@@ -0,0 +1,960 @@
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 DeriveDataTypeable #-}
18+{-# LANGUAGE FlexibleContexts #-}
19+{-# LANGUAGE MultiParamTypeClasses #-}
20+
21+module Language.PureScript.TypeChecker.Types (
22+ typesOf
23+) where
24+
25+{-
26+ The following functions represent the corresponding type checking judgements:
27+
28+ infer
29+ Synthesize a type for a value
30+
31+ check
32+ Check a value has a given type
33+
34+ checkProperties
35+ Check an object with a given type contains specified properties
36+
37+ checkFunctionApplication
38+ Check a function of a given type returns a value of another type when applied to its arguments
39+
40+ subsumes
41+ Check a type subsumes another type
42+-}
43+
44+import Data.List
45+import Data.Maybe (maybeToList, isNothing, isJust, fromMaybe)
46+import qualified Data.Data as D
47+import Data.Generics
48+ (everythingWithContext, mkM, everywhereM, everything, mkT,
49+ something, everywhere, mkQ)
50+import Data.Generics.Extras
51+
52+import Language.PureScript.Values
53+import Language.PureScript.Types
54+import Language.PureScript.Kinds
55+import Language.PureScript.Names
56+import Language.PureScript.TypeChecker.Monad
57+import Language.PureScript.TypeChecker.Kinds
58+import Language.PureScript.TypeChecker.Synonyms
59+import Language.PureScript.Pretty
60+
61+import Control.Monad.State
62+import Control.Monad.Error
63+import Control.Monad.Reader
64+import Control.Monad.Unify
65+
66+import Control.Applicative
67+import Control.Arrow (Arrow(..))
68+
69+import qualified Data.Map as M
70+import Data.Function (on)
71+import Data.Ord (comparing)
72+
73+instance Partial Type where
74+ unknown = TUnknown
75+ isUnknown (TUnknown u) = Just u
76+ isUnknown _ = Nothing
77+
78+instance Unifiable Check Type where
79+ (=?=) = unifyTypes
80+
81+-- |
82+-- Unify two types, updating the current substitution
83+--
84+unifyTypes :: Type -> Type -> UnifyT Type Check ()
85+unifyTypes t1 t2 = rethrow (\e -> "Error unifying type " ++ prettyPrintType t1 ++ " with type " ++ prettyPrintType t2 ++ ":\n" ++ e) $ do
86+ unifyTypes' t1 t2
87+ where
88+ unifyTypes' (TUnknown u1) (TUnknown u2) | u1 == u2 = return ()
89+ unifyTypes' (TUnknown u) t = u =:= t
90+ unifyTypes' t (TUnknown u) = u =:= t
91+ unifyTypes' (SaturatedTypeSynonym name args) ty = do
92+ ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ args
93+ ty1 `unifyTypes` ty
94+ unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
95+ unifyTypes' (ForAll ident1 ty1 sc1) (ForAll ident2 ty2 sc2) =
96+ case (sc1, sc2) of
97+ (Just sc1', Just sc2') -> do
98+ sko <- newSkolemConstant
99+ let sk1 = skolemize ident1 sko sc1' ty1
100+ let sk2 = skolemize ident2 sko sc2' ty2
101+ sk1 `unifyTypes` sk2
102+ _ -> throwError (prettyPrintType ty1)
103+ unifyTypes' (ForAll ident ty1 (Just sc)) ty2 = do
104+ sko <- newSkolemConstant
105+ let sk = skolemize ident sko sc ty1
106+ sk `unifyTypes` ty2
107+ unifyTypes' (ForAll _ _ _) _ = throwError "Skolem variable scope is unspecified"
108+ unifyTypes' ty f@(ForAll _ _ _) = f `unifyTypes` ty
109+ unifyTypes' (Object row1) (Object row2) = row1 =?= row2
110+ unifyTypes' (TypeVar v1) (TypeVar v2) | v1 == v2 = return ()
111+ unifyTypes' (TypeConstructor c1) (TypeConstructor c2) = do
112+ env <- getEnv
113+ Just moduleName <- checkCurrentModule <$> get
114+ guardWith ("Cannot unify " ++ show c1 ++ " with " ++ show c2 ++ ".") (typeConstructorsAreEqual env moduleName c1 c2)
115+ unifyTypes' (TypeApp t3 t4) (TypeApp t5 t6) = do
116+ t3 `unifyTypes` t5
117+ t4 `unifyTypes` t6
118+ unifyTypes' (Skolem s1 _) (Skolem s2 _) | s1 == s2 = return ()
119+ unifyTypes' r1@(RCons _ _ _) r2 = unifyRows r1 r2
120+ unifyTypes' r1 r2@(RCons _ _ _) = unifyRows r1 r2
121+ unifyTypes' r1@REmpty r2 = unifyRows r1 r2
122+ unifyTypes' r1 r2@REmpty = unifyRows r1 r2
123+ unifyTypes' t3 t4 = throwError $ "Cannot unify " ++ prettyPrintType t3 ++ " with " ++ prettyPrintType t4 ++ "."
124+
125+-- |
126+-- Unify two rows, updating the current substitution
127+--
128+-- Common labels are first identified, and unified. Remaining labels and types are unified with a
129+-- trailing row unification variable, if appropriate, otherwise leftover labels result in a unification
130+-- error.
