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))
57 sem :: AST -> Either [SemError] AST
58 sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
59 >>| foldM (const isNiceMain) () fd
61 >>| evalStateT (type fd) (defaultGamma, variableStream) of
63 Right (_,fds) = Right (AST fds)
65 hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
66 hasNoDups fds (FunDecl p n _ _ _ _)
67 # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
68 = case catMaybes mbs of
69 [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN"
71 [_:x] = Left $ SanityError p (concat
72 [n, " multiply defined at ", toString p])
74 hasMain :: [FunDecl] -> Either SemError ()
75 hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure ()
76 hasMain [_:fd] = hasMain fd
77 hasMain [] = Left $ SanityError zero "no main function defined"
79 isNiceMain :: FunDecl -> Either SemError ()
80 isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of
81 ([_:_], _) = Left $ SanityError p "main must have arity 0"
84 Just VoidType = pure ()
85 _ = Left $ SanityError p "main has to return Void")
86 isNiceMain _ = pure ()
88 class Typeable a where
90 subst :: Substitution a -> a
92 instance Typeable Scheme where
93 ftv (Forall bound t) = difference (ftv t) bound
94 subst s (Forall bound t) = Forall bound $ subst s_ t
95 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
97 instance Typeable [a] | Typeable a where
98 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
99 subst s ts = map (\t->subst s t) ts
101 instance Typeable Type where
102 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
103 ftv (ListType t) = ftv t
104 ftv (IdType tvar) = [tvar]
105 ftv (FuncType t) = ftv t
106 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
108 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
109 subst s (ListType t1) = ListType (subst s t1)
110 subst s (FuncType t) = FuncType (subst s t)
111 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
112 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
115 instance Typeable Gamma where
116 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
117 subst s gamma = Mapmap (subst s) gamma
119 extend :: String Scheme Gamma -> Gamma
120 extend k t g = 'Map'.put k t g
122 //// ------------------------
123 //// algorithm U, Unification
124 //// ------------------------
125 instance zero Substitution where zero = 'Map'.newMap
127 compose :: Substitution Substitution -> Substitution
128 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
129 //Note: just like function compositon compose does snd first
131 occurs :: TVar a -> Bool | Typeable a
132 occurs tvar a = elem tvar (ftv a)
134 unify :: Type Type -> Either SemError Substitution
135 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
136 | occurs tv t1 = Left $ InfiniteTypeError zero t1
137 | otherwise = Right $ 'Map'.singleton tv t1
138 unify t1=:(IdType tv) t2 = unify t2 t1
139 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
140 unify ta2 tb2 >>= \s2->
141 Right $ compose s1 s2
142 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
143 unify ta2 tb2 >>= \s2->
144 Right $ compose s1 s2
145 unify (ListType t1) (ListType t2) = unify t1 t2
146 unify (FuncType t1) (FuncType t2) = unify t1 t2
147 unify t1 t2 | t1 == t2 = Right zero
148 | otherwise = Left $ UnifyError zero t1 t2
150 //// ------------------------
151 //// Algorithm M, Inference and Solving
152 //// ------------------------
153 gamma :: Typing Gamma
155 putGamma :: Gamma -> Typing ()
156 putGamma g = modify (appFst $ const g) >>| pure ()
157 changeGamma :: (Gamma -> Gamma) -> Typing Gamma
158 changeGamma f = modify (appFst f) >>| gamma
159 withGamma :: (Gamma -> a) -> Typing a
160 withGamma f = f <$> gamma
162 fresh = gets snd >>= \vars->
163 modify (appSnd $ const $ tail vars) >>|
164 pure (IdType (head vars))
166 lift :: (Either SemError a) -> Typing a
167 lift (Left e) = liftT $ Left e
168 lift (Right v) = pure v
170 //instantiate maps a schemes type variables to variables with fresh names
171 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
172 instantiate :: Scheme -> Typing Type
173 instantiate (Forall bound t) =
174 mapM (const fresh) bound >>= \newVars->
175 let s = 'Map'.fromList (zip (bound,newVars)) in
178 //generalize quentifies all free type variables in a type which are not
180 generalize :: Type -> Typing Scheme
181 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
183 lookup :: String -> Typing Type
184 lookup k = gamma >>= \g-> case 'Map'.member k g of
185 False = liftT (Left $ UndeclaredVariableError zero k)
186 True = instantiate $ 'Map'.find k g
188 //The inference class
189 //When tying it all together we will treat the program is a big
190 //let x=e1 in let y=e2 in ....
