@@ -1,930 +0,0 @@
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@(_, (_, 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− return triple
208− forM tys $ \(ident, (val, ty)) -> do
209− -- Replace type class dictionary placeholders with actual dictionaries
210− val' <- replaceTypeClassDictionaries moduleName val
211− -- Check skolem variables did not escape their scope
212− skolemEscapeCheck val'
213− -- Remove type synonyms placeholders, remove duplicate row fields, and replace
214− -- top-level unification variables with named type variables.
215− let val'' = overTypes (desaturateAllTypeSynonyms . setifyAll) val'
216− ty' = varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty
217− return (ident, (val'', ty'))
218− where
219− -- Apply the substitution that was returned from runUnify to both types and (type-annotated) values
220− tidyUp (ts, sub) = map (\(i, (val, ty)) -> (i, (overTypes (sub $?) val, sub $? ty))) ts
221−
222−-- |
223−-- Check if a value introduces a function
224−--
225−isFunction :: Value -> Bool
226−isFunction (Abs _ _) = True
227−isFunction (TypedValue _ val _) = isFunction val
228−isFunction _ = False
229−
230−-- |
231−-- Check if a value contains a type annotation
232−--
233−isTyped :: (Ident, Value) -> (Ident, (Value, Maybe (Type, Bool)))
234−isTyped (name, TypedValue checkType value ty) = (name, (value, Just (ty, checkType)))
235−isTyped (name, value) = (name, (value, Nothing))
236−
237−-- |
238−-- Map a function over type annotations appearing inside a value
239−--
240−overTypes :: (Type -> Type) -> Value -> Value
241−overTypes f = everywhere (mkT f)
242−
243−-- |
244−-- Replace type class dictionary placeholders with inferred type class dictionaries
245−--
246−replaceTypeClassDictionaries :: ModuleName -> Value -> Check Value
247−replaceTypeClassDictionaries mn = everywhereM' (mkM go)
248− where
249− go (TypeClassDictionary constraint dicts) = do
250− env <- getEnv
251− entails env 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 :: Environment -> ModuleName -> [TypeClassDictionaryInScope] -> (Qualified ProperName, [Type]) -> Check Value
259−entails env moduleName context goal@(className, tys) = do
260− case go goal of
261− [] -> throwError $ "No " ++ show className ++ " instance found for " ++ intercalate ", " (map prettyPrintType tys)
262− (dict : _) -> return dict
263− where
264− go (className', tys') =
265− [ mkDictionary (canonicalizeDictionary tcd) args
266− | tcd <- context
267− -- Choose type class dictionaries in scope in the current module
268− , filterModule tcd
269− -- Make sure the type class name matches the one we are trying to satisfy
270− , className' == tcdClassName tcd
271− -- Make sure the type unifies with the type in the type instance definition
272− , subst <- maybeToList . (>>= verifySubstitution) . fmap concat $ zipWithM (typeHeadsAreEqual moduleName env) tys' (tcdInstanceTypes tcd)
273− -- Solve any necessary subgoals
274− , args <- solveSubgoals subst (tcdDependencies tcd) ]
275− -- Create dictionaries for subgoals which still need to be solved by calling go recursively
276− -- E.g. the goal (Show a, Show b) => Show (Either a b) can be satisfied if the current type
277− -- unifies with Either a b, and we can satisfy the subgoals Show a and Show b recursively.
