@@ -0,0 +1,791 @@
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+--
13+-----------------------------------------------------------------------------
14+
15+{-# OPTIONS_GHC -fno-warn-orphans #-}
16+{-# LANGUAGE DeriveDataTypeable, FlexibleContexts #-}
17+
18+module Language.PureScript.TypeChecker.Types (
19+ typesOf
20+) where
21+
22+import Data.List
23+import Data.Maybe (maybeToList, isNothing, isJust, fromMaybe)
24+import qualified Data.Data as D
25+import Data.Generics
26+ (mkM, everywhereM, everything, mkT, something, everywhere, mkQ)
27+
28+import Language.PureScript.Values
29+import Language.PureScript.Types
30+import Language.PureScript.Kinds
31+import Language.PureScript.Names
32+import Language.PureScript.TypeChecker.Monad
33+import Language.PureScript.TypeChecker.Kinds
34+import Language.PureScript.TypeChecker.Synonyms
35+import Language.PureScript.Pretty
36+import Language.PureScript.Unknown
37+
38+import Control.Monad.State
39+import Control.Monad.Error
40+import Control.Monad.Reader
41+
42+import Control.Applicative
43+import Control.Arrow (Arrow(..))
44+
45+import qualified Data.Map as M
46+import Data.Function (on)
47+
48+instance Unifiable Type where
49+ unknown = TUnknown
50+ isUnknown (TUnknown u) = Just u
51+ isUnknown _ = Nothing
52+ (~~) = unifyTypes
53+ apply s (TUnknown u) = runSubstitution s u
54+ apply s (SaturatedTypeSynonym name tys) = SaturatedTypeSynonym name $ map (apply s) tys
55+ apply s (ForAll idents ty) = ForAll idents $ apply s ty
56+ apply s (Array t) = Array (apply s t)
57+ apply s (Object r) = Object (apply s r)
58+ apply s (Function args ret) = Function (map (apply s) args) (apply s ret)
59+ apply s (TypeApp t1 t2) = TypeApp (apply s t1) (apply s t2)
60+ apply s (RCons name ty r) = RCons name (apply s ty) (apply s r)
61+ apply _ t = t
62+ unknowns (TUnknown (Unknown u)) = [u]
63+ unknowns (SaturatedTypeSynonym _ tys) = concatMap unknowns tys
64+ unknowns (ForAll _ ty) = unknowns ty
65+ unknowns (Array t) = unknowns t
66+ unknowns (Object r) = unknowns r
67+ unknowns (Function args ret) = concatMap unknowns args ++ unknowns ret
68+ unknowns (TypeApp t1 t2) = unknowns t1 ++ unknowns t2
69+ unknowns (RCons _ ty r) = unknowns ty ++ unknowns r
70+ unknowns _ = []
71+
72+unifyTypes :: Type -> Type -> Subst ()
73+unifyTypes t1 t2 = rethrow (\e -> "Error unifying type " ++ prettyPrintType t1 ++ " with type " ++ prettyPrintType t2 ++ ":\n" ++ e) $ do
74+ unifyTypes' t1 t2
75+ where
76+ unifyTypes' (TUnknown u1) (TUnknown u2) | u1 == u2 = return ()
77+ unifyTypes' (TUnknown u) t = replace u t
78+ unifyTypes' t (TUnknown u) = replace u t
79+ unifyTypes' (SaturatedTypeSynonym name args) ty = do
80+ ty1 <- expandTypeSynonym name args
81+ ty1 `unifyTypes` ty
82+ unifyTypes' ty s@(SaturatedTypeSynonym _ _) = s `unifyTypes` ty
83+ unifyTypes' (ForAll ident1 ty1) (ForAll ident2 ty2) = do
84+ sk <- skolemize ident1 ty1
85+ replaced <- replaceVarWithUnknown ident2 ty2
86+ sk `unifyTypes` replaced
87+ unifyTypes' (ForAll ident ty1) ty2 = do
88+ sk <- skolemize ident ty1
89+ sk `unifyTypes` ty2
90+ unifyTypes' ty f@(ForAll _ _) = f `unifyTypes` ty
91+ unifyTypes' Number Number = return ()
92+ unifyTypes' String String = return ()
93+ unifyTypes' Boolean Boolean = return ()
94+ unifyTypes' (Array s) (Array t) = s `unifyTypes` t
95+ unifyTypes' (Object row1) (Object row2) = row1 ~~ row2
96+ unifyTypes' (Function args1 ret1) (Function args2 ret2) = do
97+ guardWith "Function applied to incorrect number of args" $ length args1 == length args2
98+ zipWithM_ unifyTypes args1 args2
99+ ret1 `unifyTypes` ret2
100+ unifyTypes' (TypeVar v1) (TypeVar v2) | v1 == v2 = return ()
101+ unifyTypes' (TypeConstructor c1) (TypeConstructor c2) = do
102+ env <- getEnv
103+ moduleName <- substCurrentModule `fmap` ask
104+ guardWith ("Cannot unify " ++ show c1 ++ " with " ++ show c2 ++ ".") (typeConstructorsAreEqual env moduleName c1 c2)
105+ unifyTypes' (TypeApp t3 t4) (TypeApp t5 t6) = do
106+ t3 `unifyTypes` t5
107+ t4 `unifyTypes` t6
108+ unifyTypes' (Skolem s1) (Skolem s2) | s1 == s2 = return ()
109+ unifyTypes' r1@(RCons _ _ _) r2 = unifyRows r1 r2
110+ unifyTypes' r1 r2@(RCons _ _ _) = unifyRows r1 r2
111+ unifyTypes' r1@REmpty r2 = unifyRows r1 r2
112+ unifyTypes' r1 r2@REmpty = unifyRows r1 r2
113+ unifyTypes' t3 t4 = throwError $ "Cannot unify " ++ prettyPrintType t3 ++ " with " ++ prettyPrintType t4 ++ "."
