@@ -0,0 +1,486 @@
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.TypeChecker.Monad
30+import PureScript.TypeChecker.Kinds
31+import PureScript.TypeChecker.Synonyms
32+
33+import Control.Monad.State
34+import Control.Monad.Error
35+
36+import Control.Applicative
37+import Control.Arrow (Kleisli(..), (***), (&&&))
38+import qualified Control.Category as C
39+
40+import qualified Data.Map as M
41+
42+data TypeConstraint
43+ = TypeConstraint Int Type
44+ | RowConstraint Int Row deriving Show
45+
46+newtype TypeSolution = TypeSolution { runTypeSolution :: (Int -> Type, Int -> Row) }
47+
48+emptyTypeSolution :: TypeSolution
49+emptyTypeSolution = TypeSolution (TUnknown, RUnknown)
50+
51+typeOf :: String -> Value -> Check PolyType
52+typeOf name val = do
53+ me <- fresh
54+ (cs, n) <- typeConstraints (M.singleton name me) val
55+ solution <- solveTypeConstraints ((TypeConstraint me (TUnknown n)) : cs) emptyTypeSolution
56+ return $ varIfUnknown $ fst (runTypeSolution solution) n
57+
58+varIfUnknown :: Type -> PolyType
59+varIfUnknown ty =
60+ let
61+ (ty', m) = flip runState M.empty $ everywhereM (flip extM g $ mkM f) ty
62+ -- TODO : check no nested unknowns
63+ in
64+ PolyType (sort $ nub $ M.elems m) ty'
65+ where
66+ f :: Type -> State (M.Map Int String) Type
67+ f (TUnknown n) = do
68+ m <- get
69+ case M.lookup n m of
70+ Nothing -> do
71+ let name = "t" ++ show (M.size m)
72+ put $ M.insert n name m
73+ return $ TypeVar name
74+ Just name -> return $ TypeVar name
75+ f t = return t
76+ g :: Row -> State (M.Map Int String) Row
77+ g (RUnknown n) = do
78+ m <- get
79+ case M.lookup n m of
80+ Nothing -> do
81+ let name = "r" ++ show (M.size m)
82+ put $ M.insert n name m
83+ return $ RowVar name
84+ Just name -> return $ RowVar name
85+ g r = return r
86+
87+replaceVarsWithUnknowns :: [String] -> Type -> Check Type
88+replaceVarsWithUnknowns idents = flip evalStateT M.empty . everywhereM (flip extM f $ mkM g)
89+ where
90+ f :: Type -> StateT (M.Map String Int) Check Type
91+ f (TypeVar var) | var `elem` idents = do
92+ m <- get
93+ n <- lift fresh
94+ case M.lookup var m of
95+ Nothing -> do
96+ put (M.insert var n m)
97+ return $ TUnknown n
98+ Just u -> return $ TUnknown u
99+ f t = return t
100+ g :: Row -> StateT (M.Map String Int) Check Row
101+ g (RowVar var) | var `elem` idents = do
102+ m <- get
103+ n <- lift fresh
104+ case M.lookup var m of
105+ Nothing -> do
106+ put (M.insert var n m)
107+ return $ RUnknown n
108+ Just u -> return $ RUnknown u
109+ g r = return r
110+
111+replaceType :: (Data d) => Int -> Type -> d -> d
112+replaceType n t = everywhere (mkT go)
113+ where
114+ go (TUnknown m) | m == n = t
115+ go t = t
116+
117+replaceRow :: (Data d) => Int -> Row -> d -> d
118+replaceRow n r = everywhere (mkT go)
119+ where
120+ go (RUnknown m) | m == n = r
121+ go r = r
122+
123+typeOccursCheck :: Int -> Type -> Check ()
124+typeOccursCheck u (TUnknown _) = return ()
125+typeOccursCheck u t = when (occursCheck u t) $ throwError $ "Occurs check failed: " ++ show u ++ " = " ++ show t
126+
