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
30 :: Scheme = Forall [TVar] Type
31 :: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
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 sem :: AST -> Either [SemError] Constraints
52 sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
53 >>| foldM (const isNiceMain) () fd
57 //_ = case execRWST (constraints fd) zero variableStream of
59 // Right (a, b) = Right b
61 constraints :: [FunDecl] -> Typing ()
62 constraints _ = pure ()
64 //constraints fds = mapM_ funconstraint fds >>| pure ()
66 funconstraint :: FunDecl -> Typing ()
67 funconstraint fd=:(FunDecl _ ident args mt vardecls stmts) = case mt of
68 Nothing = abort "Cannot infer functions yet"
70 //Just t = inEnv (ident, (Forall [] t)) (
71 // mapM_ vardeclconstraint vardecls >>| pure ())
73 vardeclconstraint :: VarDecl -> Typing ()
74 vardeclconstraint _ = pure ()
76 //vardeclconstraint (VarDecl p mt ident expr) = infer expr
77 //>>= \it->inEnv (ident, (Forall [] it)) (pure ())
79 hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
80 hasNoDups fds (FunDecl p n _ _ _ _)
81 # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
82 = case catMaybes mbs of
83 [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN"
85 [_:x] = Left $ SanityError p (concat
86 [n, " multiply defined at ", toString p])
88 hasMain :: [FunDecl] -> Either SemError ()
89 hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure ()
90 hasMain [_:fd] = hasMain fd
91 hasMain [] = Left $ SanityError zero "no main function defined"
93 isNiceMain :: FunDecl -> Either SemError ()
94 isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of
95 ([_:_], _) = Left $ SanityError p "main must have arity 0"
98 Just VoidType = pure ()
99 _ = Left $ SanityError p "main has to return Void")
100 isNiceMain _ = pure ()
102 instance toString Scheme where
103 toString (Forall x t) =
104 concat ["Forall ": map ((+++) "\n") x] +++ toString t
106 instance toString Gamma where
108 concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
110 instance toString SemError where
111 toString (SanityError p e) = concat [toString p,
112 "SemError: SanityError: ", e]
113 toString se = "SemError: "
115 class Typeable a where
117 subst :: Substitution a -> a
119 instance Typeable Scheme where
120 ftv (Forall bound t) = difference (ftv t) bound
121 subst s (Forall bound t) = Forall bound $ subst s_ t
122 where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s
124 instance Typeable [a] | Typeable a where
125 ftv types = foldr (\t ts-> ftv t ++ ts) [] types
126 subst s ts = map (\t->subst s t) ts
128 instance Typeable Type where
129 ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
130 ftv (ListType t) = ftv t
131 ftv (IdType tvar) = [tvar]
132 ftv (t1 ->> t2) = ftv t1 ++ ftv t2
134 subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2)
135 subst s (ListType t1) = ListType (subst s t1)
136 subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
137 subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
140 instance Typeable Gamma where
141 ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
142 subst s gamma = Mapmap (subst s) gamma
144 //// ------------------------
145 //// algorithm U, Unification
146 //// ------------------------
147 instance zero Substitution where zero = 'Map'.newMap
149 compose :: Substitution Substitution -> Substitution
150 compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
151 //Note: unlike function composition, compose is left biased!
