:: Scheme = Forall [TVar] Type
:: Gamma :== 'Map'.Map String Scheme //map from Variables! to types
+:: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
:: Substitution :== 'Map'.Map TVar Type
:: Constraints :== [(Type, Type)]
:: SemError
variableStream :: [TVar]
variableStream = map toString [1..]
-sem :: AST -> Either [SemError] Constraints
+sem :: AST -> Either [SemError] AST
sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
- >>| foldM (const isNiceMain) () fd
- >>| hasMain fd of
+ >>| foldM (const isNiceMain) () fd
+ >>| hasMain fd
+ >>| evalStateT (type fd) (zero, variableStream) of
Left e = Left [e]
- _ = Right []
- //_ = case execRWST (constraints fd) zero variableStream of
- // Left e = Left [e]
- // Right (a, b) = Right b
+ Right (_,fds) = Right (AST fds)
where
- constraints :: [FunDecl] -> Typing ()
- constraints _ = pure ()
- //TODO: fix
- //constraints fds = mapM_ funconstraint fds >>| pure ()
-
- funconstraint :: FunDecl -> Typing ()
- funconstraint fd=:(FunDecl _ ident args mt vardecls stmts) = case mt of
- Nothing = abort "Cannot infer functions yet"
- _ = pure ()
- //Just t = inEnv (ident, (Forall [] t)) (
- // mapM_ vardeclconstraint vardecls >>| pure ())
-
- vardeclconstraint :: VarDecl -> Typing ()
- vardeclconstraint _ = pure ()
- //TODO: fix!
- //vardeclconstraint (VarDecl p mt ident expr) = infer expr
- //>>= \it->inEnv (ident, (Forall [] it)) (pure ())
-
hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
hasNoDups fds (FunDecl p n _ _ _ _)
# mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds
occurs tvar a = elem tvar (ftv a)
unify :: Type Type -> Either SemError Substitution
-unify t1=:(IdType tv) t2 = unify t2 t1
unify t1 t2=:(IdType tv) | t1 == (IdType tv) = Right zero
| occurs tv t1 = Left $ InfiniteTypeError zero t1
| otherwise = Right $ 'Map'.singleton tv t1
+unify t1=:(IdType tv) t2 = unify t2 t1
unify (ta1->>ta2) (tb1->>tb2) = unify ta1 tb1 >>= \s1->
- unify tb1 tb2 >>= \s2->
+ unify ta2 tb2 >>= \s2->
Right $ compose s1 s2
unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
unify ta2 tb2 >>= \s2->
//// ------------------------
//// Algorithm M, Inference and Solving
//// ------------------------
-//The typing monad
-:: Typing a :== StateT (Gamma, [TVar]) (Either SemError) a
gamma :: Typing Gamma
gamma = gets fst
putGamma :: Gamma -> Typing ()
infer el >>= \(s4, elt)->
applySubst s4 >>|
lift (unify tht elt) >>= \s5->
- pure (compose s5 $ compose s4 $ compose s3 $ compose s1 s2, subst s5 tht)
+ pure (compose s5 $ compose s4 $ compose s3 $ compose s2 s1, subst s5 tht)
WhileStmt e wh =
infer e >>= \(s1, et)->
lift (unify et BoolType) >>= \s2 ->
applySubst (compose s2 s1) >>|
infer wh >>= \(s3, wht)->
- pure (compose s3 $ compose s1 s2, subst s3 wht)
+ pure (compose s3 $ compose s2 s1, subst s3 wht)
AssStmt (VarDef k fs) e =
- infer e >>= \(s1, et)->
- applySubst s1 >>|
- changeGamma (extend k (Forall [] et)) >>| //todo: fieldselectors
- pure (s1, VoidType)
+ lookup k >>= \expected ->
+ infer e >>= \(s1, given)->
+ lift (unify expected given) >>= \s2->
+ let s = compose s2 s1 in
+ applySubst s >>|
+ changeGamma (extend k (Forall [] given)) >>| //todo: fieldselectors
+ pure (s, VoidType)
+
+ FunStmt f es = undef //what is this?