131+--
132+unifyRows :: Type -> Type -> UnifyT Type Check ()
133+unifyRows r1 r2 =
134+ let
135+ (s1, r1') = rowToList r1
136+ (s2, r2') = rowToList r2
137+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
138+ sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ]
139+ sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ]
140+ in do
141+ forM_ int (uncurry (=?=))
142+ unifyRows' sd1 r1' sd2 r2'
143+ where
144+ unifyRows' :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> UnifyT Type Check ()
145+ unifyRows' [] (TUnknown u) sd r = u =:= rowFromList (sd, r)
146+ unifyRows' sd r [] (TUnknown u) = u =:= rowFromList (sd, r)
147+ unifyRows' ((name, ty):row) r others u@(TUnknown un) = do
148+ occursCheck un ty
149+ forM_ row $ \(_, t) -> occursCheck un t
150+ u' <- fresh
151+ u =?= RCons name ty u'
152+ unifyRows' row r others u'
153+ unifyRows' [] REmpty [] REmpty = return ()
154+ unifyRows' [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = return ()
155+ unifyRows' [] (Skolem s1 _) [] (Skolem s2 _) | s1 == s2 = return ()
156+ unifyRows' sd3 r3 sd4 r4 = throwError $ "Cannot unify (" ++ prettyPrintRow (rowFromList (sd3, r3)) ++ ") with (" ++ prettyPrintRow (rowFromList (sd4, r4)) ++ ")."
157+
158+-- |
159+-- Ensure type constructors are equal after canonicalization
160+--
161+typeConstructorsAreEqual :: Environment -> ModuleName -> Qualified ProperName -> Qualified ProperName -> Bool
162+typeConstructorsAreEqual env moduleName = (==) `on` canonicalizeType moduleName env
163+
164+-- |
165+-- Infer the types of multiple mutually-recursive values, and return elaborated values including
166+-- type class dictionaries and type annotations.
167+--
168+typesOf :: Maybe ModuleName -> ModuleName -> [(Ident, Value)] -> Check [(Ident, (Value, Type))]
169+typesOf mainModuleName moduleName vals = do
170+ tys <- fmap tidyUp . liftUnify $ do
171+ let
172+ -- Map each declaration to a name/value pair, with an optional type, if the declaration is typed
173+ es = map isTyped vals
174+ -- Filter the typed and untyped declarations
175+ typed = filter (isJust . snd . snd) es
176+ untyped = filter (isNothing . snd . snd) es
177+ -- Make a map of names to typed declarations
178+ typedDict = map (\(ident, (_, Just (ty, _))) -> (ident, ty)) typed
179+ -- Create fresh unification variables for the types of untyped declarations
180+ untypedNames <- replicateM (length untyped) fresh
181+ let
182+ -- Make a map of names to the unification variables of untyped declarations
183+ untypedDict = zip (map fst untyped) untypedNames
184+ -- Create the dictionary of all name/type pairs, which will be added to the environment during type checking
185+ dict = M.fromList (map (\(ident, ty) -> ((moduleName, ident), (ty, LocalVariable))) $ typedDict ++ untypedDict)
186+ forM es $ \e@(_, (val, _)) -> do
187+ -- If the declaration is a function, it has access to other values in the binding group.
188+ -- If not, the generated code might fail at runtime since those values might be undefined.
189+ let dict' = if isFunction val then dict else M.empty
190+ triple@(_, (val, ty)) <- case e of
191+ -- Typed declarations
192+ (ident, (val, Just (ty, checkType))) -> do
193+ -- Kind check
194+ kind <- liftCheck $ kindOf moduleName ty
195+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
196+ -- Check the type with the new names in scope
197+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
198+ val' <- bindNames dict' $ if checkType
199+ then TypedValue True <$> check val ty' <*> pure ty'
200+ else return (TypedValue False val ty')
201+ return (ident, (val', ty'))
202+ -- Untyped declarations
203+ (ident, (val, Nothing)) -> do
204+ -- Infer the type with the new names in scope
205+ TypedValue _ val' ty <- bindNames dict' $ infer val
206+ ty =?= fromMaybe (error "name not found in dictionary") (lookup ident untypedDict)
207+ return (ident, (TypedValue True val' ty, ty))
208+ -- If --main is enabled, need to check that `main` has type Eff eff a for some eff, a
209+ when (Just moduleName == mainModuleName && fst e == Ident "main") $ do
210+ [eff, a] <- replicateM 2 fresh
211+ ty =?= TypeApp (TypeApp (TypeConstructor (Qualified (Just (ModuleName [ProperName "Eff"])) (ProperName "Eff"))) eff) a
212+ -- Make sure unification variables do not escape
213+ escapeCheck val ty
214+ return triple
215+ forM tys $ \(ident, (val, ty)) -> do
216+ -- Replace type class dictionary placeholders with actual dictionaries
217+ val' <- replaceTypeClassDictionaries moduleName val
218+ -- Check skolem variables did not escape their scope
219+ skolemEscapeCheck val'
220+ -- Remove type synonyms placeholders, remove duplicate row fields, and replace
221+ -- top-level unification variables with named type variables.