127+rowOccursCheck :: Int -> Row -> Check ()
128+rowOccursCheck u (RUnknown _) = return ()
129+rowOccursCheck u r = when (occursCheck u r) $ throwError $ "Occurs check failed: " ++ show u ++ " = " ++ show r
130+
131+occursCheck :: (Data d) => Int -> d -> Bool
132+occursCheck u = everything (||) $ flip extQ g $ mkQ False f
133+ where
134+ f (TUnknown u') | u' == u = True
135+ f _ = False
136+ g (RUnknown u') | u' == u = True
137+ g _ = False
138+
139+typeConstraints :: M.Map String Int -> Value -> Check ([TypeConstraint], Int)
140+typeConstraints _ (NumericLiteral _) = do
141+ me <- fresh
142+ return ([TypeConstraint me Number], me)
143+typeConstraints _ (StringLiteral _) = do
144+ me <- fresh
145+ return ([TypeConstraint me String], me)
146+typeConstraints _ (BooleanLiteral _) = do
147+ me <- fresh
148+ return ([TypeConstraint me Boolean], me)
149+typeConstraints m (ArrayLiteral vals) = do
150+ all <- mapM (typeConstraints m) vals
151+ let (cs, ns) = (concat . map fst &&& map snd) all
152+ me <- fresh
153+ return (cs ++ map (TypeConstraint me . Array . TUnknown) ns, me)
154+typeConstraints m (Unary op val) = do
155+ (cs, n1) <- typeConstraints m val
156+ me <- fresh
157+ return (cs ++ unaryOperatorConstraints op n1 me, me)
158+typeConstraints m (Binary op left right) = do
159+ (cs1, n1) <- typeConstraints m left
160+ (cs2, n2) <- typeConstraints m right
161+ me <- fresh
162+ return (cs1 ++ cs2 ++ binaryOperatorConstraints op n1 n2 me, me)
163+typeConstraints m (ObjectLiteral ps) = do
164+ all <- mapM (typeConstraints m . snd) ps
165+ let (cs, ns) = (concat . map fst &&& map snd) all
166+ me <- fresh
167+ let tys = zipWith (\(name, _) u -> (name, TUnknown u)) ps ns
168+ return ((TypeConstraint me (Object (typesToRow tys))) : cs, me)
169+ where
170+ typesToRow [] = REmpty
171+ typesToRow ((name, ty):tys) = RCons name ty (typesToRow tys)
172+typeConstraints m (Indexer index val) = do
173+ (cs1, n1) <- typeConstraints m index
174+ (cs2, n2) <- typeConstraints m val
175+ me <- fresh
176+ return ((TypeConstraint n1 Number) : (TypeConstraint n2 (Array (TUnknown me))) : cs1 ++ cs2, me)
177+typeConstraints m (Accessor prop val) = do
178+ (cs, n1) <- typeConstraints m val
179+ me <- fresh
180+ rest <- fresh
181+ return ((TypeConstraint n1 (Object (RCons prop (TUnknown me) (RUnknown rest)))) : cs, me)
182+typeConstraints m (Abs args ret) = do
183+ ns <- replicateM (length args) fresh
184+ let m' = m `M.union` M.fromList (zipWith (,) args ns)
185+ (cs, n') <- typeConstraints m' ret
186+ me <- fresh
187+ return ((TypeConstraint me (Function (map TUnknown ns) (TUnknown n'))) : cs, me)
188+typeConstraints m (App f xs) = do
189+ (cs1, n1) <- typeConstraints m f
190+ all <- mapM (typeConstraints m) xs
191+ let (cs2, ns) = (concat . map fst &&& map snd) all
192+ me <- fresh
193+ return ((TypeConstraint n1 (Function (map TUnknown ns) (TUnknown me))) : cs1 ++ cs2, me)
194+typeConstraints m (Var var) =
195+ case M.lookup var m of
196+ Nothing -> do
197+ env <- getEnv
198+ case M.lookup var (names env) of
199+ Nothing -> throwError $ var ++ " is undefined"