191 class infer a :: a -> Typing (Substitution, Type, a)
193 ////---- Inference for Expressions ----
195 instance infer Expr where
197 VarExpr _ (VarDef k fs) = lookup k >>= \t ->
198 foldM foldFieldSelectors t fs >>= \finalT ->
199 pure (zero, finalT, e)
202 infer e1 >>= \(s1, t1, e1_) ->
203 infer e2 >>= \(s2, t2, e2_) ->
205 let given = t1 ->> t2 ->> tv in
206 op2Type op >>= \expected ->
207 lift (unify expected given) >>= \s3 ->
208 pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
211 infer e1 >>= \(s1, t1, e1_) ->
213 let given = t1 ->> tv in
214 op1Type op >>= \expected ->
215 lift (unify expected given) >>= \s2 ->
216 pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
218 EmptyListExpr _ = (\tv->(zero,tv,e)) <$> fresh
220 TupleExpr p (e1, e2) =
221 infer e1 >>= \(s1, t1, e1_) ->
222 infer e2 >>= \(s2, t2, e2_) ->
223 pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
225 FunExpr p f args fs = //todo: fix print
226 lookup f >>= \expected ->
227 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
228 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
229 fresh >>= \tv->case expected of
230 FuncType t = pure (s1, t, e)
231 _ = (let given = foldr (->>) tv argTs in
232 lift (unify expected given) >>= \s2->
233 let fReturnType = subst s2 tv in
234 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
236 "print" = case head argTs of
237 IntType = pure "1printint"
238 CharType = pure "1printchar"
239 BoolType = pure "1printbool"
240 ListType (CharType) = pure "1printstr"
241 t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
242 _ = pure f) >>= \newF->
243 pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
245 IntExpr _ _ = pure $ (zero, IntType, e)
246 BoolExpr _ _ = pure $ (zero, BoolType, e)
247 CharExpr _ _ = pure $ (zero, CharType, e)
249 foldFieldSelectors :: Type FieldSelector -> Typing Type
250 foldFieldSelectors (ListType t) (FieldHd) = pure t
251 foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
252 foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
253 foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
254 foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
256 op2Type :: Op2 -> Typing Type
258 | elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
259 = pure (IntType ->> IntType ->> IntType)
260 | elem op [BiEquals, BiUnEqual]
261 = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
262 | elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
263 = pure (IntType ->> IntType ->> BoolType)
264 | elem op [BiAnd, BiOr]
265 = pure (BoolType ->> BoolType ->> BoolType)
267 = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)
269 op1Type :: Op1 -> Typing Type
270 op1Type UnNegation = pure $ (BoolType ->> BoolType)
271 op1Type UnMinus = pure $ (IntType ->> IntType)
273 ////----- Inference for Statements -----
274 applySubst :: Substitution -> Typing Gamma
275 applySubst s = changeGamma (subst s)
277 instance infer Stmt where
280 infer e >>= \(s1, et, e_)->
281 lift (unify et BoolType) >>= \s2 ->
282 applySubst (compose s2 s1) >>|
283 infer th >>= \(s3, tht, th_)->
285 infer el >>= \(s4, elt, el_)->
287 lift (unify tht elt) >>= \s5->
288 let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
289 pure (sub, subst s5 tht, IfStmt e_ th_ el_)
292 infer e >>= \(s1, et, e_)->
293 lift (unify et BoolType) >>= \s2 ->
294 applySubst (compose s2 s1) >>|
295 infer wh >>= \(s3, wht, wh_)->
296 pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
298 AssStmt vd=:(VarDef k fs) e =
299 lookup k >>= \expected ->
300 infer e >>= \(s1, given, e_)->
301 foldM reverseFs given (reverse fs) >>= \varType->
302 lift (unify expected varType) >>= \s2->
303 let s = compose s2 s1 in
305 changeGamma (extend k (Forall [] (subst s varType))) >>|
306 pure (s, VoidType, AssStmt vd e_)
309 lookup f >>= \expected ->
310 let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
311 foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
313 let given = foldr (->>) tv argTs in
314 lift (unify expected given) >>= \s2->
315 let fReturnType = subst s2 tv in
316 foldM foldFieldSelectors fReturnType fs >>= \returnType ->
318 "print" = case head argTs of
