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
29 :: Scheme = Forall [TVar] Type
30 :: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
31 :: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
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 defaultGamma :: Gamma //includes all default functions
52 defaultGamma = extend "print" (Forall ["a"] ((IdType "a") ->> VoidType))
53 $ extend "isEmpty" (Forall ["a"] ((ListType (IdType "a")) ->> BoolType))
54 $ extend "read" (Forall [] (FuncType CharType))
55 $ extend "1printchar" (Forall [] (CharType ->> VoidType))
56 $ extend "1printint" (Forall [] (IntType ->> VoidType))
57 $ extend "1printbool" (Forall [] (BoolType ->> VoidType))
60 sem :: AST -> Either [SemError] AST
61 sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
62 >>| foldM (const isNiceMain) () fd
64 >>| evalStateT (type fd) (defaultGamma, variableStream) of
66 Right (_,fds) = Right (AST fds)
68 hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
69 hasNoDups fds (FunDecl p n _ _ _ _)
70 # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
71 = case catMaybes mbs of
72 [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN"
74 [_:x] = Left $ SanityError p (concat
75 [n, " multiply defined at ", toString p])
77 hasMain :: [FunDecl] -> Either SemError ()
78 hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure ()
79 hasMain [_:fd] = hasMain fd
80 hasMain [] = Left $ SanityError zero "no main function defined"
82 isNiceMain :: FunDecl -> Either SemError ()
83 isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of
84 ([_:_], _) = Left $ SanityError p "main must have arity 0"
87 Just VoidType = pure ()
88 _ = Left $ SanityError p "main has to return Void")
89 isNiceMain _ = pure ()
91 class Typeable a where
93 subst :: Substitution a -> a
95 instance Typeable Scheme where
96 ftv (Forall bound t) = difference (ftv t) bound
97 subst s (Forall bound t) = Forall bound $ subst s_ t
98 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
100 instance Typeable [a] | Typeable a where
101 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
102 subst s ts = map (\t->subst s t) ts
104 instance Typeable Type where
105 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
106 ftv (ListType t) = ftv t
107 ftv (IdType tvar) = [tvar]
108 ftv (FuncType t) = ftv t
109 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
111 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
112 subst s (ListType t1) = ListType (subst s t1)
113 subst s (FuncType t) = FuncType (subst s t)
114 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
115 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
118 instance Typeable Gamma where
119 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
120 subst s gamma = Mapmap (subst s) gamma
122 extend :: String Scheme Gamma -> Gamma
123 extend k t g = 'Map'.put k t g
125 //// ------------------------
126 //// algorithm U, Unification
127 //// ------------------------
128 instance zero Substitution where zero = 'Map'.newMap
130 compose :: Substitution Substitution -> Substitution
131 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
132 //Note: just like function compositon compose does snd first
134 occurs :: TVar a -> Bool | Typeable a
135 occurs tvar a = elem tvar (ftv a)
137 unify :: Type Type -> Either SemError Substitution
138 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
139 | occurs tv t1 = Left $ InfiniteTypeError zero t1
140 | otherwise = Right $ 'Map'.singleton tv t1
141 unify t1=:(IdType tv) t2 = unify t2 t1
142 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
143 unify ta2 tb2 >>= \s2->
144 Right $ compose s1 s2
145 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
146 unify ta2 tb2 >>= \s2->
147 Right $ compose s1 s2
148 unify (ListType t1) (ListType t2) = unify t1 t2
149 unify (FuncType t1) (FuncType t2) = unify t1 t2
150 unify t1 t2 | t1 == t2 = Right zero
151 | otherwise = Left $ UnifyError zero t1 t2
153 //// ------------------------
154 //// Algorithm M, Inference and Solving
155 //// ------------------------
156 gamma :: Typing Gamma
158 putGamma :: Gamma -> Typing ()
159 putGamma g = modify (appFst $ const g) >>| pure ()
160 changeGamma :: (Gamma -> Gamma) -> Typing Gamma
161 changeGamma f = modify (appFst f) >>| gamma
162 withGamma :: (Gamma -> a) -> Typing a
163 withGamma f = f <$> gamma
165 fresh = gets snd >>= \vars->
166 modify (appSnd $ const $ tail vars) >>|
167 pure (IdType (head vars))
169 lift :: (Either SemError a) -> Typing a
170 lift (Left e) = liftT $ Left e
171 lift (Right v) = pure v
173 //instantiate maps a schemes type variables to variables with fresh names
174 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
175 instantiate :: Scheme -> Typing Type
176 instantiate (Forall bound t) =
177 mapM (const fresh) bound >>= \newVars->
178 let s = 'Map'.fromList (zip (bound,newVars)) in
181 //generalize quentifies all free type variables in a type which are not
183 generalize :: Type -> Typing Scheme
184 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
186 lookup :: String -> Typing Type
187 lookup k = gamma >>= \g-> case 'Map'.member k g of
188 False = liftT (Left $ UndeclaredVariableError zero k)
189 True = instantiate $ 'Map'.find k g
191 //The inference class
192 //When tying it all together we will treat the program is a big
193 //let x=e1 in let y=e2 in ....