222+ let val'' = overTypes (desaturateAllTypeSynonyms . setifyAll) val'
223+ ty' = varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty
224+ return $ (ident, (val'', ty'))
225+ where
226+ -- Apply the substitution that was returned from runUnify to both types and (type-annotated) values
227+ tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
228+
229+-- |
230+-- Check if a value introduces a function
231+--
232+isFunction :: Value -> Bool
233+isFunction (Abs _ _) = True
234+isFunction (TypedValue _ val _) = isFunction val
235+isFunction _ = False
236+
237+-- |
238+-- Check if a value contains a type annotation
239+--
240+isTyped :: (Ident, Value) -> (Ident, (Value, Maybe (Type, Bool)))
241+isTyped (name, TypedValue checkType value ty) = (name, (value, Just (ty, checkType)))
242+isTyped (name, value) = (name, (value, Nothing))
243+
244+-- |
245+-- Map a function over type annotations appearing inside a value
246+--
247+overTypes :: (Type -> Type) -> Value -> Value
248+overTypes f = everywhere (mkT f)
249+
250+-- |
251+-- Replace type class dictionary placeholders with inferred type class dictionaries
252+--
253+replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
254+replaceTypeClassDictionaries mn = everywhereM' (mkM go)
255+ where
256+ go (TypeClassDictionary constraint dicts) = entails mn dicts constraint
257+ go other = return other
258+
259+-- |
260+-- Check that the current set of type class dictionaries entail the specified type class goal, and, if so,
261+-- return a type class dictionary reference.
262+--
263+entails :: ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, Type) -> Check Value
264+entails moduleName context goal@(className, ty) = do
265+ env <- getEnv
266+ case go env goal of
267+ [] -> throwError $ "No " ++ show className ++ " instance found for " ++ prettyPrintType ty
268+ (dict : _) -> return dict
269+ where
270+ go env (className', ty') =
271+ [ mkDictionary (canonicalizeDictionary tcd) args
272+ | tcd <- context
273+ -- Choose type class dictionaries in scope in the current module
274+ , filterModule tcd
275+ -- Make sure the type class name matches the one we are trying to satisfy
276+ , typeConstructorsAreEqual env moduleName className' (tcdClassName tcd)
277+ -- Make sure the type unifies with the type in the type instance definition
278+ , subst <- maybeToList $ typeHeadsAreEqual moduleName env ty' (tcdInstanceType tcd)
279+ -- Solve any necessary subgoals
280+ , args <- solveSubgoals env subst (tcdDependencies tcd) ]
281+ -- Create dictionaries for subgoals which still need to be solved by calling go recursively
282+ -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type
283+ -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively.
284+ solveSubgoals :: Environment -> [(String, Type)] -> Maybe [(Qualified ProperName, Type)] -> [Maybe [Value]]
285+ solveSubgoals _ _ Nothing = return Nothing
286+ solveSubgoals env subst (Just subgoals) = do
287+ dict <- mapM (go env) (map (id *** replaceAllTypeVars subst) subgoals)
288+ return $ Just dict
289+ -- Make a dictionary from subgoal dictionaries by applying the correct function
290+ mkDictionary :: Qualified Ident -> Maybe [Value] -> Value
291+ mkDictionary fnName Nothing = Var fnName
292+ mkDictionary fnName (Just []) = App (Var fnName) (ObjectLiteral [])
293+ mkDictionary fnName (Just dicts) = foldl App (Var fnName) dicts
294+ -- Filter out type dictionaries which are in scope in the current module
295+ filterModule :: TypeClassDictionaryInScope -> Bool
296+ filterModule (TypeClassDictionaryInScope { tcdName = Qualified (Just mn) _ }) | mn == moduleName = True
297+ filterModule (TypeClassDictionaryInScope { tcdName = Qualified Nothing _ }) = True
298+ filterModule _ = False
299+ -- Resolve a type class dictionary in scope to an actual value by following any (TCDAlias) pointers
300+ -- which originated from module imports
301+ canonicalizeDictionary :: TypeClassDictionaryInScope -> Qualified Ident
302+ canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDRegular, tcdName = nm }) = nm
303+ canonicalizeDictionary (TypeClassDictionaryInScope { tcdType = TCDAlias nm }) = nm
304+
305+-- |
306+-- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup),
307+-- and return a substitution from type variables to types which makes the type heads unify.
308+--
309+typeHeadsAreEqual :: ModuleName -> Environment -> Type -> Type -> Maybe [(String, Type)]
310+typeHeadsAreEqual _ _ (Skolem s1 _) (Skolem s2 _) | s1 == s2 = Just []
311+typeHeadsAreEqual _ _ (TypeVar v) t = Just [(v, t)]
312+typeHeadsAreEqual _ _ t (TypeVar v) = Just [(v, t)]
313+typeHeadsAreEqual m e (TypeConstructor c1) (TypeConstructor c2) | typeConstructorsAreEqual e m c1 c2 = Just []
314+typeHeadsAreEqual m e (TypeApp h1 (TypeVar v)) (TypeApp h2 arg) = (:) (v, arg) <$> typeHeadsAreEqual m e h1 h2
315+typeHeadsAreEqual m e t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual m e t2 t1
316+typeHeadsAreEqual m e (SaturatedTypeSynonym name args) t2 = case expandTypeSynonym' e m name args of
317+ Left err -> Nothing
318+ Right t1 -> typeHeadsAreEqual m e t1 t2
319+typeHeadsAreEqual _ _ _ _ = Nothing
320+
321+-- |
322+-- Ensure unsolved unification variables do not escape
323+--
324+escapeCheck :: Value -> Type -> UnifyT Type Check ()
325+escapeCheck value ty = do
326+ subst <- unifyCurrentSubstitution <$> UnifyT get
327+ let visibleUnknowns = nub $ unknowns $ subst $? ty
328+ let allUnknowns = findAllTypes value
329+ forM_ allUnknowns $ \t -> do
330+ let unsolvedUnknowns = nub . unknowns $ subst $? t
331+ guardWith "Escape check fails" $ null $ unsolvedUnknowns \\ visibleUnknowns
332+
333+-- |
334+-- Find all type annotations occuring inside a value
335+--
336+findAllTypes :: Value -> [Type]
337+findAllTypes = everything (++) (mkQ [] go)
338+ where
339+ go (TypedValue _ _ ty) = [ty]
340+ go _ = []
341+
342+-- |
343+-- Ensure skolem variables do not escape their scope
344+--
345+skolemEscapeCheck :: Value -> Check ()
346+skolemEscapeCheck (TypedValue False _ _) = return ()
347+skolemEscapeCheck root@(TypedValue _ _ _) =
348+ -- Every skolem variable is created when a ForAll type is skolemized.
