@@ -0,0 +1,596 @@
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+{-# LANGUAGE DeriveDataTypeable #-}
16+
17+module PureScript.TypeChecker.Types (
18+ TypeConstraint(..),
19+ TypeSolution(..),
20+ typeOf
21+) where
22+
23+import Data.List
24+import Data.Function
25+import qualified Data.Data as D
26+import Data.Generics (everywhere, everywhereM, everything, mkT, mkM, mkQ, extM, extQ)
27+
28+import PureScript.Values
29+import PureScript.Types
30+import PureScript.Kinds
31+import PureScript.Names
32+import PureScript.TypeChecker.Monad
33+import PureScript.TypeChecker.Kinds
34+import PureScript.TypeChecker.Synonyms
35+import PureScript.CodeGen.Pretty.Types
36+import PureScript.CodeGen.Pretty.Kinds
37+
38+import Control.Monad.State
39+import Control.Monad.Error
40+
41+import Control.Applicative
42+import Control.Arrow (Kleisli(..), (***), (&&&))
43+import qualified Control.Category as C
44+
45+import qualified Data.Map as M
46+
47+data TypeConstraint
48+ = TypeConstraint Int Type
49+ | RowConstraint Int Row deriving (Show, D.Data, D.Typeable)
50+
51+newtype TypeSolution = TypeSolution { runTypeSolution :: (Int -> Type, Int -> Row) }
52+
53+emptyTypeSolution :: TypeSolution
54+emptyTypeSolution = TypeSolution (TUnknown, RUnknown)
55+
56+typeOf :: Ident -> Value -> Check PolyType
57+typeOf name val = do
58+ (cs, n) <- case val of
59+ Abs _ _ -> do
60+ me <- fresh
61+ (cs, n) <- typeConstraints (M.singleton name me) val
62+ return (TypeConstraint me (TUnknown n) : cs, n)
63+ _ -> typeConstraints M.empty val
64+ desugared <- replaceAllTypeSynonyms cs
65+ solution <- solveTypeConstraints desugared emptyTypeSolution
66+ let ty = fst (runTypeSolution solution) n
67+ allUnknownsBecameQuantified desugared solution ty
68+ return $ varIfUnknown $ desaturateAllTypeSynonyms ty
69+
70+allUnknownsBecameQuantified :: [TypeConstraint] -> TypeSolution -> Type -> Check ()
71+allUnknownsBecameQuantified cs solution ty = do
72+ let
73+ typesMentioned = findUnknownTypes ty
74+ unknownTypes = nub $ flip concatMap cs $ \c -> case c of
75+ TypeConstraint u t -> u : findUnknownTypes t
76+ RowConstraint _ r -> findUnknownTypes r
77+ unsolvedTypes = filter (\n -> TUnknown n == fst (runTypeSolution solution) n) unknownTypes
78+ guardWith "Unsolved type variable" $ null $ unsolvedTypes \\ typesMentioned
79+ let
80+ rowsMentioned = findUnknownRows ty
81+ unknownRows = nub $ flip concatMap cs $ \c -> case c of
82+ TypeConstraint _ t -> findUnknownRows t
83+ RowConstraint u r -> u : findUnknownRows r
84+ unsolvedRows = filter (\n -> RUnknown n == snd (runTypeSolution solution) n) unknownRows
85+ guardWith "Unsolved row variable" $ null $ unsolvedRows \\ rowsMentioned
86+
87+findUnknownTypes :: (D.Data d) => d -> [Int]
88+findUnknownTypes = everything (++) (mkQ [] f)
89+ where
90+ f :: Type -> [Int]
91+ f (TUnknown n) = [n]
92+ f _ = []
93+
94+findTypeVars :: (D.Data d) => d -> [String]
95+findTypeVars = everything (++) (mkQ [] f)
96+ where
97+ f :: Type -> [String]
98+ f (TypeVar v) = [v]
99+ f _ = []
100+
101+findUnknownRows :: (D.Data d) => d -> [Int]
102+findUnknownRows = everything (++) (mkQ [] f)
103+ where
104+ f :: Row -> [Int]
105+ f (RUnknown n) = [n]
106+ f _ = []
107+
108+varIfUnknown :: Type -> PolyType
109+varIfUnknown ty =
110+ let
111+ (ty', m) = flip runState M.empty $ everywhereM (flip extM g $ mkM f) ty
112+ in
113+ PolyType (sort $ nub $ M.elems m ++ findTypeVars ty) ty'