114+
115+unifyRows :: Type -> Type -> Subst ()
116+unifyRows r1 r2 =
117+ let
118+ (s1, r1') = rowToList r1
119+ (s2, r2') = rowToList r2
120+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
121+ sd1 = [ (name, t1) | (name, t1) <- s1, name `notElem` map fst s2 ]
122+ sd2 = [ (name, t2) | (name, t2) <- s2, name `notElem` map fst s1 ]
123+ in do
124+ forM_ int (uncurry (~~))
125+ unifyRows' sd1 r1' sd2 r2'
126+ where
127+ unifyRows' :: [(String, Type)] -> Type -> [(String, Type)] -> Type -> Subst ()
128+ unifyRows' [] (TUnknown u) sd r = replace u (rowFromList (sd, r))
129+ unifyRows' sd r [] (TUnknown u) = replace u (rowFromList (sd, r))
130+ unifyRows' ((name, ty):row) r others u@(TUnknown un) = do
131+ occursCheck un ty
132+ forM_ row $ \(_, t) -> occursCheck un t
133+ u' <- fresh
134+ u ~~ RCons name ty u'
135+ unifyRows' row r others u'
136+ unifyRows' [] REmpty [] REmpty = return ()
137+ unifyRows' [] (TypeVar v1) [] (TypeVar v2) | v1 == v2 = return ()
138+ unifyRows' [] (Skolem s1) [] (Skolem s2) | s1 == s2 = return ()
139+ unifyRows' sd3 r3 sd4 r4 = throwError $ "Cannot unify " ++ prettyPrintRow (rowFromList (sd3, r3)) ++ " with " ++ prettyPrintRow (rowFromList (sd4, r4)) ++ "."
140+
141+typeConstructorsAreEqual :: Environment -> ModuleName -> Qualified ProperName -> Qualified ProperName -> Bool
142+typeConstructorsAreEqual env moduleName = (==) `on` canonicalizeType moduleName env
143+
144+typesOf :: ModuleName -> [(Ident, Value)] -> Check [(Ident, (Value, Type))]
145+typesOf moduleName vals = do
146+ tys <- fmap (\(tys, s) -> map (\(ident, (val, ty)) -> (ident, (overTypes (apply s) val, apply s ty))) tys)
147+ . runSubst (SubstContext moduleName) $ do
148+ let es = map isTyped vals
149+ typed = filter (isJust . snd . snd) es
150+ untyped = filter (isNothing . snd . snd) es
151+ typedDict = map (\(ident, (_, Just ty)) -> (ident, ty)) typed
152+ untypedNames <- replicateM (length untyped) fresh
153+ let untypedDict = zip (map fst untyped) untypedNames
154+ dict = M.fromList (map (\(ident, ty) -> ((moduleName, ident), (ty, LocalVariable))) $ typedDict ++ untypedDict)
155+ forM es $ \e -> do
156+ triple@(_, (val, ty)) <- case e of
157+ (ident, (val, Just ty)) -> do
158+ kind <- liftCheck $ kindOf moduleName ty
159+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
160+ ty' <- replaceAllTypeSynonyms ty
161+ val' <- bindNames dict $ check val ty'
162+ return (ident, (val', ty'))
163+ (ident, (val, Nothing)) -> do
164+ TypedValue val' ty <- bindNames dict $ infer val
165+ ty ~~ fromMaybe (error "name not found in dictionary") (lookup ident untypedDict)
166+ return (ident, (val', ty))
167+ when (moduleName == ModuleName (ProperName "Main") && fst e == Ident "main") $ do
168+ [eff, a] <- replicateM 2 fresh
169+ ty ~~ TypeApp (TypeApp (TypeConstructor (Qualified (Just (ModuleName (ProperName "Eff"))) (ProperName "Eff"))) eff) a
170+ escapeCheck val ty
171+ return triple
172+ forM_ tys $ skolemEscapeCheck . snd . snd
173+ forM tys $ \(ident, (val, ty)) -> do
174+ val' <- replaceTypeClassDictionaries val
175+ return (ident, (overTypes (desaturateAllTypeSynonyms . setifyAll) $ val'
176+ , varIfUnknown . desaturateAllTypeSynonyms . setifyAll $ ty))
177+
178+isTyped :: (Ident, Value) -> (Ident, (Value, Maybe Type))
179+isTyped (name, TypedValue value ty) = (name, (value, Just ty))
180+isTyped (name, value) = (name, (value, Nothing))
181+
182+overTypes :: (Type -> Type) -> Value -> Value
183+overTypes f = everywhere (mkT f)
184+
185+replaceTypeClassDictionaries :: Value -> Check Value
186+replaceTypeClassDictionaries = everywhereM (mkM go)
187+ where
188+ go (TypeClassDictionary constraint dicts) = entails dicts constraint
189+ go other = return other
190+
191+entails :: [(Ident, [(Qualified ProperName, Type)], Qualified ProperName, Type)] -> (Qualified ProperName, Type) -> Check Value
192+entails context goal =
193+ case go goal of
194+ [] -> throwError $ "No type class instance for " ++ show goal ++ " in context " ++ show context
195+ (dict : _) -> return dict
196+ where
197+ go (className, ty) = [ App (Var (Qualified Nothing fnName)) args
198+ | (fnName, subgoals, className', ty') <- context
199+ , className == className'
200+ , subst <- maybeToList $ typeHeadsAreEqual ty ty'
