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 (type fd) (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 ()
92 unfoldLambda :: [FunDecl] -> Typing [FunDecl]
93 unfoldLambda [fd:fds] = unf_ fd >>= \fds1->
94 unfoldLambda fds >>= \fds2->
97 unf_ :: FunDecl -> Typing [FunDecl]
98 unf_ fd=:(FunDecl _ _ _ _ vds stmts) =
99 flatten <$> mapM unfv_ vds >>= \fds1->
100 flatten <$> mapM unfs_ stmts >>= \fds2->
101 pure $ [fd:fds1] ++ fds2
102 unfv_ :: VarDecl -> Typing [FunDecl]
103 unfv_ (VarDecl _ _ _ e) = pure []
104 unfs_ :: Stmt -> Typing [FunDecl]
107 class Typeable a where
109 subst :: Substitution a -> a
111 instance Typeable Scheme where
112 ftv (Forall bound t) = difference (ftv t) bound
113 subst s (Forall bound t) = Forall bound $ subst s_ t
114 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
116 instance Typeable [a] | Typeable a where
117 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
118 subst s ts = map (\t->subst s t) ts
120 instance Typeable Type where
121 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
122 ftv (ListType t) = ftv t
123 ftv (IdType tvar) = [tvar]
124 ftv (FuncType t) = ftv t
125 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
127 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
128 subst s (ListType t1) = ListType (subst s t1)
129 subst s (FuncType t) = FuncType (subst s t)
130 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
131 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
134 instance Typeable Gamma where
135 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
136 subst s gamma = Mapmap (subst s) gamma
138 extend :: String Scheme Gamma -> Gamma
139 extend k t g = 'Map'.put k t g
141 //// ------------------------
142 //// algorithm U, Unification
143 //// ------------------------
144 instance zero Substitution where zero = 'Map'.newMap
146 compose :: Substitution Substitution -> Substitution
147 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
148 //Note: just like function compositon compose does snd first
150 occurs :: TVar a -> Bool | Typeable a
151 occurs tvar a = elem tvar (ftv a)
153 unify :: Type Type -> Either SemError Substitution
154 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
155 | occurs tv t1 = Left $ InfiniteTypeError zero t1
156 | otherwise = Right $ 'Map'.singleton tv t1
157 unify t1=:(IdType tv) t2 = unify t2 t1
158 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
159 unify ta2 tb2 >>= \s2->
160 Right $ compose s1 s2
161 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
162 unify ta2 tb2 >>= \s2->
163 Right $ compose s1 s2
164 unify (ListType t1) (ListType t2) = unify t1 t2
165 unify (FuncType t1) (FuncType t2) = unify t1 t2
166 unify t1 t2 | t1 == t2 = Right zero
167 | otherwise = Left $ UnifyError zero t1 t2
169 //// ------------------------
170 //// Algorithm M, Inference and Solving
171 //// ------------------------
172 gamma :: Typing Gamma
174 putGamma :: Gamma -> Typing ()
175 putGamma g = modify (appFst $ const g) >>| pure ()
176 changeGamma :: (Gamma -> Gamma) -> Typing Gamma
177 changeGamma f = modify (appFst f) >>| gamma
178 withGamma :: (Gamma -> a) -> Typing a
179 withGamma f = f <$> gamma
181 fresh = gets snd >>= \vars->
182 modify (appSnd $ const $ tail vars) >>|
183 pure (IdType (head vars))
185 lift :: (Either SemError a) -> Typing a
186 lift (Left e) = liftT $ Left e
187 lift (Right v) = pure v
189 //instantiate maps a schemes type variables to variables with fresh names
190 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
191 instantiate :: Scheme -> Typing Type
192 instantiate (Forall bound t) =
193 mapM (const fresh) bound >>= \newVars->
194 let s = 'Map'.fromList (zip (bound,newVars)) in
197 //generalize quentifies all free type variables in a type which are not
199 generalize :: Type -> Typing Scheme
200 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
202 lookup :: String -> Typing Type
203 lookup k = gamma >>= \g-> case 'Map'.member k g of
204 False = liftT (Left $ UndeclaredVariableError zero k)
205 True = instantiate $ 'Map'.find k g
207 //The inference class
208 //When tying it all together we will treat the program is a big
209 //let x=e1 in let y=e2 in ....
