@@ -0,0 +1,566 @@
1+-----------------------------------------------------------------------------
2+--
3+-- Module : 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+module PureScript.TypeChecker.Types (
16+ TypeConstraint(..),
17+ TypeSolution(..),
18+ typeOf
19+) where
20+
21+import Data.List
22+import Data.Function
23+import Data.Data (Data(..))
24+import Data.Generics (everywhere, everywhereM, everything, mkT, mkM, mkQ, extM, extQ)
25+
26+import PureScript.Values
27+import PureScript.Types
28+import PureScript.Kinds
29+import PureScript.Names
30+import PureScript.TypeChecker.Monad
31+import PureScript.TypeChecker.Kinds
32+import PureScript.TypeChecker.Synonyms
33+
34+import Control.Monad.State
35+import Control.Monad.Error
36+
37+import Control.Applicative
38+import Control.Arrow (Kleisli(..), (***), (&&&))
39+import qualified Control.Category as C
40+
41+import qualified Data.Map as M
42+
43+data TypeConstraint
44+ = TypeConstraint Int Type
45+ | RowConstraint Int Row deriving Show
46+
47+newtype TypeSolution = TypeSolution { runTypeSolution :: (Int -> Type, Int -> Row) }
48+
49+emptyTypeSolution :: TypeSolution
50+emptyTypeSolution = TypeSolution (TUnknown, RUnknown)
51+
52+typeOf :: Ident -> Value -> Check PolyType
53+typeOf name val = do
54+ (cs, n) <- case val of
55+ Abs _ _ -> do
56+ me <- fresh
57+ (cs, n) <- typeConstraints (M.singleton name me) val
58+ return (TypeConstraint me (TUnknown n) : cs, n)
59+ _ -> typeConstraints M.empty val
60+ solution <- solveTypeConstraints cs emptyTypeSolution
61+ let ty = fst (runTypeSolution solution) n
62+ allUnknownsBecameQuantified cs solution ty
63+ return $ varIfUnknown ty
64+
65+allUnknownsBecameQuantified :: [TypeConstraint] -> TypeSolution -> Type -> Check ()
66+allUnknownsBecameQuantified cs solution ty = do
67+ let
68+ typesMentioned = findUnknownTypes ty
69+ unknownTypes = nub $ flip concatMap cs $ \c -> case c of
70+ TypeConstraint u t -> u : findUnknownTypes t
71+ RowConstraint _ r -> findUnknownTypes r
72+ unsolvedTypes = filter (\n -> TUnknown n == fst (runTypeSolution solution) n) unknownTypes
73+ guardWith "Unsolved type variable" $ null $ unsolvedTypes \\ typesMentioned
74+ let
75+ rowsMentioned = findUnknownRows ty
76+ unknownRows = nub $ flip concatMap cs $ \c -> case c of
77+ TypeConstraint _ t -> findUnknownRows t
78+ RowConstraint u r -> u : findUnknownRows r
79+ unsolvedRows = filter (\n -> RUnknown n == snd (runTypeSolution solution) n) unknownRows
80+ guardWith ("Unsolved row variable" ++ show (unsolvedRows \\ rowsMentioned) ++ ", " ++ show cs) $ null $ unsolvedRows \\ rowsMentioned
81+
82+findUnknownTypes :: (Data d) => d -> [Int]
83+findUnknownTypes = everything (++) (mkQ [] f)
84+ where
85+ f :: Type -> [Int]
86+ f (TUnknown n) = [n]
87+ f _ = []
88+
89+findTypeVars :: (Data d) => d -> [String]
90+findTypeVars = everything (++) (mkQ [] f)
91+ where
92+ f :: Type -> [String]
93+ f (TypeVar v) = [v]
94+ f _ = []
95+
96+findUnknownRows :: (Data d) => d -> [Int]
97+findUnknownRows = everything (++) (mkQ [] f)
98+ where
99+ f :: Row -> [Int]
100+ f (RUnknown n) = [n]
101+ f _ = []
102+
103+varIfUnknown :: Type -> PolyType
104+varIfUnknown ty =
105+ let
106+ (ty', m) = flip runState M.empty $ everywhereM (flip extM g $ mkM f) ty