278− solveSubgoals :: [(String, Type)] -> Maybe [(Qualified ProperName, [Type])] -> [Maybe [Value]]
279− solveSubgoals _ Nothing = return Nothing
280− solveSubgoals subst (Just subgoals) = do
281− dict <- mapM (go . second (map (replaceAllTypeVars subst))) subgoals
282− return $ Just dict
283− -- Make a dictionary from subgoal dictionaries by applying the correct function
284− mkDictionary :: Qualified Ident -> Maybe [Value] -> Value
285− mkDictionary fnName Nothing = Var fnName
286− mkDictionary fnName (Just []) = App (Var fnName) (ObjectLiteral [])
287− mkDictionary fnName (Just dicts) = foldl App (Var fnName) dicts
288− -- Filter out type dictionaries which are in scope in the current module
289− filterModule :: TypeClassDictionaryInScope -> Bool
290− filterModule (TypeClassDictionaryInScope { tcdName = Qualified (Just mn) _ }) | mn == moduleName = True
291− filterModule (TypeClassDictionaryInScope { tcdName = Qualified Nothing _ }) = True
292− filterModule _ = False
293− -- Ensure that a substitution is valid
294− verifySubstitution :: [(String, Type)] -> Maybe [(String, Type)]
295− verifySubstitution subst = do
296− let grps = groupBy ((==) `on` fst) subst
297− guard (all (pairwise (unifiesWith env) . map snd) grps)
298− return $ map head grps
299−
300−-- |
301−-- Check all values in a list pairwise match a predicate
302−--
303−pairwise :: (a -> a -> Bool) -> [a] -> Bool
304−pairwise _ [] = True
305−pairwise _ [_] = True
306−pairwise p (x : xs) = all (p x) xs && pairwise p xs
307−
308−-- |
309−-- Check that two types unify
310−--
311−unifiesWith :: Environment -> Type -> Type -> Bool
312−unifiesWith _ (TUnknown _) _ = True
313−unifiesWith _ _ (TUnknown _) = True
314−unifiesWith _ (Skolem s1 _) (Skolem s2 _) | s1 == s2 = True
315−unifiesWith _ (TypeVar v1) (TypeVar v2) | v1 == v2 = True
316−unifiesWith _ (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = True
317−unifiesWith e (TypeApp h1 t1) (TypeApp h2 t2) = unifiesWith e h1 h2 && unifiesWith e t1 t2
318−unifiesWith e (SaturatedTypeSynonym name args) t2 =
319− case expandTypeSynonym' e name args of
320− Left _ -> False
321− Right t1 -> unifiesWith e t1 t2
322−unifiesWith e t1 t2@(SaturatedTypeSynonym _ _) = unifiesWith e t2 t1
323−unifiesWith _ _ _ = False
324−
325−-- |
326−-- Check whether the type heads of two types are equal (for the purposes of type class dictionary lookup),
327−-- and return a substitution from type variables to types which makes the type heads unify.
328−--
329−typeHeadsAreEqual :: ModuleName -> Environment -> Type -> Type -> Maybe [(String, Type)]
330−typeHeadsAreEqual _ _ (Skolem s1 _) (Skolem s2 _) | s1 == s2 = Just []
331−typeHeadsAreEqual _ _ t (TypeVar v) = Just [(v, t)]
332−typeHeadsAreEqual _ _ (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = Just []
333−typeHeadsAreEqual m e (TypeApp h1 t1) (TypeApp h2 t2) = (++) <$> typeHeadsAreEqual m e h1 h2 <*> typeHeadsAreEqual m e t1 t2
334−typeHeadsAreEqual m e (SaturatedTypeSynonym name args) t2 = case expandTypeSynonym' e name args of
335− Left _ -> Nothing
336− Right t1 -> typeHeadsAreEqual m e t1 t2
337−typeHeadsAreEqual _ _ _ _ = Nothing
338−
339−-- |
340−-- Ensure skolem variables do not escape their scope
341−--
342−skolemEscapeCheck :: Value -> Check ()
343−skolemEscapeCheck (TypedValue False _ _) = return ()
344−skolemEscapeCheck root@TypedValue{} =
345− -- Every skolem variable is created when a ForAll type is skolemized.
346− -- This determines the scope of that skolem variable, which is copied from the SkolemScope
347− -- field of the ForAll constructor.
348− -- We traverse the tree top-down, and collect any SkolemScopes introduced by ForAlls.
349− -- If a Skolem is encountered whose SkolemScope is not in the current list, we have found
350− -- an escaped skolem variable.