114+ where
115+ f :: Type -> State (M.Map Int String) Type
116+ f (TUnknown n) = do
117+ m <- get
118+ case M.lookup n m of
119+ Nothing -> do
120+ let name = "t" ++ show (M.size m)
121+ put $ M.insert n name m
122+ return $ TypeVar name
123+ Just name -> return $ TypeVar name
124+ f t = return t
125+ g :: Row -> State (M.Map Int String) Row
126+ g (RUnknown n) = do
127+ m <- get
128+ case M.lookup n m of
129+ Nothing -> do
130+ let name = "r" ++ show (M.size m)
131+ put $ M.insert n name m
132+ return $ RowVar name
133+ Just name -> return $ RowVar name
134+ g r = return r
135+
136+replaceTypeVars :: M.Map String Type -> Type -> Type
137+replaceTypeVars m = everywhere (mkT replace)
138+ where
139+ replace (TypeVar v) = case M.lookup v m of
140+ Just ty -> ty
141+ _ -> TypeVar v
142+ replace t = t
143+
144+replaceVarsWithUnknowns :: [String] -> Type -> Check Type
145+replaceVarsWithUnknowns idents = flip evalStateT M.empty . everywhereM (flip extM f $ mkM g)
146+ where
147+ f :: Type -> StateT (M.Map String Int) Check Type
148+ f (TypeVar var) | var `elem` idents = do
149+ m <- get
150+ n <- lift fresh
151+ case M.lookup var m of
152+ Nothing -> do
153+ put (M.insert var n m)
154+ return $ TUnknown n
155+ Just u -> return $ TUnknown u
156+ f t = return t
157+ g :: Row -> StateT (M.Map String Int) Check Row
158+ g (RowVar var) | var `elem` idents = do
159+ m <- get
160+ n <- lift fresh
161+ case M.lookup var m of
162+ Nothing -> do
163+ put (M.insert var n m)
164+ return $ RUnknown n
165+ Just u -> return $ RUnknown u
166+ g r = return r
167+
168+replaceAllTypeSynonyms :: (D.Data d) => d -> Check d
169+replaceAllTypeSynonyms d = do
170+ env <- getEnv
171+ let syns = map (\(name, (args, _)) -> (name, length args)) . M.toList $ typeSynonyms env
172+ either throwError return $ saturateAllTypeSynonyms syns d
173+
174+desaturateAllTypeSynonyms :: (D.Data d) => d -> d
175+desaturateAllTypeSynonyms = everywhere (mkT $ replace)
176+ where
177+ replace (SaturatedTypeSynonym name args) = foldl (\t arg -> TypeApp t arg) (TypeConstructor name) args
178+ replace t = t
179+
180+replaceType :: (D.Data d) => Int -> Type -> d -> d
181+replaceType n t = everywhere (mkT go)
182+ where
183+ go (TUnknown m) | m == n = t
184+ go t = t
185+
186+replaceRow :: (D.Data d) => Int -> Row -> d -> d
187+replaceRow n r = everywhere (mkT go)
188+ where
189+ go (RUnknown m) | m == n = r
190+ go r = r
191+
192+typeOccursCheck :: Int -> Type -> Check ()
193+typeOccursCheck u (TUnknown _) = return ()
194+typeOccursCheck u t = when (occursCheck u t) $ throwError $ "Occurs check failed: " ++ show u ++ " = " ++ prettyPrintType t
195+
196+rowOccursCheck :: Int -> Row -> Check ()
197+rowOccursCheck u (RUnknown _) = return ()
198+rowOccursCheck u r = when (occursCheck u r) $ throwError $ "Occurs check failed: " ++ show u ++ " = " ++ prettyPrintRow r
199+
200+occursCheck :: (D.Data d) => Int -> d -> Bool
201+occursCheck u = everything (||) $ flip extQ g $ mkQ False f
202+ where
203+ f (TUnknown u') | u' == u = True
204+ f _ = False
205+ g (RUnknown u') | u' == u = True
206+ g _ = False
207+
208+typeConstraints :: M.Map Ident Int -> Value -> Check ([TypeConstraint], Int)
209+typeConstraints _ (NumericLiteral _) = do
210+ me <- fresh
211+ return ([TypeConstraint me Number], me)
212+typeConstraints _ (StringLiteral _) = do
213+ me <- fresh
214+ return ([TypeConstraint me String], me)