107+ in
108+ PolyType (sort $ nub $ M.elems m ++ findTypeVars ty) ty'
109+ where
110+ f :: Type -> State (M.Map Int String) Type
111+ f (TUnknown n) = do
112+ m <- get
113+ case M.lookup n m of
114+ Nothing -> do
115+ let name = "t" ++ show (M.size m)
116+ put $ M.insert n name m
117+ return $ TypeVar name
118+ Just name -> return $ TypeVar name
119+ f t = return t
120+ g :: Row -> State (M.Map Int String) Row
121+ g (RUnknown n) = do
122+ m <- get
123+ case M.lookup n m of
124+ Nothing -> do
125+ let name = "r" ++ show (M.size m)
126+ put $ M.insert n name m
127+ return $ RowVar name
128+ Just name -> return $ RowVar name
129+ g r = return r
130+
131+replaceVarsWithUnknowns :: [String] -> Type -> Check Type
132+replaceVarsWithUnknowns idents = flip evalStateT M.empty . everywhereM (flip extM f $ mkM g)
133+ where
134+ f :: Type -> StateT (M.Map String Int) Check Type
135+ f (TypeVar var) | var `elem` idents = do
136+ m <- get
137+ n <- lift fresh
138+ case M.lookup var m of
139+ Nothing -> do
140+ put (M.insert var n m)
141+ return $ TUnknown n
142+ Just u -> return $ TUnknown u
143+ f t = return t
144+ g :: Row -> StateT (M.Map String Int) Check Row
145+ g (RowVar var) | var `elem` idents = do
146+ m <- get
147+ n <- lift fresh
148+ case M.lookup var m of
149+ Nothing -> do
150+ put (M.insert var n m)
151+ return $ RUnknown n
152+ Just u -> return $ RUnknown u
153+ g r = return r
154+
155+replaceType :: (Data d) => Int -> Type -> d -> d
156+replaceType n t = everywhere (mkT go)
157+ where
158+ go (TUnknown m) | m == n = t
159+ go t = t
160+
161+replaceRow :: (Data d) => Int -> Row -> d -> d
162+replaceRow n r = everywhere (mkT go)
163+ where
164+ go (RUnknown m) | m == n = r
165+ go r = r
166+
167+typeOccursCheck :: Int -> Type -> Check ()
168+typeOccursCheck u (TUnknown _) = return ()
169+typeOccursCheck u t = when (occursCheck u t) $ throwError $ "Occurs check failed: " ++ show u ++ " = " ++ show t
170+
171+rowOccursCheck :: Int -> Row -> Check ()
172+rowOccursCheck u (RUnknown _) = return ()
173+rowOccursCheck u r = when (occursCheck u r) $ throwError $ "Occurs check failed: " ++ show u ++ " = " ++ show r
174+
175+occursCheck :: (Data d) => Int -> d -> Bool
176+occursCheck u = everything (||) $ flip extQ g $ mkQ False f
177+ where
178+ f (TUnknown u') | u' == u = True
179+ f _ = False
180+ g (RUnknown u') | u' == u = True
181+ g _ = False
182+
183+typeConstraints :: M.Map Ident Int -> Value -> Check ([TypeConstraint], Int)
184+typeConstraints _ (NumericLiteral _) = do
185+ me <- fresh
186+ return ([TypeConstraint me Number], me)
187+typeConstraints _ (StringLiteral _) = do
188+ me <- fresh
189+ return ([TypeConstraint me String], me)
190+typeConstraints _ (BooleanLiteral _) = do
191+ me <- fresh
192+ return ([TypeConstraint me Boolean], me)
193+typeConstraints m (ArrayLiteral vals) = do
194+ all <- mapM (typeConstraints m) vals
195+ let (cs, ns) = (concat . map fst &&& map snd) all
196+ me <- fresh
197+ return (cs ++ map (TypeConstraint me . Array . TUnknown) ns, me)
198+typeConstraints m (Unary op val) = do
199+ (cs, n1) <- typeConstraints m val
200+ me <- fresh
201+ return (cs ++ unaryOperatorConstraints op n1 me, me)
202+typeConstraints m (Binary op left right) = do
