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_ e = pure ([], e)
143 class Typeable a where
145 subst :: Substitution a -> a
147 instance Typeable Scheme where
148 ftv (Forall bound t) = difference (ftv t) bound
149 subst s (Forall bound t) = Forall bound $ subst s_ t
150 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
152 instance Typeable [a] | Typeable a where
153 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
154 subst s ts = map (\t->subst s t) ts
156 instance Typeable Type where
157 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
158 ftv (ListType t) = ftv t
159 ftv (IdType tvar) = [tvar]
160 ftv (FuncType t) = ftv t
161 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
163 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
164 subst s (ListType t1) = ListType (subst s t1)
165 subst s (FuncType t) = FuncType (subst s t)
166 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
167 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
170 instance Typeable Gamma where
171 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
172 subst s gamma = Mapmap (subst s) gamma
174 extend :: String Scheme Gamma -> Gamma
175 extend k t g = 'Map'.put k t g
177 //// ------------------------
178 //// algorithm U, Unification
179 //// ------------------------
180 instance zero Substitution where zero = 'Map'.newMap
182 compose :: Substitution Substitution -> Substitution
183 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
184 //Note: just like function compositon compose does snd first
186 occurs :: TVar a -> Bool | Typeable a
187 occurs tvar a = elem tvar (ftv a)
189 unify :: Type Type -> Either SemError Substitution
190 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
191 | occurs tv t1 = Left $ InfiniteTypeError zero t1
192 | otherwise = Right $ 'Map'.singleton tv t1
193 unify t1=:(IdType tv) t2 = unify t2 t1
194 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
195 unify ta2 tb2 >>= \s2->
196 Right $ compose s1 s2
197 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
198 unify ta2 tb2 >>= \s2->
199 Right $ compose s1 s2
200 unify (ListType t1) (ListType t2) = unify t1 t2
201 unify (FuncType t1) (FuncType t2) = unify t1 t2
202 unify t1 t2 | t1 == t2 = Right zero
203 | otherwise = Left $ UnifyError zero t1 t2
205 //// ------------------------
206 //// Algorithm M, Inference and Solving
207 //// ------------------------
208 gamma :: Typing Gamma
210 putGamma :: Gamma -> Typing ()
211 putGamma g = modify (appFst $ const g) >>| pure ()
212 changeGamma :: (Gamma -> Gamma) -> Typing Gamma
213 changeGamma f = modify (appFst f) >>| gamma
214 withGamma :: (Gamma -> a) -> Typing a
215 withGamma f = f <$> gamma
217 fresh = gets snd >>= \vars->
218 modify (appSnd $ const $ tail vars) >>|
219 pure (IdType (head vars))
221 lift :: (Either SemError a) -> Typing a
222 lift (Left e) = liftT $ Left e
223 lift (Right v) = pure v
225 //instantiate maps a schemes type variables to variables with fresh names
226 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
227 instantiate :: Scheme -> Typing Type
228 instantiate (Forall bound t) =
229 mapM (const fresh) bound >>= \newVars->
230 let s = 'Map'.fromList (zip (bound,newVars)) in
233 //generalize quentifies all free type variables in a type which are not
235 generalize :: Type -> Typing Scheme
236 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
238 lookup :: String -> Typing Type
239 lookup k = gamma >>= \g-> case 'Map'.member k g of
240 False = liftT (Left $ UndeclaredVariableError zero k)
241 True = instantiate $ 'Map'.find k g
243 //The inference class
244 //When tying it all together we will treat the program is a big
245 //let x=e1 in let y=e2 in ....