200+ Just (PolyType idents ty, _) -> do
201+ me <- fresh
202+ replaced <- replaceVarsWithUnknowns idents ty
203+ return ([TypeConstraint me replaced], me)
204+ Just u -> do
205+ me <- fresh
206+ return ([TypeConstraint u (TUnknown me)], me)
207+typeConstraints m (Block ss) = do
208+ ret <- fresh
209+ (cs, allCodePathsReturn, _) <- typeConstraintsForBlock m M.empty ret ss
210+ guardWith "Block is missing a return statement" allCodePathsReturn
211+ return (cs, ret)
212+typeConstraints m (Constructor c) = do
213+ env <- getEnv
214+ case M.lookup c (dataConstructors env) of
215+ Nothing -> throwError $ "Constructor " ++ c ++ " is undefined"
216+ Just (PolyType idents ty) -> do
217+ me <- fresh
218+ replaced <- replaceVarsWithUnknowns idents ty
219+ return ([TypeConstraint me replaced], me)
220+typeConstraints m (Case val binders) = do
221+ (cs1, n1) <- typeConstraints m val
222+ ret <- fresh
223+ cs2 <- typeConstraintsForBinders m n1 ret binders
224+ return (cs1 ++ cs2, ret)
225+typeConstraints m (TypedValue val poly@(PolyType idents ty)) = do
226+ kind <- kindOf poly
227+ guardWith ("Expected type of kind *, was " ++ show kind) $ kind == Star
228+ desugared <- replaceAllTypeSynonyms ty
229+ (cs, n1) <- typeConstraints m val
230+ return (TypeConstraint n1 desugared : cs, n1)
231+
232+replaceAllTypeSynonyms :: Type -> Check Type
233+replaceAllTypeSynonyms ty = do
234+ env <- getEnv
235+ go (M.toList $ typeSynonyms env) ty
236+ where
237+ go [] ty = return ty
238+ go ((name, (args, repl)):rest) ty = do
239+ ty' <- either throwError return (substituteTypeSynonym name args repl ty)
240+ go rest ty'
241+
242+unaryOperatorConstraints :: UnaryOperator -> Int -> Int -> [TypeConstraint]
243+unaryOperatorConstraints Negate val result = [TypeConstraint val Number, TypeConstraint result Number]
244+unaryOperatorConstraints Not val result = [TypeConstraint val Boolean, TypeConstraint result Boolean]
245+unaryOperatorConstraints BitwiseNot val result = [TypeConstraint val Number, TypeConstraint result Number]
246+
247+binaryOperatorConstraints :: BinaryOperator -> Int -> Int -> Int -> [TypeConstraint]
248+binaryOperatorConstraints Add = symBinOpConstraints Number
249+binaryOperatorConstraints Subtract = symBinOpConstraints Number
250+binaryOperatorConstraints Multiply = symBinOpConstraints Number
251+binaryOperatorConstraints Divide = symBinOpConstraints Number
252+binaryOperatorConstraints Modulus = symBinOpConstraints Number
253+binaryOperatorConstraints LessThan = asymBinOpConstraints Number Boolean
254+binaryOperatorConstraints LessThanOrEqualTo = asymBinOpConstraints Number Boolean
255+binaryOperatorConstraints GreaterThan = asymBinOpConstraints Number Boolean
256+binaryOperatorConstraints GreaterThanOrEqualTo = asymBinOpConstraints Number Boolean
257+binaryOperatorConstraints BitwiseAnd = symBinOpConstraints Number
258+binaryOperatorConstraints BitwiseOr = symBinOpConstraints Number
259+binaryOperatorConstraints BitwiseXor = symBinOpConstraints Number
260+binaryOperatorConstraints ShiftLeft = symBinOpConstraints Number
