsWithUnknowns' t
87+ replaceVarsWithUnknowns' (Object row) = Object <$> replaceVarsWithUnknowns'' row
88+ replaceVarsWithUnknowns' (Function args ret) = Function <$> mapM replaceVarsWithUnknowns' args <*> replaceVarsWithUnknowns' ret
89+ replaceVarsWithUnknowns' (TypeApp t1 t2) = TypeApp <$> replaceVarsWithUnknowns' t1 <*> replaceVarsWithUnknowns' t2
90+ replaceVarsWithUnknowns' (TypeVar var) = do
93+ case M.lookup var m of
95+ put (M.insert var n m)
97+ Just u -> return $ TUnknown u
98+ replaceVarsWithUnknowns' t = return t
99+ replaceVarsWithUnknowns'' :: Row -> StateT (M.Map String Int) Check Row
100+ replaceVarsWithUnknowns'' (RowVar var) = do
103+ case M.lookup var m of
105+ put (M.insert var n m)
107+ Just u -> return $ RUnknown u
108+ replaceVarsWithUnknowns'' (RCons name ty row) = RCons name <$> replaceVarsWithUnknowns' ty <*> replaceVarsWithUnknowns'' row
109+ replaceVarsWithUnknowns'' r = return r
111+typeConstraints :: M.Map String Int -> Value -> Check ([TypeConstraint], Int)
112+typeConstraints _ (NumericLiteral _) = do
114+ return ([TypeConstraint me Number], me)
115+typeConstraints _ (StringLiteral _) = do
117+ return ([TypeConstraint me String], me)
118+typeConstraints _ (BooleanLiteral _) = do
120+ return ([TypeConstraint me Boolean], me)
121+typeConstraints m (ArrayLiteral vals) = do
122+ all <- mapM (typeConstraints m) vals
123+ let (cs, ns) = (concat . map fst &&& map snd) all
125+ return (cs ++ map (TypeConstraint me . Array . TUnknown) ns, me)
126+typeConstraints m (Unary op val) = do
127+ (cs, n1) <- typeConstraints m val
129+ return (cs ++ unaryOperatorConstraints op n1 me, me)
130+typeConstraints m (Binary op left right) = do
131+ (cs1, n1) <- typeConstraints m left
132+ (cs2, n2) <- typeConstraints m right
134+ return (cs1 ++ cs2 ++ binaryOperatorConstraints op n1 n2 me, me)
135+typeConstraints m (ObjectLiteral ps) = do
136+ all <- mapM (typeConstraints m . snd) ps
137+ let (cs, ns) = (concat . map fst &&& map snd) all
139+ let tys = zipWith (\(name, _) u -> (name, TUnknown u)) ps ns
140+ return ((TypeConstraint me (Object (typesToRow tys))) : cs, me)
142+ typesToRow [] = REmpty
143+ typesToRow ((name, ty):tys) = RCons name ty (typesToRow tys)
144+typeConstraints m (Indexer index val) = do
145+ (cs1, n1) <- typeConstraints m index
146+ (cs2, n2) <- typeConstraints m val
148+ return ((TypeConstraint n1 Number) : (TypeConstraint n2 (Array (TUnknown me))) : cs1 ++ cs2, me)
149+typeConstraints m (Accessor prop val) = do
150+ (cs, n1) <- typeConstraints m val
153+ return ((TypeConstraint n1 (Object (RCons prop (TUnknown me) (RUnknown rest)))) : cs, me)
154+typeConstraints m (Abs args ret) = do
155+ ns <- replicateM (length args) fresh
156+ let m' = m `M.union` M.fromList (zipWith (,) args ns)
157+ (cs, n') <- typeConstraints m' ret
159+ return ((TypeConstraint me (Function (map TUnknown ns) (TUnknown n'))) : cs, me)
160+typeConstraints m (App f xs) = do
161+ (cs1, n1) <- typeConstraints m f
162+ all <- mapM (typeConstraints m) xs
163+ let (cs2, ns) = (concat . map fst &&& map snd) all
165+ return ((TypeConstraint n1 (Function (map TUnknown ns) (TUnknown me))) : cs1 ++ cs2, me)
166+typeConstraints m (Var var) =
167+ case M.lookup var m of
170+ case M.lookup var (names env) of
171+ Nothing -> throwError $ var ++ " is undefined"
174+ replaced <- replaceVarsWithUnknowns ty
175+ return ([TypeConstraint me replaced], me)
178+ return ([TypeConstraint u (TUnknown me)], me)
179+typeConstraints m (Block ss) = do
181+ (cs, allCodePathsReturn, _) <- typeConstraintsForBlock m M.empty ret ss
182+ guardWith "Block is missing a return statement" allCodePathsReturn
184+typeConstraints m (Constructor c) = do
186+ case M.lookup c (names env) of