215+typeConstraints _ (BooleanLiteral _) = do
216+ me <- fresh
217+ return ([TypeConstraint me Boolean], me)
218+typeConstraints m (ArrayLiteral vals) = do
219+ all <- mapM (typeConstraints m) vals
220+ let (cs, ns) = (concat . map fst &&& map snd) all
221+ me <- fresh
222+ return (cs ++ map (TypeConstraint me . Array . TUnknown) ns, me)
223+typeConstraints m (Unary op val) = do
224+ (cs, n1) <- typeConstraints m val
225+ me <- fresh
226+ return (cs ++ unaryOperatorConstraints op n1 me, me)
227+typeConstraints m (Binary op left right) = do
228+ (cs1, n1) <- typeConstraints m left
229+ (cs2, n2) <- typeConstraints m right
230+ me <- fresh
231+ return (cs1 ++ cs2 ++ binaryOperatorConstraints op n1 n2 me, me)
232+typeConstraints m (ObjectLiteral ps) = do
233+ all <- mapM (typeConstraints m . snd) ps
234+ let (cs, ns) = (concat . map fst &&& map snd) all
235+ me <- fresh
236+ let tys = zipWith (\(name, _) u -> (name, TUnknown u)) ps ns
237+ return ((TypeConstraint me (Object (typesToRow tys))) : cs, me)
238+ where
239+ typesToRow [] = REmpty
240+ typesToRow ((name, ty):tys) = RCons name ty (typesToRow tys)
241+typeConstraints m (Indexer index val) = do
242+ (cs1, n1) <- typeConstraints m index
243+ (cs2, n2) <- typeConstraints m val
244+ me <- fresh
245+ return ((TypeConstraint n1 Number) : (TypeConstraint n2 (Array (TUnknown me))) : cs1 ++ cs2, me)
246+typeConstraints m (Accessor prop val) = do
247+ (cs, n1) <- typeConstraints m val
248+ me <- fresh
249+ rest <- fresh
250+ return ((TypeConstraint n1 (Object (RCons prop (TUnknown me) (RUnknown rest)))) : cs, me)
251+typeConstraints m (Abs args ret) = do
252+ ns <- replicateM (length args) fresh
253+ let m' = m `M.union` M.fromList (zipWith (,) args ns)
254+ (cs, n') <- typeConstraints m' ret
255+ me <- fresh
256+ return ((TypeConstraint me (Function (map TUnknown ns) (TUnknown n'))) : cs, me)
257+typeConstraints m (App f xs) = do
258+ (cs1, n1) <- typeConstraints m f
259+ all <- mapM (typeConstraints m) xs
260+ let (cs2, ns) = (concat . map fst &&& map snd) all
261+ me <- fresh
262+ return ((TypeConstraint n1 (Function (map TUnknown ns) (TUnknown me))) : cs1 ++ cs2, me)
263+typeConstraints m (Var var) =
264+ case M.lookup var m of
265+ Nothing -> do
266+ env <- getEnv
267+ case M.lookup var (names env) of
268+ Nothing -> throwError $ show var ++ " is undefined"
269+ Just (PolyType idents ty, _) -> do
270+ me <- fresh
271+ replaced <- replaceVarsWithUnknowns idents ty
272+ return ([TypeConstraint me replaced], me)
273+ Just u -> do
274+ me <- fresh
275+ return ([TypeConstraint u (TUnknown me)], me)
276+typeConstraints m (Block ss) = do
277+ ret <- fresh
278+ (cs, allCodePathsReturn, _) <- typeConstraintsForBlock m M.empty ret ss
279+ guardWith "Block is missing a return statement" allCodePathsReturn
280+ return (cs, ret)
281+typeConstraints m (Constructor c) = do
282+ env <- getEnv
283+ case M.lookup c (dataConstructors env) of
284+ Nothing -> throwError $ "Constructor " ++ c ++ " is undefined"
285+ Just (PolyType idents ty) -> do
286+ me <- fresh
287+ replaced <- replaceVarsWithUnknowns idents ty
288+ return ([TypeConstraint me replaced], me)
289+typeConstraints m (Case val binders) = do
290+ (cs1, n1) <- typeConstraints m val
291+ ret <- fresh
292+ cs2 <- typeConstraintsForBinders m n1 ret binders
293+ return (cs1 ++ cs2, ret)
294+typeConstraints m (IfThenElse cond th el) = do