349+ -- This determines the scope of that skolem variable, which is copied from the SkolemScope
350+ -- field of the ForAll constructor.
351+ -- We traverse the tree top-down, and collect any SkolemScopes introduced by ForAlls.
352+ -- If a Skolem is encountered whose SkolemScope is not in the current list, we have found
353+ -- an escaped skolem variable.
354+ case everythingWithContext [] (++) (mkQ ((,) []) go) root of
355+ [] -> return ()
356+ ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
357+ where
358+ go :: Value -> [(SkolemScope, Value)] -> ([(Maybe Value, Value)], [(SkolemScope, Value)])
359+ go val@(TypedValue _ _ (ForAll _ _ (Just sco))) scos = ([], (sco, val) : scos)
360+ go val@(TypedValue _ _ ty) scos = case collectSkolems ty \\ map fst scos of
361+ (sco : _) -> ([(findBindingScope sco, val)], scos)
362+ _ -> ([], scos)
363+ where
364+ collectSkolems :: Type -> [SkolemScope]
365+ collectSkolems = nub . everything (++) (mkQ [] collect)
366+ where
367+ collect (Skolem _ scope) = [scope]
368+ collect _ = []
369+ go _ scos = ([], scos)
370+ findBindingScope :: SkolemScope -> Maybe Value
371+ findBindingScope sco = something (mkQ Nothing go) root
372+ where
373+ go val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
374+ go _ = Nothing
375+skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
376+
377+-- |
378+-- Ensure a row contains no duplicate labels
379+--
380+setify :: Type -> Type
381+setify = rowFromList . first (M.toList . M.fromList) . rowToList
382+
383+-- |
384+-- \"Setify\" all rows occuring inside a value
385+--
386+setifyAll :: (D.Data d) => d -> d
387+setifyAll = everywhere (mkT setify)
388+
389+-- |
390+-- Replace outermost unsolved unification variables with named type variables
391+--
392+varIfUnknown :: Type -> Type
393+varIfUnknown ty =
394+ let unks = nub $ unknowns ty
395+ toName = (:) 't' . show
396+ ty' = everywhere (mkT typeToVar) $ ty
397+ typeToVar :: Type -> Type
398+ typeToVar (TUnknown (Unknown u)) = TypeVar (toName u)
399+ typeToVar t = t
400+ in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
401+
402+-- |
403+-- Replace named type variables with types
404+--
405+replaceAllTypeVars :: [(String, Type)] -> Type -> Type
406+replaceAllTypeVars = foldl' (\f (name, ty) -> replaceTypeVars name ty . f) id
407+
408+-- |
409+-- Remove any ForAlls and ConstrainedType constructors in a type by introducing new unknowns
410+-- or TypeClassDictionary values.
411+--
412+-- This is necessary during type checking to avoid unifying a polymorphic type with a
413+-- unification variable.
414+--
415+instantiatePolyTypeWithUnknowns :: Value -> Type -> UnifyT Type Check (Value, Type)
416+instantiatePolyTypeWithUnknowns val (ForAll ident ty _) = do
417+ ty' <- replaceVarWithUnknown ident ty
418+ instantiatePolyTypeWithUnknowns val ty'
419+instantiatePolyTypeWithUnknowns val (ConstrainedType constraints ty) = do
420+ env <- getEnv
421+ Just moduleName <- checkCurrentModule <$> get
422+ dicts <- getTypeClassDictionaries
423+ (_, ty') <- instantiatePolyTypeWithUnknowns (error "Types under a constraint cannot themselves be constrained") ty
424+ return (foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints)), ty')
425+instantiatePolyTypeWithUnknowns val ty = return (val, ty)
426+
427+-- |
428+-- Replace a single type variable with a new unification variable
429+--
430+replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
431+replaceVarWithUnknown ident ty = do
432+ tu <- fresh
433+ return $ replaceTypeVars ident tu $ ty
434+
435+-- |
436+-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
437+-- better error messages during unification.
