1 implementation module sem
3 import qualified Data.Map as Map
5 from Data.Func import $
6 from StdFunc import o, flip, const, id
8 import Control.Applicative
10 import Control.Monad.Trans
11 import Control.Monad.State
26 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 :: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
33 :: Substitution :== 'Map'.Map TVar Type
34 :: Constraints :== [(Type, Type)]
36 = ParseError Pos String
37 | UnifyError Pos Type Type
38 | InfiniteTypeError Pos Type
39 | FieldSelectorError Pos Type FieldSelector
40 | OperatorError Pos Op2 Type
41 | UndeclaredVariableError Pos String
42 | ArgumentMisMatchError Pos String
43 | SanityError Pos String
46 instance zero Gamma where
49 variableStream :: [TVar]
50 variableStream = map toString [1..]
52 defaultGamma :: Gamma //includes all default functions
53 defaultGamma = extend "print" (Forall ["a"] ((IdType "a") ->> VoidType))
54 $ extend "isEmpty" (Forall ["a"] ((ListType (IdType "a")) ->> BoolType))
55 $ extend "read" (Forall [] (FuncType CharType))
56 $ extend "1printchar" (Forall [] (CharType ->> VoidType))
57 $ extend "1printint" (Forall [] (IntType ->> VoidType))
58 $ extend "1printbool" (Forall [] (BoolType ->> VoidType))
61 sem :: AST -> Either [SemError] (AST, Gamma)
62 sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
63 >>| foldM (const isNiceMain) () fd
65 >>| runStateT (unfoldLambda fd >>= type) (defaultGamma, variableStream) of
67 Right ((_,fds),(gam,_)) = Right (AST fds, gam)
69 hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
70 hasNoDups fds (FunDecl p n _ _ _ _)
71 # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
72 = case catMaybes mbs of
73 [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN"
75 [_:x] = Left $ SanityError p (concat
76 [n, " multiply defined at ", toString p])
78 hasMain :: [FunDecl] -> Either SemError ()
79 hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure ()
80 hasMain [_:fd] = hasMain fd
81 hasMain [] = Left $ SanityError zero "no main function defined"
83 isNiceMain :: FunDecl -> Either SemError ()
84 isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of
85 ([_:_], _) = Left $ SanityError p "main must have arity 0"
88 Just VoidType = pure ()
89 _ = Left $ SanityError p "main has to return Void")
90 isNiceMain _ = pure ()
96 unfoldLambda :: [FunDecl] -> Typing [FunDecl]
97 unfoldLambda [] = pure []
98 unfoldLambda [fd:fds] = unfoldL_ fd >>= \(gen1, fs_)->
99 unfoldLambda fds >>= \gen2->
100 pure $ gen1 ++ [fs_] ++ gen2
102 flattenT :: [([a],b)] -> ([a],[b])
103 flattenT ts = (flatten $ map fst ts, map snd ts)
105 class unfoldL_ a :: a -> Typing ([FunDecl], a)
107 instance unfoldL_ FunDecl where
108 unfoldL_ (FunDecl p f args mt vds stmts) =
109 flattenT <$> mapM unfoldL_ vds >>= \(fds1,vds_) ->
110 flattenT <$> mapM unfoldL_ stmts >>= \(fds2,stmts_)->
111 pure (fds1 ++ fds2, FunDecl p f args mt vds_ stmts_)
113 instance unfoldL_ VarDecl where
114 unfoldL_ (VarDecl p mt v e) = unfoldL_ e >>= \(fds, e_)->pure (fds, VarDecl p mt v e_)
116 instance unfoldL_ Stmt where
117 unfoldL_ (IfStmt e th el) = unfoldL_ e >>= \(fds, e_)->pure (fds, IfStmt e_ th el)
118 unfoldL_ (WhileStmt e c) = unfoldL_ e >>= \(fds, e_)->pure (fds, WhileStmt e_ c)
119 unfoldL_ (AssStmt vd e) = unfoldL_ e >>= \(fds, e_)->pure (fds, AssStmt vd e_)
120 unfoldL_ (FunStmt f es fs) = flattenT <$> mapM unfoldL_ es >>= \(fds, es_)->
121 pure (fds, FunStmt f es_ fs)
122 unfoldL_ (ReturnStmt (Just e)) = unfoldL_ e >>= \(fds, e_) ->
123 pure (fds, ReturnStmt (Just e_))
124 unfoldL_ (ReturnStmt Nothing) = pure ([], ReturnStmt Nothing)
126 instance unfoldL_ Expr where
127 unfoldL_ (LambdaExpr p args e) =
128 fresh >>= \(IdType n) ->
129 let f = ("2lambda_"+++n) in
130 let fd = FunDecl p f args Nothing [] [ReturnStmt $ Just e] in
131 let fe = VarExpr p (VarDef f []) in
133 unfoldL_ (FunExpr p f es fs) = flattenT <$> mapM unfoldL_ es >>= \(fds, es_)->
134 pure (fds, FunExpr p f es_ fs)
135 unfoldL_ (Op2Expr p e1 op e2) = unfoldL_ e1 >>= \(fds1, e1_)->