187+ Nothing -> throwError $ c ++ " is undefined"
190+ replaced <- replaceVarsWithUnknowns ty
191+ return ([TypeConstraint me replaced], me)
192+typeConstraints m (Case val binders) = do
193+ (cs1, n1) <- typeConstraints m val
195+ cs2 <- typeConstraintsForBinders m n1 ret binders
196+ return (cs1 ++ cs2, ret)
197+typeConstraints m (TypedValue val ty) = do
198+ (cs, n1) <- typeConstraints m val
199+ return ([TypeConstraint n1 ty], n1)
200+ -- TODO: Kind-check the type
202+unaryOperatorConstraints :: UnaryOperator -> Int -> Int -> [TypeConstraint]
203+unaryOperatorConstraints Negate val result = [TypeConstraint val Number, TypeConstraint result Number]
204+unaryOperatorConstraints Not val result = [TypeConstraint val Boolean, TypeConstraint result Boolean]
205+unaryOperatorConstraints BitwiseNot val result = [TypeConstraint val Number, TypeConstraint result Number]
207+binaryOperatorConstraints :: BinaryOperator -> Int -> Int -> Int -> [TypeConstraint]
208+binaryOperatorConstraints Add = symBinOpConstraints Number
209+binaryOperatorConstraints Subtract = symBinOpConstraints Number
210+binaryOperatorConstraints Multiply = symBinOpConstraints Number
211+binaryOperatorConstraints Divide = symBinOpConstraints Number
212+binaryOperatorConstraints Modulus = symBinOpConstraints Number
213+binaryOperatorConstraints LessThan = symBinOpConstraints Number
214+binaryOperatorConstraints LessThanOrEqualTo = symBinOpConstraints Number
215+binaryOperatorConstraints GreaterThan = symBinOpConstraints Number
216+binaryOperatorConstraints GreaterThanOrEqualTo = symBinOpConstraints Number
217+binaryOperatorConstraints BitwiseAnd = symBinOpConstraints Number
218+binaryOperatorConstraints BitwiseOr = symBinOpConstraints Number
219+binaryOperatorConstraints BitwiseXor = symBinOpConstraints Number
220+binaryOperatorConstraints ShiftLeft = symBinOpConstraints Number
221+binaryOperatorConstraints ShiftRight = symBinOpConstraints Number
222+binaryOperatorConstraints ZeroFillShiftRight = symBinOpConstraints Number
223+binaryOperatorConstraints EqualTo = equalityBinOpConstraints
224+binaryOperatorConstraints NotEqualTo = equalityBinOpConstraints
225+binaryOperatorConstraints And = symBinOpConstraints Boolean
226+binaryOperatorConstraints Or = symBinOpConstraints Boolean
227+binaryOperatorConstraints Concat = symBinOpConstraints String
229+equalityBinOpConstraints :: Int -> Int -> Int -> [TypeConstraint]
230+equalityBinOpConstraints left right result = [TypeConstraint left (TUnknown right), TypeConstraint result Boolean]
232+symBinOpConstraints :: Type -> Int -> Int -> Int -> [TypeConstraint]
233+symBinOpConstraints ty left right result = [TypeConstraint left ty, TypeConstraint right ty, TypeConstraint result ty]
235+typeConstraintsForBinder :: Int -> Binder -> Check ([TypeConstraint], M.Map String Int)
236+typeConstraintsForBinder val (StringBinder _) = constantBinder val String
237+typeConstraintsForBinder val (NumberBinder _) = constantBinder val Number
238+typeConstraintsForBinder val (BooleanBinder _) = constantBinder val Boolean
239+typeConstraintsForBinder val (VarBinder name) = do
241+ return ([TypeConstraint me (TUnknown val)], M.singleton name me)
242+typeConstraintsForBinder val (NullaryBinder ctor) = do
244+ case M.lookup ctor (names env) of
246+ ret' <- replaceVarsWithUnknowns ret
247+ return ([TypeConstraint val ret'], M.empty)
248+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
249+typeConstraintsForBinder val (UnaryBinder ctor binder) = do
251+ case M.lookup ctor (names env) of
252+ Just f@(Function [ty] ret) -> do
254+ Function [ty'] ret' <- replaceVarsWithUnknowns f
255+ (cs, m1) <- typeConstraintsForBinder obj binder