261+binaryOperatorConstraints ShiftRight = symBinOpConstraints Number
262+binaryOperatorConstraints ZeroFillShiftRight = symBinOpConstraints Number
263+binaryOperatorConstraints EqualTo = equalityBinOpConstraints
264+binaryOperatorConstraints NotEqualTo = equalityBinOpConstraints
265+binaryOperatorConstraints And = symBinOpConstraints Boolean
266+binaryOperatorConstraints Or = symBinOpConstraints Boolean
267+binaryOperatorConstraints Concat = symBinOpConstraints String
268+
269+equalityBinOpConstraints :: Int -> Int -> Int -> [TypeConstraint]
270+equalityBinOpConstraints left right result = [TypeConstraint left (TUnknown right), TypeConstraint result Boolean]
271+
272+symBinOpConstraints :: Type -> Int -> Int -> Int -> [TypeConstraint]
273+symBinOpConstraints ty left right result = asymBinOpConstraints ty ty left right result
274+
275+asymBinOpConstraints :: Type -> Type -> Int -> Int -> Int -> [TypeConstraint]
276+asymBinOpConstraints ty res left right result = [TypeConstraint left ty, TypeConstraint right ty, TypeConstraint result res]
277+
278+typeConstraintsForBinder :: Int -> Binder -> Check ([TypeConstraint], M.Map String Int)
279+typeConstraintsForBinder val (StringBinder _) = constantBinder val String
280+typeConstraintsForBinder val (NumberBinder _) = constantBinder val Number
281+typeConstraintsForBinder val (BooleanBinder _) = constantBinder val Boolean
282+typeConstraintsForBinder val (VarBinder name) = do
283+ me <- fresh
284+ return ([TypeConstraint me (TUnknown val)], M.singleton name me)
285+typeConstraintsForBinder val (NullaryBinder ctor) = do
286+ env <- getEnv
287+ case M.lookup ctor (dataConstructors env) of
288+ Just (PolyType args ret) -> do
289+ ret' <- replaceVarsWithUnknowns args ret
290+ return ([TypeConstraint val ret'], M.empty)
291+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
292+typeConstraintsForBinder val (UnaryBinder ctor binder) = do
293+ env <- getEnv
294+ case M.lookup ctor (dataConstructors env) of
295+ Just (PolyType idents f@(Function [_] _)) -> do
296+ obj <- fresh
297+ (Function [ty] ret) <- replaceVarsWithUnknowns idents f
298+ (cs, m1) <- typeConstraintsForBinder obj binder
299+ return ((TypeConstraint val ret) : (TypeConstraint obj ty) : cs, m1)
300+ Just _ -> throwError $ ctor ++ " is not a unary constructor"
301+ _ -> throwError $ "Constructor " ++ ctor ++ " is not defined"
302+typeConstraintsForBinder val (ObjectBinder props) = do
303+ row <- fresh
304+ rest <- fresh
305+ (cs, m1) <- typeConstraintsForProperties row (RUnknown rest) props
306+ return ((TypeConstraint val (Object (RUnknown row))) : cs, m1)
307+ where
308+ typeConstraintsForProperties :: Int -> Row -> [(String, Binder)] -> Check ([TypeConstraint], M.Map String Int)
309+ typeConstraintsForProperties nrow row [] = return ([RowConstraint nrow row], M.empty)
310+ typeConstraintsForProperties nrow row ((name, binder):binders) = do
311+ propTy <- fresh
312+ (cs1, m1) <- typeConstraintsForBinder propTy binder
313+ (cs2, m2) <- typeConstraintsForProperties nrow (RCons name (TUnknown propTy) row) binders