136 unfoldL_ e2 >>= \(fds2, e2_)->
137 pure (fds1++fds2, Op2Expr p e1_ op e2_)
138 unfoldL_ (Op1Expr p op e1) = unfoldL_ e1 >>= \(fds, e1_)->pure (fds, Op1Expr p op e1_)
139 unfoldL_ (TupleExpr p (e1, e2)) = unfoldL_ e1 >>= \(fds1, e1_)->
140 unfoldL_ e2 >>= \(fds2, e2_)->
141 pure (fds1++fds2, TupleExpr p (e1_, e2_))
142 unfoldL_ e = pure ([], e)
150 class Typeable a where
152 subst :: Substitution a -> a
154 instance Typeable Scheme where
155 ftv (Forall bound t) = difference (ftv t) bound
156 subst s (Forall bound t) = Forall bound $ subst s_ t
157 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
159 instance Typeable [a] | Typeable a where
160 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
161 subst s ts = map (\t->subst s t) ts
163 instance Typeable Type where
164 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
165 ftv (ListType t) = ftv t
166 ftv (IdType tvar) = [tvar]
167 ftv (FuncType t) = ftv t
168 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
170 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
171 subst s (ListType t1) = ListType (subst s t1)
172 subst s (FuncType t) = FuncType (subst s t)
173 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
174 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
177 instance Typeable Gamma where
178 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
179 subst s gamma = Mapmap (subst s) gamma
181 extend :: String Scheme Gamma -> Gamma
182 extend k t g = 'Map'.put k t g
184 //// ------------------------
185 //// algorithm U, Unification
186 //// ------------------------
187 instance zero Substitution where zero = 'Map'.newMap
189 compose :: Substitution Substitution -> Substitution
190 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
191 //Note: just like function compositon compose does snd first
193 occurs :: TVar a -> Bool | Typeable a
194 occurs tvar a = elem tvar (ftv a)
196 unify :: Type Type -> Either SemError Substitution
197 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
198 | occurs tv t1 = Left $ InfiniteTypeError zero t1
199 | otherwise = Right $ 'Map'.singleton tv t1
200 unify t1=:(IdType tv) t2 = unify t2 t1
201 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
202 unify (subst s1 ta2) (subst s1 tb2) >>= \s2->
203 Right $ compose s2 s1
204 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
205 unify (subst s1 ta2) (subst s1 tb2) >>= \s2->
206 Right $ compose s2 s1
207 unify (ListType t1) (ListType t2) = unify t1 t2
208 unify (FuncType t1) (FuncType t2) = unify t1 t2
209 unify t1 t2 | t1 == t2 = Right zero
210 | otherwise = Left $ UnifyError zero t1 t2
212 //// ------------------------
213 //// Algorithm M, Inference and Solving
214 //// ------------------------
215 gamma :: Typing Gamma
217 putGamma :: Gamma -> Typing ()
218 putGamma g = modify (appFst $ const g) >>| pure ()
219 changeGamma :: (Gamma -> Gamma) -> Typing Gamma
220 changeGamma f = modify (appFst f) >>| gamma
221 withGamma :: (Gamma -> a) -> Typing a
222 withGamma f = f <$> gamma
224 fresh = gets snd >>= \vars->
225 modify (appSnd $ const $ tail vars) >>|
226 pure (IdType (head vars))
228 lift :: (Either SemError a) -> Typing a
229 lift (Left e) = liftT $ Left e
230 lift (Right v) = pure v
232 //instantiate maps a schemes type variables to variables with fresh names
233 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
234 instantiate :: Scheme -> Typing Type
235 instantiate (Forall bound t) =
236 mapM (const fresh) bound >>= \newVars->
237 let s = 'Map'.fromList (zip (bound,newVars)) in
240 //generalize quentifies all free type variables in a type which are not
242 generalize :: Type -> Typing Scheme
243 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
245 lookup :: String -> Typing Type
246 lookup k = gamma >>= \g-> case 'Map'.member k g of
247 False = liftT (Left $ UndeclaredVariableError zero k)
248 True = instantiate $ 'Map'.find k g
250 //The inference class
251 //When tying it all together we will treat the program is a big
252 //let x=e1 in let y=e2 in ....