256+ return ((TypeConstraint val ret') : (TypeConstraint obj ty') : cs, m1)
257+ Just _ -> throwError $ ctor ++ " is not a unary constructor"
258+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
259+typeConstraintsForBinder val (ObjectBinder props) = do
262+ (cs, m1) <- typeConstraintsForProperties row (RUnknown rest) props
263+ return ((TypeConstraint val (Object (RUnknown row))) : cs, m1)
265+ typeConstraintsForProperties :: Int -> Row -> [(String, Binder)] -> Check ([TypeConstraint], M.Map String Int)
266+ typeConstraintsForProperties nrow row [] = return ([RowConstraint nrow row], M.empty)
267+ typeConstraintsForProperties nrow row ((name, binder):binders) = do
269+ (cs1, m1) <- typeConstraintsForBinder propTy binder
270+ (cs2, m2) <- typeConstraintsForProperties nrow (RCons name (TUnknown propTy) row) binders
271+ return (cs1 ++ cs2, M.union m1 m2)
272+typeConstraintsForBinder val (ArrayBinder binders rest) = do
274+ all <- mapM (typeConstraintsForBinder el) binders
275+ let (cs1, m1) = (concat . map fst &&& M.unions . map snd) all
276+ let arrayConstraint = TypeConstraint val (Array (TUnknown el))
278+ Nothing -> return (arrayConstraint : cs1, m1)
280+ (cs2, m2) <- typeConstraintsForBinder val binder
281+ return (arrayConstraint : cs1 ++ cs2, M.union m1 m2)
283+constantBinder :: Int -> Type -> Check ([TypeConstraint], M.Map String Int)
284+constantBinder val ty = return ([TypeConstraint val ty], M.empty)
286+typeConstraintsForBinders :: M.Map String Int -> Int -> Int -> [(Binder, Value)] -> Check [TypeConstraint]
287+typeConstraintsForBinders _ _ _ [] = return []
288+typeConstraintsForBinders m nval ret ((binder, val):bs) = do
289+ (cs1, m1) <- typeConstraintsForBinder nval binder
290+ (cs2, n2) <- typeConstraints (M.union m m1) val
291+ cs3 <- typeConstraintsForBinders m nval ret bs
292+ return ((TypeConstraint n2 (TUnknown ret)) : cs1 ++ cs2 ++ cs3)
294+typeConstraintsForStatement :: M.Map String Int -> M.Map String Int -> Int -> Statement -> Check ([TypeConstraint], Bool, M.Map String Int)
295+typeConstraintsForStatement m mass ret (VariableIntroduction name val) = do
296+ case M.lookup name (m `M.union` mass) of
298+ (cs1, n1) <- typeConstraints m val
299+ return $ (cs1, False, M.insert name n1 mass)
300+ Just ty -> throwError $ "Variable with name " ++ name ++ " already exists."
301+typeConstraintsForStatement m mass ret (Assignment name val) = do
302+ case M.lookup name (m `M.union` mass) of
303+ Nothing -> throwError $ "No local variable with name " ++ name
305+ (cs1, n1) <- typeConstraints m val
306+ return ((TypeConstraint n1 (TUnknown ty)) : cs1, False, mass)
307+typeConstraintsForStatement m mass ret (While val inner) = do
308+ (cs1, n1) <- typeConstraints m val
309+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret inner
310+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn, mass)
311+typeConstraintsForStatement m mass ret (IfThenElse val thens Nothing) = do
312+ (cs1, n1) <- typeConstraints m val
313+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret thens
314+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn, mass)
315+typeConstraintsForStatement m mass ret (IfThenElse val thens (Just elses)) = do
316+ (cs1, n1) <- typeConstraints m val
317+ (cs2, allCodePathsReturn1, _) <- typeConstraintsForBlock m mass ret thens
318+ (cs3, allCodePathsReturn2, _) <- typeConstraintsForBlock m mass ret elses
319+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2 ++ cs3, allCodePathsReturn1 && allCodePathsReturn2, mass)
320+typeConstraintsForStatement m mass ret (For (init, cond, cont) inner) = do
321+ (cs1, b1, mass1) <- typeConstraintsForStatement m mass ret init
322+ guardWith "Cannot return from inside for" $ not b1