203+ (cs1, n1) <- typeConstraints m left
204+ (cs2, n2) <- typeConstraints m right
205+ me <- fresh
206+ return (cs1 ++ cs2 ++ binaryOperatorConstraints op n1 n2 me, me)
207+typeConstraints m (ObjectLiteral ps) = do
208+ all <- mapM (typeConstraints m . snd) ps
209+ let (cs, ns) = (concat . map fst &&& map snd) all
210+ me <- fresh
211+ let tys = zipWith (\(name, _) u -> (name, TUnknown u)) ps ns
212+ return ((TypeConstraint me (Object (typesToRow tys))) : cs, me)
213+ where
214+ typesToRow [] = REmpty
215+ typesToRow ((name, ty):tys) = RCons name ty (typesToRow tys)
216+typeConstraints m (Indexer index val) = do
217+ (cs1, n1) <- typeConstraints m index
218+ (cs2, n2) <- typeConstraints m val
219+ me <- fresh
220+ return ((TypeConstraint n1 Number) : (TypeConstraint n2 (Array (TUnknown me))) : cs1 ++ cs2, me)
221+typeConstraints m (Accessor prop val) = do
222+ (cs, n1) <- typeConstraints m val
223+ me <- fresh
224+ rest <- fresh
225+ return ((TypeConstraint n1 (Object (RCons prop (TUnknown me) (RUnknown rest)))) : cs, me)
226+typeConstraints m (Abs args ret) = do
227+ ns <- replicateM (length args) fresh
228+ let m' = m `M.union` M.fromList (zipWith (,) args ns)
229+ (cs, n') <- typeConstraints m' ret
230+ me <- fresh
231+ return ((TypeConstraint me (Function (map TUnknown ns) (TUnknown n'))) : cs, me)
232+typeConstraints m (App f xs) = do
233+ (cs1, n1) <- typeConstraints m f
234+ all <- mapM (typeConstraints m) xs
235+ let (cs2, ns) = (concat . map fst &&& map snd) all
236+ me <- fresh
237+ return ((TypeConstraint n1 (Function (map TUnknown ns) (TUnknown me))) : cs1 ++ cs2, me)
238+typeConstraints m (Var var) =
239+ case M.lookup var m of
240+ Nothing -> do
241+ env <- getEnv
242+ case M.lookup var (names env) of
243+ Nothing -> throwError $ show var ++ " is undefined"
244+ Just (PolyType idents ty, _) -> do
245+ me <- fresh
246+ replaced <- replaceVarsWithUnknowns idents ty
247+ return ([TypeConstraint me replaced], me)
248+ Just u -> do
249+ me <- fresh
250+ return ([TypeConstraint u (TUnknown me)], me)
251+typeConstraints m (Block ss) = do
252+ ret <- fresh
253+ (cs, allCodePathsReturn, _) <- typeConstraintsForBlock m M.empty ret ss
254+ guardWith "Block is missing a return statement" allCodePathsReturn
255+ return (cs, ret)
256+typeConstraints m (Constructor c) = do
257+ env <- getEnv
258+ case M.lookup c (dataConstructors env) of
259+ Nothing -> throwError $ "Constructor " ++ c ++ " is undefined"
260+ Just (PolyType idents ty) -> do
261+ me <- fresh
262+ replaced <- replaceVarsWithUnknowns idents ty
263+ return ([TypeConstraint me replaced], me)
264+typeConstraints m (Case val binders) = do
265+ (cs1, n1) <- typeConstraints m val
266+ ret <- fresh
267+ cs2 <- typeConstraintsForBinders m n1 ret binders
268+ return (cs1 ++ cs2, ret)
269+typeConstraints m (TypedValue val poly@(PolyType idents ty)) = do
270+ kind <- kindOf poly
271+ guardWith ("Expected type of kind *, was " ++ show kind) $ kind == Star
272+ desugared <- replaceAllTypeSynonyms ty
273+ (cs, n1) <- typeConstraints m val
274+ return (TypeConstraint n1 desugared : cs, n1)
275+
276+replaceAllTypeSynonyms :: Type -> Check Type
277+replaceAllTypeSynonyms ty = do
278+ env <- getEnv
279+ go (M.toList $ typeSynonyms env) ty
280+ where