295+ (cs1, n1) <- typeConstraints m cond
296+ (cs2, n2) <- typeConstraints m th
297+ (cs3, n3) <- typeConstraints m el
298+ return (TypeConstraint n1 Boolean : TypeConstraint n2 (TUnknown n3) : cs1 ++ cs2 ++ cs3, n2)
299+typeConstraints m (TypedValue val poly@(PolyType idents ty)) = do
300+ kind <- kindOf poly
301+ guardWith ("Expected type of kind *, was " ++ prettyPrintKind kind) $ kind == Star
302+ (cs, n1) <- typeConstraints m val
303+ return (TypeConstraint n1 ty : cs, n1)
304+
305+unaryOperatorConstraints :: UnaryOperator -> Int -> Int -> [TypeConstraint]
306+unaryOperatorConstraints Negate val result = [TypeConstraint val Number, TypeConstraint result Number]
307+unaryOperatorConstraints Not val result = [TypeConstraint val Boolean, TypeConstraint result Boolean]
308+unaryOperatorConstraints BitwiseNot val result = [TypeConstraint val Number, TypeConstraint result Number]
309+
310+binaryOperatorConstraints :: BinaryOperator -> Int -> Int -> Int -> [TypeConstraint]
311+binaryOperatorConstraints Add = symBinOpConstraints Number
312+binaryOperatorConstraints Subtract = symBinOpConstraints Number
313+binaryOperatorConstraints Multiply = symBinOpConstraints Number
314+binaryOperatorConstraints Divide = symBinOpConstraints Number
315+binaryOperatorConstraints Modulus = symBinOpConstraints Number
316+binaryOperatorConstraints LessThan = asymBinOpConstraints Number Boolean
317+binaryOperatorConstraints LessThanOrEqualTo = asymBinOpConstraints Number Boolean
318+binaryOperatorConstraints GreaterThan = asymBinOpConstraints Number Boolean
319+binaryOperatorConstraints GreaterThanOrEqualTo = asymBinOpConstraints Number Boolean
320+binaryOperatorConstraints BitwiseAnd = symBinOpConstraints Number
321+binaryOperatorConstraints BitwiseOr = symBinOpConstraints Number
322+binaryOperatorConstraints BitwiseXor = symBinOpConstraints Number
323+binaryOperatorConstraints ShiftLeft = symBinOpConstraints Number
324+binaryOperatorConstraints ShiftRight = symBinOpConstraints Number
325+binaryOperatorConstraints ZeroFillShiftRight = symBinOpConstraints Number
326+binaryOperatorConstraints EqualTo = equalityBinOpConstraints
327+binaryOperatorConstraints NotEqualTo = equalityBinOpConstraints
328+binaryOperatorConstraints And = symBinOpConstraints Boolean
329+binaryOperatorConstraints Or = symBinOpConstraints Boolean
330+binaryOperatorConstraints Concat = symBinOpConstraints String
331+
332+equalityBinOpConstraints :: Int -> Int -> Int -> [TypeConstraint]
333+equalityBinOpConstraints left right result = [TypeConstraint left (TUnknown right), TypeConstraint result Boolean]
334+
335+symBinOpConstraints :: Type -> Int -> Int -> Int -> [TypeConstraint]
336+symBinOpConstraints ty left right result = asymBinOpConstraints ty ty left right result
337+
338+asymBinOpConstraints :: Type -> Type -> Int -> Int -> Int -> [TypeConstraint]
339+asymBinOpConstraints ty res left right result = [TypeConstraint left ty, TypeConstraint right ty, TypeConstraint result res]
340+
341+typeConstraintsForBinder :: Int -> Binder -> Check ([TypeConstraint], M.Map Ident Int)
342+typeConstraintsForBinder _ NullBinder = return ([], M.empty)
343+typeConstraintsForBinder val (StringBinder _) = constantBinder val String
344+typeConstraintsForBinder val (NumberBinder _) = constantBinder val Number
345+typeConstraintsForBinder val (BooleanBinder _) = constantBinder val Boolean
346+typeConstraintsForBinder val (VarBinder name) = do
