1 implementation module sem
3 import qualified Data.Map as Map
5 from Data.Func import $
6 from StdFunc import o, flip, const, id
9 import Control.Monad.Trans
10 import Control.Monad.State
25 from Text import class Text(concat), instance Text String
30 :: Scheme = Forall [TVar] Type
31 :: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
32 :: Substitution :== 'Map'.Map TVar Type
33 :: Constraints :== [(Type, Type)]
35 = ParseError Pos String
36 | UnifyError Pos Type Type
37 | InfiniteTypeError Pos Type
38 | FieldSelectorError Pos Type FieldSelector
39 | OperatorError Pos Op2 Type
40 | UndeclaredVariableError Pos String
41 | ArgumentMisMatchError Pos String
42 | SanityError Pos String
45 instance zero Gamma where
48 variableStream :: [TVar]
49 variableStream = map toString [1..]
51 sem :: AST -> Either [SemError] Constraints
52 sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
53 >>| foldM (const isNiceMain) () fd
57 //_ = case execRWST (constraints fd) zero variableStream of
59 // Right (a, b) = Right b
61 constraints :: [FunDecl] -> Typing ()
62 constraints _ = pure ()
64 //constraints fds = mapM_ funconstraint fds >>| pure ()
66 funconstraint :: FunDecl -> Typing ()
67 funconstraint fd=:(FunDecl _ ident args mt vardecls stmts) = case mt of
68 Nothing = abort "Cannot infer functions yet"
70 //Just t = inEnv (ident, (Forall [] t)) (
71 // mapM_ vardeclconstraint vardecls >>| pure ())
73 vardeclconstraint :: VarDecl -> Typing ()
74 vardeclconstraint _ = pure ()
76 //vardeclconstraint (VarDecl p mt ident expr) = infer expr
77 //>>= \it->inEnv (ident, (Forall [] it)) (pure ())
79 hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
80 hasNoDups fds (FunDecl p n _ _ _ _)
81 # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
82 = case catMaybes mbs of
83 [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN"
85 [_:x] = Left $ SanityError p (concat
86 [n, " multiply defined at ", toString p])
88 hasMain :: [FunDecl] -> Either SemError ()
89 hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure ()
90 hasMain [_:fd] = hasMain fd
91 hasMain [] = Left $ SanityError zero "no main function defined"
93 isNiceMain :: FunDecl -> Either SemError ()
94 isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of
95 ([_:_], _) = Left $ SanityError p "main must have arity 0"
98 Just VoidType = pure ()
99 _ = Left $ SanityError p "main has to return Void")
100 isNiceMain _ = pure ()
102 class Typeable a where
104 subst :: Substitution a -> a
106 instance Typeable Scheme where
107 ftv (Forall bound t) = difference (ftv t) bound
108 subst s (Forall bound t) = Forall bound $ subst s_ t
109 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
111 instance Typeable [a] | Typeable a where
112 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
113 subst s ts = map (\t->subst s t) ts
115 instance Typeable Type where
116 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
117 ftv (ListType t) = ftv t
118 ftv (IdType tvar) = [tvar]
119 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
121 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
122 subst s (ListType t1) = ListType (subst s t1)
123 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
124 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
127 instance Typeable Gamma where
128 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
129 subst s gamma = Mapmap (subst s) gamma
131 extend :: String Scheme Gamma -> Gamma
132 extend k t g = 'Map'.put k t g
134 //// ------------------------
135 //// algorithm U, Unification
136 //// ------------------------
137 instance zero Substitution where zero = 'Map'.newMap
139 compose :: Substitution Substitution -> Substitution
140 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
141 //Note: just like function compositon compose does snd first
143 occurs :: TVar a -> Bool | Typeable a
144 occurs tvar a = elem tvar (ftv a)
146 unify :: Type Type -> Either SemError Substitution
147 unify t1=:(IdType tv) t2 = unify t2 t1
148 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
149 | occurs tv t1 = Left $ InfiniteTypeError zero t1
150 | otherwise = Right $ 'Map'.singleton tv t1
151 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
152 unify tb1 tb2 >>= \s2->
153 Right $ compose s1 s2
154 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
155 unify ta2 tb2 >>= \s2->
156 Right $ compose s1 s2
157 unify (ListType t1) (ListType t2) = unify t1 t2
158 unify t1 t2 | t1 == t2 = Right zero
159 | otherwise = Left $ UnifyError zero t1 t2
161 //// ------------------------
162 //// Algorithm M, Inference and Solving
163 //// ------------------------
165 :: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
166 gamma :: Typing Gamma
168 putGamma :: Gamma -> Typing ()
169 putGamma g = modify (appFst $ const g) >>| pure ()
170 changeGamma :: (Gamma -> Gamma) -> Typing Gamma
171 changeGamma f = modify (appFst f) >>| gamma
172 withGamma :: (Gamma -> a) -> Typing a
173 withGamma f = f <$> gamma
175 fresh = gets snd >>= \vars->
176 modify (appSnd $ const $ tail vars) >>|
177 pure (IdType (head vars))
179 lift :: (Either SemError a) -> Typing a
180 lift (Left e) = liftT $ Left e
181 lift (Right v) = pure v
183 //instantiate maps a schemes type variables to variables with fresh names
184 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
185 instantiate :: Scheme -> Typing Type
186 instantiate (Forall bound t) =
187 mapM (const fresh) bound >>= \newVars->
188 let s = 'Map'.fromList (zip (bound,newVars)) in
191 //generalize quentifies all free type variables in a type which are not
193 generalize :: Type -> Typing Scheme
194 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
196 lookup :: String -> Typing Type
197 lookup k = gamma >>= \g-> case 'Map'.member k g of
198 False = liftT (Left $ UndeclaredVariableError zero k)
199 True = instantiate $ 'Map'.find k g
201 //The inference class
202 //When tying it all together we will treat the program is a big
203 //let x=e1 in let y=e2 in ....