281+ go [] ty = return ty
282+ go ((name, (args, repl)):rest) ty = do
283+ ty' <- either throwError return (substituteTypeSynonym name args repl ty)
284+ go rest ty'
285+
286+unaryOperatorConstraints :: UnaryOperator -> Int -> Int -> [TypeConstraint]
287+unaryOperatorConstraints Negate val result = [TypeConstraint val Number, TypeConstraint result Number]
288+unaryOperatorConstraints Not val result = [TypeConstraint val Boolean, TypeConstraint result Boolean]
289+unaryOperatorConstraints BitwiseNot val result = [TypeConstraint val Number, TypeConstraint result Number]
290+
291+binaryOperatorConstraints :: BinaryOperator -> Int -> Int -> Int -> [TypeConstraint]
292+binaryOperatorConstraints Add = symBinOpConstraints Number
293+binaryOperatorConstraints Subtract = symBinOpConstraints Number
294+binaryOperatorConstraints Multiply = symBinOpConstraints Number
295+binaryOperatorConstraints Divide = symBinOpConstraints Number
296+binaryOperatorConstraints Modulus = symBinOpConstraints Number
297+binaryOperatorConstraints LessThan = asymBinOpConstraints Number Boolean
298+binaryOperatorConstraints LessThanOrEqualTo = asymBinOpConstraints Number Boolean
299+binaryOperatorConstraints GreaterThan = asymBinOpConstraints Number Boolean
300+binaryOperatorConstraints GreaterThanOrEqualTo = asymBinOpConstraints Number Boolean
301+binaryOperatorConstraints BitwiseAnd = symBinOpConstraints Number
302+binaryOperatorConstraints BitwiseOr = symBinOpConstraints Number
303+binaryOperatorConstraints BitwiseXor = symBinOpConstraints Number
304+binaryOperatorConstraints ShiftLeft = symBinOpConstraints Number
305+binaryOperatorConstraints ShiftRight = symBinOpConstraints Number
306+binaryOperatorConstraints ZeroFillShiftRight = symBinOpConstraints Number
307+binaryOperatorConstraints EqualTo = equalityBinOpConstraints
308+binaryOperatorConstraints NotEqualTo = equalityBinOpConstraints
309+binaryOperatorConstraints And = symBinOpConstraints Boolean
310+binaryOperatorConstraints Or = symBinOpConstraints Boolean
311+binaryOperatorConstraints Concat = symBinOpConstraints String
312+
313+equalityBinOpConstraints :: Int -> Int -> Int -> [TypeConstraint]
314+equalityBinOpConstraints left right result = [TypeConstraint left (TUnknown right), TypeConstraint result Boolean]
315+
316+symBinOpConstraints :: Type -> Int -> Int -> Int -> [TypeConstraint]
317+symBinOpConstraints ty left right result = asymBinOpConstraints ty ty left right result
318+
319+asymBinOpConstraints :: Type -> Type -> Int -> Int -> Int -> [TypeConstraint]
320+asymBinOpConstraints ty res left right result = [TypeConstraint left ty, TypeConstraint right ty, TypeConstraint result res]
321+
322+typeConstraintsForBinder :: Int -> Binder -> Check ([TypeConstraint], M.Map Ident Int)
323+typeConstraintsForBinder _ NullBinder = return ([], M.empty)
324+typeConstraintsForBinder val (StringBinder _) = constantBinder val String
325+typeConstraintsForBinder val (NumberBinder _) = constantBinder val Number
326+typeConstraintsForBinder val (BooleanBinder _) = constantBinder val Boolean
327+typeConstraintsForBinder val (VarBinder name) = do
328+ me <- fresh
329+ return ([TypeConstraint me (TUnknown val)], M.singleton name me)
330+typeConstraintsForBinder val (NullaryBinder ctor) = do