253 class infer a :: a -> Typing (Substitution, Type, a)
255 ////---- Inference for Expressions ----
257 instance infer Expr where
259 VarExpr _ (VarDef k fs) = lookup k >>= \t ->
260 foldM foldFieldSelectors t fs >>= \finalT ->
261 pure (zero, finalT, e)
264 infer e1 >>= \(s1, t1, e1_) ->
266 infer e2 >>= \(s2, t2, e2_) ->
269 let given = t1 ->> t2 ->> tv in
270 op2Type op >>= \expected ->
271 lift (unify expected given) >>= \s3 ->
273 pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
276 infer e1 >>= \(s1, t1, e1_) ->
279 let given = t1 ->> tv in
280 op1Type op >>= \expected ->
281 lift (unify expected given) >>= \s2 ->
283 pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
285 EmptyListExpr _ = (\tv->(zero,ListType tv,e)) <$> fresh
287 TupleExpr p (e1, e2) =
288 infer e1 >>= \(s1, t1, e1_) ->
290 infer e2 >>= \(s2, t2, e2_) ->
292 pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
294 LambdaExpr _ _ _ = liftT $ Left $ Error "PANIC: lambdas should be Unfolded"
296 FunExpr p f args fs =
297 lookup f >>= \expected ->
298 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
299 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
302 "print" = case head argTs of
303 IntType = pure "1printint"
304 CharType = pure "1printchar"
305 BoolType = pure "1printbool"
306 ListType (CharType) = pure "1printstr"
307 t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
310 fresh >>= \tv->case expected of
311 FuncType t = foldM foldFieldSelectors t fs >>= \returnType ->
312 pure (s1, returnType, (FunExpr p newF args fs))
313 _ = (let given = foldr (->>) tv argTs in
314 lift (unify expected given) >>= \s2->
316 let fReturnType = subst s2 tv in
317 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
318 pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
320 IntExpr _ _ = pure $ (zero, IntType, e)
321 BoolExpr _ _ = pure $ (zero, BoolType, e)
322 CharExpr _ _ = pure $ (zero, CharType, e)
324 foldFieldSelectors :: Type FieldSelector -> Typing Type
325 foldFieldSelectors (ListType t) (FieldHd) = pure t
326 foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
327 foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
328 foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
329 foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
331 op2Type :: Op2 -> Typing Type
333 | elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
334 = pure (IntType ->> IntType ->> IntType)
335 | elem op [BiEquals, BiUnEqual]
336 = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
337 | elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
338 = pure (IntType ->> IntType ->> BoolType)
339 | elem op [BiAnd, BiOr]
340 = pure (BoolType ->> BoolType ->> BoolType)
342 = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
344 op1Type :: Op1 -> Typing Type
345 op1Type UnNegation = pure $ (BoolType ->> BoolType)
346 op1Type UnMinus = pure $ (IntType ->> IntType)
348 ////----- Inference for Statements -----
349 applySubst :: Substitution -> Typing Gamma
350 applySubst s = changeGamma (subst s)
352 instance infer Stmt where
355 infer e >>= \(s1, et, e_)->
356 lift (unify et BoolType) >>= \s2 ->
357 applySubst (compose s2 s1) >>|
358 infer th >>= \(s3, tht, th_)->
360 infer el >>= \(s4, elt, el_)->
362 lift (unify tht elt) >>= \s5->
363 let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
364 pure (sub, subst s5 tht, IfStmt e_ th_ el_)
367 infer e >>= \(s1, et, e_)->
368 lift (unify et BoolType) >>= \s2 ->
369 applySubst (compose s2 s1) >>|
370 infer wh >>= \(s3, wht, wh_)->
371 pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
373 AssStmt vd=:(VarDef k fs) e =
374 lookup k >>= \expected ->
375 infer e >>= \(s1, given, e_)->
376 foldM reverseFs given (reverse fs) >>= \varType->
377 lift (unify expected varType) >>= \s2->
378 let s = compose s2 s1 in
380 changeGamma (extend k (Forall [] (subst s varType))) >>|
381 pure (s, VoidType, AssStmt vd e_)
384 lookup f >>= \expected ->
385 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
386 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
388 let given = foldr (->>) tv argTs in
389 lift (unify expected given) >>= \s2->
390 let fReturnType = subst s2 tv in
391 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
393 "print" = case head argTs of
394 IntType = pure "1printint"
395 CharType = pure "1printchar"