438+--
439+replaceAllTypeSynonyms' :: (D.Data d) => Environment -> ModuleName -> d -> Either String d
440+replaceAllTypeSynonyms' env moduleName d =
441+ let
442+ syns = map (\((path, name), (args, _)) -> ((path, name), length args)) . M.toList $ typeSynonyms env
443+ in
444+ saturateAllTypeSynonyms env moduleName syns d
445+
446+replaceAllTypeSynonyms :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
447+replaceAllTypeSynonyms d = do
448+ env <- getEnv
449+ Just moduleName <- checkCurrentModule <$> get
450+ either throwError return $ replaceAllTypeSynonyms' env moduleName d
451+
452+-- |
453+-- \"Desaturate\" @SaturatedTypeSynonym@s
454+--
455+desaturateAllTypeSynonyms :: (D.Data d) => d -> d
456+desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
457+ where
458+ replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
459+ replaceSaturatedTypeSynonym t = t
460+
461+-- |
462+-- Replace a type synonym and its arguments with the aliased type
463+--
464+expandTypeSynonym' :: Environment -> ModuleName -> Qualified ProperName -> [Type] -> Either String Type
465+expandTypeSynonym' env moduleName name args =
466+ case M.lookup (canonicalizeType moduleName env name) (typeSynonyms env) of
467+ Just (synArgs, body) -> do
468+ let repl = replaceAllTypeVars (zip synArgs args) body
469+ replaceAllTypeSynonyms' env moduleName repl
470+ Nothing -> error "Type synonym was not defined"
471+
472+expandTypeSynonym :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => Qualified ProperName -> [Type] -> m Type
473+expandTypeSynonym name args = do
474+ env <- getEnv
475+ Just moduleName <- checkCurrentModule <$> get
476+ either throwError return $ expandTypeSynonym' env moduleName name args
477+
478+-- |
479+-- Ensure a set of property names and value does not contain duplicate labels
480+--
481+ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
482+ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
483+
484+-- |
485+-- Infer a type for a value, rethrowing any error to provide a more useful error message
486+--
487+infer :: Value -> UnifyT Type Check Value
488+infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
489+
490+-- |
491+-- Infer a type for a value
492+--
493+infer' :: Value -> UnifyT Type Check Value
494+infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
495+infer' v@(StringLiteral _) = return $ TypedValue True v tyString
496+infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
497+infer' (ArrayLiteral vals) = do
498+ ts <- mapM infer vals
499+ els <- fresh
500+ forM_ ts $ \(TypedValue _ _ t) -> els =?= TypeApp tyArray t
501+ return $ TypedValue True (ArrayLiteral ts) els
502+infer' (ObjectLiteral ps) = do
503+ ensureNoDuplicateProperties ps
504+ ts <- mapM (infer . snd) ps
505+ let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
506+ ty = Object $ rowFromList (fields, REmpty)
507+ return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
508+infer' (ObjectUpdate o ps) = do
509+ ensureNoDuplicateProperties ps
510+ row <- fresh
511+ newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
512+ let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
513+ oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
514+ let oldTy = Object $ rowFromList (oldTys, row)
515+ o' <- TypedValue True <$> check o oldTy <*> pure oldTy
516+ return $ TypedValue True (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
517+infer' (Accessor prop val) = do
518+ typed@(TypedValue _ _ objTy) <- infer val
519+ propTy <- inferProperty objTy prop
520+ case propTy of
521+ Nothing -> do
522+ field <- fresh
523+ rest <- fresh
524+ _ <- subsumes Nothing objTy (Object (RCons prop field rest))
525+ return $ TypedValue True (Accessor prop typed) field
526+ Just ty -> return $ TypedValue True (Accessor prop typed) ty
527+infer' (Abs arg ret) = do
528+ ty <- fresh
529+ Just moduleName <- checkCurrentModule <$> get
530+ bindLocalVariables moduleName [(arg, ty)] $ do
531+ body@(TypedValue _ _ bodyTy) <- infer' ret
532+ return $ TypedValue True (Abs arg body) $ function ty bodyTy
533+infer' (App f arg) = do
534+ f'@(TypedValue _ _ ft) <- infer f
535+ (ret, app) <- checkFunctionApplication f' ft arg
536+ return $ TypedValue True app ret
537+infer' (Var var) = do
538+ Just moduleName <- checkCurrentModule <$> get
539+ ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
540+ case ty of
541+ ConstrainedType constraints ty' -> do
542+ env <- getEnv
543+ dicts <- getTypeClassDictionaries
544+ return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) ty'
545+ _ -> return $ TypedValue True (Var var) ty
546+infer' v@(Constructor c) = do
547+ env <- getEnv
548+ Just moduleName <- checkCurrentModule <$> get
549+ case M.lookup (qualify moduleName c) (dataConstructors env) of
550+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
