@@ -0,0 +1,952 @@
1+-----------------------------------------------------------------------------
2+--
3+-- Module : Language.PureScript.TypeChecker.Types
4+-- Copyright : (c) Phil Freeman 2013
5+-- License : MIT
6+--
7+-- Maintainer : Phil Freeman <paf31@cantab.net>
8+-- Stability : experimental
9+-- Portability :
10+--
11+-- |
12+-- This module implements the type checker
13+--
14+-----------------------------------------------------------------------------
15+
16+{-# OPTIONS_GHC -fno-warn-orphans #-}
17+{-# LANGUAGE FlexibleContexts #-}
18+{-# LANGUAGE MultiParamTypeClasses #-}
19+
20+module Language.PureScript.TypeChecker.Types (
21+ typesOf
22+) where
23+
24+{-
25+ The following functions represent the corresponding type checking judgements:
26+
27+ infer
28+ Synthesize a type for a value
29+
30+ check
31+ Check a value has a given type
32+
33+ checkProperties
34+ Check an object with a given type contains specified properties
35+
36+ checkFunctionApplication
37+ Check a function of a given type returns a value of another type when applied to its arguments
38+
39+ subsumes
40+ Check a type subsumes another type
41+-}
42+
43+import Data.List
44+import Data.Maybe (maybeToList, isNothing, isJust, fromMaybe)
45+import qualified Data.Data as D
46+import Data.Generics
47+ (everythingWithContext, mkM, everywhereM, everything, mkT,
48+ something, everywhere, mkQ)
49+import Data.Generics.Extras
50+
51+import Language.PureScript.Values
52+import Language.PureScript.Types
53+import Language.PureScript.Kinds
54+import Language.PureScript.Names
55+import Language.PureScript.TypeChecker.Monad
56+import Language.PureScript.TypeChecker.Kinds
57+import Language.PureScript.TypeChecker.Synonyms
58+import Language.PureScript.Pretty
59+import Language.PureScript.Prim
60+
61+import Control.Monad.State
62+import Control.Monad.Error
63+import Control.Monad.Unify
64+
65+import Control.Applicative
66+import Control.Arrow (Arrow(..))
67+
68+import qualified Data.Map as M
69+import Data.Function (on)
70+import Data.Ord (comparing)
71+
72+instance Partial Type where
73+ unknown = TUnknown
74+ isUnknown (TUnknown u) = Just u
75+ isUnknown _ = Nothing
76+
77+instance Unifiable Check Type where
78+ (=?=) = unifyTypes
79+
80+-- |
81+-- Unify two types, updating the current substitution
82+--
83+unifyTypes :: Type -> Type -> UnifyT Type Check ()
84+unifyTypes t1 t2 = rethrow (\e -> "Error unifying type " ++ prettyPrintType t1 ++ " with type " ++ prettyPrintType t2 ++ ":\n" ++ e) $
85+ unifyTypes' t1 t2
86+ where
87+ unifyTypes' (TUnknown u1) (TUnknown u2) | u1 == u2 = return ()
88+ unifyTypes' (TUnknown u) t = u =:= t
89+ unifyTypes' t (TUnknown u) = u =:= t
90+ unifyTypes' (SaturatedTypeSynonym name args) ty = do
91+ ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ args
92+ ty1 `unifyTypes` ty
93+ unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
94+ unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
95+ case (sc1, sc2) of
96+ (Just sc1', Just sc2') -> do
97+ sko <- newSkolemConstant
98+ let sk1 = skolemize ident1 sko sc1' ty1
99+ let sk2 = skolemize ident2 sko sc2' ty2
100+ sk1 `unifyTypes` sk2
101+ _ -> throwError (prettyPrintType ty1)
102+ unifyTypes' (ForAll ident ty1 (Just sc)) ty2 = do
103+ sko <- newSkolemConstant
104+ let sk = skolemize ident sko sc ty1
105+ sk `unifyTypes` ty2
106+ unifyTypes' ForAll{} _ = throwError "Skolem variable scope is unspecified"
107+ unifyTypes' ty f@ForAll{} = f `unifyTypes` ty
108+ unifyTypes' (Object row1) (Object row2) = row1 =?= row2
109+ unifyTypes' (TypeVar v1) (TypeVar v2) | v1 == v2 = return ()
110+ unifyTypes' (TypeConstructor c1) (TypeConstructor c2) = do
111+ env <- getEnv
112+ Just moduleName <- checkCurrentModule <$> get
113+ guardWith ("Cannot unify " ++ show c1 ++ " with " ++ show c2 ++ ".") (c1 == c2)
114+ unifyTypes' (TypeApp t3 t4) (TypeApp t5 t6) = do
115+ t3 `unifyTypes` t5
116+ t4 `unifyTypes` t6
117+ unifyTypes' (Skolem s1 _) (Skolem s2 _) | s1 == s2 = return ()
118+ unifyTypes' r1@RCons{} r2 = unifyRows r1 r2
119+ unifyTypes' r1 r2@RCons{} = unifyRows r1 r2
120+ unifyTypes' r1@REmpty r2 = unifyRows r1 r2
121+ unifyTypes' r1 r2@REmpty = unifyRows r1 r2
122+ unifyTypes' t3 t4 = throwError $ "Cannot unify " ++ prettyPrintType t3 ++ " with " ++ prettyPrintType t4 ++ "."