+ ReturnStmt Nothing = pure (zero, VoidType)
+ ReturnStmt (Just e) = infer e
+//The type of a list of statements is either an encountered
+//return, or VoidType
instance infer [a] | infer a where
- infer _ = undef
+ infer [] = pure (zero, VoidType)
+ infer [stmt:ss] =
+ infer stmt >>= \(s1, t1) ->
+ applySubst s1 >>|
+ infer ss >>= \(s2, t2) ->
+ applySubst s2 >>|
+ case t1 of
+ VoidType = pure (compose s2 s1, t2)
+ _ = case t2 of
+ VoidType = pure (compose s2 s1, t1)
+ _ = lift (unify t1 t2) >>= \s3 ->
+ pure (compose s3 $ compose s2 s1, t1)
+
+//the type class inferes the type of an AST element (VarDecl or FunDecl)
+//and adds it to the AST element
+class type a :: a -> Typing (Substitution, a)
+
+instance type VarDecl where
+ type (VarDecl p expected k e) =
+ infer e >>= \(s1, given) ->
+ applySubst s1 >>|
+ case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given)
+ >>= \s2->
+ applySubst s2 >>|
+ let vtype = subst (compose s2 s1) given in
+ generalize vtype >>= \t ->
+ changeGamma (extend k t) >>|
+ pure (compose s2 s1, VarDecl p (Just vtype) k e)
+
+instance type FunDecl where
+ type (FunDecl p f args expected vds stmts) =
+ gamma >>= \outerScope-> //functions are infered in their own scopde
+ introduce f >>|
+ mapM introduce args >>= \argTs->
+ type vds >>= \(s1, tVds)->
+ applySubst s1 >>|
+ infer stmts >>= \(s2, result)->
+ applySubst s1 >>|
+ let argTs_ = map (subst $ compose s2 s1) argTs in
+ //abort (concat $ intersperse "\n" $ map toString argTs_) >>|
+ let given = foldr (->>) result argTs_ in
+ (case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given))
+ >>= \s3 ->
+ let ftype = subst (compose s3 $ compose s2 s1) given in
+ generalize ftype >>= \t->
+ putGamma outerScope >>|
+ changeGamma (extend f t) >>|
+ pure (compose s3 $ compose s2 s1, FunDecl p f args (Just ftype) tVds stmts)
+
+instance type [a] | type a where
+ type [] = pure (zero, [])
+ type [v:vs] =
+ type v >>= \(s1, v_)->
+ applySubst s1 >>|
+ type vs >>= \(s2, vs_)->
+ applySubst (compose s2 s1) >>|
+ pure (compose s2 s1, [v_:vs_])
-Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
-Mapmap _ 'Map'.Tip = 'Map'.Tip
-Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)
- (Mapmap f ml)
- (Mapmap f mr)
+introduce :: String -> Typing Type
+introduce k =
+ fresh >>= \tv ->
+ changeGamma (extend k (Forall [] tv)) >>|
+ pure tv
instance toString Scheme where
toString (Forall x t) =
- concat ["Forall ": map ((+++) "\n") x] +++ toString t
+ concat ["Forall ": intersperse "," x] +++ concat [". ", toString t];
instance toString Gamma where
toString mp =
concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
+instance toString Substitution where
+ toString subs =
+ concat [concat [k, ": ", toString t, "\n"]\\(k, t)<-'Map'.toList subs]
+
instance toString SemError where
toString (SanityError p e) = concat [toString p,
"SemError: SanityError: ", e]
- toString se = "SemError: "
+ toString (ParseError p s) = concat [toString p,
+ "ParseError: ", s]
+ toString (UnifyError p t1 t2) = concat [toString p,
+ "Can not unify types, expected|given:\n", toString t1,
+ "\n", toString t2]
+ toString (InfiniteTypeError p t) = concat [toString p,
+ "Infinite type: ", toString t]
+ toString (FieldSelectorError p t fs) = concat [toString p,
+ "Can not run fieldselector '", toString fs, "' on type: ",
+ toString t]
+ toString (OperatorError p op t) = concat [toString p,
+ "Operator error, operator '", toString op, "' can not be",
+ "used on type: ", toString t]
+ toString (UndeclaredVariableError p k) = concat [toString p,
+ "Undeclared identifier: ", k]
+ toString (ArgumentMisMatchError p str) = concat [toString p,