314+ return (cs1 ++ cs2, M.union m1 m2)
315+typeConstraintsForBinder val (ArrayBinder binders rest) = do
316+ el <- fresh
317+ all <- mapM (typeConstraintsForBinder el) binders
318+ let (cs1, m1) = (concat . map fst &&& M.unions . map snd) all
319+ let arrayConstraint = TypeConstraint val (Array (TUnknown el))
320+ case rest of
321+ Nothing -> return (arrayConstraint : cs1, m1)
322+ Just binder -> do
323+ (cs2, m2) <- typeConstraintsForBinder val binder
324+ return (arrayConstraint : cs1 ++ cs2, M.union m1 m2)
325+
326+constantBinder :: Int -> Type -> Check ([TypeConstraint], M.Map String Int)
327+constantBinder val ty = return ([TypeConstraint val ty], M.empty)
328+
329+typeConstraintsForBinders :: M.Map String Int -> Int -> Int -> [(Binder, Value)] -> Check [TypeConstraint]
330+typeConstraintsForBinders _ _ _ [] = return []
331+typeConstraintsForBinders m nval ret ((binder, val):bs) = do
332+ (cs1, m1) <- typeConstraintsForBinder nval binder
333+ (cs2, n2) <- typeConstraints (M.union m m1) val
334+ cs3 <- typeConstraintsForBinders m nval ret bs
335+ return ((TypeConstraint n2 (TUnknown ret)) : cs1 ++ cs2 ++ cs3)
336+
337+typeConstraintsForStatement :: M.Map String Int -> M.Map String Int -> Int -> Statement -> Check ([TypeConstraint], Bool, M.Map String Int)
338+typeConstraintsForStatement m mass ret (VariableIntroduction name val) = do
339+ case M.lookup name (m `M.union` mass) of
340+ Nothing -> do
341+ (cs1, n1) <- typeConstraints m val
342+ return $ (cs1, False, M.insert name n1 mass)
343+ Just ty -> throwError $ "Variable with name " ++ name ++ " already exists."
344+typeConstraintsForStatement m mass ret (Assignment tgt val) = do
345+ (cs1, n1) <- typeConstraints m val
346+ cs2 <- typeConstraintsForAssignmentTarget m mass n1 tgt
347+ return (cs1 ++ cs2, False, mass)
348+typeConstraintsForStatement m mass ret (While val inner) = do
349+ (cs1, n1) <- typeConstraints m val
350+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret inner
351+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn, mass)
352+typeConstraintsForStatement m mass ret (IfThenElse val thens Nothing) = do
353+ (cs1, n1) <- typeConstraints m val
354+ (cs2, allCodePathsReturn, _) <- typeConstraintsForBlock m mass ret thens
355+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2, allCodePathsReturn, mass)
356+typeConstraintsForStatement m mass ret (IfThenElse val thens (Just elses)) = do
357+ (cs1, n1) <- typeConstraints m val
358+ (cs2, allCodePathsReturn1, _) <- typeConstraintsForBlock m mass ret thens
359+ (cs3, allCodePathsReturn2, _) <- typeConstraintsForBlock m mass ret elses
360+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2 ++ cs3, allCodePathsReturn1 && allCodePathsReturn2, mass)
361+typeConstraintsForStatement m mass ret (For (init, cond, cont) inner) = do
362+ (cs1, b1, mass1) <- typeConstraintsForStatement m mass ret init
363+ guardWith "Cannot return from inside for" $ not b1
364+ (cs2, n1) <- typeConstraints (m `M.union` mass1) cond
365+ (cs3, b2, mass2) <- typeConstraintsForStatement (m `M.union` mass1) mass1 ret cont