123+
124+-- |
125+-- Unify two rows, updating the current substitution
126+--
127+-- Common labels are first identified, and unified. Remaining labels and types are unified with a
128+-- trailing row unification variable, if appropriate, otherwise leftover labels result in a unification
129+-- error.
130+--
131+unifyRows :: Type -> Type -> UnifyT Type Check ()
132+unifyRows r1 r2 =
133+ let
134+ (s1, r1') = rowToList r1
135+ (s2, r2') = rowToList r2
136+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
137+ sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ]
138+ sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ]
139+ in do
140+ forM_ int (uncurry (=?=))
141+ unifyRows' sd1 r1' sd2 r2'
142+ where
143+ unifyRows' :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> UnifyT Type Check ()
144+ unifyRows' [] (TUnknown u) sd r = u =:= rowFromList (sd, r)
145+ unifyRows' sd r [] (TUnknown u) = u =:= rowFromList (sd, r)
146+ unifyRows' ((name, ty):row) r others u@(TUnknown un) = do
147+ occursCheck un ty
148+ forM_ row $ \(_, t) -> occursCheck un t
149+ u' <- fresh
150+ u =?= RCons name ty u'
151+ unifyRows' row r others u'
152+ unifyRows' [] REmpty [] REmpty = return ()
153+ unifyRows' [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = return ()
154+ unifyRows' [] (Skolem s1 _) [] (Skolem s2 _) | s1 == s2 = return ()
155+ unifyRows' sd3 r3 sd4 r4 = throwError $ "Cannot unify (" ++ prettyPrintRow (rowFromList (sd3, r3)) ++ ") with (" ++ prettyPrintRow (rowFromList (sd4, r4)) ++ ")."
156+
157+-- |
158+-- Infer the types of multiple mutually-recursive values, and return elaborated values including
159+-- type class dictionaries and type annotations.
160+--
161+typesOf :: Maybe ModuleName -> ModuleName -> [(Ident, Value)] -> Check [(Ident, (Value, Type))]
162+typesOf mainModuleName moduleName vals = do
163+ tys <- fmap tidyUp . liftUnify $ do
164+ let
165+ -- Map each declaration to a name/value pair, with an optional type, if the declaration is typed
166+ es = map isTyped vals
167+ -- Filter the typed and untyped declarations
168+ typed = filter (isJust . snd . snd) es
169+ untyped = filter (isNothing . snd . snd) es
170+ -- Make a map of names to typed declarations
171+ typedDict = map (\(ident, (_, Just (ty, _))) -> (ident, ty)) typed
172+ -- Create fresh unification variables for the types of untyped declarations
173+ untypedNames <- replicateM (length untyped) fresh
174+ let
175+ -- Make a map of names to the unification variables of untyped declarations
176+ untypedDict = zip (map fst untyped) untypedNames
177+ -- Create the dictionary of all name/type pairs, which will be added to the environment during type checking
178+ dict = M.fromList (map (\(ident, ty) -> ((moduleName, ident), (ty, LocalVariable))) $ typedDict ++ untypedDict)
179+ forM es $ \e@(_, (val, _)) -> do
180+ -- If the declaration is a function, it has access to other values in the binding group.
181+ -- If not, the generated code might fail at runtime since those values might be undefined.
182+ let dict' = if isFunction val then dict else M.empty
183+ triple@(_, (val', ty)) <- case e of
184+ -- Typed declarations
185+ (ident, (val', Just (ty, checkType))) -> do
186+ -- Kind check
187+ kind <- liftCheck $ kindOf moduleName ty
188+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
189+ -- Check the type with the new names in scope
190+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
191+ val'' <- bindNames dict' $ if checkType
192+ then TypedValue True <$> check val' ty' <*> pure ty'
193+ else return (TypedValue False val' ty')
194+ return (ident, (val'', ty'))
195+ -- Untyped declarations
196+ (ident, (val', Nothing)) -> do
197+ -- Infer the type with the new names in scope
198+ TypedValue _ val'' ty <- bindNames dict' $ infer val'
199+ ty =?= fromMaybe (error "name not found in dictionary") (lookup ident untypedDict)
200+ return (ident, (TypedValue True val'' ty, ty))
201+ -- If --main is enabled, need to check that `main` has type Eff eff a for some eff, a
202+ when (Just moduleName == mainModuleName && fst e == Ident "main") $ do
203+ [eff, a] <- replicateM 2 fresh
204+ ty =?= TypeApp (TypeApp (TypeConstructor (Qualified (Just (ModuleName [ProperName "Control", ProperName "Monad", ProperName "Eff"])) (ProperName "Eff"))) eff) a
205+ -- Make sure unification variables do not escape
206+ escapeCheck val' ty
207+ return triple
208+ forM tys $ \(ident, (val, ty)) -> do
209+ -- Replace type class dictionary placeholders with actual dictionaries
210+ val' <- replaceTypeClassDictionaries moduleName val
211+ -- Check skolem variables did not escape their scope
212+ skolemEscapeCheck val'
213+ -- Remove type synonyms placeholders, remove duplicate row fields, and replace
214+ -- top-level unification variables with named type variables.