331+ env <- getEnv
332+ case M.lookup ctor (dataConstructors env) of
333+ Just (PolyType args ret) -> do
334+ ret' <- replaceVarsWithUnknowns args ret
335+ return ([TypeConstraint val ret'], M.empty)
336+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
337+typeConstraintsForBinder val (UnaryBinder ctor binder) = do
338+ env <- getEnv
339+ case M.lookup ctor (dataConstructors env) of
340+ Just (PolyType idents f@(Function [_] _)) -> do
341+ obj <- fresh
342+ (Function [ty] ret) <- replaceVarsWithUnknowns idents f
343+ (cs, m1) <- typeConstraintsForBinder obj binder
344+ return ((TypeConstraint val ret) : (TypeConstraint obj ty) : cs, m1)
345+ Just _ -> throwError $ ctor ++ " is not a unary constructor"
346+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
347+typeConstraintsForBinder val (ObjectBinder props) = do
348+ row <- fresh
349+ rest <- fresh
350+ (cs, m1) <- typeConstraintsForProperties row (RUnknown rest) props
351+ return ((TypeConstraint val (Object (RUnknown row))) : cs, m1)
352+ where
353+ typeConstraintsForProperties :: Int -> Row -> [(String, Binder)] -> Check ([TypeConstraint], M.Map Ident Int)
354+ typeConstraintsForProperties nrow row [] = return ([RowConstraint nrow row], M.empty)
355+ typeConstraintsForProperties nrow row ((name, binder):binders) = do
356+ propTy <- fresh
357+ (cs1, m1) <- typeConstraintsForBinder propTy binder
358+ (cs2, m2) <- typeConstraintsForProperties nrow (RCons name (TUnknown propTy) row) binders
359+ return (cs1 ++ cs2, M.union m1 m2)
360+typeConstraintsForBinder val (ArrayBinder binders rest) = do
361+ el <- fresh
362+ all <- mapM (typeConstraintsForBinder el) binders
363+ let (cs1, m1) = (concat . map fst &&& M.unions . map snd) all
364+ let arrayConstraint = TypeConstraint val (Array (TUnknown el))
365+ case rest of
366+ Nothing -> return (arrayConstraint : cs1, m1)
367+ Just binder -> do
368+ (cs2, m2) <- typeConstraintsForBinder val binder
369+ return (arrayConstraint : cs1 ++ cs2, M.union m1 m2)
370+typeConstraintsForBinder val (NamedBinder name binder) = do
371+ me <- fresh
372+ (cs, m) <- typeConstraintsForBinder val binder
373+ return (TypeConstraint me (TUnknown val) : cs, M.insert name me m)
374+typeConstraintsForBinder val (GuardedBinder cond binder) = do
375+ (cs1, m) <- typeConstraintsForBinder val binder
376+ (cs2, n) <- typeConstraints m cond
377+ return (TypeConstraint n Boolean : cs1 ++ cs2, m)
378+
379+constantBinder :: Int -> Type -> Check ([TypeConstraint], M.Map Ident Int)
380+constantBinder val ty = return ([TypeConstraint val ty], M.empty)
381+
382+typeConstraintsForBinders :: M.Map Ident Int -> Int -> Int -> [(Binder, Value)] -> Check [TypeConstraint]
383+typeConstraintsForBinders _ _ _ [] = return []
384+typeConstraintsForBinders m nval ret ((binder, val):bs) = do
385+ (cs1, m1) <- typeConstraintsForBinder nval binder
386+ (cs2, n2) <- typeConstraints (M.union m m1) val
387+ cs3 <- typeConstraintsForBinders m nval ret bs
388+ return ((TypeConstraint n2 (TUnknown ret)) : cs1 ++ cs2 ++ cs3)
389+
390+assignVariable :: Ident -> M.Map Ident Int -> Check ()
391+assignVariable name m =
392+ case M.lookup name m of
393+ Nothing -> return ()
394+ Just _ -> throwError $ "Variable with name " ++ show name ++ " already exists."