201+ , args <- forM (replaceAllTypeVars subst subgoals) go ]
202+ typeHeadsAreEqual :: Type -> Type -> Maybe [(String, Type)]
203+ typeHeadsAreEqual String String = Just []
204+ typeHeadsAreEqual Number Number = Just []
205+ typeHeadsAreEqual Boolean Boolean = Just []
206+ typeHeadsAreEqual (Skolem s1) (Skolem s2) | s1 == s2 = Just []
207+ typeHeadsAreEqual (Array ty1) (Array ty2) = typeHeadsAreEqual ty1 ty2
208+ typeHeadsAreEqual (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = Just []
209+ typeHeadsAreEqual (TypeApp h1 (TypeVar v)) (TypeApp h2 arg) = do
210+ m <- typeHeadsAreEqual h1 h2
211+ return $ (v, arg) : m
212+ typeHeadsAreEqual t1@(TypeApp _ _) t2@(TypeApp _ (TypeVar _)) = typeHeadsAreEqual t2 t1
213+ typeHeadsAreEqual _ _ = Nothing
214+
215+escapeCheck :: Value -> Type -> Subst ()
216+escapeCheck value ty = do
217+ subst <- substSubst <$> getSubstState
218+ let visibleUnknowns = nub $ unknowns $ apply subst ty
219+ let allUnknowns = findAllTypes value
220+ forM_ allUnknowns $ \t -> do
221+ let unsolvedUnknowns = nub . unknowns $ apply subst t
222+ guardWith "Escape check fails" $ null $ unsolvedUnknowns \\ visibleUnknowns
223+
224+findAllTypes :: Value -> [Type]
225+findAllTypes = everything (++) (mkQ [] go)
226+ where
227+ go (TypedValue _ ty) = [ty]
228+ go _ = []
229+
230+skolemEscapeCheck :: Type -> Check ()
231+skolemEscapeCheck ty =
232+ case something (mkQ Nothing findSkolems) ty of
233+ Nothing -> return ()
234+ Just _ -> throwError $ "Skolem variables cannot escape. Consider adding a type signature." ++ show ty
235+ where
236+ findSkolems (Skolem _) = return ()
237+ findSkolems _ = mzero
238+
239+setify :: Type -> Type
240+setify = rowFromList . first (M.toList . M.fromList) . rowToList
241+
242+setifyAll :: (D.Data d) => d -> d
243+setifyAll = everywhere (mkT setify)
244+
245+varIfUnknown :: Type -> Type
246+varIfUnknown ty =
247+ let unks = nub $ unknowns ty
248+ toName = (:) 't' . show
249+ ty' = everywhere (mkT typeToVar) $ ty
250+ typeToVar :: Type -> Type
251+ typeToVar (TUnknown (Unknown u)) = TypeVar (toName u)
252+ typeToVar t = t
253+ in mkForAll (sort . map toName $ unks) ty'
254+
255+replaceAllTypeVars :: (D.Data d) => [(String, Type)] -> d -> d
256+replaceAllTypeVars = foldl' (\f (name, ty) -> replaceTypeVars name ty . f) id
257+
258+replaceAllVarsWithUnknowns :: Type -> Subst Type
259+replaceAllVarsWithUnknowns (ForAll ident ty) = replaceVarWithUnknown ident ty >>= replaceAllVarsWithUnknowns
260+replaceAllVarsWithUnknowns ty = return ty
261+
262+replaceVarWithUnknown :: String -> Type -> Subst Type
263+replaceVarWithUnknown ident ty = do
264+ tu <- fresh
265+ return $ replaceTypeVars ident tu $ ty
266+
267+replaceAllTypeSynonyms :: (Functor m, MonadState CheckState m, MonadReader SubstContext m, MonadError String m) => (D.Data d) => d -> m d
268+replaceAllTypeSynonyms d = do
269+ env <- getEnv
270+ moduleName <- substCurrentModule <$> ask
271+ let syns = map (\((path, name), (args, _)) -> ((path, name), length args)) . M.toList $ typeSynonyms env
272+ either throwError return $ saturateAllTypeSynonyms env moduleName syns d
273+
274+desaturateAllTypeSynonyms :: (D.Data d) => d -> d
275+desaturateAllTypeSynonyms = everywhere (mkT replaceSaturatedTypeSynonym)
276+ where
277+ replaceSaturatedTypeSynonym (SaturatedTypeSynonym name args) = foldl TypeApp (TypeConstructor name) args
278+ replaceSaturatedTypeSynonym t = t
279+
280+expandTypeSynonym :: Qualified ProperName -> [Type] -> Subst Type
281+expandTypeSynonym name args = do
282+ env <- getEnv
283+ moduleName <- substCurrentModule `fmap` ask
284+ case M.lookup (canonicalizeType moduleName env name) (typeSynonyms env) of
285+ Just (synArgs, body) -> return $ replaceAllTypeVars (zip synArgs args) body
286+ Nothing -> error "Type synonym was not defined"
287+
288+ensureNoDuplicateProperties :: (MonadError String m) => [(String, Value)] -> m ()
289+ensureNoDuplicateProperties ps = guardWith "Duplicate property names" $ length (nub . map fst $ ps) == length ps
290+
291+infer :: Value -> Subst Value
292+infer val = rethrow (\e -> "Error inferring type of term " ++ prettyPrintValue val ++ ":\n" ++ e) $ infer' val
293+
294+infer' :: Value -> Subst Value