551+ Just (ty, _) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
552+ return $ TypedValue True v ty'
553+infer' (Case vals binders) = do
554+ ts <- mapM infer vals
555+ ret <- fresh
556+ binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
557+ return $ TypedValue True (Case ts binders') ret
558+infer' (IfThenElse cond th el) = do
559+ cond' <- check cond tyBoolean
560+ v2@(TypedValue _ _ t2) <- infer th
561+ v3@(TypedValue _ _ t3) <- infer el
562+ t2 =?= t3
563+ return $ TypedValue True (IfThenElse cond' v2 v3) t2
564+infer' (TypedValue checkType val ty) = do
565+ Just moduleName <- checkCurrentModule <$> get
566+ kind <- liftCheck $ kindOf moduleName ty
567+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
568+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
569+ val' <- if checkType then check val ty' else return val
570+ return $ TypedValue True val' ty'
571+infer' _ = error "Invalid argument to infer"
572+
573+-- |
574+-- Infer the type of a property inside a record with a given type
575+--
576+inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
577+inferProperty (Object row) prop = do
578+ let (props, _) = rowToList row
579+ return $ lookup prop props
580+inferProperty (SaturatedTypeSynonym name args) prop = do
581+ replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
582+ inferProperty replaced prop
583+inferProperty (ForAll ident ty _) prop = do
584+ replaced <- replaceVarWithUnknown ident ty
585+ inferProperty replaced prop
586+inferProperty _ _ = return Nothing
587+
588+-- |
589+-- Infer the types of variables brought into scope by a binder
590+--
591+inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
592+inferBinder _ NullBinder = return M.empty
593+inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
594+inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
595+inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
596+inferBinder val (VarBinder name) = return $ M.singleton name val
597+inferBinder val (ConstructorBinder ctor binders) = do
598+ env <- getEnv
599+ Just moduleName <- checkCurrentModule <$> get
600+ case M.lookup (qualify moduleName ctor) (dataConstructors env) of
601+ Just (ty, _) -> do
602+ (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contains constraints") ty
603+ go binders fn
604+ where
605+ go [] ty = do
606+ subsumes Nothing val ty
607+ return M.empty
608+ go (binder : binders) (TypeApp (TypeApp t obj) ret) | t == tyFunction =
609+ M.union <$> inferBinder obj binder <*> go binders ret
610+ go _ _ = throwError $ "Wrong number of arguments to constructor " ++ show ctor
611+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
612+inferBinder val (ObjectBinder props) = do
613+ row <- fresh
614+ rest <- fresh
615+ m1 <- inferRowProperties row rest props
616+ val =?= Object row
617+ return m1
618+ where
619+ inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
620+ inferRowProperties nrow row [] = nrow =?= row >> return M.empty
621+ inferRowProperties nrow row ((name, binder):binders) = do
622+ propTy <- fresh
623+ m1 <- inferBinder propTy binder
624+ m2 <- inferRowProperties nrow (RCons name propTy row) binders
625+ return $ m1 `M.union` m2
626+inferBinder val (ArrayBinder binders) = do
627+ el <- fresh
628+ m1 <- M.unions <$> mapM (inferBinder el) binders
629+ val =?= TypeApp tyArray el
630+ return m1
631+inferBinder val (ConsBinder headBinder tailBinder) = do
632+ el <- fresh
633+ m1 <- inferBinder el headBinder
634+ m2 <- inferBinder val tailBinder
635+ val =?= TypeApp tyArray el
636+ return $ m1 `M.union` m2
637+inferBinder val (NamedBinder name binder) = do
638+ m <- inferBinder val binder
639+ return $ M.insert name val m
640+
641+-- |
642+-- Check the types of the return values in a set of binders in a case statement
643+--
644+checkBinders :: [Type] -> Type -> [([Binder], Maybe Guard, Value)] -> UnifyT Type Check [([Binder], Maybe Guard, Value)]
645+checkBinders _ _ [] = return []
646+checkBinders nvals ret ((binders, grd, val):bs) = do
647+ Just moduleName <- checkCurrentModule <$> get
648+ m1 <- M.unions <$> zipWithM inferBinder nvals binders
649+ r <- bindLocalVariables moduleName (M.toList m1) $ do
650+ val' <- TypedValue True <$> check val ret <*> pure ret
651+ case grd of
652+ Nothing -> return (binders, Nothing, val')
653+ Just g -> do
654+ g' <- check g tyBoolean
655+ return (binders, Just g', val')
656+ rs <- checkBinders nvals ret bs
657+ return $ r : rs
658+
659+-- |
660+-- Check that a local variable name is not already used
661+--
662+assignVariable :: Ident -> UnifyT Type Check ()
663+assignVariable name = do
664+ env <- checkEnv <$> get
665+ Just moduleName <- checkCurrentModule <$> get
666+ case M.lookup (moduleName, name) (names env) of
667+ Just _ -> UnifyT . lift . throwError $ "Variable with name " ++ show name ++ " already exists."