210 class infer a :: a -> Typing (Substitution, Type, a)
212 ////---- Inference for Expressions ----
214 instance infer Expr where
216 VarExpr _ (VarDef k fs) = lookup k >>= \t ->
217 foldM foldFieldSelectors t fs >>= \finalT ->
218 pure (zero, finalT, e)
221 infer e1 >>= \(s1, t1, e1_) ->
222 infer e2 >>= \(s2, t2, e2_) ->
224 let given = t1 ->> t2 ->> tv in
225 op2Type op >>= \expected ->
226 lift (unify expected given) >>= \s3 ->
227 pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
230 infer e1 >>= \(s1, t1, e1_) ->
232 let given = t1 ->> tv in
233 op1Type op >>= \expected ->
234 lift (unify expected given) >>= \s2 ->
235 pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
237 EmptyListExpr _ = (\tv->(zero,tv,e)) <$> fresh
239 TupleExpr p (e1, e2) =
240 infer e1 >>= \(s1, t1, e1_) ->
241 infer e2 >>= \(s2, t2, e2_) ->
242 pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
244 LambdaExpr _ _ _ = liftT $ Left $ Error "PANIC: lambdas should be Unfolded"
246 FunExpr p f args fs =
247 lookup f >>= \expected ->
248 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
249 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
250 fresh >>= \tv->case expected of
251 FuncType t = pure (s1, t, e)
252 _ = (let given = foldr (->>) tv argTs in
253 lift (unify expected given) >>= \s2->
254 let fReturnType = subst s2 tv in
255 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
257 "print" = case head argTs of
258 IntType = pure "1printint"
259 CharType = pure "1printchar"
260 BoolType = pure "1printbool"
261 ListType (CharType) = pure "1printstr"
262 t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
263 _ = pure f) >>= \newF->
264 pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
266 IntExpr _ _ = pure $ (zero, IntType, e)
267 BoolExpr _ _ = pure $ (zero, BoolType, e)
268 CharExpr _ _ = pure $ (zero, CharType, e)
270 foldFieldSelectors :: Type FieldSelector -> Typing Type
271 foldFieldSelectors (ListType t) (FieldHd) = pure t
272 foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
273 foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
274 foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
275 foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
277 op2Type :: Op2 -> Typing Type
279 | elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
280 = pure (IntType ->> IntType ->> IntType)
281 | elem op [BiEquals, BiUnEqual]
282 = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
283 | elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
284 = pure (IntType ->> IntType ->> BoolType)
285 | elem op [BiAnd, BiOr]
286 = pure (BoolType ->> BoolType ->> BoolType)
288 = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
290 op1Type :: Op1 -> Typing Type
291 op1Type UnNegation = pure $ (BoolType ->> BoolType)
292 op1Type UnMinus = pure $ (IntType ->> IntType)
294 ////----- Inference for Statements -----
295 applySubst :: Substitution -> Typing Gamma
296 applySubst s = changeGamma (subst s)
298 instance infer Stmt where
301 infer e >>= \(s1, et, e_)->
302 lift (unify et BoolType) >>= \s2 ->
303 applySubst (compose s2 s1) >>|
304 infer th >>= \(s3, tht, th_)->
306 infer el >>= \(s4, elt, el_)->
308 lift (unify tht elt) >>= \s5->
309 let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
310 pure (sub, subst s5 tht, IfStmt e_ th_ el_)
313 infer e >>= \(s1, et, e_)->
314 lift (unify et BoolType) >>= \s2 ->
315 applySubst (compose s2 s1) >>|
316 infer wh >>= \(s3, wht, wh_)->
317 pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
319 AssStmt vd=:(VarDef k fs) e =
320 lookup k >>= \expected ->
321 infer e >>= \(s1, given, e_)->
322 foldM reverseFs given (reverse fs) >>= \varType->
323 lift (unify expected varType) >>= \s2->
324 let s = compose s2 s1 in
326 changeGamma (extend k (Forall [] (subst s varType))) >>|
327 pure (s, VoidType, AssStmt vd e_)
330 lookup f >>= \expected ->
331 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
332 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
334 let given = foldr (->>) tv argTs in
335 lift (unify expected given) >>= \s2->
336 let fReturnType = subst s2 tv in
337 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
339 "print" = case head argTs of
340 IntType = pure "1printint"