366+ guardWith "Cannot return from inside for" $ not b2
367+ (cs4, allCodePathsReturn, _) <- typeConstraintsForBlock (m `M.union` mass2) mass2 ret inner
368+ return $ ((TypeConstraint n1 Boolean) : cs1 ++ cs2 ++ cs3 ++ cs4, allCodePathsReturn, mass)
369+typeConstraintsForStatement m mass ret (Return val) = do
370+ (cs1, n1) <- typeConstraints (m `M.union` mass) val
371+ return ((TypeConstraint n1 (TUnknown ret)) : cs1, True, mass)
372+
373+typeConstraintsForAssignmentTarget :: M.Map String Int -> M.Map String Int -> Int -> AssignmentTarget -> Check [TypeConstraint]
374+typeConstraintsForAssignmentTarget m mass nval (AssignVariable var) =
375+ case M.lookup var mass of
376+ Nothing -> throwError $ "No local variable with name " ++ var
377+ Just ty -> do
378+ return [TypeConstraint nval (TUnknown ty)]
379+typeConstraintsForAssignmentTarget m mass nval (AssignArrayIndex index tgt) = do
380+ arr <- fresh
381+ (cs1, n1) <- typeConstraints (m `M.union` mass) index
382+ cs2 <- typeConstraintsForAssignmentTarget m mass arr tgt
383+ return $ (TypeConstraint arr (Array (TUnknown nval))) : (TypeConstraint n1 Number) : cs1 ++ cs2
384+typeConstraintsForAssignmentTarget m mass nval (AssignObjectProperty prop tgt) = do
385+ obj <- fresh
386+ row <- fresh
387+ cs <- typeConstraintsForAssignmentTarget m mass obj tgt
388+ return $ (TypeConstraint obj (Object (RCons prop (TUnknown nval) $ RUnknown row))) : cs
389+
390+typeConstraintsForBlock :: M.Map String Int -> M.Map String Int -> Int -> [Statement] -> Check ([TypeConstraint], Bool, M.Map String Int)
391+typeConstraintsForBlock _ mass _ [] = return ([], False, mass)
392+typeConstraintsForBlock m mass ret (s:ss) = do
393+ (cs1, b1, mass1) <- typeConstraintsForStatement (m `M.union` mass) mass ret s
394+ case (b1, ss) of
395+ (True, []) -> return (cs1, True, mass1)
396+ (True, _) -> throwError "Unreachable code"
397+ (False, ss) -> do
398+ (cs2, b2, mass2) <- typeConstraintsForBlock m mass1 ret ss
399+ return (cs1 ++ cs2, b2, mass2)
400+
401+solveTypeConstraints :: [TypeConstraint] -> TypeSolution -> Check TypeSolution
402+solveTypeConstraints [] s = return s
403+solveTypeConstraints all@(TypeConstraint n t:cs) s = do
404+ typeOccursCheck n t
405+ let s' = let (f, g) = runTypeSolution s
406+ in TypeSolution (replaceType n t . f, replaceType n t . g)
407+ cs' <- fmap concat $ mapM (substituteTypeInConstraint n t) cs
408+ solveTypeConstraints cs' s'
409+solveTypeConstraints (RowConstraint n r:cs) s = do
410+ rowOccursCheck n r
411+ let s' = let (f, g) = runTypeSolution s
412+ in TypeSolution $ (replaceRow n r . f, replaceRow n r . g)
413+ cs' <- fmap concat $ mapM (substituteRowInConstraint n r) cs
414+ solveTypeConstraints cs' s'
415+
416+substituteTypeInConstraint :: Int -> Type -> TypeConstraint -> Check [TypeConstraint]
417+substituteTypeInConstraint n s (TypeConstraint m t)
418+ | n == m = unifyTypes s t
419+ | otherwise = return [TypeConstraint m (replaceType n s t)]
420+substituteTypeInConstraint n s (RowConstraint m r)
421+ = return [RowConstraint m (replaceType n s r)]
422+