215+ let val'' = overTypes (desaturateAllTypeSynonyms . setifyAll) val'
216+ ty' = varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty
217+ return (ident, (val'', ty'))
218+ where
219+ -- Apply the substitution that was returned from runUnify to both types and (type-annotated) values
220+ tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
221+
222+-- |
223+-- Check if a value introduces a function
224+--
225+isFunction :: Value -> Bool
226+isFunction (Abs _ _) = True
227+isFunction (TypedValue _ val _) = isFunction val
228+isFunction _ = False
229+
230+-- |
231+-- Check if a value contains a type annotation
232+--
233+isTyped :: (Ident, Value) -> (Ident, (Value, Maybe (Type, Bool)))
234+isTyped (name, TypedValue checkType value ty) = (name, (value, Just (ty, checkType)))
235+isTyped (name, value) = (name, (value, Nothing))
236+
237+-- |
238+-- Map a function over type annotations appearing inside a value
239+--
240+overTypes :: (Type -> Type) -> Value -> Value
241+overTypes f = everywhere (mkT f)
242+
243+-- |
244+-- Replace type class dictionary placeholders with inferred type class dictionaries
245+--
246+replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
247+replaceTypeClassDictionaries mn = everywhereM' (mkM go)
248+ where
249+ go (TypeClassDictionary constraint dicts) = entails mn dicts constraint
250+ go other = return other
251+
252+-- |
253+-- Check that the current set of type class dictionaries entail the specified type class goal, and, if so,
254+-- return a type class dictionary reference.
255+--
256+entails :: ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, [Type]) -> Check Value
257+entails moduleName context goal@(className, tys) = do
258+ env <- getEnv
259+ case go env goal of
260+ [] -> throwError $ "No " ++ show className ++ " instance found for " ++ intercalate ", " (map prettyPrintType tys)
261+ (dict : _) -> return dict
262+ where
263+ go env (className', tys') =
264+ [ mkDictionary (canonicalizeDictionary tcd) args
265+ | tcd <- context
266+ -- Choose type class dictionaries in scope in the current module
267+ , filterModule tcd
268+ -- Make sure the type class name matches the one we are trying to satisfy
269+ , className' == tcdClassName tcd
270+ -- Make sure the type unifies with the type in the type instance definition
271+ , subst <- maybeToList . (>>= verifySubstitution) . fmap concat $ zipWithM (typeHeadsAreEqual moduleName env) tys' (tcdInstanceTypes tcd)
272+ -- Solve any necessary subgoals
273+ , args <- solveSubgoals env subst (tcdDependencies tcd) ]
274+ -- Create dictionaries for subgoals which still need to be solved by calling go recursively
275+ -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type
276+ -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively.
277+ solveSubgoals :: Environment -> [(String, Type)] -> Maybe [(Qualified ProperName, [Type])] -> [Maybe [Value]]
278+ solveSubgoals _ _ Nothing = return Nothing
279+ solveSubgoals env subst (Just subgoals) = do
280+ dict <- mapM (go env . second (map (replaceAllTypeVars subst))) subgoals
281+ return $ Just dict
282+ -- Make a dictionary from subgoal dictionaries by applying the correct function
283+ mkDictionary :: Qualified Ident -> Maybe [Value] -> Value
284+ mkDictionary fnName Nothing = Var fnName
285+ mkDictionary fnName (Just []) = App (Var fnName) (ObjectLiteral [])
286+ mkDictionary fnName (Just dicts) = foldl App (Var fnName) dicts
287+ -- Filter out type dictionaries which are in scope in the current module
288+ filterModule :: TypeClassDictionaryInScope -> Bool
289+ filterModule (TypeClassDictionaryInScope { tcdName = Qualified (Just mn) _ }) | mn == moduleName = True
290+ filterModule (TypeClassDictionaryInScope { tcdName = Qualified Nothing _ }) = True
291+ filterModule _ = False
292+ canonicalizeDictionary :: TypeClassDictionaryInScope -> Qualified Ident
293+ canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDRegular, tcdName = nm }) = nm
294+ canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDAlias nm }) = nm
295+ -- Ensure that a substitution is valid
296+ verifySubstitution :: [(String, Type)] -> Maybe [(String, Type)]
297+ verifySubstitution subst = do
298+ let grps = groupBy ((==) `on` fst) subst
299+ guard (all ((==) 1 . length . nubBy ((==) `on` snd)) grps)
300+ return $ map head grps
301+
302+-- |
303+-- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup),
304+-- and return a substitution from type variables to types which makes the type heads unify.