396 BoolType = pure "1printbool"
397 ListType (CharType) = pure "1printstr"
398 t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
399 _ = pure f) >>= \newF->
400 pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
402 ReturnStmt Nothing = pure (zero, VoidType, s)
403 //hier ook sub applyen
404 ReturnStmt (Just e) = infer e >>= \(sub, t, e_)-> pure (sub, t, ReturnStmt (Just e_))
406 reverseFs :: Type FieldSelector -> Typing Type
407 reverseFs t FieldHd = pure $ ListType t
408 reverseFs t FieldTl = pure t
409 reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
410 reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
412 //The type of a list of statements is either an encountered
413 //return, or VoidType
414 instance infer [a] | infer a where
415 infer [] = pure (zero, VoidType, [])
417 infer stmt >>= \(s1, t1, s_) ->
419 infer ss >>= \(s2, t2, ss_) ->
422 VoidType = pure (compose s2 s1, t2, [s_:ss_])
424 VoidType = pure (compose s2 s1, t1, [s_:ss_])
425 _ = lift (unify t1 t2) >>= \s3 ->
426 pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
428 //the type class inferes the type of an AST element (VarDecl or FunDecl)
429 //and adds it to the AST element
430 class type a :: a -> Typing (Substitution, a)
432 instance type VarDecl where
433 type (VarDecl p expected k e) =
434 infer e >>= \(s1, given, e_) ->
438 Just expected_ = lift (unify expected_ given)
441 let vtype = subst (compose s2 s1) given in
442 generalize vtype >>= \t ->
443 changeGamma (extend k t) >>|
444 pure (compose s2 s1, VarDecl p (Just vtype) k e_)
446 instance type FunDecl where
447 type fd=:(FunDecl p f args expected vds stmts) =
448 gamma >>= \outerScope-> //functions are infered in their own scopde
450 mapM introduce args >>= \argTs->
452 let temp = foldr (->>) tempTv argTs in
454 Just expected_ = lift (unify expected_ temp)
458 type vds >>= \(s1, tVds)->
460 infer stmts >>= \(s2, result, stmts_)->
462 let argTs_ = map (subst $ compose s2 $ compose s1 s0) argTs in
463 let given = foldr (->>) result argTs_ in
466 Just (FuncType expected_) = lift (unify expected_ given)
467 Just expected_ = lift (unify expected_ given)
469 let ftype = subst (compose s3 $ compose s2 $ compose s1 s0) given in
472 _ = pure $ FuncType ftype
474 generalize ftype_ >>= \t->
475 putGamma outerScope >>|
476 changeGamma (extend f t) >>|
477 pure (compose s3 $ compose s2 $ compose s1 s0,
478 FunDecl p f args (Just ftype_) tVds stmts_)
480 instance type [a] | type a where
481 type [] = pure (zero, [])
483 type v >>= \(s1, v_)->
485 type vs >>= \(s2, vs_)->
486 applySubst (compose s2 s1) >>|
487 pure (compose s2 s1, [v_:vs_])
489 introduce :: String -> Typing Type
492 changeGamma (extend k (Forall [] tv)) >>|
495 instance toString Scheme where
496 toString (Forall x t) =
497 concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
499 instance toString Gamma where
501 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
503 instance toString Substitution where
505 concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
507 instance toString SemError where
508 toString (SanityError p e) = concat [toString p,
509 "SemError: SanityError: ", e]
510 toString (ParseError p s) = concat [toString p,
512 toString (UnifyError p t1 t2) = concat [toString p,
513 "Can not unify types, expected|given:\n", toString t1,
515 toString (InfiniteTypeError p t) = concat [toString p,
516 "Infinite type: ", toString t]
517 toString (FieldSelectorError p t fs) = concat [toString p,
518 "Can not run fieldselector '", toString fs, "' on type: ",
520 toString (OperatorError p op t) = concat [toString p,
521 "Operator error, operator '", toString op, "' can not be",
522 "used on type: ", toString t]
523 toString (UndeclaredVariableError p k) = concat [toString p,
524 "Undeclared identifier: ", k]
525 toString (ArgumentMisMatchError p str) = concat [toString p,
526 "Argument mismatch: ", str]
527 toString (Error e) = concat ["Unknown error during semantical",
530 instance toString (Maybe a) | toString a where
531 toString Nothing = "Nothing"
532 toString (Just e) = concat ["Just ", toString e]
534 instance MonadTrans (StateT (Gamma, [TVar])) where
535 liftT m = StateT \s-> m >>= \a-> return (a, s)
537 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
538 Mapmap _ 'Map'.Tip = 'Map'.Tip
539 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)