423+substituteRowInConstraint :: Int -> Row -> TypeConstraint -> Check [TypeConstraint]
424+substituteRowInConstraint n r (TypeConstraint m t)
425+ = return [TypeConstraint m (replaceRow n r t)]
426+substituteRowInConstraint n r (RowConstraint m r1)
427+ | m == n = unifyRows r r1
428+ | otherwise = return [RowConstraint m (replaceRow n r r1)]
429+
430+unifyTypes :: Type -> Type -> Check [TypeConstraint]
431+unifyTypes (TUnknown u1) (TUnknown u2) | u1 == u2 = return []
432+unifyTypes (TUnknown u) t = do
433+ typeOccursCheck u t
434+ return [TypeConstraint u t]
435+unifyTypes t (TUnknown u) = do
436+ typeOccursCheck u t
437+ return [TypeConstraint u t]
438+unifyTypes Number Number = return []
439+unifyTypes String String = return []
440+unifyTypes Boolean Boolean = return []
441+unifyTypes (Array s) (Array t) = unifyTypes s t
442+unifyTypes (Object row1) (Object row2) = unifyRows row1 row2
443+unifyTypes (Function args1 ret1) (Function args2 ret2) = do
444+ guardWith "Function applied to incorrect number of args" $ length args1 == length args2
445+ cs1 <- fmap concat $ zipWithM unifyTypes args1 args2
446+ cs2 <- unifyTypes ret1 ret2
447+ return $ cs1 ++ cs2
448+unifyTypes (TypeVar v1) (TypeVar v2) | v1 == v2 = return []
449+unifyTypes (TypeConstructor c1) (TypeConstructor c2) | c1 == c2 = return []
450+unifyTypes (TypeVar v1) (TypeVar v2) = return []
451+unifyTypes (TypeApp t1 t2) (TypeApp t3 t4) = do
452+ cs1 <- unifyTypes t1 t3
453+ cs2 <- unifyTypes t2 t4
454+ return $ cs1 ++ cs2
455+unifyTypes t1 t2 = throwError $ "Cannot unify " ++ show t1 ++ " with " ++ show t2 ++ "."
456+
457+unifyRows :: Row -> Row -> Check [TypeConstraint]
458+unifyRows r1 r2 =
459+ let
460+ (s1, r1') = toList r1
461+ (s2, r2') = toList r2
462+ int = [ (t1, t2) | (name, t1) <- s1, (name', t2) <- s2, name == name' ]
463+ sd1 = [ (name, t1) | (name, t1) <- s1, not (elem name (map fst s2)) ]
464+ sd2 = [ (name, t2) | (name, t2) <- s2, not (elem name (map fst s1)) ]
465+ in rethrow (\e -> "Cannot unify " ++ show r1 ++ " with " ++ show r2 ++ ": " ++ e) $ do
466+ cs1 <- fmap concat $ mapM (uncurry unifyTypes) int
467+ cs2 <- unifyRows' sd1 r1' sd2 r2'
468+ return $ cs1 ++ cs2
469+ where
470+ unifyRows' :: [(String, Type)] -> Row -> [(String, Type)] -> Row -> Check [TypeConstraint]
471+ unifyRows' [] (RUnknown u) sd r = do
472+ rowOccursCheck u r
473+ return [RowConstraint u (fromList (sd, r))]
474+ unifyRows' ((name, ty):row) r others (RUnknown u) = do
475+ u' <- fresh
476+ cs <- unifyRows' row r others (RUnknown u')
477+ return [ RowConstraint u (RCons name ty (RUnknown u')) ]
478+ unifyRows' [] REmpty [] REmpty = return []
479+ unifyRows' sd1 r1 sd2 r2 = throwError $ "Cannot unify " ++ show (fromList (sd1, r1)) ++ " with " ++ show (fromList (sd2, r2)) ++ "."
480+ toList :: Row -> ([(String, Type)], Row)
481+ toList (RCons name ty row) = let (tys, rest) = toList row
482+ in ((name, ty):tys, rest)
483+ toList r = ([], r)
484+ fromList :: ([(String, Type)], Row) -> Row
485+ fromList ([], r) = r
486+ fromList ((name, t):ts, r) = RCons name t (fromList (ts, r))