305+--
306+typeHeadsAreEqual :: ModuleName -> Environment -> Type -> Type -> Maybe [(String, Type)]
307+typeHeadsAreEqual _ _ (Skolem s1 _) (Skolem s2 _) | s1 == s2 = Just []
308+typeHeadsAreEqual _ _ (TypeVar v) t = Just [(v, t)]
309+typeHeadsAreEqual _ _ t (TypeVar v) = Just [(v, t)]
310+typeHeadsAreEqual m e (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = Just []
311+typeHeadsAreEqual m e (TypeApp h1 (TypeVar v)) (TypeApp h2 arg) = (:) (v, arg) <$> typeHeadsAreEqual m e h1 h2
312+typeHeadsAreEqual m e t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual m e t2 t1
313+typeHeadsAreEqual m e (SaturatedTypeSynonym name args) t2 = case expandTypeSynonym' e m name args of
314+ Left _ -> Nothing
315+ Right t1 -> typeHeadsAreEqual m e t1 t2
316+typeHeadsAreEqual _ _ _ _ = Nothing
317+
318+-- |
319+-- Ensure unsolved unification variables do not escape
320+--
321+escapeCheck :: Value -> Type -> UnifyT Type Check ()
322+escapeCheck value ty = do
323+ subst <- unifyCurrentSubstitution <$> UnifyT get
324+ let visibleUnknowns = nub $ unknowns $ subst $? ty
325+ let allUnknowns = findAllTypes value
326+ forM_ allUnknowns $ \t -> do
327+ let unsolvedUnknowns = nub . unknowns $ subst $? t
328+ guardWith "Escape check fails" $ null $ unsolvedUnknowns \\ visibleUnknowns
329+
330+-- |
331+-- Find all type annotations occuring inside a value
332+--
333+findAllTypes :: Value -> [Type]
334+findAllTypes = everything (++) (mkQ [] go)
335+ where
336+ go (TypedValue _ _ ty) = [ty]
337+ go _ = []
338+
339+-- |
340+-- Ensure skolem variables do not escape their scope
341+--
342+skolemEscapeCheck :: Value -> Check ()
343+skolemEscapeCheck (TypedValue False _ _) = return ()
344+skolemEscapeCheck root@TypedValue{} =
345+ -- Every skolem variable is created when a ForAll type is skolemized.
346+ -- This determines the scope of that skolem variable, which is copied from the SkolemScope
347+ -- field of the ForAll constructor.
348+ -- We traverse the tree top-down, and collect any SkolemScopes introduced by ForAlls.
349+ -- If a Skolem is encountered whose SkolemScope is not in the current list, we have found
350+ -- an escaped skolem variable.
351+ case everythingWithContext [] (++) (mkQ ((,) []) go) root of
352+ [] -> return ()
353+ ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
354+ where
355+ go :: Value -> [(SkolemScope, Value)] -> ([(Maybe Value, Value)], [(SkolemScope, Value)])
356+ go val@(TypedValue _ _ (ForAll _ _ (Just sco))) scos = ([], (sco, val) : scos)
357+ go val@(TypedValue _ _ ty) scos = case collectSkolems ty \\ map fst scos of
358+ (sco : _) -> ([(findBindingScope sco, val)], scos)
359+ _ -> ([], scos)
360+ where
361+ collectSkolems :: Type -> [SkolemScope]
362+ collectSkolems = nub . everything (++) (mkQ [] collect)
363+ where
364+ collect (Skolem _ scope) = [scope]
365+ collect _ = []
366+ go _ scos = ([], scos)
367+ findBindingScope :: SkolemScope -> Maybe Value
368+ findBindingScope sco = something (mkQ Nothing go') root
369+ where
370+ go' val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
371+ go' _ = Nothing
372+skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
373+
374+-- |
375+-- Ensure a row contains no duplicate labels
376+--
377+setify :: Type -> Type
378+setify = rowFromList . first (M.toList . M.fromList) . rowToList
379+
380+-- |
381+-- \"Setify\" all rows occuring inside a value
382+--
383+setifyAll :: (D.Data d) => d -> d
384+setifyAll = everywhere (mkT setify)
385+
386+-- |
387+-- Replace outermost unsolved unification variables with named type variables
388+--
389+varIfUnknown :: Type -> Type
390+varIfUnknown ty =
391+ let unks = nub $ unknowns ty
392+ toName = (:) 't' . show
393+ ty' = everywhere (mkT typeToVar) ty
394+ typeToVar :: Type -> Type
395+ typeToVar (TUnknown (Unknown u)) = TypeVar (toName u)
396+ typeToVar t = t
397+ in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
398+
399+-- |
400+-- Remove any ForAlls and ConstrainedType constructors in a type by introducing new unknowns
401+-- or TypeClassDictionary values.
402+--
403+-- This is necessary during type checking to avoid unifying a polymorphic type with a
404+-- unification variable.
405+--
406+instantiatePolyTypeWithUnknowns :: Value -> Type -> UnifyT Type Check (Value, Type)
407+instantiatePolyTypeWithUnknowns val (ForAll ident ty _) = do
408+ ty' <- replaceVarWithUnknown ident ty
409+ instantiatePolyTypeWithUnknowns val ty'
410+instantiatePolyTypeWithUnknowns val (ConstrainedType constraints ty) = do
411+ env <- getEnv
412+ Just moduleName <- checkCurrentModule <$> get
413+ dicts <- getTypeClassDictionaries
414+ (_, ty') <- instantiatePolyTypeWithUnknowns (error "Types under a constraint cannot themselves be constrained") ty
415+ return (foldl App val (map (flip TypeClassDictionary dicts) constraints), ty')
416+instantiatePolyTypeWithUnknowns val ty = return (val, ty)
417+
418+-- |
419+-- Replace a single type variable with a new unification variable
420+--
421+replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
422+replaceVarWithUnknown ident ty = do
423+ tu <- fresh
424+ return $ replaceTypeVars ident tu ty
425+
426+-- |
427+-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
428+-- better error messages during unification.