295+infer' v@(NumericLiteral _) = return $ TypedValue v Number
296+infer' v@(StringLiteral _) = return $ TypedValue v String
297+infer' v@(BooleanLiteral _) = return $ TypedValue v Boolean
298+infer' (ArrayLiteral vals) = do
299+ ts <- mapM infer vals
300+ els <- fresh
301+ forM_ ts $ \(TypedValue _ t) -> els ~~ Array t
302+ return $ TypedValue (ArrayLiteral ts) els
303+infer' (Unary op val) = do
304+ v <- infer val
305+ inferUnary op v
306+infer' (Binary op left right) = do
307+ v1 <- infer left
308+ v2 <- infer right
309+ inferBinary op v1 v2
310+infer' (ObjectLiteral ps) = do
311+ ensureNoDuplicateProperties ps
312+ ts <- mapM (infer . snd) ps
313+ let fields = zipWith (\name (TypedValue _ t) -> (name, t)) (map fst ps) ts
314+ ty = Object $ rowFromList (fields, REmpty)
315+ return $ TypedValue (ObjectLiteral (zip (map fst ps) ts)) ty
316+infer' (ObjectUpdate o ps) = do
317+ ensureNoDuplicateProperties ps
318+ row <- fresh
319+ newVals <- zipWith (\(name, _) t -> (name, t)) ps <$> mapM (infer . snd) ps
320+ let newTys = map (\(name, TypedValue _ ty) -> (name, ty)) newVals
321+ oldTys <- zip (map fst ps) <$> replicateM (length ps) fresh
322+ o' <- check o $ Object $ rowFromList (oldTys, row)
323+ return $ TypedValue (ObjectUpdate o' newVals) $ Object $ rowFromList (newTys, row)
324+infer' (Indexer index val) = do
325+ el <- fresh
326+ index' <- check index Number
327+ val' <- check val (Array el)
328+ return $ TypedValue (Indexer (TypedValue index' Number) (TypedValue val' (Array el))) el
329+infer' (Accessor prop val) = do
330+ typed@(TypedValue _ objTy) <- infer val
331+ propTy <- inferProperty objTy prop
332+ case propTy of
333+ Nothing -> do
334+ field <- fresh
335+ rest <- fresh
336+ objTy `subsumes` Object (RCons prop field rest)
337+ return $ TypedValue (Accessor prop typed) field
338+ Just ty -> return $ TypedValue (Accessor prop typed) ty
339+infer' (Abs args ret) = do
340+ ts <- replicateM (length args) fresh
341+ moduleName <- substCurrentModule <$> ask
342+ bindLocalVariables moduleName (zip args ts) $ do
343+ body@(TypedValue _ bodyTy) <- infer' ret
344+ return $ TypedValue (Abs args body) $ Function ts bodyTy
345+infer' (App f args) = do
346+ f'@(TypedValue _ ft) <- infer f
347+ ret <- fresh
348+ app <- checkFunctionApplication f' ft args ret
349+ return $ TypedValue app ret
350+infer' (Var var) = do
351+ moduleName <- substCurrentModule <$> ask
352+ ty <- lookupVariable moduleName var
353+ ty' <- replaceAllTypeSynonyms ty
354+ case ty' of
355+ ConstrainedType constraints _ -> do
356+ dicts <- getTypeClassDictionaries
357+ return $ TypedValue (App (Var var) (map (flip TypeClassDictionary dicts) constraints)) ty'
358+ _ -> return $ TypedValue (Var var) ty'
359+infer' (Block ss) = do
360+ ret <- fresh
361+ (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
362+ guardWith "Block is missing a return statement" allCodePathsReturn
363+ return $ TypedValue (Block ss') ret
364+infer' v@(Constructor c) = do
365+ env <- getEnv
366+ moduleName <- substCurrentModule `fmap` ask
367+ case M.lookup (qualify moduleName c) (dataConstructors env) of
368+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
369+ Just (ty, _) -> do ty' <- replaceAllTypeSynonyms ty
370+ return $ TypedValue v ty'
371+infer' (Case vals binders) = do
372+ ts <- mapM infer vals
373+ ret <- fresh
374+ binders' <- checkBinders (map (\(TypedValue _ t) -> t) ts) ret binders
375+ return $ TypedValue (Case ts binders') ret
376+infer' (IfThenElse cond th el) = do
377+ cond' <- check cond Boolean
378+ v2@(TypedValue _ t2) <- infer th
379+ v3@(TypedValue _ t3) <- infer el
380+ t2 ~~ t3
381+ return $ TypedValue (IfThenElse cond' v2 v3) t2
382+infer' (TypedValue val ty) = do
383+ moduleName <- substCurrentModule <$> ask
384+ kind <- liftCheck $ kindOf moduleName ty
385+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
386+ ty' <- replaceAllTypeSynonyms ty
387+ val' <- check val ty'
388+ return $ TypedValue val' ty
389+infer' _ = error "Invalid argument to infer"
390+
391+inferProperty :: Type -> String -> Subst (Maybe Type)
392+inferProperty (Object row) prop = do
393+ let (props, _) = rowToList row
394+ return $ lookup prop props
395+inferProperty (SaturatedTypeSynonym name args) prop = do