395+
396+typeConstraintsForStatement :: M.Map Ident Int -> M.Map Ident Int -> Int -> Statement -> Check ([TypeConstraint], Bool, M.Map Ident Int)
397+typeConstraintsForStatement m mass ret (VariableIntroduction name val) = do
398+ assignVariable name (m `M.union` mass)
399+ (cs1, n1) <- typeConstraints m val
400+ return $ (cs1, False, M.insert name n1 mass)
401+typeConstraintsForStatement m mass ret (Assignment tgt val) = do
402+ (cs1, n1) <- typeConstraints m val
403+ cs2 <- typeConstraintsForAssignmentTarget m mass n1 tgt
404+ return (cs1 ++ cs2, False, mass)
405+typeConstraintsForStatement m mass ret (While val inner) = do
406+ (cs1, n1) <- typeConstraints m val
407+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret inner
408+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn, mass)
409+typeConstraintsForStatement m mass ret (If ifst) = do
410+ (cs, allCodePathsReturn) <- typeConstraintsForIfStatement m mass ret ifst
411+ return $ (cs, allCodePathsReturn, mass)
412+typeConstraintsForStatement m mass ret (For ident start end inner) = do
413+ assignVariable ident (m `M.union` mass)
414+ (cs1, n1) <- typeConstraints (m `M.union` mass) start
415+ (cs2, n2) <- typeConstraints (m `M.union` mass) end
416+ let mass1 = M.insert ident n1 mass
417+ (cs3, allCodePathsReturn, _) <- typeConstraintsForBlock (m `M.union` mass1) mass1 ret inner
418+ return $ ((TypeConstraint n1 Number) : (TypeConstraint n2 Number) : cs1 ++ cs2 ++ cs3, allCodePathsReturn, mass)
419+typeConstraintsForStatement m mass ret (ForEach ident vals inner) = do
420+ assignVariable ident (m `M.union` mass)
421+ val <- fresh
422+ (cs1, n1) <- typeConstraints (m `M.union` mass) vals
423+ let mass1 = M.insert ident val mass
424+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock (m `M.union` mass1) mass1 ret inner
425+ guardWith "Cannot return from within a foreach block" $ not allCodePathsReturn
426+ return $ ((TypeConstraint n1 (Array (TUnknown val))) : cs1 ++ cs2, False, mass)
427+typeConstraintsForStatement m mass ret (Return val) = do
428+ (cs1, n1) <- typeConstraints (m `M.union` mass) val
429+ return ((TypeConstraint n1 (TUnknown ret)) : cs1, True, mass)
430+
431+typeConstraintsForIfStatement :: M.Map Ident Int -> M.Map Ident Int -> Int -> IfStatement -> Check ([TypeConstraint], Bool)
432+typeConstraintsForIfStatement m mass ret (IfStatement val thens Nothing) = do
433+ (cs1, n1) <- typeConstraints m val
434+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret thens
435+ return ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn)
436+typeConstraintsForIfStatement m mass ret (IfStatement val thens (Just elses)) = do
437+ (cs1, n1) <- typeConstraints m val
438+ (cs2, allCodePathsReturn1, _) <- typeConstraintsForBlock m mass ret thens
439+ (cs3, allCodePathsReturn2) <- typeConstraintsForElseStatement m mass ret elses
440+ return ((TypeConstraint n1 Boolean) : cs1 ++ cs2 ++ cs3, allCodePathsReturn1 && allCodePathsReturn2)
441+
442+typeConstraintsForElseStatement :: M.Map Ident Int -> M.Map Ident Int -> Int -> ElseStatement -> Check ([TypeConstraint], Bool)