204 class infer a :: a -> Typing (Substitution, Type)
206 ////---- Inference for Expressions ----
208 instance infer Expr where
210 VarExpr _ (VarDef k fs) = (\t->(zero,t)) <$> lookup k
211 //instantiate is key for the let polymorphism!
212 //TODO: field selectors
215 infer e1 >>= \(s1, t1) ->
216 infer e2 >>= \(s2, t2) ->
218 let given = t1 ->> t2 ->> tv in
219 op2Type op >>= \expected ->
220 lift (unify expected given) >>= \s3 ->
221 pure ((compose s3 $ compose s2 s1), subst s3 tv)
224 infer e1 >>= \(s1, t1) ->
226 let given = t1 ->> tv in
227 op1Type op >>= \expected ->
228 lift (unify expected given) >>= \s2 ->
229 pure (compose s2 s1, subst s2 tv)
231 EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
233 TupleExpr _ (e1, e2) =
234 infer e1 >>= \(s1, t1) ->
235 infer e2 >>= \(s2, t2) ->
236 pure (compose s2 s1, TupleType (t1,t2))
238 FunExpr _ f args fs = //todo: fieldselectors
239 lookup f >>= \expected ->
240 let accST = (\(s,ts) e->infer e >>= \(s_,et)->pure (compose s_ s,ts++[et])) in
241 foldM accST (zero,[]) args >>= \(s1, argTs)->
243 let given = foldr (->>) tv argTs in
244 lift (unify expected given) >>= \s2->
245 pure (compose s2 s1, subst s2 tv)
247 IntExpr _ _ = pure $ (zero, IntType)
248 BoolExpr _ _ = pure $ (zero, BoolType)
249 CharExpr _ _ = pure $ (zero, CharType)
252 op2Type :: Op2 -> Typing Type
254 | elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
255 = pure (IntType ->> IntType ->> IntType)
256 | elem op [BiEquals, BiUnEqual]
257 = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
258 | elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
259 = pure (IntType ->> IntType ->> BoolType)
260 | elem op [BiAnd, BiOr]
261 = pure (BoolType ->> BoolType ->> BoolType)
263 = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
265 op1Type :: Op1 -> Typing Type
266 op1Type UnNegation = pure $ (BoolType ->> BoolType)
267 op1Type UnMinus = pure $ (IntType ->> IntType)
269 ////----- Inference for Statements -----
270 applySubst :: Substitution -> Typing Gamma
271 applySubst s = changeGamma (subst s)
273 instance infer Stmt where
276 infer e >>= \(s1, et)->
277 lift (unify et BoolType) >>= \s2 ->
278 applySubst (compose s2 s1) >>|
279 infer th >>= \(s3, tht)->
281 infer el >>= \(s4, elt)->
283 lift (unify tht elt) >>= \s5->
284 pure (compose s5 $ compose s4 $ compose s3 $ compose s2 s1, subst s5 tht)
287 infer e >>= \(s1, et)->
288 lift (unify et BoolType) >>= \s2 ->
289 applySubst (compose s2 s1) >>|
290 infer wh >>= \(s3, wht)->
291 pure (compose s3 $ compose s2 s1, subst s3 wht)