246 class infer a :: a -> Typing (Substitution, Type, a)
248 ////---- Inference for Expressions ----
250 instance infer Expr where
252 VarExpr _ (VarDef k fs) = lookup k >>= \t ->
253 foldM foldFieldSelectors t fs >>= \finalT ->
254 pure (zero, finalT, e)
257 infer e1 >>= \(s1, t1, e1_) ->
258 infer e2 >>= \(s2, t2, e2_) ->
260 let given = t1 ->> t2 ->> tv in
261 op2Type op >>= \expected ->
262 lift (unify expected given) >>= \s3 ->
263 pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
266 infer e1 >>= \(s1, t1, e1_) ->
268 let given = t1 ->> tv in
269 op1Type op >>= \expected ->
270 lift (unify expected given) >>= \s2 ->
271 pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
273 EmptyListExpr _ = (\tv->(zero,tv,e)) <$> fresh
275 TupleExpr p (e1, e2) =
276 infer e1 >>= \(s1, t1, e1_) ->
277 infer e2 >>= \(s2, t2, e2_) ->
278 pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
280 LambdaExpr _ _ _ = liftT $ Left $ Error "PANIC: lambdas should be Unfolded"
282 FunExpr p f args fs =
283 lookup f >>= \expected ->
284 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
285 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
287 "print" = case head argTs of
288 IntType = pure "1printint"
289 CharType = pure "1printchar"
290 BoolType = pure "1printbool"
291 ListType (CharType) = pure "1printstr"
292 t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
295 fresh >>= \tv->case expected of
296 FuncType t = pure (s1, t, (FunExpr p newF args fs))
297 _ = (let given = foldr (->>) tv argTs in
298 lift (unify expected given) >>= \s2->
299 let fReturnType = subst s2 tv in
300 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
301 pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
303 IntExpr _ _ = pure $ (zero, IntType, e)
304 BoolExpr _ _ = pure $ (zero, BoolType, e)
305 CharExpr _ _ = pure $ (zero, CharType, e)
307 foldFieldSelectors :: Type FieldSelector -> Typing Type
308 foldFieldSelectors (ListType t) (FieldHd) = pure t
309 foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
310 foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
311 foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
312 foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
314 op2Type :: Op2 -> Typing Type
316 | elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
317 = pure (IntType ->> IntType ->> IntType)
318 | elem op [BiEquals, BiUnEqual]
319 = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
320 | elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
321 = pure (IntType ->> IntType ->> BoolType)
322 | elem op [BiAnd, BiOr]
323 = pure (BoolType ->> BoolType ->> BoolType)
325 = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
327 op1Type :: Op1 -> Typing Type
328 op1Type UnNegation = pure $ (BoolType ->> BoolType)
329 op1Type UnMinus = pure $ (IntType ->> IntType)
331 ////----- Inference for Statements -----
332 applySubst :: Substitution -> Typing Gamma
333 applySubst s = changeGamma (subst s)
335 instance infer Stmt where
338 infer e >>= \(s1, et, e_)->
339 lift (unify et BoolType) >>= \s2 ->
340 applySubst (compose s2 s1) >>|
341 infer th >>= \(s3, tht, th_)->
343 infer el >>= \(s4, elt, el_)->
345 lift (unify tht elt) >>= \s5->
346 let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
347 pure (sub, subst s5 tht, IfStmt e_ th_ el_)
350 infer e >>= \(s1, et, e_)->
351 lift (unify et BoolType) >>= \s2 ->
352 applySubst (compose s2 s1) >>|
353 infer wh >>= \(s3, wht, wh_)->
354 pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
356 AssStmt vd=:(VarDef k fs) e =
357 lookup k >>= \expected ->
358 infer e >>= \(s1, given, e_)->
359 foldM reverseFs given (reverse fs) >>= \varType->
360 lift (unify expected varType) >>= \s2->
361 let s = compose s2 s1 in
363 changeGamma (extend k (Forall [] (subst s varType))) >>|
364 pure (s, VoidType, AssStmt vd e_)
367 lookup f >>= \expected ->
368 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
369 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
371 let given = foldr (->>) tv argTs in
372 lift (unify expected given) >>= \s2->
373 let fReturnType = subst s2 tv in
374 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
376 "print" = case head argTs of
377 IntType = pure "1printint"
378 CharType = pure "1printchar"
