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