443+typeConstraintsForElseStatement m mass ret (Else elses) = do
444+ (cs, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret elses
445+ return (cs, allCodePathsReturn)
446+typeConstraintsForElseStatement m mass ret (ElseIf ifst) = do
447+ (cs, allCodePathsReturn) <- typeConstraintsForIfStatement m mass ret ifst
448+ return (cs, allCodePathsReturn)
449+
450+typeConstraintsForAssignmentTarget :: M.Map Ident Int -> M.Map Ident Int -> Int -> AssignmentTarget -> Check [TypeConstraint]
451+typeConstraintsForAssignmentTarget m mass nval (AssignVariable var) =
452+ case M.lookup var mass of
453+ Nothing -> throwError $ "No local variable with name " ++ show var
454+ Just ty -> do
455+ return [TypeConstraint nval (TUnknown ty)]
456+typeConstraintsForAssignmentTarget m mass nval (AssignArrayIndex index tgt) = do
457+ arr <- fresh
458+ (cs1, n1) <- typeConstraints (m `M.union` mass) index
459+ cs2 <- typeConstraintsForAssignmentTarget m mass arr tgt
460+ return $ (TypeConstraint arr (Array (TUnknown nval))) : (TypeConstraint n1 Number) : cs1 ++ cs2
461+typeConstraintsForAssignmentTarget m mass nval (AssignObjectProperty prop tgt) = do
462+ obj <- fresh
463+ row <- fresh
464+ cs <- typeConstraintsForAssignmentTarget m mass obj tgt
465+ return $ (TypeConstraint obj (Object (RCons prop (TUnknown nval) $ RUnknown row))) : cs
466+
467+typeConstraintsForBlock :: M.Map Ident Int -> M.Map Ident Int -> Int -> [Statement] -> Check ([TypeConstraint], Bool, M.Map Ident Int)
468+typeConstraintsForBlock _ mass _ [] = return ([], False, mass)
469+typeConstraintsForBlock m mass ret (s:ss) = do
470+ (cs1, b1, mass1) <- typeConstraintsForStatement (m `M.union` mass) mass ret s
471+ case (b1, ss) of
472+ (True, []) -> return (cs1, True, mass1)
473+ (True, _) -> throwError "Unreachable code"
474+ (False, ss) -> do
475+ (cs2, b2, mass2) <- typeConstraintsForBlock m mass1 ret ss
476+ return (cs1 ++ cs2, b2, mass2)
477+
478+solveTypeConstraints :: [TypeConstraint] -> TypeSolution -> Check TypeSolution
479+solveTypeConstraints [] s = return s
480+solveTypeConstraints all@(TypeConstraint n t:cs) s = do
481+ typeOccursCheck n t
482+ let s' = let (f, g) = runTypeSolution s
483+ in TypeSolution (replaceType n t . f, replaceType n t . g)
484+ cs' <- fmap concat $ mapM (substituteTypeInConstraint n t) cs
485+ solveTypeConstraints cs' s'
486+solveTypeConstraints (RowConstraint n r:cs) s = do
487+ rowOccursCheck n r
488+ let s' = let (f, g) = runTypeSolution s
489+ in TypeSolution $ (replaceRow n r . f, replaceRow n r . g)
490+ cs' <- fmap concat $ mapM (substituteRowInConstraint n r) cs
491+ solveTypeConstraints cs' s'
492+
493+substituteTypeInConstraint :: Int -> Type -> TypeConstraint -> Check [TypeConstraint]
494+substituteTypeInConstraint n s (TypeConstraint m t)
495+ | n == m = unifyTypes s t
496+ | otherwise = return [TypeConstraint m (replaceType n s t)]
497+substituteTypeInConstraint n s (RowConstraint m r)
498+ = return [RowConstraint m (replaceType n s r)]
499+
500+substituteRowInConstraint :: Int -> Row -> TypeConstraint -> Check [TypeConstraint]