319 IntType = pure "1printint"
320 CharType = pure "1printchar"
321 BoolType = pure "1printbool"
322 ListType (CharType) = pure "1printstr"
323 t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
324 _ = pure f) >>= \newF->
325 pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
327 ReturnStmt Nothing = pure (zero, VoidType, s)
328 ReturnStmt (Just e) = infer e >>= \(sub, t, _)-> pure (sub, t, s)
330 reverseFs :: Type FieldSelector -> Typing Type
331 reverseFs t FieldHd = pure $ ListType t
332 reverseFs t FieldTl = pure $ ListType t
333 reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
334 reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
336 //The type of a list of statements is either an encountered
337 //return, or VoidType
338 instance infer [a] | infer a where
339 infer [] = pure (zero, VoidType, [])
341 infer stmt >>= \(s1, t1, s_) ->
343 infer ss >>= \(s2, t2, ss_) ->
346 VoidType = pure (compose s2 s1, t2, [s_:ss_])
348 VoidType = pure (compose s2 s1, t1, [s_:ss_])
349 _ = lift (unify t1 t2) >>= \s3 ->
350 pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
352 //the type class inferes the type of an AST element (VarDecl or FunDecl)
353 //and adds it to the AST element
354 class type a :: a -> Typing (Substitution, a)
356 instance type VarDecl where
357 type (VarDecl p expected k e) =
358 infer e >>= \(s1, given, e_) ->
362 Just expected_ = lift (unify expected_ given)
365 let vtype = subst (compose s2 s1) given in
366 generalize vtype >>= \t ->
367 changeGamma (extend k t) >>|
368 pure (compose s2 s1, VarDecl p (Just vtype) k e_)
370 instance type FunDecl where
371 type (FunDecl p f args expected vds stmts) =
372 gamma >>= \outerScope-> //functions are infered in their own scopde
374 mapM introduce args >>= \argTs->
375 type vds >>= \(s1, tVds)->
377 infer stmts >>= \(s2, result, stmts_)->
379 let argTs_ = map (subst $ compose s2 s1) argTs in
380 let given = foldr (->>) result argTs_ in
383 Just expected_ = lift (unify expected_ given))
385 let ftype = subst (compose s3 $ compose s2 s1) given in
386 generalize ftype >>= \t->
387 putGamma outerScope >>|
388 changeGamma (extend f t) >>|
389 pure (compose s3 $ compose s2 s1, FunDecl p f args (Just ftype) tVds stmts_)
391 instance type [a] | type a where
392 type [] = pure (zero, [])
394 type v >>= \(s1, v_)->
396 type vs >>= \(s2, vs_)->
397 applySubst (compose s2 s1) >>|
398 pure (compose s2 s1, [v_:vs_])
400 introduce :: String -> Typing Type
403 changeGamma (extend k (Forall [] tv)) >>|
406 instance toString Scheme where
407 toString (Forall x t) =
408 concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
410 instance toString Gamma where
412 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
414 instance toString Substitution where
416 concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
418 instance toString SemError where
419 toString (SanityError p e) = concat [toString p,
420 "SemError: SanityError: ", e]
421 toString (ParseError p s) = concat [toString p,
423 toString (UnifyError p t1 t2) = concat [toString p,
424 "Can not unify types, expected|given:\n", toString t1,
426 toString (InfiniteTypeError p t) = concat [toString p,
427 "Infinite type: ", toString t]
428 toString (FieldSelectorError p t fs) = concat [toString p,
429 "Can not run fieldselector '", toString fs, "' on type: ",
431 toString (OperatorError p op t) = concat [toString p,
432 "Operator error, operator '", toString op, "' can not be",
433 "used on type: ", toString t]
434 toString (UndeclaredVariableError p k) = concat [toString p,
435 "Undeclared identifier: ", k]
436 toString (ArgumentMisMatchError p str) = concat [toString p,
437 "Argument mismatch: ", str]
438 toString (Error e) = concat ["Unknown error during semantical",
441 instance toString (Maybe a) | toString a where
442 toString Nothing = "Nothing"
443 toString (Just e) = concat ["Just ", toString e]
445 instance MonadTrans (StateT (Gamma, [TVar])) where
446 liftT m = StateT \s-> m >>= \a-> return (a, s)
448 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
449 Mapmap _ 'Map'.Tip = 'Map'.Tip
450 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)