351− case everythingWithContext [] (++) (mkQ ((,) []) go) root of
352− [] -> return ()
353− ((binding, val) : _) -> throwError $ "Rigid/skolem type variable bound by " ++ maybe "<unknown>" prettyPrintValue binding ++ " has escaped at " ++ prettyPrintValue val
354− where
355− go :: Value -> [(SkolemScope, Value)] -> ([(Maybe Value, Value)], [(SkolemScope, Value)])
356− go val@(TypedValue _ _ (ForAll _ _ (Just sco))) scos = ([], (sco, val) : scos)
357− go val@(TypedValue _ _ ty) scos = case collectSkolems ty \\ map fst scos of
358− (sco : _) -> ([(findBindingScope sco, val)], scos)
359− _ -> ([], scos)
360− where
361− collectSkolems :: Type -> [SkolemScope]
362− collectSkolems = nub . everything (++) (mkQ [] collect)
363− where
364− collect (Skolem _ scope) = [scope]
365− collect _ = []
366− go _ scos = ([], scos)
367− findBindingScope :: SkolemScope -> Maybe Value
368− findBindingScope sco = something (mkQ Nothing go') root
369− where
370− go' val@(TypedValue _ _ (ForAll _ _ (Just sco'))) | sco == sco' = Just val
371− go' _ = Nothing
372−skolemEscapeCheck val = throwError $ "Untyped value passed to skolemEscapeCheck: " ++ prettyPrintValue val
373−
374−-- |
375−-- Ensure a row contains no duplicate labels
376−--
377−setify :: Type -> Type
378−setify = rowFromList . first (M.toList . M.fromList) . rowToList
379−
380−-- |
381−-- \"Setify\" all rows occuring inside a value
382−--
383−setifyAll :: (D.Data d) => d -> d
384−setifyAll = everywhere (mkT setify)
385−
386−-- |
387−-- Replace outermost unsolved unification variables with named type variables
388−--
389−varIfUnknown :: Type -> Type
390−varIfUnknown ty =
391− let unks = nub $ unknowns ty
392− toName = (:) 't' . show
393− ty' = everywhere (mkT typeToVar) ty
394− typeToVar :: Type -> Type
395− typeToVar (TUnknown (Unknown u)) = TypeVar (toName u)
396− typeToVar t = t
397− in mkForAll (sort . map (toName . runUnknown) $ unks) ty'
398−
399−-- |
400−-- Remove any ForAlls and ConstrainedType constructors in a type by introducing new unknowns
401−-- or TypeClassDictionary values.
402−--
403−-- This is necessary during type checking to avoid unifying a polymorphic type with a
404−-- unification variable.
405−--
406−instantiatePolyTypeWithUnknowns :: Value -> Type -> UnifyT Type Check (Value, Type)
407−instantiatePolyTypeWithUnknowns val (ForAll ident ty _) = do
408− ty' <- replaceVarWithUnknown ident ty
409− instantiatePolyTypeWithUnknowns val ty'
410−instantiatePolyTypeWithUnknowns val (ConstrainedType constraints ty) = do
411− dicts <- getTypeClassDictionaries
412− (_, ty') <- instantiatePolyTypeWithUnknowns (error "Types under a constraint cannot themselves be constrained") ty
413− return (foldl App val (map (flip TypeClassDictionary dicts) constraints), ty')
414−instantiatePolyTypeWithUnknowns val ty = return (val, ty)
415−
416−-- |
417−-- Replace a single type variable with a new unification variable
418−--
419−replaceVarWithUnknown :: String -> Type -> UnifyT Type Check Type
420−replaceVarWithUnknown ident ty = do
421− tu <- fresh
422− return $ replaceTypeVars ident tu ty
423−
424−-- |
425−-- Replace fully applied type synonyms with the @SaturatedTypeSynonym@ data constructor, which helps generate
426−-- better error messages during unification.
427−--
428−replaceAllTypeSynonyms' :: (D.Data d) => Environment -> d -> Either String d
429−replaceAllTypeSynonyms' env d =
430− let
431− syns = map (\(name, (args, _)) -> (name, length args)) . M.toList $ typeSynonyms env
432− in
433− saturateAllTypeSynonyms syns d
434−
435−replaceAllTypeSynonyms :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => (D.Data d) => d -> m d
436−replaceAllTypeSynonyms d = do
437− env <- getEnv
438− either throwError return $ replaceAllTypeSynonyms' env d
439−
440−-- |
441−-- \"Desaturate\" @SaturatedTypeSynonym@s
442−--
443−desaturateAllTypeSynonyms :: (D.Data d) => d -> d
444−desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
445− where
446− replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
447− replaceSaturatedTypeSynonym t = t
448−
449−-- |