347+ me <- fresh
348+ return ([TypeConstraint me (TUnknown val)], M.singleton name me)
349+typeConstraintsForBinder val (NullaryBinder ctor) = do
350+ env <- getEnv
351+ case M.lookup ctor (dataConstructors env) of
352+ Just (PolyType args ret) -> do
353+ ret' <- replaceVarsWithUnknowns args ret
354+ return ([TypeConstraint val ret'], M.empty)
355+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
356+typeConstraintsForBinder val (UnaryBinder ctor binder) = do
357+ env <- getEnv
358+ case M.lookup ctor (dataConstructors env) of
359+ Just (PolyType idents f@(Function [_] _)) -> do
360+ obj <- fresh
361+ (Function [ty] ret) <- replaceVarsWithUnknowns idents f
362+ (cs, m1) <- typeConstraintsForBinder obj binder
363+ return ((TypeConstraint val ret) : (TypeConstraint obj ty) : cs, m1)
364+ Just _ -> throwError $ ctor ++ " is not a unary constructor"
365+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
366+typeConstraintsForBinder val (ObjectBinder props) = do
367+ row <- fresh
368+ rest <- fresh
369+ (cs, m1) <- typeConstraintsForProperties row (RUnknown rest) props
370+ return ((TypeConstraint val (Object (RUnknown row))) : cs, m1)
371+ where
372+ typeConstraintsForProperties :: Int -> Row -> [(String, Binder)] -> Check ([TypeConstraint], M.Map Ident Int)
373+ typeConstraintsForProperties nrow row [] = return ([RowConstraint nrow row], M.empty)
374+ typeConstraintsForProperties nrow row ((name, binder):binders) = do
375+ propTy <- fresh
376+ (cs1, m1) <- typeConstraintsForBinder propTy binder
377+ (cs2, m2) <- typeConstraintsForProperties nrow (RCons name (TUnknown propTy) row) binders
378+ return (cs1 ++ cs2, M.union m1 m2)
379+typeConstraintsForBinder val (ArrayBinder binders rest) = do
380+ el <- fresh
381+ all <- mapM (typeConstraintsForBinder el) binders
382+ let (cs1, m1) = (concat . map fst &&& M.unions . map snd) all
383+ let arrayConstraint = TypeConstraint val (Array (TUnknown el))
384+ case rest of
385+ Nothing -> return (arrayConstraint : cs1, m1)
386+ Just binder -> do
387+ (cs2, m2) <- typeConstraintsForBinder val binder
388+ return (arrayConstraint : cs1 ++ cs2, M.union m1 m2)
389+typeConstraintsForBinder val (NamedBinder name binder) = do
390+ me <- fresh
391+ (cs, m) <- typeConstraintsForBinder val binder
392+ return (TypeConstraint me (TUnknown val) : cs, M.insert name me m)
393+typeConstraintsForBinder val (GuardedBinder cond binder) = do
394+ (cs1, m) <- typeConstraintsForBinder val binder
395+ (cs2, n) <- typeConstraints m cond
396+ return (TypeConstraint n Boolean : cs1 ++ cs2, m)
397+
398+constantBinder :: Int -> Type -> Check ([TypeConstraint], M.Map Ident Int)
399+constantBinder val ty = return ([TypeConstraint val ty], M.empty)
400+
401+typeConstraintsForBinders :: M.Map Ident Int -> Int -> Int -> [(Binder, Value)] -> Check [TypeConstraint]
402+typeConstraintsForBinders _ _ _ [] = return []
403+typeConstraintsForBinders m nval ret ((binder, val):bs) = do
404+ (cs1, m1) <- typeConstraintsForBinder nval binder
405+ (cs2, n2) <- typeConstraints (M.union m m1) val
406+ cs3 <- typeConstraintsForBinders m nval ret bs
407+ return ((TypeConstraint n2 (TUnknown ret)) : cs1 ++ cs2 ++ cs3)
408+
409+assignVariable :: Ident -> M.Map Ident Int -> Check ()
410+assignVariable name m =
411+ case M.lookup name m of
412+ Nothing -> return ()
413+ Just _ -> throwError $ "Variable with name " ++ show name ++ " already exists."