323+ (cs2, n1) <- typeConstraints (m `M.union` mass1) cond
324+ (cs3, b2, mass2) <- typeConstraintsForStatement (m `M.union` mass1) mass1 ret cont
325+ guardWith "Cannot return from inside for" $ not b2
326+ (cs4, allCodePathsReturn, _) <- typeConstraintsForBlock (m `M.union` mass2) mass2 ret inner
327+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2 ++ cs3 ++ cs4, allCodePathsReturn, mass)
328+typeConstraintsForStatement m mass ret (Return val) = do
329+ (cs1, n1) <- typeConstraints m val
330+ return ((TypeConstraint n1 (TUnknown ret)) : cs1, True, mass)
332+typeConstraintsForBlock :: M.Map String Int -> M.Map String Int -> Int -> [Statement] -> Check ([TypeConstraint], Bool, M.Map String Int)
333+typeConstraintsForBlock _ mass _ [] = return ([], False, mass)
334+typeConstraintsForBlock m mass ret (s:ss) = do
335+ (cs1, b1, mass1) <- typeConstraintsForStatement (m `M.union` mass) mass ret s
337+ (True, []) -> return (cs1, True, mass1)
338+ (True, _) -> throwError "Unreachable code"
340+ (cs2, b2, mass2) <- typeConstraintsForBlock m mass1 ret ss
341+ return (cs1 ++ cs2, b2, mass2)
343+solveTypeConstraints :: [TypeConstraint] -> TypeSolution -> Check TypeSolution
344+solveTypeConstraints [] s = return s
345+solveTypeConstraints all@(TypeConstraint n t:cs) s = do
346+ guardWith "Occurs check failed" $ not $ typeOccursCheck False n t
347+ let s' = let (f, g) = runTypeSolution s
348+ in TypeSolution (replaceTypeInType n t . f, replaceTypeInRow n t . g)
349+ cs' <- fmap concat $ mapM (substituteTypeInConstraint n t) cs
350+ solveTypeConstraints cs' s'
351+solveTypeConstraints (RowConstraint n r:cs) s = do
352+ guardWith "Occurs check failed" $ not $ rowOccursCheck False n r
353+ let s' = let (f, g) = runTypeSolution s
354+ in TypeSolution $ (replaceRowInType n r . f, replaceRowInRow n r . g)
355+ cs' <- fmap concat $ mapM (substituteRowInConstraint n r) cs
356+ solveTypeConstraints cs' s'
358+substituteTypeInConstraint :: Int -> Type -> TypeConstraint -> Check [TypeConstraint]
359+substituteTypeInConstraint n s (TypeConstraint m t)
360+ | n == m = unifyTypes s t
361+ | otherwise = return [TypeConstraint m (replaceTypeInType n s t)]
362+substituteTypeInConstraint n s (RowConstraint m r)
363+ = return [RowConstraint m (replaceTypeInRow n s r)]
365+substituteRowInConstraint :: Int -> Row -> TypeConstraint -> Check [TypeConstraint]
366+substituteRowInConstraint n r (TypeConstraint m t)
367+ = return [TypeConstraint m (replaceRowInType n r t)]
368+substituteRowInConstraint n r (RowConstraint m r1)
369+ | m == n = unifyRows r r1
370+ | otherwise = return [RowConstraint m (replaceRowInRow n r r1)]
372+replaceTypeInType :: Int -> Type -> Type -> Type
373+replaceTypeInType n t (TUnknown m) | m == n = t
374+replaceTypeInType n t (Array t1) = Array $ replaceTypeInType n t t1
375+replaceTypeInType n t (Object row) = Object $ replaceTypeInRow n t row
376+replaceTypeInType n t (Function args ret) = Function (map (replaceTypeInType n t) args) (replaceTypeInType n t ret)
377+replaceTypeInType n t (TypeApp t1 t2) = TypeApp (replaceTypeInType n t t1) (replaceTypeInType n t t2)
378+replaceTypeInType _ _ other = other
380+replaceTypeInRow :: Int -> Type -> Row -> Row
381+replaceTypeInRow n t (RCons name ty row) = RCons name (replaceTypeInType n t ty) (replaceTypeInRow n t row)
382+replaceTypeInRow n t other = other
384+replaceRowInType :: Int -> Row -> Type -> Type
385+replaceRowInType n r (Array t1) = Array $ replaceRowInType n r t1
386+replaceRowInType n r (Object row) = Object $ replaceRowInRow n r row
387+replaceRowInType n r (Function args ret) = Function (map (replaceRowInType n r) args) (replaceRowInType n r ret)
388+replaceRowInType n r (TypeApp t1 t2) = TypeApp (replaceRowInType n r t1) (replaceRowInType n r t2)