450−-- Replace a type synonym and its arguments with the aliased type
451−--
452−expandTypeSynonym' :: Environment -> Qualified ProperName -> [Type] -> Either String Type
453−expandTypeSynonym' env name args =
454− case M.lookup name (typeSynonyms env) of
455− Just (synArgs, body) -> do
456− let repl = replaceAllTypeVars (zip synArgs args) body
457− replaceAllTypeSynonyms' env repl
458− Nothing -> error "Type synonym was not defined"
459−
460−expandTypeSynonym :: (Functor m, Monad m, MonadState CheckState m, MonadError String m) => Qualified ProperName -> [Type] -> m Type
461−expandTypeSynonym name args = do
462− env <- getEnv
463− either throwError return $ expandTypeSynonym' env name args
464−
465−-- |
466−-- Ensure a set of property names and value does not contain duplicate labels
467−--
468−ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
469−ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
470−
471−-- |
472−-- Infer a type for a value, rethrowing any error to provide a more useful error message
473−--
474−infer :: Value -> UnifyT Type Check Value
475−infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
476−
477−-- |
478−-- Infer a type for a value
479−--
480−infer' :: Value -> UnifyT Type Check Value
481−infer' v@(NumericLiteral _) = return $ TypedValue True v tyNumber
482−infer' v@(StringLiteral _) = return $ TypedValue True v tyString
483−infer' v@(BooleanLiteral _) = return $ TypedValue True v tyBoolean
484−infer' (ArrayLiteral vals) = do
485− ts <- mapM infer vals
486− els <- fresh
487− forM_ ts $ \(TypedValue _ _ t) -> els =?= TypeApp tyArray t
488− return $ TypedValue True (ArrayLiteral ts) els
489−infer' (ObjectLiteral ps) = do
490− ensureNoDuplicateProperties ps
491− ts <- mapM (infer . snd) ps
492− let fields = zipWith (\name (TypedValue _ _ t) -> (name, t)) (map fst ps) ts
493− ty = Object $ rowFromList (fields, REmpty)
494− return $ TypedValue True (ObjectLiteral (zip (map fst ps) ts)) ty
495−infer' (ObjectUpdate o ps) = do
496− ensureNoDuplicateProperties ps
497− row <- fresh
498− newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
499− let newTys = map (\(name, TypedValue _ _ ty) -> (name, ty)) newVals
500− oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
501− let oldTy = Object $ rowFromList (oldTys, row)
502− o' <- TypedValue True <$> check o oldTy <*> pure oldTy
503− return $ TypedValue True (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
504−infer' (Accessor prop val) = do
505− typed@(TypedValue _ _ objTy) <- infer val
506− propTy <- inferProperty objTy prop
507− case propTy of
508− Nothing -> do
509− field <- fresh
510− rest <- fresh
511− _ <- subsumes Nothing objTy (Object (RCons prop field rest))
512− return $ TypedValue True (Accessor prop typed) field
513− Just ty -> return $ TypedValue True (Accessor prop typed) ty
514−infer' (Abs (Left arg) ret) = do
515− ty <- fresh
516− Just moduleName <- checkCurrentModule <$> get
517− bindLocalVariables moduleName [(arg, ty)] $ do
518− body@(TypedValue _ _ bodyTy) <- infer' ret
519− return $ TypedValue True (Abs (Left arg) body) $ function ty bodyTy
520−infer' (Abs (Right _) _) = error "Binder was not desugared"
521−infer' (App f arg) = do
522− f'@(TypedValue _ _ ft) <- infer f
523− (ret, app) <- checkFunctionApplication f' ft arg Nothing
524− return $ TypedValue True app ret
525−infer' (Var var) = do
526− Just moduleName <- checkCurrentModule <$> get
527− ty <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
528− case ty of
529− ConstrainedType constraints ty' -> do
530− dicts <- getTypeClassDictionaries
531− return $ TypedValue True (foldl App (Var var) (map (flip TypeClassDictionary dicts) constraints)) ty'
532− _ -> return $ TypedValue True (Var var) ty
533−infer' v@(Constructor c) = do
534− env <- getEnv
535− case M.lookup c (dataConstructors env) of
536− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
537− Just (_, ty) -> do ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
538− return $ TypedValue True v ty'
539−infer' (Case vals binders) = do
540− ts <- mapM infer vals
541− ret <- fresh