414+
415+typeConstraintsForStatement :: M.Map Ident Int -> M.Map Ident Int -> Int -> Statement -> Check ([TypeConstraint], Bool, M.Map Ident Int)
416+typeConstraintsForStatement m mass ret (VariableIntroduction name val) = do
417+ assignVariable name (m `M.union` mass)
418+ (cs1, n1) <- typeConstraints m val
419+ return $ (cs1, False, M.insert name n1 mass)
420+typeConstraintsForStatement m mass ret (Assignment tgt val) = do
421+ (cs1, n1) <- typeConstraints m val
422+ cs2 <- typeConstraintsForAssignmentTarget m mass n1 tgt
423+ return (cs1 ++ cs2, False, mass)
424+typeConstraintsForStatement m mass ret (While val inner) = do
425+ (cs1, n1) <- typeConstraints m val
426+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret inner
427+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn, mass)
428+typeConstraintsForStatement m mass ret (If ifst) = do
429+ (cs, allCodePathsReturn) <- typeConstraintsForIfStatement m mass ret ifst
430+ return $ (cs, allCodePathsReturn, mass)
431+typeConstraintsForStatement m mass ret (For ident start end inner) = do
432+ assignVariable ident (m `M.union` mass)
433+ (cs1, n1) <- typeConstraints (m `M.union` mass) start
434+ (cs2, n2) <- typeConstraints (m `M.union` mass) end
435+ let mass1 = M.insert ident n1 mass
436+ (cs3, allCodePathsReturn, _) <- typeConstraintsForBlock (m `M.union` mass1) mass1 ret inner
437+ return $ ((TypeConstraint n1 Number) : (TypeConstraint n2 Number) : cs1 ++ cs2 ++ cs3, allCodePathsReturn, mass)
438+typeConstraintsForStatement m mass ret (ForEach ident vals inner) = do
439+ assignVariable ident (m `M.union` mass)
440+ val <- fresh
441+ (cs1, n1) <- typeConstraints (m `M.union` mass) vals
442+ let mass1 = M.insert ident val mass
443+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock (m `M.union` mass1) mass1 ret inner
444+ guardWith "Cannot return from within a foreach block" $ not allCodePathsReturn
445+ return $ ((TypeConstraint n1 (Array (TUnknown val))) : cs1 ++ cs2, False, mass)
446+typeConstraintsForStatement m mass ret (Return val) = do
447+ (cs1, n1) <- typeConstraints (m `M.union` mass) val
448+ return ((TypeConstraint n1 (TUnknown ret)) : cs1, True, mass)
449+
450+typeConstraintsForIfStatement :: M.Map Ident Int -> M.Map Ident Int -> Int -> IfStatement -> Check ([TypeConstraint], Bool)
451+typeConstraintsForIfStatement m mass ret (IfStatement val thens Nothing) = do
452+ (cs1, n1) <- typeConstraints m val
453+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret thens
454+ return ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn)
455+typeConstraintsForIfStatement m mass ret (IfStatement val thens (Just elses)) = do
456+ (cs1, n1) <- typeConstraints m val
457+ (cs2, allCodePathsReturn1, _) <- typeConstraintsForBlock m mass ret thens
458+ (cs3, allCodePathsReturn2) <- typeConstraintsForElseStatement m mass ret elses
459+ return ((TypeConstraint n1 Boolean) : cs1 ++ cs2 ++ cs3, allCodePathsReturn1 && allCodePathsReturn2)
460+
461+typeConstraintsForElseStatement :: M.Map Ident Int -> M.Map Ident Int -> Int -> ElseStatement -> Check ([TypeConstraint], Bool)
462+typeConstraintsForElseStatement m mass ret (Else elses) = do
463+ (cs, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret elses
464+ return (cs, allCodePathsReturn)