429+--
430+replaceAllTypeSynonyms' :: (D.Data d) => Environment -> ModuleName -> d -> Either String d
431+replaceAllTypeSynonyms' env moduleName d =
432+ let
433+ syns = map (\(name, (args, _)) -> (name, length args)) . M.toList $ typeSynonyms env
434+ in
435+ saturateAllTypeSynonyms env moduleName syns d
436+
437+replaceAllTypeSynonyms :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
438+replaceAllTypeSynonyms d = do
439+ env <- getEnv
440+ Just moduleName <- checkCurrentModule <$> get
441+ either throwError return $ replaceAllTypeSynonyms' env moduleName d
442+
443+-- |
444+-- \"Desaturate\" @SaturatedTypeSynonym@s
445+--
446+desaturateAllTypeSynonyms :: (D.Data d) => d -> d
447+desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
448+ where
449+ replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
450+ replaceSaturatedTypeSynonym t = t
451+
452+-- |
453+-- Replace a type synonym and its arguments with the aliased type
454+--
455+expandTypeSynonym' :: Environment -> ModuleName -> Qualified ProperName -> [Type] -> Either String Type
456+expandTypeSynonym' env moduleName name args =
457+ case M.lookup name (typeSynonyms env) of
458+ Just (synArgs, body) -> do
459+ let repl = replaceAllTypeVars (zip synArgs args) body
460+ replaceAllTypeSynonyms' env moduleName repl
461+ Nothing -> error "Type synonym was not defined"
462+
463+expandTypeSynonym :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => Qualified ProperName -> [Type] -> m Type
464+expandTypeSynonym name args = do
465+ env <- getEnv
466+ Just moduleName <- checkCurrentModule <$> get
467+ either throwError return $ expandTypeSynonym' env moduleName name args
468+
469+-- |
470+-- Ensure a set of property names and value does not contain duplicate labels
471+--
472+ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
473+ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
474+
475+-- |
476+-- Infer a type for a value, rethrowing any error to provide a more useful error message
477+--
478+infer :: Value -> UnifyT Type Check Value
479+infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
480+
481+-- |
482+-- Infer a type for a value
483+--
484+infer' :: Value -> UnifyT Type Check Value
485+infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
486+infer' v@(StringLiteral _) = return $ TypedValue True v tyString
487+infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
488+infer' (ArrayLiteral vals) = do
489+ ts <- mapM infer vals
490+ els <- fresh
491+ forM_ ts $ \(TypedValue _ _ t) -> els =?= TypeApp tyArray t
492+ return $ TypedValue True (ArrayLiteral ts) els
493+infer' (ObjectLiteral ps) = do
494+ ensureNoDuplicateProperties ps
495+ ts <- mapM (infer . snd) ps
496+ let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
497+ ty = Object $ rowFromList (fields, REmpty)
498+ return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
499+infer' (ObjectUpdate o ps) = do
500+ ensureNoDuplicateProperties ps
501+ row <- fresh
502+ newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
503+ let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
504+ oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
505+ let oldTy = Object $ rowFromList (oldTys, row)
506+ o' <- TypedValue True <$> check o oldTy <*> pure oldTy
507+ return $ TypedValue True (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
508+infer' (Accessor prop val) = do
509+ typed@(TypedValue _ _ objTy) <- infer val
510+ propTy <- inferProperty objTy prop
511+ case propTy of
512+ Nothing -> do
513+ field <- fresh
514+ rest <- fresh
515+ _ <- subsumes Nothing objTy (Object (RCons prop field rest))
516+ return $ TypedValue True (Accessor prop typed) field
517+ Just ty -> return $ TypedValue True (Accessor prop typed) ty
518+infer' (Abs (Left arg) ret) = do
519+ ty <- fresh
520+ Just moduleName <- checkCurrentModule <$> get
521+ bindLocalVariables moduleName [(arg, ty)] $ do
522+ body@(TypedValue _ _ bodyTy) <- infer' ret
523+ return $ TypedValue True (Abs (Left arg) body) $ function ty bodyTy
524+infer' (Abs (Right _) _) = error "Binder was not desugared"
525+infer' (App f arg) = do
526+ f'@(TypedValue _ _ ft) <- infer f
527+ (ret, app) <- checkFunctionApplication f' ft arg
528+ return $ TypedValue True app ret
529+infer' (Var var) = do
530+ Just moduleName <- checkCurrentModule <$> get
531+ ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
532+ case ty of
533+ ConstrainedType constraints ty' -> do
534+ env <- getEnv
535+ dicts <- getTypeClassDictionaries
536+ return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) constraints)) ty'
537+ _ -> return $ TypedValue True (Var var) ty
538+infer' v@(Constructor c) = do
539+ env <- getEnv
540+ Just moduleName <- checkCurrentModule <$> get
541+ case M.lookup c (dataConstructors env) of
542+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