194 class infer a :: a -> Typing (Substitution, Type, a)
196 ////---- Inference for Expressions ----
198 instance infer Expr where
200 VarExpr _ (VarDef k fs) = lookup k >>= \t ->
201 foldM foldFieldSelectors t fs >>= \finalT ->
202 pure (zero, finalT, e)
205 infer e1 >>= \(s1, t1, e1_) ->
206 infer e2 >>= \(s2, t2, e2_) ->
208 let given = t1 ->> t2 ->> tv in
209 op2Type op >>= \expected ->
210 lift (unify expected given) >>= \s3 ->
211 pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
214 infer e1 >>= \(s1, t1, e1_) ->
216 let given = t1 ->> tv in
217 op1Type op >>= \expected ->
218 lift (unify expected given) >>= \s2 ->
219 pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
221 EmptyListExpr _ = (\tv->(zero,tv,e)) <$> fresh
223 TupleExpr p (e1, e2) =
224 infer e1 >>= \(s1, t1, e1_) ->
225 infer e2 >>= \(s2, t2, e2_) ->
226 pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
228 FunExpr p f args fs = //todo: fix print
229 lookup f >>= \expected ->
230 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
231 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
232 fresh >>= \tv->case expected of
233 FuncType t = pure (s1, t, e)
234 _ = (let given = foldr (->>) tv argTs in
235 lift (unify expected given) >>= \s2->
236 let fReturnType = subst s2 tv in
237 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
239 "print" = case head argTs of
240 IntType = pure "1printint"
241 CharType = pure "1printchar"
242 BoolType = pure "1printbool"
243 ListType (CharType) = pure "1printstr"
244 t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
245 _ = pure f) >>= \newF->
246 pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
248 IntExpr _ _ = pure $ (zero, IntType, e)
249 BoolExpr _ _ = pure $ (zero, BoolType, e)
250 CharExpr _ _ = pure $ (zero, CharType, e)
252 foldFieldSelectors :: Type FieldSelector -> Typing Type
253 foldFieldSelectors (ListType t) (FieldHd) = pure t
254 foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
255 foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
256 foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
257 foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
259 op2Type :: Op2 -> Typing Type
261 | elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
262 = pure (IntType ->> IntType ->> IntType)
263 | elem op [BiEquals, BiUnEqual]
264 = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
265 | elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
266 = pure (IntType ->> IntType ->> BoolType)
267 | elem op [BiAnd, BiOr]
268 = pure (BoolType ->> BoolType ->> BoolType)
270 = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
272 op1Type :: Op1 -> Typing Type
273 op1Type UnNegation = pure $ (BoolType ->> BoolType)
274 op1Type UnMinus = pure $ (IntType ->> IntType)
276 ////----- Inference for Statements -----
277 applySubst :: Substitution -> Typing Gamma
278 applySubst s = changeGamma (subst s)
280 instance infer Stmt where
283 infer e >>= \(s1, et, e_)->
284 lift (unify et BoolType) >>= \s2 ->
285 applySubst (compose s2 s1) >>|
286 infer th >>= \(s3, tht, th_)->
288 infer el >>= \(s4, elt, el_)->
290 lift (unify tht elt) >>= \s5->
291 let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
292 pure (sub, subst s5 tht, IfStmt e_ th_ el_)
295 infer e >>= \(s1, et, e_)->
296 lift (unify et BoolType) >>= \s2 ->
297 applySubst (compose s2 s1) >>|
298 infer wh >>= \(s3, wht, wh_)->
299 pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
301 AssStmt vd=:(VarDef k fs) e =
302 lookup k >>= \expected ->
303 infer e >>= \(s1, given, e_)->
304 foldM reverseFs given (reverse fs) >>= \varType->
305 lift (unify expected varType) >>= \s2->
306 let s = compose s2 s1 in
308 changeGamma (extend k (Forall [] (subst s varType))) >>|
309 pure (s, VoidType, AssStmt vd e_)
312 lookup f >>= \expected ->
313 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
314 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
316 let given = foldr (->>) tv argTs in
317 lift (unify expected given) >>= \s2->
318 let fReturnType = subst s2 tv in
319 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
321 "print" = case head argTs of