542− binders' <- checkBinders (map (\(TypedValue _ _ t) -> t) ts) ret binders
543− return $ TypedValue True (Case ts binders') ret
544−infer' (IfThenElse cond th el) = do
545− cond' <- check cond tyBoolean
546− v2@(TypedValue _ _ t2) <- infer th
547− v3@(TypedValue _ _ t3) <- infer el
548− t2 =?= t3
549− return $ TypedValue True (IfThenElse cond' v2 v3) t2
550−infer' (TypedValue checkType val ty) = do
551− Just moduleName <- checkCurrentModule <$> get
552− kind <- liftCheck $ kindOf moduleName ty
553− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
554− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
555− val' <- if checkType then check val ty' else return val
556− return $ TypedValue True val' ty'
557−infer' _ = error "Invalid argument to infer"
558−
559−-- |
560−-- Infer the type of a property inside a record with a given type
561−--
562−inferProperty :: Type -> String -> UnifyT Type Check (Maybe Type)
563−inferProperty (Object row) prop = do
564− let (props, _) = rowToList row
565− return $ lookup prop props
566−inferProperty (SaturatedTypeSynonym name args) prop = do
567− replaced <- introduceSkolemScope <=< expandTypeSynonym name $ args
568− inferProperty replaced prop
569−inferProperty (ForAll ident ty _) prop = do
570− replaced <- replaceVarWithUnknown ident ty
571− inferProperty replaced prop
572−inferProperty _ _ = return Nothing
573−
574−-- |
575−-- Infer the types of variables brought into scope by a binder
576−--
577−inferBinder :: Type -> Binder -> UnifyT Type Check (M.Map Ident Type)
578−inferBinder _ NullBinder = return M.empty
579−inferBinder val (StringBinder _) = val =?= tyString >> return M.empty
580−inferBinder val (NumberBinder _) = val =?= tyNumber >> return M.empty
581−inferBinder val (BooleanBinder _) = val =?= tyBoolean >> return M.empty
582−inferBinder val (VarBinder name) = return $ M.singleton name val
583−inferBinder val (ConstructorBinder ctor binders) = do
584− env <- getEnv
585− case M.lookup ctor (dataConstructors env) of
586− Just (_, ty) -> do
587− (_, fn) <- instantiatePolyTypeWithUnknowns (error "Data constructor types cannot contain constraints") ty
588− fn' <- replaceAllTypeSynonyms fn
589− go binders fn'
590− where
591− go [] ty' = do
592− _ <- subsumes Nothing val ty'
593− return M.empty
594− go (binder : binders') (TypeApp (TypeApp t obj) ret) | t == tyFunction =
595− M.union <$> inferBinder obj binder <*> go binders' ret
596− go _ _ = throwError $ "Wrong number of arguments to constructor " ++ show ctor
597− _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
598−inferBinder val (ObjectBinder props) = do
599− row <- fresh
600− rest <- fresh
601− m1 <- inferRowProperties row rest props
602− val =?= Object row
603− return m1
604− where
605− inferRowProperties :: Type -> Type -> [(String, Binder)] -> UnifyT Type Check (M.Map Ident Type)
606− inferRowProperties nrow row [] = nrow =?= row >> return M.empty
607− inferRowProperties nrow row ((name, binder):binders) = do
608− propTy <- fresh
609− m1 <- inferBinder propTy binder
610− m2 <- inferRowProperties nrow (RCons name propTy row) binders
611− return $ m1 `M.union` m2
612−inferBinder val (ArrayBinder binders) = do
613− el <- fresh
614− m1 <- M.unions <$> mapM (inferBinder el) binders
615− val =?= TypeApp tyArray el
616− return m1
617−inferBinder val (ConsBinder headBinder tailBinder) = do
618− el <- fresh
619− m1 <- inferBinder el headBinder
620− m2 <- inferBinder val tailBinder
621− val =?= TypeApp tyArray el
622− return $ m1 `M.union` m2
623−inferBinder val (NamedBinder name binder) = do
624− m <- inferBinder val binder
625− return $ M.insert name val m
626−
627−-- |
628−-- Check the types of the return values in a set of binders in a case statement
629−--
630−checkBinders :: [Type] -> Type -> [CaseAlternative] -> UnifyT Type Check [CaseAlternative]
631−checkBinders _ _ [] = return []
632−checkBinders nvals ret (CaseAlternative binders grd val : bs) = do
633− Just moduleName <- checkCurrentModule <$> get
634− m1 <- M.unions <$> zipWithM inferBinder nvals binders
635− r <- bindLocalVariables moduleName (M.toList m1) $ do