543+ Just ty -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
544+ return $ TypedValue True v ty'
545+infer' (Case vals binders) = do
546+ ts <- mapM infer vals
547+ ret <- fresh
548+ binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
549+ return $ TypedValue True (Case ts binders') ret
550+infer' (IfThenElse cond th el) = do
551+ cond' <- check cond tyBoolean
552+ v2@(TypedValue _ _ t2) <- infer th
553+ v3@(TypedValue _ _ t3) <- infer el
554+ t2 =?= t3
555+ return $ TypedValue True (IfThenElse cond' v2 v3) t2
556+infer' (TypedValue checkType val ty) = do
557+ Just moduleName <- checkCurrentModule <$> get
558+ kind <- liftCheck $ kindOf moduleName ty
559+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
560+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
561+ val' <- if checkType then check val ty' else return val
562+ return $ TypedValue True val' ty'
563+infer' _ = error "Invalid argument to infer"
564+
565+-- |
566+-- Infer the type of a property inside a record with a given type
567+--
568+inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
569+inferProperty (Object row) prop = do
570+ let (props, _) = rowToList row
571+ return $ lookup prop props
572+inferProperty (SaturatedTypeSynonym name args) prop = do
573+ replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
574+ inferProperty replaced prop
575+inferProperty (ForAll ident ty _) prop = do
576+ replaced <- replaceVarWithUnknown ident ty
577+ inferProperty replaced prop
578+inferProperty _ _ = return Nothing
579+
580+-- |
581+-- Infer the types of variables brought into scope by a binder
582+--
583+inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
584+inferBinder _ NullBinder = return M.empty
585+inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
586+inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
587+inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
588+inferBinder val (VarBinder name) = return $ M.singleton name val
589+inferBinder val (ConstructorBinder ctor binders) = do
590+ env <- getEnv
591+ Just moduleName <- checkCurrentModule <$> get
592+ case M.lookup ctor (dataConstructors env) of
593+ Just ty -> do
594+ (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contains constraints") ty
595+ go binders fn
596+ where
597+ go [] ty' = do
598+ subsumes Nothing val ty'
599+ return M.empty
600+ go (binder : binders') (TypeApp (TypeApp t obj) ret) | t == tyFunction =
601+ M.union <$> inferBinder obj binder <*> go binders' ret
602+ go _ _ = throwError $ "Wrong number of arguments to constructor " ++ show ctor
603+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
604+inferBinder val (ObjectBinder props) = do
605+ row <- fresh
606+ rest <- fresh
607+ m1 <- inferRowProperties row rest props
608+ val =?= Object row
609+ return m1
610+ where
611+ inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
612+ inferRowProperties nrow row [] = nrow =?= row >> return M.empty
613+ inferRowProperties nrow row ((name, binder):binders) = do
614+ propTy <- fresh
615+ m1 <- inferBinder propTy binder
616+ m2 <- inferRowProperties nrow (RCons name propTy row) binders
617+ return $ m1 `M.union` m2
618+inferBinder val (ArrayBinder binders) = do
619+ el <- fresh
620+ m1 <- M.unions <$> mapM (inferBinder el) binders
621+ val =?= TypeApp tyArray el
622+ return m1
623+inferBinder val (ConsBinder headBinder tailBinder) = do
624+ el <- fresh
625+ m1 <- inferBinder el headBinder
626+ m2 <- inferBinder val tailBinder
627+ val =?= TypeApp tyArray el
628+ return $ m1 `M.union` m2
629+inferBinder val (NamedBinder name binder) = do
630+ m <- inferBinder val binder
631+ return $ M.insert name val m
632+
633+-- |
634+-- Check the types of the return values in a set of binders in a case statement
635+--
636+checkBinders :: [Type] -> Type -> [CaseAlternative] -> UnifyT Type Check [CaseAlternative]
637+checkBinders _ _ [] = return []
638+checkBinders nvals ret (CaseAlternative binders grd val : bs) = do
639+ Just moduleName <- checkCurrentModule <$> get
640+ m1 <- M.unions <$> zipWithM inferBinder nvals binders
641+ r <- bindLocalVariables moduleName (M.toList m1) $ do
642+ val' <- TypedValue True <$> check val ret <*> pure ret
643+ case grd of
644+ Nothing -> return $ CaseAlternative binders Nothing val'
645+ Just g -> do
646+ g' <- check g tyBoolean
647+ return $ CaseAlternative binders (Just g') val'
648+ rs <- checkBinders nvals ret bs
649+ return $ r : rs
650+
651+-- |
652+-- Check that a local variable name is not already used
653+--
654+assignVariable :: Ident -> UnifyT Type Check ()
655+assignVariable name = do
656+ env <- checkEnv <$> get
657+ Just moduleName <- checkCurrentModule <$> get
658+ case M.lookup (moduleName, name) (names env) of
659+ Just _ -> UnifyT . lift . throwError $ "Variable with name " ++ show name ++ " already exists."