396+ replaced <- expandTypeSynonym name args
397+ inferProperty replaced prop
398+inferProperty (ForAll ident ty) prop = do
399+ replaced <- replaceVarWithUnknown ident ty
400+ inferProperty replaced prop
401+inferProperty _ _ = return Nothing
402+
403+inferUnary :: UnaryOperator -> Value -> Subst Value
404+inferUnary op (TypedValue val valTy) =
405+ case fromMaybe (error "Invalid operator") $ lookup op unaryOps of
406+ (valTy', resTy) -> do
407+ valTy' ~~ valTy
408+ return $ TypedValue (Unary op val) resTy
409+inferUnary _ _ = error "Invalid arguments to inferUnary"
410+
411+checkUnary :: UnaryOperator -> Value -> Type -> Subst Value
412+checkUnary op val res =
413+ case fromMaybe (error "Invalid operator") $ lookup op unaryOps of
414+ (valTy, resTy) -> do
415+ res ~~ resTy
416+ val' <- check val valTy
417+ return $ Unary op val'
418+
419+unaryOps :: [(UnaryOperator, (Type, Type))]
420+unaryOps = [ (Negate, (Number, Number))
421+ , (Not, (Boolean, Boolean))
422+ , (BitwiseNot, (Number, Number))
423+ ]
424+
425+inferBinary :: BinaryOperator -> Value -> Value -> Subst Value
426+inferBinary op left@(TypedValue _ leftTy) right@(TypedValue _ rightTy) | isEqualityTest op = do
427+ leftTy ~~ rightTy
428+ return $ TypedValue (Binary op left right) Boolean
429+inferBinary op left@(TypedValue _ leftTy) right@(TypedValue _ rightTy) =
430+ case fromMaybe (error "Invalid operator") $ lookup op binaryOps of
431+ (valTy, resTy) -> do
432+ leftTy ~~ valTy
433+ rightTy ~~ valTy
434+ return $ TypedValue (Binary op left right) resTy
435+inferBinary _ _ _ = error "Invalid arguments to inferBinary"
436+
437+checkBinary :: BinaryOperator -> Value -> Value -> Type -> Subst Value
438+checkBinary op left right res | isEqualityTest op = do
439+ res ~~ Boolean
440+ left'@(TypedValue _ t1) <- infer left
441+ right'@(TypedValue _ t2) <- infer right
442+ t1 ~~ t2
443+ return $ Binary op left' right'
444+checkBinary op left right res =
445+ case fromMaybe (error "Invalid operator") $ lookup op binaryOps of
446+ (valTy, resTy) -> do
447+ res ~~ resTy
448+ left' <- check left valTy
449+ right' <- check right valTy
450+ return $ Binary op left' right'
451+
452+isEqualityTest :: BinaryOperator -> Bool
453+isEqualityTest EqualTo = True
454+isEqualityTest NotEqualTo = True
455+isEqualityTest _ = False
456+
457+binaryOps :: [(BinaryOperator, (Type, Type))]
458+binaryOps = [ (Add, (Number, Number))
459+ , (Subtract, (Number, Number))
460+ , (Multiply, (Number, Number))
461+ , (Divide, (Number, Number))
462+ , (Modulus, (Number, Number))
463+ , (BitwiseAnd, (Number, Number))
464+ , (BitwiseOr, (Number, Number))
465+ , (BitwiseXor, (Number, Number))
466+ , (ShiftRight, (Number, Number))
467+ , (ZeroFillShiftRight, (Number, Number))
468+ , (And, (Boolean, Boolean))
469+ , (Or, (Boolean, Boolean))
470+ , (Concat, (String, String))
471+ , (Modulus, (Number, Number))
472+ , (LessThan, (Number, Boolean))
473+ , (LessThanOrEqualTo, (Number, Boolean))
474+ , (GreaterThan, (Number, Boolean))
475+ , (GreaterThanOrEqualTo, (Number, Boolean))
476+ ]
477+
478+inferBinder :: Type -> Binder -> Subst (M.Map Ident Type)
479+inferBinder _ NullBinder = return M.empty
480+inferBinder val (StringBinder _) = val ~~ String >> return M.empty
481+inferBinder val (NumberBinder _) = val ~~ Number >> return M.empty
482+inferBinder val (BooleanBinder _) = val ~~ Boolean >> return M.empty
483+inferBinder val (VarBinder name) = return $ M.singleton name val
484+inferBinder val (NullaryBinder ctor) = do
485+ env <- getEnv
486+ moduleName <- substCurrentModule <$> ask
487+ case M.lookup (qualify moduleName ctor) (dataConstructors env) of
488+ Just (ty, _) -> do
489+ ty `subsumes` val
490+ return M.empty
491+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
492+inferBinder val (UnaryBinder ctor binder) = do
493+ env <- getEnv
494+ moduleName <- substCurrentModule <$> ask
495+ case M.lookup (qualify moduleName ctor) (dataConstructors env) of
496+ Just (ty, _) -> do
497+ fn <- replaceAllVarsWithUnknowns ty
498+ case fn of
499+ Function [obj] ret -> do
500+ val `subsumes` ret
501+ inferBinder obj binder
502+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not a unary constructor"
503+ _ -> throwError $ "Constructor " ++ show ctor ++ " is not defined"