636− val' <- TypedValue True <$> check val ret <*> pure ret
637− case grd of
638− Nothing -> return $ CaseAlternative binders Nothing val'
639− Just g -> do
640− g' <- check g tyBoolean
641− return $ CaseAlternative binders (Just g') val'
642− rs <- checkBinders nvals ret bs
643− return $ r : rs
644−
645−-- |
646−-- Generate a new skolem constant
647−--
648−newSkolemConstant :: UnifyT Type Check Int
649−newSkolemConstant = runUnknown <$> fresh'
650−
651−-- |
652−-- Generate a new skolem scope
653−--
654−newSkolemScope :: UnifyT Type Check SkolemScope
655−newSkolemScope = SkolemScope . runUnknown <$> fresh'
656−
657−-- |
658−-- Skolemize a type variable by replacing its instances with fresh skolem constants
659−--
660−skolemize :: String -> Int -> SkolemScope -> Type -> Type
661−skolemize ident sko scope = replaceTypeVars ident (Skolem sko scope)
662−
663−-- |
664−-- Introduce skolem scope at every occurence of a ForAll
665−--
666−introduceSkolemScope :: Type -> UnifyT Type Check Type
667−introduceSkolemScope = everywhereM (mkM go)
668− where
669− go (ForAll ident ty Nothing) = ForAll ident ty <$> (Just <$> newSkolemScope)
670− go other = return other
671−
672−-- |
673−-- Check the type of a value, rethrowing errors to provide a better error message
674−--
675−check :: Value -> Type -> UnifyT Type Check Value
676−check val ty = rethrow errorMessage $ check' val ty
677− where
678− errorMessage msg =
679− "Error checking type of term " ++
680− prettyPrintValue val ++
681− " against type " ++
682− prettyPrintType ty ++
683− ":\n" ++
684− msg
685−
686−-- |
687−-- Check the type of a value
688−--
689−check' :: Value -> Type -> UnifyT Type Check Value
690−check' val (ForAll ident ty _) = do
691− scope <- newSkolemScope
692− sko <- newSkolemConstant
693− let sk = skolemize ident sko scope ty
694− val' <- check val sk
695− return $ TypedValue True val' (ForAll ident ty (Just scope))
696−check' val t@(ConstrainedType constraints ty) = do
697− dictNames <- forM constraints $ \(Qualified _ (ProperName className), _) -> do
698− n <- liftCheck freshDictionaryName
699− return $ Ident $ "__dict_" ++ className ++ "_" ++ show n
700− val' <- withTypeClassDictionaries (zipWith (\name (className, instanceTy) ->
701− TypeClassDictionaryInScope name className instanceTy Nothing TCDRegular) (map (Qualified Nothing) dictNames)
702− constraints) $ check val ty
703− return $ TypedValue True (foldr (Abs . Left) val' dictNames) t
704−check' val (SaturatedTypeSynonym name args) = do
705− ty <- introduceSkolemScope <=< expandTypeSynonym name $ args
706− val' <- check val ty
707− return $ TypedValue True val' ty
708−check' val u@(TUnknown _) = do
709− val'@(TypedValue _ _ ty) <- infer val
710− -- Don't unify an unknown with an inferred polytype
711− (val'', ty') <- instantiatePolyTypeWithUnknowns val' ty
712− ty' =?= u
713− return $ TypedValue True val'' ty'
714−check' v@(NumericLiteral _) t | t == tyNumber =
715− return $ TypedValue True v t
716−check' v@(StringLiteral _) t | t == tyString =
717− return $ TypedValue True v t
718−check' v@(BooleanLiteral _) t | t == tyBoolean =
719− return $ TypedValue True v t
720−check' (ArrayLiteral vals) t@(TypeApp a ty) = do
721− a =?= tyArray
722− array <- ArrayLiteral <$> forM vals (`check` ty)
723− return $ TypedValue True array t
724−check' (Abs (Left arg) ret) ty@(TypeApp (TypeApp t argTy) retTy) | t == tyFunction = do
725− Just moduleName <- checkCurrentModule <$> get
726− ret' <- bindLocalVariables moduleName [(arg, argTy)] $ check ret retTy
727− return $ TypedValue True (Abs (Left arg) ret') ty
728−check' (Abs (Right _) _) _ = error "Binder was not desugared"
729−check' (App f arg) ret = do
730− f'@(TypedValue _ _ ft) <- infer f
731− (_, app) <- checkFunctionApplication f' ft arg (Just ret)
732− return $ TypedValue True app ret
733−check' v@(Var var) ty = do
734− Just moduleName <- checkCurrentModule <$> get
735− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms <=< lookupVariable moduleName $ var
736− ty' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty
737− v' <- subsumes (Just v) repl ty'