153 occurs :: TVar a -> Bool | Typeable a
154 occurs tvar a = elem tvar (ftv a)
156 unify :: Type Type -> Either SemError Substitution
157 unify t1=:(IdType tv) t2 = unify t2 t1
158 unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
159 | occurs tv t1 = Left $ InfiniteTypeError zero t1
160 | otherwise = Right $ 'Map'.singleton tv t1
161 unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
162 unify tb1 tb2 >>= \s2->
163 Right $ compose s1 s2
164 unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
165 unify ta2 tb2 >>= \s2->
166 Right $ compose s1 s2
167 unify (ListType t1) (ListType t2) = unify t1 t2
168 unify t1 t2 | t1 == t2 = Right zero
169 | otherwise = Left $ UnifyError zero t1 t2
171 //// ------------------------
172 //// Algorithm M, Inference and Solving
173 //// ------------------------
175 :: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
176 gamma :: Typing Gamma
178 putGamma :: Gamma -> Typing ()
179 putGamma g = modify (appFst $ const g) >>| pure ()
180 withGamma :: (Gamma -> Gamma) -> Typing ()
181 withGamma f = modify (appFst f) >>| pure ()
183 fresh = gets snd >>= \vars->
184 modify (appSnd $ const $ tail vars) >>|
185 pure (IdType (head vars))
187 //instantiate maps a schemes type variables to variables with fresh names
188 //and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
189 instantiate :: Scheme -> Typing Type
190 instantiate (Forall bound t) =
191 mapM (const fresh) bound >>= \newVars->
192 let s = 'Map'.fromList (zip (bound,newVars)) in
194 //generalize quentifies all free type variables in a type which are not
196 generalize :: Type -> Typing Scheme
197 generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
203 Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
204 Mapmap _ 'Map'.Tip = 'Map'.Tip
205 Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)
209 //// ------------------------
210 //// First step: Inference
211 //// ------------------------//
213 //unify :: Type Type -> Infer ()
214 //unify t1 t2 = tell [(t1, t2)]//
216 //fresh :: Infer Type
217 //fresh = (gets id) >>= \vars-> (put $ tail vars) >>| (pure $ IdType $ head vars)//
219 //op2Type :: Op2 -> Infer Type
221 //| elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
222 // = pure (IntType ->> IntType ->> IntType)
223 //| elem op [BiEquals, BiUnEqual]
224 // = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
225 //| elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
226 // = pure (IntType ->> IntType ->> BoolType)
227 //| elem op [BiAnd, BiOr]
228 // = pure (BoolType ->> BoolType ->> BoolType)
230 // = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)//
232 //op1Type :: Op1 -> Infer Type
233 //op1Type UnNegation = pure $ (BoolType ->> BoolType)
234 //op1Type UnMinus = pure $ (IntType ->> IntType)//
236 ////instantiate :: Scheme -> Infer Type
237 ////instantiate (Forall as t) = mapM (const fresh) as//
239 //lookupEnv :: String -> Infer Type
240 //lookupEnv ident = asks ('Map'.get ident)
242 // Nothing = liftT $ Left $ UndeclaredVariableError zero ident
243 // Just (Forall as t) = pure t //instantiate ???//
245 //class infer a :: a -> Infer Type
246 //instance infer Expr where
247 // infer (VarExpr _ (VarDef ident fs)) = lookupEnv ident
248 // infer (Op2Expr _ e1 op e2) =
249 // infer e1 >>= \t1 ->
250 // infer e2 >>= \t2 ->
251 // fresh >>= \frsh ->
252 // let given = t1 ->> (t2 ->> frsh) in
253 // op2Type op >>= \expected ->
254 // unify expected given >>|
256 // infer (Op1Expr _ op e) =
257 // infer e >>= \t1 ->
258 // fresh >>= \frsh ->
259 // let given = t1 ->> frsh in
260 // op1Type op >>= \expected ->
261 // unify expected given >>|
263 // infer (IntExpr _ _) = pure IntType
264 // infer (CharExpr _ _) = pure CharType
265 // infer (BoolExpr _ _) = pure BoolType
266 // infer (FunExpr _ f args sels) = //todo, iets met field selectors
267 // lookupEnv f >>= \expected ->
268 // fresh >>= \frsh ->
269 // mapM infer args >>= \argTypes ->
270 // let given = foldr (->>) frsh argTypes in
271 // unify expected given >>|
273 // infer (EmptyListExpr _) = ListType <$> fresh
274 // infer (TupleExpr _ (e1, e2)) =
275 // infer e1 >>= \et1->infer e2 >>= \et2->pure $ TupleType (et1, et2)//
277 ////:: VarDef = VarDef String [FieldSelector]
278 ////:: FieldSelector = FieldHd | FieldTl | FieldFst | FieldSnd
279 ////:: Op1 = UnNegation | UnMinus
280 ////:: Op2 = BiPlus | BiMinus | BiTimes | BiDivide | BiMod | BiEquals | BiLesser |
281 //// BiGreater | BiLesserEq | BiGreaterEq | BiUnEqual | BiAnd | BiOr | BiCons
282 ////:: FunDecl = FunDecl Pos String [String] (Maybe Type) [VarDecl] [Stmt]
283 ////:: FunCall = FunCall String [Expr]
285 //// = IfStmt Expr [Stmt] [Stmt]
286 //// | WhileStmt Expr [Stmt]
287 //// | AssStmt VarDef Expr
288 //// | FunStmt FunCall
289 //// | ReturnStmt (Maybe Expr)
290 ////:: Pos = {line :: Int, col :: Int}
291 ////:: AST = AST [VarDecl] [FunDecl]
292 ////:: VarDecl = VarDecl Pos Type String Expr
294 //// = TupleType (Type, Type)
302 //// | (->>) infixl 7 Type Type