504+inferBinder val (ObjectBinder props) = do
505+ row <- fresh
506+ rest <- fresh
507+ m1 <- inferRowProperties row rest props
508+ val ~~ Object row
509+ return m1
510+ where
511+ inferRowProperties :: Type -> Type -> [(String, Binder)] -> Subst (M.Map Ident Type)
512+ inferRowProperties nrow row [] = nrow ~~ row >> return M.empty
513+ inferRowProperties nrow row ((name, binder):binders) = do
514+ propTy <- fresh
515+ m1 <- inferBinder propTy binder
516+ m2 <- inferRowProperties nrow (RCons name propTy row) binders
517+ return $ m1 `M.union` m2
518+inferBinder val (ArrayBinder binders) = do
519+ el <- fresh
520+ m1 <- M.unions <$> mapM (inferBinder el) binders
521+ val ~~ Array el
522+ return m1
523+inferBinder val (ConsBinder headBinder tailBinder) = do
524+ el <- fresh
525+ m1 <- inferBinder el headBinder
526+ m2 <- inferBinder val tailBinder
527+ val ~~ Array el
528+ return $ m1 `M.union` m2
529+inferBinder val (NamedBinder name binder) = do
530+ m <- inferBinder val binder
531+ return $ M.insert name val m
532+
533+checkBinders :: [Type] -> Type -> [([Binder], Maybe Guard, Value)] -> Subst [([Binder], Maybe Guard, Value)]
534+checkBinders _ _ [] = return []
535+checkBinders nvals ret ((binders, grd, val):bs) = do
536+ moduleName <- substCurrentModule <$> ask
537+ m1 <- M.unions <$> zipWithM inferBinder nvals binders
538+ r <- bindLocalVariables moduleName (M.toList m1) $ do
539+ val' <- check val ret
540+ case grd of
541+ Nothing -> return (binders, Nothing, val')
542+ Just g -> do
543+ g' <- check g Boolean
544+ return (binders, Just g', val')
545+ rs <- checkBinders nvals ret bs
546+ return $ r : rs
547+
548+assignVariable :: Ident -> Subst ()
549+assignVariable name = do
550+ env <- checkEnv <$> get
551+ moduleName <- substCurrentModule <$> ask
552+ case M.lookup (moduleName, name) (names env) of
553+ Just (_, LocalVariable) -> throwError $ "Variable with name " ++ show name ++ " already exists."
554+ _ -> return ()
555+
556+checkStatement :: M.Map Ident Type -> Type -> Statement -> Subst (Bool, M.Map Ident Type, Statement)
557+checkStatement mass _ (VariableIntroduction name val) = do
558+ assignVariable name
559+ val'@(TypedValue _ t) <- infer val
560+ return (False, M.insert name t mass, VariableIntroduction name val')
561+checkStatement mass _ (Assignment ident val) = do
562+ val'@(TypedValue _ t) <- infer val
563+ case M.lookup ident mass of
564+ Nothing -> throwError $ "No local variable with name " ++ show ident
565+ Just ty -> do t ~~ ty
566+ return (False, mass, Assignment ident val')
567+checkStatement mass ret (While val inner) = do
568+ val' <- check val Boolean
569+ (allCodePathsReturn, _, inner') <- checkBlock mass ret inner
570+ return (allCodePathsReturn, mass, While val' inner')
571+checkStatement mass ret (If ifst) = do
572+ (allCodePathsReturn, ifst') <- checkIfStatement mass ret ifst
573+ return (allCodePathsReturn, mass, If ifst')
574+checkStatement mass ret (For ident start end inner) = do
575+ moduleName <- substCurrentModule <$> ask
576+ assignVariable ident
577+ start' <- check start Number
578+ end' <- check end Number
579+ (allCodePathsReturn, _, inner') <- bindLocalVariables moduleName [(ident, Number)] $ checkBlock mass ret inner
580+ return (allCodePathsReturn, mass, For ident start' end' inner')
581+checkStatement mass ret (Return val) = do
582+ val' <- check val ret
583+ return (True, mass, Return val')
584+
585+checkIfStatement :: M.Map Ident Type -> Type -> IfStatement -> Subst (Bool, IfStatement)
586+checkIfStatement mass ret (IfStatement val thens Nothing) = do
587+ val' <- check val Boolean
588+ (_, _, thens') <- checkBlock mass ret thens
589+ return (False, IfStatement val' thens' Nothing)
590+checkIfStatement mass ret (IfStatement val thens (Just elses)) = do
591+ val' <- check val Boolean
592+ (allCodePathsReturn1, _, thens') <- checkBlock mass ret thens
593+ (allCodePathsReturn2, elses') <- checkElseStatement mass ret elses
594+ return (allCodePathsReturn1 && allCodePathsReturn2, IfStatement val' thens' (Just elses'))
595+
596+checkElseStatement :: M.Map Ident Type -> Type -> ElseStatement -> Subst (Bool, ElseStatement)
597+checkElseStatement mass ret (Else elses) = do