738− case v' of
739− Nothing -> throwError "Unable to check type subsumption"
740− Just v'' -> return $ TypedValue True v'' ty'
741−check' (TypedValue checkType val ty1) ty2 = do
742− Just moduleName <- checkCurrentModule <$> get
743− kind <- liftCheck $ kindOf moduleName ty1
744− guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
745− ty1' <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
746− val' <- subsumes (Just val) ty1' ty2
747− case val' of
748− Nothing -> throwError "Unable to check type subsumption"
749− Just val'' -> do
750− val''' <- if checkType then check val'' ty1' else return val''
751− return $ TypedValue checkType (TypedValue True val''' ty1) ty2
752−check' (Case vals binders) ret = do
753− vals' <- mapM infer vals
754− let ts = map (\(TypedValue _ _ t) -> t) vals'
755− binders' <- checkBinders ts ret binders
756− return $ TypedValue True (Case vals' binders') ret
757−check' (IfThenElse cond th el) ty = do
758− cond' <- check cond tyBoolean
759− th' <- check th ty
760− el' <- check el ty
761− return $ TypedValue True (IfThenElse cond' th' el') ty
762−check' (ObjectLiteral ps) t@(Object row) = do
763− ensureNoDuplicateProperties ps
764− ps' <- checkProperties ps row False
765− return $ TypedValue True (ObjectLiteral ps') t
766−check' (ObjectUpdate obj ps) t@(Object row) = do
767− ensureNoDuplicateProperties ps
768− us <- zip (map fst ps) <$> replicateM (length ps) fresh
769− let (propsToCheck, rest) = rowToList row
770− propsToRemove = map fst ps
771− remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
772− obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
773− ps' <- checkProperties ps row True
774− return $ TypedValue True (ObjectUpdate obj' ps') t
775−check' (Accessor prop val) ty = do
776− rest <- fresh
777− val' <- check val (Object (RCons prop ty rest))
778− return $ TypedValue True (Accessor prop val') ty
779−check' (Constructor c) ty = do
780− env <- getEnv
781− case M.lookup c (dataConstructors env) of
782− Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
783− Just (_, ty1) -> do
784− repl <- introduceSkolemScope <=< replaceAllTypeSynonyms $ ty1
785− _ <- subsumes Nothing repl ty
786− return $ TypedValue True (Constructor c) ty
787−check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
788−
789−-- |
790−-- Check the type of a collection of named record fields
791−--
792−-- The @lax@ parameter controls whether or not every record member has to be provided. For object updates, this is not the case.
793−--
794−checkProperties :: [(String, Value)] -> Type -> Bool -> UnifyT Type Check [(String, Value)]
795−checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
796− go [] [] REmpty = return []
797− go [] [] u@(TUnknown _) = do u =?= REmpty
798− return []
799− go [] [] (Skolem _ _) | lax = return []
800− go [] ((p, _): _) _ | lax = return []
801− | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
802− go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
803− go ((p,v):ps') [] u@(TUnknown _) = do
804− v'@(TypedValue _ _ ty) <- infer v
805− rest <- fresh
806− u =?= RCons p ty rest
807− ps'' <- go ps' [] rest
808− return $ (p, v') : ps''
809− go ((p,v):ps') ts r =
810− case lookup p ts of
811− Nothing -> do
812− v'@(TypedValue _ _ ty) <- infer v
813− rest <- fresh
814− r =?= RCons p ty rest
815− ps'' <- go ps' ts rest
816− return $ (p, v') : ps''
817− Just ty -> do
818− v' <- check v ty
819− ps'' <- go ps' (delete (p, ty) ts) r
820− return $ (p, v') : ps''
821− go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
822−
823−-- |
824−-- Check the type of a function application, rethrowing errors to provide a better error message
825−--
826−checkFunctionApplication :: Value -> Type -> Value -> Maybe Type -> UnifyT Type Check (Type, Value)
827−checkFunctionApplication fn fnTy arg ret = rethrow errorMessage $ checkFunctionApplication' fn fnTy arg ret
828− where
829− errorMessage msg = "Error applying function of type "
830− ++ prettyPrintType fnTy
831− ++ " to argument " ++ prettyPrintValue arg
832− ++ ":\n" ++ msg
833−
834−-- |