501+substituteRowInConstraint n r (TypeConstraint m t)
502+ = return [TypeConstraint m (replaceRow n r t)]
503+substituteRowInConstraint n r (RowConstraint m r1)
504+ | m == n = unifyRows r r1
505+ | otherwise = return [RowConstraint m (replaceRow n r r1)]
506+
507+unifyTypes :: Type -> Type -> Check [TypeConstraint]
508+unifyTypes (TUnknown u1) (TUnknown u2) | u1 == u2 = return []
509+unifyTypes (TUnknown u) t = do
510+ typeOccursCheck u t
511+ return [TypeConstraint u t]
512+unifyTypes t (TUnknown u) = do
513+ typeOccursCheck u t
514+ return [TypeConstraint u t]
515+unifyTypes Number Number = return []
516+unifyTypes String String = return []
517+unifyTypes Boolean Boolean = return []
518+unifyTypes (Array s) (Array t) = unifyTypes s t
519+unifyTypes (Object row1) (Object row2) = unifyRows row1 row2
520+unifyTypes (Function args1 ret1) (Function args2 ret2) = do
521+ guardWith "Function applied to incorrect number of args" $ length args1 == length args2
522+ cs1 <- fmap concat $ zipWithM unifyTypes args1 args2
523+ cs2 <- unifyTypes ret1 ret2
524+ return $ cs1 ++ cs2
525+unifyTypes (TypeVar v1) (TypeVar v2) | v1 == v2 = return []
526+unifyTypes (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = return []
527+unifyTypes (TypeVar v1) (TypeVar v2) = return []
528+unifyTypes (TypeApp t1 t2) (TypeApp t3 t4) = do
529+ cs1 <- unifyTypes t1 t3
530+ cs2 <- unifyTypes t2 t4
531+ return $ cs1 ++ cs2
532+unifyTypes t1 t2 = throwError $ "Cannot unify " ++ show t1 ++ " with " ++ show t2 ++ "."
533+
534+unifyRows :: Row -> Row -> Check [TypeConstraint]
535+unifyRows r1 r2 =
536+ let
537+ (s1, r1') = toList r1
538+ (s2, r2') = toList r2
539+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
540+ sd1 = [ (name, t1) | (name, t1) <- s1, not (elem name (map fst s2)) ]
541+ sd2 = [ (name, t2) | (name, t2) <- s2, not (elem name (map fst s1)) ]
542+ in rethrow (\e -> "Cannot unify " ++ show r1 ++ " with " ++ show r2 ++ ": " ++ e) $ do
543+ cs1 <- fmap concat $ mapM (uncurry unifyTypes) int
544+ cs2 <- unifyRows' sd1 r1' sd2 r2'
545+ return $ cs1 ++ cs2
546+ where
547+ unifyRows' :: [(String, Type)] -> Row -> [(String, Type)] -> Row -> Check [TypeConstraint]
548+ unifyRows' [] (RUnknown u) sd r = do
549+ rowOccursCheck u r
550+ return [RowConstraint u (fromList (sd, r))]
551+ unifyRows' sd r [] (RUnknown u) = do
552+ rowOccursCheck u r
553+ return [RowConstraint u (fromList (sd, r))]
554+ unifyRows' ((name, ty):row) r others (RUnknown u) = do
555+ u' <- fresh
556+ cs <- unifyRows' row r others (RUnknown u')
557+ return (RowConstraint u (RCons name ty (RUnknown u')) : cs)
558+ unifyRows' [] REmpty [] REmpty = return []
559+ unifyRows' sd1 r1 sd2 r2 = throwError $ "Cannot unify " ++ show (fromList (sd1, r1)) ++ " with " ++ show (fromList (sd2, r2)) ++ "."
560+ toList :: Row -> ([(String, Type)], Row)
561+ toList (RCons name ty row) = let (tys, rest) = toList row
562+ in ((name, ty):tys, rest)
563+ toList r = ([], r)
564+ fromList :: ([(String, Type)], Row) -> Row
565+ fromList ([], r) = r
566+ fromList ((name, t):ts, r) = RCons name t (fromList (ts, r))