668+ _ -> return ()
669+
670+-- |
671+-- Generate a new skolem constant
672+--
673+newSkolemConstant :: UnifyT Type Check Int
674+newSkolemConstant = runUnknown <$> fresh'
675+
676+-- |
677+-- Generate a new skolem scope
678+--
679+newSkolemScope :: UnifyT Type Check SkolemScope
680+newSkolemScope = SkolemScope . runUnknown <$> fresh'
681+
682+-- |
683+-- Skolemize a type variable by replacing its instances with fresh skolem constants
684+--
685+skolemize :: String -> Int -> SkolemScope -> Type -> Type
686+skolemize ident sko scope = replaceTypeVars ident (Skolem sko scope)
687+
688+-- |
689+-- Introduce skolem scope at every occurence of a ForAll
690+--
691+introduceSkolemScope :: Type -> UnifyT Type Check Type
692+introduceSkolemScope = everywhereM (mkM go)
693+ where
694+ go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
695+ go other = return other
696+
697+-- |
698+-- Check the type of a value, rethrowing errors to provide a better error message
699+--
700+check :: Value -> Type -> UnifyT Type Check Value
701+check val ty = rethrow errorMessage $ check' val ty
702+ where
703+ errorMessage msg =
704+ "Error checking type of term " ++
705+ prettyPrintValue val ++
706+ " against type " ++
707+ prettyPrintType ty ++
708+ ":\n" ++
709+ msg
710+
711+-- |
712+-- Check the type of a value
713+--
714+check' :: Value -> Type -> UnifyT Type Check Value
715+check' val t@(ForAll ident ty _) = do
716+ scope <- newSkolemScope
717+ sko <- newSkolemConstant
718+ let sk = skolemize ident sko scope ty
719+ val' <- check val sk
720+ return $ TypedValue True val' (ForAll ident ty (Just scope))
721+check' val t@(ConstrainedType constraints ty) = do
722+ env <- getEnv
723+ Just moduleName <- checkCurrentModule <$> get
724+ dictNames <- flip mapM constraints $ \(Qualified _ (ProperName className), _) -> do
725+ n <- liftCheck freshDictionaryName
726+ return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
727+ val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
728+ TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
729+ (qualifyAllUnqualifiedNames moduleName env constraints)) $
730+ check val ty
731+ return $ TypedValue True (foldr Abs val' dictNames) t
732+check' val t@(SaturatedTypeSynonym name args) = do
733+ ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
734+ val' <- check val ty
735+ return $ TypedValue True val' ty
736+check' val u@(TUnknown _) = do
737+ val'@(TypedValue _ _ ty) <- infer val
738+ -- Don't unify an unknown with an inferred polytype
739+ (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
740+ ty' =?= u
741+ return $ TypedValue True val'' ty'
742+check' v@(NumericLiteral _) t | t == tyNumber =
743+ return $ TypedValue True v t
744+check' v@(StringLiteral _) t | t == tyString =
745+ return $ TypedValue True v t
746+check' v@(BooleanLiteral _) t | t == tyBoolean =
747+ return $ TypedValue True v t
748+check' (ArrayLiteral vals) t@(TypeApp a ty) | a == tyArray = do
749+ arr <- ArrayLiteral <$> forM vals (\val -> check val ty)
750+ return $ TypedValue True arr t
751+check' (Abs arg ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
752+ Just moduleName <- checkCurrentModule <$> get
753+ ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
754+ return $ TypedValue True (Abs arg ret') ty
755+check' (App f arg) ret = do
756+ f'@(TypedValue _ _ ft) <- infer f
757+ (ret', app) <- checkFunctionApplication f' ft arg
758+ subsumes Nothing ret' ret
759+ return $ TypedValue True app ret
760+check' v@(Var var) ty = do
761+ Just moduleName <- checkCurrentModule <$> get
762+ repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
763+ ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
764+ v' <- subsumes (Just v) repl ty'
765+ case v' of
766+ Nothing -> throwError "Unable to check type subsumption"
767+ Just v'' -> return $ TypedValue True v'' ty'
768+check' (TypedValue checkType val ty1) ty2 = do
769+ Just moduleName <- checkCurrentModule <$> get
770+ kind <- liftCheck $ kindOf moduleName ty1
771+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
772+ ty1' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
773+ val' <- subsumes (Just val) ty1' ty2
774+ case val' of
775+ Nothing -> throwError "Unable to check type subsumption"
776+ Just val'' -> do
777+ val''' <- if checkType then check val'' ty1 else return val''
778+ return $ TypedValue checkType (TypedValue True val''' ty1) ty2
779+check' (Case vals binders) ret = do
780+ vals' <- mapM infer vals
781+ let ts = map (\(TypedValue _ _ t) -> t) vals'
782+ binders' <- checkBinders ts ret binders
783+ return $ TypedValue True (Case vals' binders') ret
784+check' (IfThenElse cond th el) ty = do
785+ cond' <- check cond tyBoolean
786+ th' <- check th ty
787+ el' <- check el ty
788+ return $ TypedValue True (IfThenElse cond' th' el') ty
789+check' (ObjectLiteral ps) t@(Object row) = do
790+ ensureNoDuplicateProperties ps
791+ ps' <- checkProperties ps row False
792+ return $ TypedValue True (ObjectLiteral ps') t
793+check' (ObjectUpdate obj ps) t@(Object row) = do
794+ ensureNoDuplicateProperties ps
795+ us <- zip (map fst ps) <$> replicateM (length ps) fresh
796+ let (propsToCheck, rest) = rowToList row
797+ propsToRemove = map fst ps
798+ remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
799+ obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
800+ ps' <- checkProperties ps row True
801+ return $ TypedValue True (ObjectUpdate obj' ps') t
802+check' (Accessor prop val) ty = do
803+ rest <- fresh
804+ val' <- check val (Object (RCons prop ty rest))
805+ return $ TypedValue True (Accessor prop val') ty
806+check' (Constructor c) ty = do
807+ env <- getEnv
808+ Just moduleName <- checkCurrentModule <$> get
809+ case M.lookup (qualify moduleName c) (dataConstructors env) of