660+ _ -> return ()
661+
662+-- |
663+-- Generate a new skolem constant
664+--
665+newSkolemConstant :: UnifyT Type Check Int
666+newSkolemConstant = runUnknown <$> fresh'
667+
668+-- |
669+-- Generate a new skolem scope
670+--
671+newSkolemScope :: UnifyT Type Check SkolemScope
672+newSkolemScope = SkolemScope . runUnknown <$> fresh'
673+
674+-- |
675+-- Skolemize a type variable by replacing its instances with fresh skolem constants
676+--
677+skolemize :: String -> Int -> SkolemScope -> Type -> Type
678+skolemize ident sko scope = replaceTypeVars ident (Skolem sko scope)
679+
680+-- |
681+-- Introduce skolem scope at every occurence of a ForAll
682+--
683+introduceSkolemScope :: Type -> UnifyT Type Check Type
684+introduceSkolemScope = everywhereM (mkM go)
685+ where
686+ go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
687+ go other = return other
688+
689+-- |
690+-- Check the type of a value, rethrowing errors to provide a better error message
691+--
692+check :: Value -> Type -> UnifyT Type Check Value
693+check val ty = rethrow errorMessage $ check' val ty
694+ where
695+ errorMessage msg =
696+ "Error checking type of term " ++
697+ prettyPrintValue val ++
698+ " against type " ++
699+ prettyPrintType ty ++
700+ ":\n" ++
701+ msg
702+
703+-- |
704+-- Check the type of a value
705+--
706+check' :: Value -> Type -> UnifyT Type Check Value
707+check' val (ForAll ident ty _) = do
708+ scope <- newSkolemScope
709+ sko <- newSkolemConstant
710+ let sk = skolemize ident sko scope ty
711+ val' <- check val sk
712+ return $ TypedValue True val' (ForAll ident ty (Just scope))
713+check' val t@(ConstrainedType constraints ty) = do
714+ env <- getEnv
715+ Just moduleName <- checkCurrentModule <$> get
716+ dictNames <- forM constraints $ \(Qualified _ (ProperName className), _) -> do
717+ n <- liftCheck freshDictionaryName
718+ return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
719+ val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
720+ TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
721+ constraints) $ check val ty
722+ return $ TypedValue True (foldr (Abs . Left) val' dictNames) t
723+check' val (SaturatedTypeSynonym name args) = do
724+ ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
725+ val' <- check val ty
726+ return $ TypedValue True val' ty
727+check' val u@(TUnknown _) = do
728+ val'@(TypedValue _ _ ty) <- infer val
729+ -- Don't unify an unknown with an inferred polytype
730+ (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
731+ ty' =?= u
732+ return $ TypedValue True val'' ty'
733+check' v@(NumericLiteral _) t | t == tyNumber =
734+ return $ TypedValue True v t
735+check' v@(StringLiteral _) t | t == tyString =
736+ return $ TypedValue True v t
737+check' v@(BooleanLiteral _) t | t == tyBoolean =
738+ return $ TypedValue True v t
739+check' (ArrayLiteral vals) t@(TypeApp a ty) | a == tyArray = do
740+ array <- ArrayLiteral <$> forM vals (`check` ty)
741+ return $ TypedValue True array t
742+check' (Abs (Left arg) ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
743+ Just moduleName <- checkCurrentModule <$> get
744+ ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
745+ return $ TypedValue True (Abs (Left arg) ret') ty
746+check' (Abs (Right _) _) _ = error "Binder was not desugared"
747+check' (App f arg) ret = do
748+ f'@(TypedValue _ _ ft) <- infer f
749+ (ret', app) <- checkFunctionApplication f' ft arg
750+ subsumes Nothing ret' ret
751+ return $ TypedValue True app ret
752+check' v@(Var var) ty = do
753+ Just moduleName <- checkCurrentModule <$> get
754+ repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
755+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
756+ v' <- subsumes (Just v) repl ty'
757+ case v' of
758+ Nothing -> throwError "Unable to check type subsumption"
759+ Just v'' -> return $ TypedValue True v'' ty'
760+check' (TypedValue checkType val ty1) ty2 = do
761+ Just moduleName <- checkCurrentModule <$> get
762+ kind <- liftCheck $ kindOf moduleName ty1
763+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
764+ ty1' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
765+ val' <- subsumes (Just val) ty1' ty2
766+ case val' of
767+ Nothing -> throwError "Unable to check type subsumption"
768+ Just val'' -> do
769+ val''' <- if checkType then check val'' ty1 else return val''
770+ return $ TypedValue checkType (TypedValue True val''' ty1) ty2
771+check' (Case vals binders) ret = do
772+ vals' <- mapM infer vals
773+ let ts = map (\(TypedValue _ _ t) -> t) vals'
774+ binders' <- checkBinders ts ret binders
775+ return $ TypedValue True (Case vals' binders') ret
776+check' (IfThenElse cond th el) ty = do
777+ cond' <- check cond tyBoolean
778+ th' <- check th ty
779+ el' <- check el ty
780+ return $ TypedValue True (IfThenElse cond' th' el') ty
781+check' (ObjectLiteral ps) t@(Object row) = do
782+ ensureNoDuplicateProperties ps
783+ ps' <- checkProperties ps row False
784+ return $ TypedValue True (ObjectLiteral ps') t
785+check' (ObjectUpdate obj ps) t@(Object row) = do
786+ ensureNoDuplicateProperties ps
787+ us <- zip (map fst ps) <$> replicateM (length ps) fresh
788+ let (propsToCheck, rest) = rowToList row
789+ propsToRemove = map fst ps
790+ remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
791+ obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
792+ ps' <- checkProperties ps row True
793+ return $ TypedValue True (ObjectUpdate obj' ps') t
794+check' (Accessor prop val) ty = do
795+ rest <- fresh
796+ val' <- check val (Object (RCons prop ty rest))
797+ return $ TypedValue True (Accessor prop val') ty
798+check' (Constructor c) ty = do
799+ env <- getEnv
800+ Just moduleName <- checkCurrentModule <$> get
801+ case M.lookup c (dataConstructors env) of