465+typeConstraintsForElseStatement m mass ret (ElseIf ifst) = do
466+ (cs, allCodePathsReturn) <- typeConstraintsForIfStatement m mass ret ifst
467+ return (cs, allCodePathsReturn)
468+
469+typeConstraintsForAssignmentTarget :: M.Map Ident Int -> M.Map Ident Int -> Int -> AssignmentTarget -> Check [TypeConstraint]
470+typeConstraintsForAssignmentTarget m mass nval (AssignVariable var) =
471+ case M.lookup var mass of
472+ Nothing -> throwError $ "No local variable with name " ++ show var
473+ Just ty -> do
474+ return [TypeConstraint nval (TUnknown ty)]
475+typeConstraintsForAssignmentTarget m mass nval (AssignArrayIndex index tgt) = do
476+ arr <- fresh
477+ (cs1, n1) <- typeConstraints (m `M.union` mass) index
478+ cs2 <- typeConstraintsForAssignmentTarget m mass arr tgt
479+ return $ (TypeConstraint arr (Array (TUnknown nval))) : (TypeConstraint n1 Number) : cs1 ++ cs2
480+typeConstraintsForAssignmentTarget m mass nval (AssignObjectProperty prop tgt) = do
481+ obj <- fresh
482+ row <- fresh
483+ cs <- typeConstraintsForAssignmentTarget m mass obj tgt
484+ return $ (TypeConstraint obj (Object (RCons prop (TUnknown nval) $ RUnknown row))) : cs
485+
486+typeConstraintsForBlock :: M.Map Ident Int -> M.Map Ident Int -> Int -> [Statement] -> Check ([TypeConstraint], Bool, M.Map Ident Int)
487+typeConstraintsForBlock _ mass _ [] = return ([], False, mass)
488+typeConstraintsForBlock m mass ret (s:ss) = do
489+ (cs1, b1, mass1) <- typeConstraintsForStatement (m `M.union` mass) mass ret s
490+ case (b1, ss) of
491+ (True, []) -> return (cs1, True, mass1)
492+ (True, _) -> throwError "Unreachable code"
493+ (False, ss) -> do
494+ (cs2, b2, mass2) <- typeConstraintsForBlock m mass1 ret ss
495+ return (cs1 ++ cs2, b2, mass2)
496+
497+solveTypeConstraints :: [TypeConstraint] -> TypeSolution -> Check TypeSolution
498+solveTypeConstraints [] s = return s
499+solveTypeConstraints all@(TypeConstraint n t:cs) s = do
500+ typeOccursCheck n t
501+ let s' = let (f, g) = runTypeSolution s
502+ in TypeSolution (replaceType n t . f, replaceType n t . g)
503+ cs' <- fmap concat $ mapM (substituteTypeInConstraint n t) cs
504+ solveTypeConstraints cs' s'
505+solveTypeConstraints (RowConstraint n r:cs) s = do
506+ rowOccursCheck n r
507+ let s' = let (f, g) = runTypeSolution s
508+ in TypeSolution $ (replaceRow n r . f, replaceRow n r . g)
509+ cs' <- fmap concat $ mapM (substituteRowInConstraint n r) cs
510+ solveTypeConstraints cs' s'
511+
512+substituteTypeInConstraint :: Int -> Type -> TypeConstraint -> Check [TypeConstraint]
513+substituteTypeInConstraint n s (TypeConstraint m t)
514+ | n == m = unifyTypes s t
515+ | otherwise = return [TypeConstraint m (replaceType n s t)]
516+substituteTypeInConstraint n s (RowConstraint m r)
517+ = return [RowConstraint m (replaceType n s r)]
518+
519+substituteRowInConstraint :: Int -> Row -> TypeConstraint -> Check [TypeConstraint]
520+substituteRowInConstraint n r (TypeConstraint m t)
521+ = return [TypeConstraint m (replaceRow n r t)]
522+substituteRowInConstraint n r (RowConstraint m r1)
523+ | m == n = unifyRows r r1
524+ | otherwise = return [RowConstraint m (replaceRow n r r1)]
525+
526+unifyTypes :: Type -> Type -> Check [TypeConstraint]
527+unifyTypes (TUnknown u1) (TUnknown u2) | u1 == u2 = return []
528+unifyTypes (TUnknown u) t = do
