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