802+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
803+ Just ty1 -> do
804+ repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
805+ _ <- subsumes Nothing repl ty
806+ return $ TypedValue True (Constructor c) ty
807+check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
808+
809+-- |
810+-- Check the type of a collection of named record fields
811+--
812+-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
813+--
814+checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
815+checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
816+ go [] [] REmpty = return []
817+ go [] [] u@(TUnknown _) = do u =?= REmpty
818+ return []
819+ go [] [] (Skolem _ _) | lax = return []
820+ go [] ((p, _): _) _ | lax = return []
821+ | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
822+ go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
823+ go ((p,v):ps') [] u@(TUnknown _) = do
824+ v'@(TypedValue _ _ ty) <- infer v
825+ rest <- fresh
826+ u =?= RCons p ty rest
827+ ps'' <- go ps' [] rest
828+ return $ (p, v') : ps''
829+ go ((p,v):ps') ts r =
830+ case lookup p ts of
831+ Nothing -> do
832+ v'@(TypedValue _ _ ty) <- infer v
833+ rest <- fresh
834+ r =?= RCons p ty rest
835+ ps'' <- go ps' ts rest
836+ return $ (p, v') : ps''
837+ Just ty -> do
838+ v' <- check v ty
839+ ps'' <- go ps' (delete (p, ty) ts) r
840+ return $ (p, v') : ps''
841+ go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
842+
843+-- |
844+-- Check the type of a function application, rethrowing errors to provide a better error message
845+--
846+checkFunctionApplication :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
847+checkFunctionApplication fn fnTy arg = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg
848+ where
849+ errorMessage msg = "Error applying function of type "
850+ ++ prettyPrintType fnTy
851+ ++ " to argument " ++ prettyPrintValue arg
852+ ++ ":\n" ++ msg
853+
854+-- |
855+-- Check the type of a function application
856+--
857+checkFunctionApplication' :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
858+checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg = do
859+ tyFunction' =?= tyFunction
860+ arg' <- check arg argTy
861+ return (retTy, App fn arg')
862+checkFunctionApplication' fn (ForAll ident ty _) arg = do
863+ replaced <- replaceVarWithUnknown ident ty
864+ checkFunctionApplication fn replaced arg
865+checkFunctionApplication' fn u@(TUnknown _) arg = do
866+ arg' <- do
867+ TypedValue _ arg' t <- infer arg
868+ (arg'', t') <- instantiatePolyTypeWithUnknowns arg' t
869+ return $ TypedValue True arg'' t'
870+ let ty = (\(TypedValue _ _ t) -> t) arg'
871+ ret <- fresh
872+ u =?= function ty ret
873+ return (ret, App fn arg')
874+checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg = do
875+ ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
876+ checkFunctionApplication fn ty arg
877+checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg = do
878+ env <- getEnv
879+ dicts <- getTypeClassDictionaries
880+ Just moduleName <- checkCurrentModule <$> get
881+ checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) constraints)) fnTy arg
882+checkFunctionApplication' _ fnTy arg = throwError $ "Cannot apply a function of type "
883+ ++ prettyPrintType fnTy
884+ ++ " to argument " ++ prettyPrintValue arg
885+
886+-- |
887+-- Check whether one type subsumes another, rethrowing errors to provide a better error message
888+--
889+subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
890+subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
891+ where
892+ errorMessage msg = "Error checking that type "
893+ ++ prettyPrintType ty1
894+ ++ " subsumes type "
895+ ++ prettyPrintType ty2
896+ ++ ":\n" ++ msg
897+
898+-- |
899+-- Check whether one type subsumes another
900+--
901+subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
902+subsumes' val (ForAll ident ty1 _) ty2 = do
903+ replaced <- replaceVarWithUnknown ident ty1
904+ subsumes val replaced ty2
905+subsumes' val ty1 (ForAll ident ty2 sco) =
906+ case sco of
907+ Just sco' -> do
908+ sko <- newSkolemConstant
909+ let sk = skolemize ident sko sco' ty2
910+ subsumes val ty1 sk
911+ Nothing -> throwError "Skolem variable scope is unspecified"
912+subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
913+ subsumes Nothing arg2 arg1
914+ subsumes Nothing ret1 ret2
915+ return val
916+subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
917+ ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
918+ subsumes val ty1 ty2
919+subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
920+ ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
921+ subsumes val ty1 ty2
922+subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
923+ env <- getEnv
924+ dicts <- getTypeClassDictionaries
925+ Just moduleName <- checkCurrentModule <$> get
926+ _ <- subsumes' Nothing ty1 ty2
927+ return . Just $ foldl App val (map (flip TypeClassDictionary dicts) constraints)
928+subsumes' val (Object r1) (Object r2) = do
929+ let
930+ (ts1, r1') = rowToList r1
931+ (ts2, r2') = rowToList r2
932+ ts1' = sortBy (comparing fst) ts1
933+ ts2' = sortBy (comparing fst) ts2
934+ go ts1' ts2' r1' r2'
935+ return val
936+ where
937+ go [] ts2 r1' r2' = r1' =?= rowFromList (ts2, r2')
938+ go ts1 [] r1' r2' = r2' =?= rowFromList (ts1, r1')
939+ go ((p1, ty1) : ts1) ((p2, ty2) : ts2) r1' r2'
940+ | p1 == p2 = do subsumes Nothing ty1 ty2
941+ go ts1 ts2 r1' r2'
942+ | p1 < p2 = do rest <- fresh
943+ r2' =?= RCons p1 ty1 rest
944+ go ts1 ((p2, ty2) : ts2) r1' rest
945+ | p1 > p2 = do rest <- fresh
946+ r1' =?= RCons p2 ty2 rest
947+ go ((p1, ty1) : ts1) ts2 rest r2'
948+subsumes' val ty1 ty2@(Object _) = subsumes val ty2 ty1
949+subsumes' val ty1 ty2 = do
950+ ty1 =?= ty2
951+ return val
952+