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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−