293 AssStmt (VarDef k fs) e =
294 infer e >>= \(s1, et)->
296 changeGamma (extend k (Forall [] et)) >>| //todo: fieldselectors
299 FunStmt f es = undef //what is this?
301 ReturnStmt Nothing = pure (zero, VoidType)
302 ReturnStmt (Just e) = infer e
304 //The type of a list of statements is either an encountered
305 //return, or VoidType
306 instance infer [a] | infer a where
307 infer [] = pure (zero, VoidType)
309 infer stmt >>= \(s1, t1) ->
310 infer ss >>= \(s2, t2) ->
312 VoidType = pure (compose s2 s1, t2)
314 VoidType = pure (compose s2 s1, t1)
315 _ = lift (unify t1 t2) >>= \s3 ->
316 pure (compose s3 $ compose s2 s1, t1)
318 //the type class inferes the type of an AST element (VarDecl or FunDecl)
319 //and adds it to the AST element
320 class type a :: a -> Typing a
322 instance type VarDecl where
323 type (VarDecl p expected k e) =
324 infer e >>= \(s, given) ->
328 Just expected_ = lift (unify expected_ given)
330 generalize given >>= \t ->
331 changeGamma (extend k t) >>|
332 pure (VarDecl p (Just given) k e)
334 instance type FunDecl where
335 type (FunDecl p f args expected vds stmts) =
337 infer stmts >>= \(s, given)->
341 Just expected_ = lift (unify expected_ given))
343 generalize given >>= \t->
344 changeGamma (extend f t) >>|
345 pure (FunDecl p f args (Just given) tVds stmts)
347 instance type [a] | type a where
348 type dcls = mapM type dcls
352 instance toString Scheme where
353 toString (Forall x t) =
354 concat ["Forall ": map ((+++) "\n") x] +++ toString t
356 instance toString Gamma where
358 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
360 instance toString SemError where
361 toString (SanityError p e) = concat [toString p,
362 "SemError: SanityError: ", e]
363 toString se = "SemError: "
365 instance MonadTrans (StateT (Gamma, [TVar])) where
366 liftT m = StateT \s-> m >>= \a-> return (a, s)
368 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
369 Mapmap _ 'Map'.Tip = 'Map'.Tip
370 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)
374 //// ------------------------
375 //// First step: Inference
376 //// ------------------------//
378 //unify :: Type Type -> Infer ()
379 //unify t1 t2 = tell [(t1, t2)]//
381 //fresh :: Infer Type
382 //fresh = (gets id) >>= \vars-> (put $ tail vars) >>| (pure $ IdType $ head vars)//
384 //op2Type :: Op2 -> Infer Type
386 //| elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
387 // = pure (IntType ->> IntType ->> IntType)
388 //| elem op [BiEquals, BiUnEqual]
389 // = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
390 //| elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
391 // = pure (IntType ->> IntType ->> BoolType)
392 //| elem op [BiAnd, BiOr]
393 // = pure (BoolType ->> BoolType ->> BoolType)
395 // = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)//
397 //op1Type :: Op1 -> Infer Type
398 //op1Type UnNegation = pure $ (BoolType ->> BoolType)
399 //op1Type UnMinus = pure $ (IntType ->> IntType)//
401 ////instantiate :: Scheme -> Infer Type
402 ////instantiate (Forall as t) = mapM (const fresh) as//
404 //lookupEnv :: String -> Infer Type
405 //lookupEnv ident = asks ('Map'.get ident)
407 // Nothing = liftT $ Left $ UndeclaredVariableError zero ident
408 // Just (Forall as t) = pure t //instantiate ???//
410 //class infer a :: a -> Infer Type
411 //instance infer Expr where
412 // infer (VarExpr _ (VarDef ident fs)) = lookupEnv ident
413 // infer (Op2Expr _ e1 op e2) =
414 // infer e1 >>= \t1 ->
415 // infer e2 >>= \t2 ->
416 // fresh >>= \frsh ->
417 // let given = t1 ->> (t2 ->> frsh) in
418 // op2Type op >>= \expected ->
419 // unify expected given >>|
421 // infer (Op1Expr _ op e) =
422 // infer e >>= \t1 ->
423 // fresh >>= \frsh ->
424 // let given = t1 ->> frsh in
425 // op1Type op >>= \expected ->
426 // unify expected given >>|
428 // infer (IntExpr _ _) = pure IntType
429 // infer (CharExpr _ _) = pure CharType
430 // infer (BoolExpr _ _) = pure BoolType
431 // infer (FunExpr _ f args sels) = //todo, iets met field selectors
432 // lookupEnv f >>= \expected ->
433 // fresh >>= \frsh ->
434 // mapM infer args >>= \argTypes ->
435 // let given = foldr (->>) frsh argTypes in
436 // unify expected given >>|
438 // infer (EmptyListExpr _) = ListType <$> fresh
439 // infer (TupleExpr _ (e1, e2)) =
440 // infer e1 >>= \et1->infer e2 >>= \et2->pure $ TupleType (et1, et2)//
442 ////:: VarDef = VarDef String [FieldSelector]
443 ////:: FieldSelector = FieldHd | FieldTl | FieldFst | FieldSnd
444 ////:: Op1 = UnNegation | UnMinus
445 ////:: Op2 = BiPlus | BiMinus | BiTimes | BiDivide | BiMod | BiEquals | BiLesser |
446 //// BiGreater | BiLesserEq | BiGreaterEq | BiUnEqual | BiAnd | BiOr | BiCons
447 ////:: FunDecl = FunDecl Pos String [String] (Maybe Type) [VarDecl] [Stmt]
448 ////:: FunCall = FunCall String [Expr]
450 //// = IfStmt Expr [Stmt] [Stmt]
451 //// | WhileStmt Expr [Stmt]
452 //// | AssStmt VarDef Expr
453 //// | FunStmt FunCall
454 //// | ReturnStmt (Maybe Expr)
455 ////:: Pos = {line :: Int, col :: Int}
456 ////:: AST = AST [VarDecl] [FunDecl]
457 ////:: VarDecl = VarDecl Pos Type String Expr
459 //// = TupleType (Type, Type)
467 //// | (->>) infixl 7 Type Type