810+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
811+ Just (ty1, _) -> do
812+ repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
813+ _ <- subsumes Nothing repl ty
814+ return $ TypedValue True (Constructor c) ty
815+check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
816+
817+-- |
818+-- Check the type of a collection of named record fields
819+--
820+-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
821+--
822+checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
823+checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
824+ go [] [] REmpty = return []
825+ go [] [] u@(TUnknown _) = do u =?= REmpty
826+ return []
827+ go [] [] (Skolem _ _) | lax = return []
828+ go [] ((p, _): _) _ | lax = return []
829+ | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
830+ go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
831+ go ((p,v):ps') [] u@(TUnknown _) = do
832+ v'@(TypedValue _ _ ty) <- infer v
833+ rest <- fresh
834+ u =?= RCons p ty rest
835+ ps'' <- go ps' [] rest
836+ return $ (p, v') : ps''
837+ go ((p,v):ps') ts r =
838+ case lookup p ts of
839+ Nothing -> do
840+ v'@(TypedValue _ _ ty) <- infer v
841+ rest <- fresh
842+ r =?= RCons p ty rest
843+ ps'' <- go ps' ts rest
844+ return $ (p, v') : ps''
845+ Just ty -> do
846+ v' <- check v ty
847+ ps'' <- go ps' (delete (p, ty) ts) r
848+ return $ (p, v') : ps''
849+ go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
850+
851+-- |
852+-- Check the type of a function application, rethrowing errors to provide a better error message
853+--
854+checkFunctionApplication :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
855+checkFunctionApplication fn fnTy arg = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg
856+ where
857+ errorMessage msg = "Error applying function of type "
858+ ++ prettyPrintType fnTy
859+ ++ " to argument " ++ prettyPrintValue arg
860+ ++ ":\n" ++ msg
861+
862+-- |
863+-- Check the type of a function application
864+--
865+checkFunctionApplication' :: Value -> Type -> Value -> UnifyT Type Check (Type, Value)
866+checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg = do
867+ tyFunction' =?= tyFunction
868+ arg' <- check arg argTy
869+ return (retTy, App fn arg')
870+checkFunctionApplication' fn (ForAll ident ty _) arg = do
871+ replaced <- replaceVarWithUnknown ident ty
872+ checkFunctionApplication fn replaced arg
873+checkFunctionApplication' fn u@(TUnknown _) arg = do
874+ arg' <- do
875+ TypedValue _ arg' t <- infer arg
876+ (arg'', t') <- instantiatePolyTypeWithUnknowns arg' t
877+ return $ TypedValue True arg'' t'
878+ let ty = (\(TypedValue _ _ t) -> t) arg'
879+ ret <- fresh
880+ u =?= function ty ret
881+ return (ret, App fn arg')
882+checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg = do
883+ ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
884+ checkFunctionApplication fn ty arg
885+checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg = do
886+ env <- getEnv
887+ dicts <- getTypeClassDictionaries
888+ Just moduleName <- checkCurrentModule <$> get
889+ checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))) fnTy arg
890+checkFunctionApplication' _ fnTy arg = throwError $ "Cannot apply a function of type "
891+ ++ prettyPrintType fnTy
892+ ++ " to argument " ++ prettyPrintValue arg
893+
894+-- |
895+-- Check whether one type subsumes another, rethrowing errors to provide a better error message
896+--
897+subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
898+subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
899+ where
900+ errorMessage msg = "Error checking that type "
901+ ++ prettyPrintType ty1
902+ ++ " subsumes type "
903+ ++ prettyPrintType ty2
904+ ++ ":\n" ++ msg
905+
906+-- |
907+-- Check whether one type subsumes another
908+--
909+subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
910+subsumes' val (ForAll ident ty1 _) ty2 = do
911+ replaced <- replaceVarWithUnknown ident ty1
912+ subsumes val replaced ty2
913+subsumes' val ty1 (ForAll ident ty2 sco) =
914+ case sco of
915+ Just sco' -> do
916+ sko <- newSkolemConstant
917+ let sk = skolemize ident sko sco' ty2
918+ subsumes val ty1 sk
919+ Nothing -> throwError "Skolem variable scope is unspecified"
920+subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
921+ subsumes Nothing arg2 arg1
922+ subsumes Nothing ret1 ret2
923+ return val
924+subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
925+ ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
926+ subsumes val ty1 ty2
927+subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
928+ ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
929+ subsumes val ty1 ty2
930+subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
931+ env <- getEnv
932+ dicts <- getTypeClassDictionaries
933+ Just moduleName <- checkCurrentModule <$> get
934+ _ <- subsumes' Nothing ty1 ty2
935+ return . Just $ foldl App val (map (flip TypeClassDictionary dicts) (qualifyAllUnqualifiedNames moduleName env constraints))
936+subsumes' val (Object r1) (Object r2) = do
937+ let
938+ (ts1, r1') = rowToList r1
939+ (ts2, r2') = rowToList r2
940+ ts1' = sortBy (comparing fst) ts1
941+ ts2' = sortBy (comparing fst) ts2
942+ go ts1' ts2' r1' r2'
943+ return val
944+ where
945+ go [] ts2 r1 r2 = r1 =?= rowFromList (ts2, r2)
946+ go ts1 [] r1 r2 = r2 =?= rowFromList (ts1, r1)
947+ go ((p1, ty1) : ts1) ((p2, ty2) : ts2) r1 r2
948+ | p1 == p2 = do subsumes Nothing ty1 ty2
949+ go ts1 ts2 r1 r2
950+ | p1 < p2 = do rest <- fresh
951+ r2 =?= RCons p1 ty1 rest
952+ go ts1 ((p2, ty2) : ts2) r1 rest
953+ | p1 > p2 = do rest <- fresh
954+ r1 =?= RCons p2 ty2 rest
955+ go ((p1, ty1) : ts1) ts2 rest r2
956+subsumes' val ty1 ty2@(Object _) = subsumes val ty2 ty1
957+subsumes' val ty1 ty2 = do
958+ ty1 =?= ty2
959+ return val
960+