598+ (allCodePathsReturn, _, elses') <- checkBlock mass ret elses
599+ return (allCodePathsReturn, Else elses')
600+checkElseStatement mass ret (ElseIf ifst) = (id *** ElseIf) <$> checkIfStatement mass ret ifst
601+
602+checkBlock :: M.Map Ident Type -> Type -> [Statement] -> Subst (Bool, M.Map Ident Type, [Statement])
603+checkBlock mass _ [] = return (False, mass, [])
604+checkBlock mass ret (s:ss) = do
605+ moduleName <- substCurrentModule <$> ask
606+ (b1, mass1, s') <- checkStatement mass ret s
607+ bindLocalVariables moduleName (M.toList mass1) $ case (b1, ss) of
608+ (True, []) -> return (True, mass1, [s'])
609+ (True, _) -> throwError "Unreachable code"
610+ (False, ss') -> do
611+ (b, m, ss'') <- checkBlock mass1 ret ss'
612+ return (b, m, s':ss'')
613+
614+skolemize :: String -> Type -> Subst Type
615+skolemize ident ty = do
616+ tsk <- Skolem <$> fresh'
617+ return $ replaceTypeVars ident tsk ty
618+
619+check :: Value -> Type -> Subst Value
620+check val ty = rethrow errorMessage $ check' val ty
621+ where
622+ errorMessage msg =
623+ "Error checking type of term " ++
624+ prettyPrintValue val ++
625+ " against type " ++
626+ prettyPrintType ty ++
627+ ":\n" ++
628+ msg
629+
630+check' :: Value -> Type -> Subst Value
631+check' val (ForAll idents ty) = do
632+ sk <- skolemize idents ty
633+ check val sk
634+check' val (ConstrainedType constraints ty) = do
635+ let dictName = Ident "__dict" -- TODO
636+ val' <- withTypeClassDictionaries (map (\(className, instanceTy) -> (dictName, [], className, instanceTy)) constraints) $ check val ty
637+ return $ Abs (map (\_ -> dictName) constraints) val'
638+check' val u@(TUnknown _) = do
639+ val'@(TypedValue _ ty) <- infer val
640+ -- Don't unify an unknown with an inferred polytype
641+ ty' <- replaceAllVarsWithUnknowns ty
642+ ty' ~~ u
643+ return val'
644+check' v@(NumericLiteral _) Number = return v
645+check' v@(StringLiteral _) String = return v
646+check' v@(BooleanLiteral _) Boolean = return v
647+check' (Unary op val) ty = checkUnary op val ty
648+check' (Binary op left right) ty = checkBinary op left right ty
649+check' (ArrayLiteral vals) (Array ty) = ArrayLiteral <$> forM vals (\val -> check val ty)
650+check' (Indexer index vals) ty = do
651+ index' <- check index Number
652+ vals' <- check vals (Array ty)
653+ return $ Indexer index' vals'
654+check' (Abs args ret) (Function argTys retTy) = do
655+ moduleName <- substCurrentModule <$> ask
656+ guardWith "Incorrect number of function arguments" (length args == length argTys)
657+ ret' <- bindLocalVariables moduleName (zip args argTys) $ check ret retTy
658+ return $ Abs args ret'
659+check' (App f args) ret = do
660+ f'@(TypedValue _ ft) <- infer f
661+ app <- checkFunctionApplication f' ft args ret
662+ return $ app
663+check' (Var var) ty = do
664+ moduleName <- substCurrentModule <$> ask
665+ ty1 <- lookupVariable moduleName var
666+ repl <- replaceAllTypeSynonyms ty1
667+ repl `subsumes` ty
668+ return $ Var var
669+check' (TypedValue val ty1) ty2 = do
670+ moduleName <- substCurrentModule <$> ask
671+ kind <- liftCheck $ kindOf moduleName ty1
672+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
673+ ty1 `subsumes` ty2
674+ val' <- check val ty1
675+ return $ TypedValue val' ty1
676+check' (Case vals binders) ret = do
677+ vals' <- mapM infer vals
678+ let ts = map (\(TypedValue _ t) -> t) vals'
679+ binders' <- checkBinders ts ret binders
680+ return $ Case vals' binders'
681+check' (IfThenElse cond th el) ty = do
682+ cond' <- check cond Boolean
683+ th' <- check th ty
684+ el' <- check el ty
685+ return $ IfThenElse cond' th' el'
686+check' (ObjectLiteral ps) (Object row) = do
687+ ensureNoDuplicateProperties ps
688+ ps' <- checkProperties ps row False
689+ return $ ObjectLiteral ps'
690+check' (ObjectUpdate obj ps) (Object row) = do
691+ ensureNoDuplicateProperties ps
692+ us <- zip (map fst ps) <$> replicateM (length ps) fresh
693+ let (propsToCheck, rest) = rowToList row
694+ propsToRemove = map fst ps
695+ remainingProps = filter (\(p, _) -> p `notElem` propsToRemove) propsToCheck
696+ obj' <- check obj (Object (rowFromList (us ++ remainingProps, rest)))
697+ ps' <- checkProperties ps row True
698+ return $ ObjectUpdate obj' ps'
699+check' (Accessor prop val) ty = do