341 CharType = pure "1printchar"
342 BoolType = pure "1printbool"
343 ListType (CharType) = pure "1printstr"
344 t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
345 _ = pure f) >>= \newF->
346 pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
348 ReturnStmt Nothing = pure (zero, VoidType, s)
349 ReturnStmt (Just e) = infer e >>= \(sub, t, _)-> pure (sub, t, s)
351 reverseFs :: Type FieldSelector -> Typing Type
352 reverseFs t FieldHd = pure $ ListType t
353 reverseFs t FieldTl = pure $ ListType t
354 reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
355 reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
357 //The type of a list of statements is either an encountered
358 //return, or VoidType
359 instance infer [a] | infer a where
360 infer [] = pure (zero, VoidType, [])
362 infer stmt >>= \(s1, t1, s_) ->
364 infer ss >>= \(s2, t2, ss_) ->
367 VoidType = pure (compose s2 s1, t2, [s_:ss_])
369 VoidType = pure (compose s2 s1, t1, [s_:ss_])
370 _ = lift (unify t1 t2) >>= \s3 ->
371 pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
373 //the type class inferes the type of an AST element (VarDecl or FunDecl)
374 //and adds it to the AST element
375 class type a :: a -> Typing (Substitution, a)
377 instance type VarDecl where
378 type (VarDecl p expected k e) =
379 infer e >>= \(s1, given, e_) ->
383 Just expected_ = lift (unify expected_ given)
386 let vtype = subst (compose s2 s1) given in
387 generalize vtype >>= \t ->
388 changeGamma (extend k t) >>|
389 pure (compose s2 s1, VarDecl p (Just vtype) k e_)
391 instance type FunDecl where
392 type (FunDecl p f args expected vds stmts) =
393 gamma >>= \outerScope-> //functions are infered in their own scopde
395 mapM introduce args >>= \argTs->
396 type vds >>= \(s1, tVds)->
398 infer stmts >>= \(s2, result, stmts_)->
400 let argTs_ = map (subst $ compose s2 s1) argTs in
401 let given = foldr (->>) result argTs_ in
404 Just (FuncType expected_) = lift (unify expected_ given)
405 Just expected_ = lift (unify expected_ given)
407 let ftype = subst (compose s3 $ compose s2 s1) given in
410 _ = pure $ FuncType ftype
412 generalize ftype_ >>= \t->
413 putGamma outerScope >>|
414 changeGamma (extend f t) >>|
415 pure (compose s3 $ compose s2 s1, FunDecl p f args (Just ftype_) tVds stmts_)
417 instance type [a] | type a where
418 type [] = pure (zero, [])
420 type v >>= \(s1, v_)->
422 type vs >>= \(s2, vs_)->
423 applySubst (compose s2 s1) >>|
424 pure (compose s2 s1, [v_:vs_])
426 introduce :: String -> Typing Type
429 changeGamma (extend k (Forall [] tv)) >>|
432 instance toString Scheme where
433 toString (Forall x t) =
434 concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
436 instance toString Gamma where
438 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
440 instance toString Substitution where
442 concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
444 instance toString SemError where
445 toString (SanityError p e) = concat [toString p,
446 "SemError: SanityError: ", e]
447 toString (ParseError p s) = concat [toString p,
449 toString (UnifyError p t1 t2) = concat [toString p,
450 "Can not unify types, expected|given:\n", toString t1,
452 toString (InfiniteTypeError p t) = concat [toString p,
453 "Infinite type: ", toString t]
454 toString (FieldSelectorError p t fs) = concat [toString p,
455 "Can not run fieldselector '", toString fs, "' on type: ",
457 toString (OperatorError p op t) = concat [toString p,
458 "Operator error, operator '", toString op, "' can not be",
459 "used on type: ", toString t]
460 toString (UndeclaredVariableError p k) = concat [toString p,
461 "Undeclared identifier: ", k]
462 toString (ArgumentMisMatchError p str) = concat [toString p,
463 "Argument mismatch: ", str]
464 toString (Error e) = concat ["Unknown error during semantical",
467 instance toString (Maybe a) | toString a where
468 toString Nothing = "Nothing"
469 toString (Just e) = concat ["Just ", toString e]
471 instance MonadTrans (StateT (Gamma, [TVar])) where
472 liftT m = StateT \s-> m >>= \a-> return (a, s)
474 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
475 Mapmap _ 'Map'.Tip = 'Map'.Tip
476 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)