322 IntType = pure "1printint"
323 CharType = pure "1printchar"
324 BoolType = pure "1printbool"
325 ListType (CharType) = pure "1printstr"
326 t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
327 _ = pure f) >>= \newF->
328 pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
330 ReturnStmt Nothing = pure (zero, VoidType, s)
331 ReturnStmt (Just e) = infer e >>= \(sub, t, _)-> pure (sub, t, s)
333 reverseFs :: Type FieldSelector -> Typing Type
334 reverseFs t FieldHd = pure $ ListType t
335 reverseFs t FieldTl = pure $ ListType t
336 reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
337 reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
339 //The type of a list of statements is either an encountered
340 //return, or VoidType
341 instance infer [a] | infer a where
342 infer [] = pure (zero, VoidType, [])
344 infer stmt >>= \(s1, t1, s_) ->
346 infer ss >>= \(s2, t2, ss_) ->
349 VoidType = pure (compose s2 s1, t2, [s_:ss_])
351 VoidType = pure (compose s2 s1, t1, [s_:ss_])
352 _ = lift (unify t1 t2) >>= \s3 ->
353 pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
355 //the type class inferes the type of an AST element (VarDecl or FunDecl)
356 //and adds it to the AST element
357 class type a :: a -> Typing (Substitution, a)
359 instance type VarDecl where
360 type (VarDecl p expected k e) =
361 infer e >>= \(s1, given, e_) ->
365 Just expected_ = lift (unify expected_ given)
368 let vtype = subst (compose s2 s1) given in
369 generalize vtype >>= \t ->
370 changeGamma (extend k t) >>|
371 pure (compose s2 s1, VarDecl p (Just vtype) k e_)
373 instance type FunDecl where
374 type (FunDecl p f args expected vds stmts) =
375 gamma >>= \outerScope-> //functions are infered in their own scopde
377 mapM introduce args >>= \argTs->
378 type vds >>= \(s1, tVds)->
380 infer stmts >>= \(s2, result, stmts_)->
382 let argTs_ = map (subst $ compose s2 s1) argTs in
383 let given = foldr (->>) result argTs_ in
386 Just expected_ = lift (unify expected_ given))
388 let ftype = subst (compose s3 $ compose s2 s1) given in
389 generalize ftype >>= \t->
390 putGamma outerScope >>|
391 changeGamma (extend f t) >>|
392 pure (compose s3 $ compose s2 s1, FunDecl p f args (Just ftype) tVds stmts_)
394 instance type [a] | type a where
395 type [] = pure (zero, [])
397 type v >>= \(s1, v_)->
399 type vs >>= \(s2, vs_)->
400 applySubst (compose s2 s1) >>|
401 pure (compose s2 s1, [v_:vs_])
403 introduce :: String -> Typing Type
406 changeGamma (extend k (Forall [] tv)) >>|
409 instance toString Scheme where
410 toString (Forall x t) =
411 concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
413 instance toString Gamma where
415 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
417 instance toString Substitution where
419 concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
421 instance toString SemError where
422 toString (SanityError p e) = concat [toString p,
423 "SemError: SanityError: ", e]
424 toString (ParseError p s) = concat [toString p,
426 toString (UnifyError p t1 t2) = concat [toString p,
427 "Can not unify types, expected|given:\n", toString t1,
429 toString (InfiniteTypeError p t) = concat [toString p,
430 "Infinite type: ", toString t]
431 toString (FieldSelectorError p t fs) = concat [toString p,
432 "Can not run fieldselector '", toString fs, "' on type: ",
434 toString (OperatorError p op t) = concat [toString p,
435 "Operator error, operator '", toString op, "' can not be",
436 "used on type: ", toString t]
437 toString (UndeclaredVariableError p k) = concat [toString p,
438 "Undeclared identifier: ", k]
439 toString (ArgumentMisMatchError p str) = concat [toString p,
440 "Argument mismatch: ", str]
441 toString (Error e) = concat ["Unknown error during semantical",
444 instance toString (Maybe a) | toString a where
445 toString Nothing = "Nothing"
446 toString (Just e) = concat ["Just ", toString e]
448 instance MonadTrans (StateT (Gamma, [TVar])) where
449 liftT m = StateT \s-> m >>= \a-> return (a, s)
451 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
452 Mapmap _ 'Map'.Tip = 'Map'.Tip
453 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)