835−-- Check the type of a function application
836−--
837−checkFunctionApplication' :: Value -> Type -> Value -> Maybe Type -> UnifyT Type Check (Type, Value)
838−checkFunctionApplication' fn (TypeApp (TypeApp tyFunction' argTy) retTy) arg ret = do
839− tyFunction' =?= tyFunction
840− _ <- maybe (return Nothing) (subsumes Nothing retTy) ret
841− subst <- unifyCurrentSubstitution <$> UnifyT get
842− arg' <- check arg (subst $? argTy)
843− return (retTy, App fn arg')
844−checkFunctionApplication' fn (ForAll ident ty _) arg ret = do
845− replaced <- replaceVarWithUnknown ident ty
846− checkFunctionApplication fn replaced arg ret
847−checkFunctionApplication' fn u@(TUnknown _) arg ret = do
848− arg' <- do
849− TypedValue _ arg' t <- infer arg
850− (arg'', t') <- instantiatePolyTypeWithUnknowns arg' t
851− return $ TypedValue True arg'' t'
852− let ty = (\(TypedValue _ _ t) -> t) arg'
853− ret' <- maybe fresh return ret
854− u =?= function ty ret'
855− return (ret', App fn arg')
856−checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) arg ret = do
857− ty <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
858− checkFunctionApplication fn ty arg ret
859−checkFunctionApplication' fn (ConstrainedType constraints fnTy) arg ret = do
860− dicts <- getTypeClassDictionaries
861− checkFunctionApplication' (foldl App fn (map (flip TypeClassDictionary dicts) constraints)) fnTy arg ret
862−checkFunctionApplication' _ fnTy arg _ = throwError $ "Cannot apply a function of type "
863− ++ prettyPrintType fnTy
864− ++ " to argument " ++ prettyPrintValue arg
865−
866−-- |
867−-- Check whether one type subsumes another, rethrowing errors to provide a better error message
868−--
869−subsumes :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
870−subsumes val ty1 ty2 = rethrow errorMessage $ subsumes' val ty1 ty2
871− where
872− errorMessage msg = "Error checking that type "
873− ++ prettyPrintType ty1
874− ++ " subsumes type "
875− ++ prettyPrintType ty2
876− ++ ":\n" ++ msg
877−
878−-- |
879−-- Check whether one type subsumes another
880−--
881−subsumes' :: Maybe Value -> Type -> Type -> UnifyT Type Check (Maybe Value)
882−subsumes' val (ForAll ident ty1 _) ty2 = do
883− replaced <- replaceVarWithUnknown ident ty1
884− subsumes val replaced ty2
885−subsumes' val ty1 (ForAll ident ty2 sco) =
886− case sco of
887− Just sco' -> do
888− sko <- newSkolemConstant
889− let sk = skolemize ident sko sco' ty2
890− subsumes val ty1 sk
891− Nothing -> throwError "Skolem variable scope is unspecified"
892−subsumes' val (TypeApp (TypeApp f1 arg1) ret1) (TypeApp (TypeApp f2 arg2) ret2) | f1 == tyFunction && f2 == tyFunction = do
893− _ <- subsumes Nothing arg2 arg1
894− _ <- subsumes Nothing ret1 ret2
895− return val
896−subsumes' val (SaturatedTypeSynonym name tyArgs) ty2 = do
897− ty1 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
898− subsumes val ty1 ty2
899−subsumes' val ty1 (SaturatedTypeSynonym name tyArgs) = do
900− ty2 <- introduceSkolemScope <=< expandTypeSynonym name $ tyArgs
901− subsumes val ty1 ty2
902−subsumes' (Just val) (ConstrainedType constraints ty1) ty2 = do
903− dicts <- getTypeClassDictionaries
904− _ <- subsumes' Nothing ty1 ty2
905− return . Just $ foldl App val (map (flip TypeClassDictionary dicts) constraints)
906−subsumes' val (Object r1) (Object r2) = do
907− let
908− (ts1, r1') = rowToList r1
909− (ts2, r2') = rowToList r2
910− ts1' = sortBy (comparing fst) ts1
911− ts2' = sortBy (comparing fst) ts2
912− go ts1' ts2' r1' r2'
913− return val
914− where
915− go [] ts2 r1' r2' = r1' =?= rowFromList (ts2, r2')
916− go ts1 [] r1' r2' = r2' =?= rowFromList (ts1, r1')
917− go ((p1, ty1) : ts1) ((p2, ty2) : ts2) r1' r2'
918− | p1 == p2 = do _ <- subsumes Nothing ty1 ty2
919− go ts1 ts2 r1' r2'
920− | p1 < p2 = do rest <- fresh
921− r2' =?= RCons p1 ty1 rest
922− go ts1 ((p2, ty2) : ts2) r1' rest
923− | otherwise = do rest <- fresh
924− r1' =?= RCons p2 ty2 rest
925− go ((p1, ty1) : ts1) ts2 rest r2'
926−subsumes' val ty1 ty2@(Object _) = subsumes val ty2 ty1
927−subsumes' val ty1 ty2 = do
928− ty1 =?= ty2
929− return val
930−