389+replaceRowInType _ _ other = other
391+replaceRowInRow :: Int -> Row -> Row -> Row
392+replaceRowInRow n r (RUnknown m) | m == n = r
393+replaceRowInRow n r (RCons name ty row) = RCons name (replaceRowInType n r ty) (replaceRowInRow n r row)
394+replaceRowInRow _ _ other = other
396+unifyTypes :: Type -> Type -> Check [TypeConstraint]
397+unifyTypes (TUnknown u1) (TUnknown u2) | u1 == u2 = return []
398+unifyTypes (TUnknown u) t = do
399+ guardWith "Occurs check failed" $ not $ typeOccursCheck False u t
400+ return [TypeConstraint u t]
401+unifyTypes t (TUnknown u) = do
402+ guardWith "Occurs check failed" $ not $ typeOccursCheck False u t
403+ return [TypeConstraint u t]
404+unifyTypes Number Number = return []
405+unifyTypes String String = return []
406+unifyTypes Boolean Boolean = return []
407+unifyTypes (Array s) (Array t) = unifyTypes s t
408+unifyTypes (Object row1) (Object row2) = unifyRows row1 row2
409+unifyTypes (Function args1 ret1) (Function args2 ret2) = do
410+ guardWith "Function applied to incorrect number of args" $ length args1 == length args2
411+ cs1 <- fmap concat $ zipWithM unifyTypes args1 args2
412+ cs2 <- unifyTypes ret1 ret2
414+unifyTypes (TypeVar v1) (TypeVar v2) | v1 == v2 = return []
415+unifyTypes (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = return []
416+unifyTypes (TypeVar v1) (TypeVar v2) = return []
417+unifyTypes (TypeApp t1 t2) (TypeApp t3 t4) = do
418+ cs1 <- unifyTypes t1 t3
419+ cs2 <- unifyTypes t2 t4
421+unifyTypes t1 t2 = throwError $ "Cannot unify " ++ show t1 ++ " with " ++ show t2 ++ "."
423+unifyRows :: Row -> Row -> Check [TypeConstraint]
426+ (s1, r1') = toList r1
427+ (s2, r2') = toList r2
428+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
429+ sd1 = [ (name, t1) | (name, t1) <- s1, not (elem name (map fst s2)) ]
430+ sd2 = [ (name, t2) | (name, t2) <- s2, not (elem name (map fst s1)) ]
431+ in rethrow (const $ "Cannot unify " ++ show r1 ++ " with " ++ show r2) $ do
432+ cs1 <- fmap concat $ mapM (uncurry unifyTypes) int
433+ cs2 <- unifyRows' sd1 r1' sd2 r2'
436+ unifyRows' :: [(String, Type)] -> Row -> [(String, Type)] -> Row -> Check [TypeConstraint]
437+ unifyRows' [] (RUnknown u) sd r = do
438+ guardWith "Occurs check failed" $ not $ rowOccursCheck False u r
439+ return [RowConstraint u (fromList (sd, r))]
440+ unifyRows' ((name, ty):row) r others (RUnknown u) = do
442+ cs <- unifyRows' row r others (RUnknown u')
443+ return [ RowConstraint u (RCons name ty (RUnknown u')) ]
444+ unifyRows' [] REmpty [] REmpty = return []
445+ unifyRows' sd1 r1 sd2 r2 = throwError $ "Cannot unify " ++ show (fromList (sd1, r1)) ++ " with " ++ show (fromList (sd2, r2)) ++ "."
446+ toList :: Row -> ([(String, Type)], Row)
447+ toList (RCons name ty row) = let (tys, rest) = toList row
448+ in ((name, ty):tys, rest)
450+ fromList :: ([(String, Type)], Row) -> Row
451+ fromList ([], r) = r
452+ fromList ((name, t):ts, r) = RCons name t (fromList (ts, r))
454+typeOccursCheck :: Bool -> Int -> Type -> Bool
455+typeOccursCheck b u (TUnknown u') | u == u' = b
456+typeOccursCheck _ u (Array t) = typeOccursCheck True u t
457+typeOccursCheck _ u (Object row) = rowOccursCheck True u row
458+typeOccursCheck _ u (Function args ret) = any (typeOccursCheck True u) args || typeOccursCheck True u ret
459+typeOccursCheck _ u (TypeApp s t) = typeOccursCheck True u s || typeOccursCheck True u t
460+typeOccursCheck _ _ _ = False
462+rowOccursCheck :: Bool -> Int -> Row -> Bool
463+rowOccursCheck b u (RUnknown u') | u == u' = b
464+rowOccursCheck _ u (RCons name ty row) = typeOccursCheck True u ty || rowOccursCheck True u row
465+rowOccursCheck _ _ _ = False