529+ typeOccursCheck u t
530+ return [TypeConstraint u t]
531+unifyTypes t (TUnknown u) = do
532+ typeOccursCheck u t
533+ return [TypeConstraint u t]
534+unifyTypes (SaturatedTypeSynonym name1 args1) (SaturatedTypeSynonym name2 args2) | name1 == name2 =
535+ fmap concat $ zipWithM unifyTypes args1 args2
536+unifyTypes (SaturatedTypeSynonym name args) ty = do
537+ env <- getEnv
538+ case M.lookup name (typeSynonyms env) of
539+ Just (synArgs, body) -> do
540+ let m = M.fromList $ zip synArgs args
541+ let replaced = replaceTypeVars m body
542+ unifyTypes replaced ty
543+ Nothing -> error "Type synonym was not defined"
544+unifyTypes ty s@(SaturatedTypeSynonym _ _) = unifyTypes s ty
545+unifyTypes Number Number = return []
546+unifyTypes String String = return []
547+unifyTypes Boolean Boolean = return []
548+unifyTypes (Array s) (Array t) = unifyTypes s t
549+unifyTypes (Object row1) (Object row2) = unifyRows row1 row2
550+unifyTypes (Function args1 ret1) (Function args2 ret2) = do
551+ guardWith "Function applied to incorrect number of args" $ length args1 == length args2
552+ cs1 <- fmap concat $ zipWithM unifyTypes args1 args2
553+ cs2 <- unifyTypes ret1 ret2
554+ return $ cs1 ++ cs2
555+unifyTypes (TypeVar v1) (TypeVar v2) | v1 == v2 = return []
556+unifyTypes (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = return []
557+unifyTypes (TypeVar v1) (TypeVar v2) = return []
558+unifyTypes (TypeApp t1 t2) (TypeApp t3 t4) = do
559+ cs1 <- unifyTypes t1 t3
560+ cs2 <- unifyTypes t2 t4
561+ return $ cs1 ++ cs2
562+unifyTypes t1 t2 = throwError $ "Cannot unify " ++ prettyPrintType t1 ++ " with " ++ prettyPrintType t2 ++ "."
563+
564+unifyRows :: Row -> Row -> Check [TypeConstraint]
565+unifyRows r1 r2 =
566+ let
567+ (s1, r1') = toList r1
568+ (s2, r2') = toList r2
569+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
570+ sd1 = [ (name, t1) | (name, t1) <- s1, not (elem name (map fst s2)) ]
571+ sd2 = [ (name, t2) | (name, t2) <- s2, not (elem name (map fst s1)) ]
572+ in rethrow (\e -> "Cannot unify " ++ prettyPrintRow r1 ++ " with " ++ prettyPrintRow r2 ++ ": " ++ e) $ do
573+ cs1 <- fmap concat $ mapM (uncurry unifyTypes) int
574+ cs2 <- unifyRows' sd1 r1' sd2 r2'
575+ return $ cs1 ++ cs2
576+ where
577+ unifyRows' :: [(String, Type)] -> Row -> [(String, Type)] -> Row -> Check [TypeConstraint]
578+ unifyRows' [] (RUnknown u) sd r = do
579+ rowOccursCheck u r
580+ return [RowConstraint u (fromList (sd, r))]
581+ unifyRows' sd r [] (RUnknown u) = do
582+ rowOccursCheck u r
583+ return [RowConstraint u (fromList (sd, r))]
584+ unifyRows' ((name, ty):row) r others (RUnknown u) = do
585+ u' <- fresh
586+ cs <- unifyRows' row r others (RUnknown u')
587+ return (RowConstraint u (RCons name ty (RUnknown u')) : cs)
588+ unifyRows' [] REmpty [] REmpty = return []
589+ unifyRows' sd1 r1 sd2 r2 = throwError $ "Cannot unify " ++ prettyPrintRow (fromList (sd1, r1)) ++ " with " ++ prettyPrintRow (fromList (sd2, r2)) ++ "."
590+ toList :: Row -> ([(String, Type)], Row)
591+ toList (RCons name ty row) = let (tys, rest) = toList row
592+ in ((name, ty):tys, rest)
593+ toList r = ([], r)
594+ fromList :: ([(String, Type)], Row) -> Row
595+ fromList ([], r) = r
596+ fromList ((name, t):ts, r) = RCons name t (fromList (ts, r))