379 BoolType = pure "1printbool"
380 ListType (CharType) = pure "1printstr"
381 t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
382 _ = pure f) >>= \newF->
383 pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
385 ReturnStmt Nothing = pure (zero, VoidType, s)
386 ReturnStmt (Just e) = infer e >>= \(sub, t, e_)-> pure (sub, t, ReturnStmt (Just e_))
388 reverseFs :: Type FieldSelector -> Typing Type
389 reverseFs t FieldHd = pure $ ListType t
390 reverseFs t FieldTl = pure $ ListType t
391 reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
392 reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
394 //The type of a list of statements is either an encountered
395 //return, or VoidType
396 instance infer [a] | infer a where
397 infer [] = pure (zero, VoidType, [])
399 infer stmt >>= \(s1, t1, s_) ->
401 infer ss >>= \(s2, t2, ss_) ->
404 VoidType = pure (compose s2 s1, t2, [s_:ss_])
406 VoidType = pure (compose s2 s1, t1, [s_:ss_])
407 _ = lift (unify t1 t2) >>= \s3 ->
408 pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
410 //the type class inferes the type of an AST element (VarDecl or FunDecl)
411 //and adds it to the AST element
412 class type a :: a -> Typing (Substitution, a)
414 instance type VarDecl where
415 type (VarDecl p expected k e) =
416 infer e >>= \(s1, given, e_) ->
420 Just expected_ = lift (unify expected_ given)
423 let vtype = subst (compose s2 s1) given in
424 generalize vtype >>= \t ->
425 changeGamma (extend k t) >>|
426 pure (compose s2 s1, VarDecl p (Just vtype) k e_)
428 instance type FunDecl where
429 type fd=:(FunDecl p f args expected vds stmts) =
430 //if (f=="main") (abort (toString fd)) (pure ()) >>|
431 gamma >>= \outerScope-> //functions are infered in their own scopde
433 mapM introduce args >>= \argTs->
434 type vds >>= \(s1, tVds)->
436 infer stmts >>= \(s2, result, stmts_)->
438 let argTs_ = map (subst $ compose s2 s1) argTs in
439 let given = foldr (->>) result argTs_ in
442 Just (FuncType expected_) = lift (unify expected_ given)
443 Just expected_ = lift (unify expected_ given)
445 let ftype = subst (compose s3 $ compose s2 s1) given in
448 _ = pure $ FuncType ftype
450 generalize ftype_ >>= \t->
451 putGamma outerScope >>|
452 changeGamma (extend f t) >>|
453 pure (compose s3 $ compose s2 s1, FunDecl p f args (Just ftype_) tVds stmts_)
455 instance type [a] | type a where
456 type [] = pure (zero, [])
458 type v >>= \(s1, v_)->
460 type vs >>= \(s2, vs_)->
461 applySubst (compose s2 s1) >>|
462 pure (compose s2 s1, [v_:vs_])
464 introduce :: String -> Typing Type
467 changeGamma (extend k (Forall [] tv)) >>|
470 instance toString Scheme where
471 toString (Forall x t) =
472 concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
474 instance toString Gamma where
476 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
478 instance toString Substitution where
480 concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
482 instance toString SemError where
483 toString (SanityError p e) = concat [toString p,
484 "SemError: SanityError: ", e]
485 toString (ParseError p s) = concat [toString p,
487 toString (UnifyError p t1 t2) = concat [toString p,
488 "Can not unify types, expected|given:\n", toString t1,
490 toString (InfiniteTypeError p t) = concat [toString p,
491 "Infinite type: ", toString t]
492 toString (FieldSelectorError p t fs) = concat [toString p,
493 "Can not run fieldselector '", toString fs, "' on type: ",
495 toString (OperatorError p op t) = concat [toString p,
496 "Operator error, operator '", toString op, "' can not be",
497 "used on type: ", toString t]
498 toString (UndeclaredVariableError p k) = concat [toString p,
499 "Undeclared identifier: ", k]
500 toString (ArgumentMisMatchError p str) = concat [toString p,
501 "Argument mismatch: ", str]
502 toString (Error e) = concat ["Unknown error during semantical",
505 instance toString (Maybe a) | toString a where
506 toString Nothing = "Nothing"
507 toString (Just e) = concat ["Just ", toString e]
509 instance MonadTrans (StateT (Gamma, [TVar])) where
510 liftT m = StateT \s-> m >>= \a-> return (a, s)
512 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
513 Mapmap _ 'Map'.Tip = 'Map'.Tip
514 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)