700+ rest <- fresh
701+ val' <- check val (Object (RCons prop ty rest))
702+ return $ Accessor prop val'
703+check' (Block ss) ret = do
704+ (allCodePathsReturn, _, ss') <- checkBlock M.empty ret ss
705+ guardWith "Block is missing a return statement" allCodePathsReturn
706+ return $ Block ss'
707+check' (Constructor c) ty = do
708+ env <- getEnv
709+ moduleName <- substCurrentModule <$> ask
710+ case M.lookup (qualify moduleName c) (dataConstructors env) of
711+ Nothing -> throwError $ "Constructor " ++ show c ++ " is undefined"
712+ Just (ty1, _) -> do
713+ repl <- replaceAllTypeSynonyms ty1
714+ repl `subsumes` ty
715+ return $ Constructor c
716+check' val (SaturatedTypeSynonym name args) = do
717+ ty <- expandTypeSynonym name args
718+ check val ty
719+check' val ty = throwError $ prettyPrintValue val ++ " does not have type " ++ prettyPrintType ty
720+
721+checkProperties :: [(String, Value)] -> Type -> Bool -> Subst [(String, Value)]
722+checkProperties ps row lax = let (ts, r') = rowToList row in go ps ts r' where
723+ go [] [] REmpty = return []
724+ go [] [] u@(TUnknown _) = do u ~~ REmpty
725+ return []
726+ go [] [] (Skolem _) | lax = return []
727+ go [] ((p, _): _) _ | lax = return []
728+ | otherwise = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have property " ++ p
729+ go ((p,_):_) [] REmpty = throwError $ "Property " ++ p ++ " is not present in closed object type " ++ prettyPrintRow row
730+ go ((p,v):ps') [] u@(TUnknown _) = do
731+ v'@(TypedValue _ ty) <- infer v
732+ rest <- fresh
733+ u ~~ RCons p ty rest
734+ ps'' <- go ps' [] rest
735+ return $ (p, v') : ps''
736+ go ((p,v):ps') ts r =
737+ case lookup p ts of
738+ Nothing -> do
739+ v'@(TypedValue _ ty) <- infer v
740+ rest <- fresh
741+ r ~~ RCons p ty rest
742+ ps'' <- go ps' ts rest
743+ return $ (p, v') : ps''
744+ Just ty -> do
745+ v' <- check v ty
746+ ps'' <- go ps' (delete (p, ty) ts) r
747+ return $ (p, v') : ps''
748+ go _ _ _ = throwError $ prettyPrintValue (ObjectLiteral ps) ++ " does not have type " ++ prettyPrintType (Object row)
749+
750+checkFunctionApplication :: Value -> Type -> [Value] -> Type -> Subst Value
751+checkFunctionApplication fn fnTy args ret = rethrow errorMessage $ checkFunctionApplication' fn fnTy args ret
752+ where
753+ errorMessage msg = "Error applying function of type "
754+ ++ prettyPrintType fnTy
755+ ++ " to arguments " ++ intercalate ", " (map prettyPrintValue args)
756+ ++ ":\n" ++ msg
757+
758+checkFunctionApplication' :: Value -> Type -> [Value] -> Type -> Subst Value
759+checkFunctionApplication' fn (Function argTys retTy) args ret = do
760+ guardWith "Incorrect number of function arguments" (length args == length argTys)
761+ args' <- zipWithM check args argTys
762+ retTy `subsumes` ret
763+ return $ App fn args'
764+checkFunctionApplication' fn (ForAll ident ty) args ret = do
765+ replaced <- replaceVarWithUnknown ident ty
766+ checkFunctionApplication fn replaced args ret
767+checkFunctionApplication' fn u@(TUnknown _) args ret = do
768+ args' <- mapM (\arg -> infer arg >>= \(TypedValue v t) -> TypedValue v <$> replaceAllVarsWithUnknowns t) args
769+ let tys = map (\(TypedValue _ t) -> t) args'
770+ u ~~ Function tys ret
771+ return $ App fn args'
772+checkFunctionApplication' fn (SaturatedTypeSynonym name tyArgs) args ret = do
773+ ty <- expandTypeSynonym name tyArgs
774+ checkFunctionApplication fn ty args ret
775+checkFunctionApplication' fn (ConstrainedType constraints fnTy) args ret = do
776+ dicts <- getTypeClassDictionaries
777+ checkFunctionApplication' (App fn (map (flip TypeClassDictionary dicts) constraints)) fnTy args ret
778+checkFunctionApplication' _ fnTy args ret = throwError $ "Applying a function of type "
779+ ++ prettyPrintType fnTy
780+ ++ " to argument(s) " ++ intercalate ", " (map prettyPrintValue args)
781+ ++ " does not yield a value of type " ++ prettyPrintType ret ++ "."
782+
783+subsumes :: Type -> Type -> Subst ()
784+subsumes (ForAll ident ty1) ty2 = do
785+ replaced <- replaceVarWithUnknown ident ty1
786+ replaced `subsumes` ty2
787+subsumes (Function args1 ret1) (Function args2 ret2) = do
788+ zipWithM_ subsumes args2 args1
789+ ret1 `subsumes` ret2
790+subsumes ty1 ty2 = ty1 ~~ ty2
791+