+ "Argument mismatch: ", str]
+ toString (Error e) = concat ["Unknown error during semantical",
+ "analysis: ", e]
+
+instance toString (Maybe a) | toString a where
+ toString Nothing = "Nothing"
+ toString (Just e) = concat ["Just ", toString e]
instance MonadTrans (StateT (Gamma, [TVar])) where
liftT m = StateT \s-> m >>= \a-> return (a, s)
-//// ------------------------
-//// First step: Inference
-//// ------------------------//
-
-//unify :: Type Type -> Infer ()
-//unify t1 t2 = tell [(t1, t2)]//
-
-//fresh :: Infer Type
-//fresh = (gets id) >>= \vars-> (put $ tail vars) >>| (pure $ IdType $ head vars)//
-
-//op2Type :: Op2 -> Infer Type
-//op2Type op
-//| elem op [BiPlus, BiMinus, BiTimes, BiDivide, BiMod]
-// = pure (IntType ->> IntType ->> IntType)
-//| elem op [BiEquals, BiUnEqual]
-// = fresh >>= \t1-> fresh >>= \t2-> pure (t1 ->> t2 ->> BoolType)
-//| elem op [BiLesser, BiGreater, BiLesserEq, BiGreaterEq]
-// = pure (IntType ->> IntType ->> BoolType)
-//| elem op [BiAnd, BiOr]
-// = pure (BoolType ->> BoolType ->> BoolType)
-//| op == BiCons
-// = fresh >>= \t1-> pure (t1 ->> ListType t1 ->> ListType t1)//
-
-//op1Type :: Op1 -> Infer Type
-//op1Type UnNegation = pure $ (BoolType ->> BoolType)
-//op1Type UnMinus = pure $ (IntType ->> IntType)//
-
-////instantiate :: Scheme -> Infer Type
-////instantiate (Forall as t) = mapM (const fresh) as//
-
-//lookupEnv :: String -> Infer Type
-//lookupEnv ident = asks ('Map'.get ident)
-// >>= \m->case m of
-// Nothing = liftT $ Left $ UndeclaredVariableError zero ident
-// Just (Forall as t) = pure t //instantiate ???//
-
-//class infer a :: a -> Infer Type
-//instance infer Expr where
-// infer (VarExpr _ (VarDef ident fs)) = lookupEnv ident
-// infer (Op2Expr _ e1 op e2) =
-// infer e1 >>= \t1 ->
-// infer e2 >>= \t2 ->
-// fresh >>= \frsh ->
-// let given = t1 ->> (t2 ->> frsh) in
-// op2Type op >>= \expected ->
-// unify expected given >>|
-// return frsh
-// infer (Op1Expr _ op e) =
-// infer e >>= \t1 ->
-// fresh >>= \frsh ->
-// let given = t1 ->> frsh in
-// op1Type op >>= \expected ->
-// unify expected given >>|
-// pure frsh
-// infer (IntExpr _ _) = pure IntType
-// infer (CharExpr _ _) = pure CharType
-// infer (BoolExpr _ _) = pure BoolType
-// infer (FunExpr _ f args sels) = //todo, iets met field selectors
-// lookupEnv f >>= \expected ->
-// fresh >>= \frsh ->
-// mapM infer args >>= \argTypes ->
-// let given = foldr (->>) frsh argTypes in
-// unify expected given >>|
-// pure frsh
-// infer (EmptyListExpr _) = ListType <$> fresh
-// infer (TupleExpr _ (e1, e2)) =
-// infer e1 >>= \et1->infer e2 >>= \et2->pure $ TupleType (et1, et2)//
-
-////:: VarDef = VarDef String [FieldSelector]
-////:: FieldSelector = FieldHd | FieldTl | FieldFst | FieldSnd
-////:: Op1 = UnNegation | UnMinus
-////:: Op2 = BiPlus | BiMinus | BiTimes | BiDivide | BiMod | BiEquals | BiLesser |
-//// BiGreater | BiLesserEq | BiGreaterEq | BiUnEqual | BiAnd | BiOr | BiCons
-////:: FunDecl = FunDecl Pos String [String] (Maybe Type) [VarDecl] [Stmt]
-////:: FunCall = FunCall String [Expr]
-////:: Stmt
-//// = IfStmt Expr [Stmt] [Stmt]
-//// | WhileStmt Expr [Stmt]
-//// | AssStmt VarDef Expr
-//// | FunStmt FunCall
-//// | ReturnStmt (Maybe Expr)
-////:: Pos = {line :: Int, col :: Int}
-////:: AST = AST [VarDecl] [FunDecl]
-////:: VarDecl = VarDecl Pos Type String Expr
-////:: Type
-//// = TupleType (Type, Type)
-//// | ListType Type
-//// | IdType String
-//// | IntType
-//// | BoolType
-//// | CharType
-//// | VarType
-//// | VoidType
-//// | (->>) infixl 7 Type Type
+Mapmap :: (a->b) ('Map'.Map k a) -> ('Map'.Map k b)
+Mapmap _ 'Map'.Tip = 'Map'.Tip
+Mapmap f ('Map'.Bin sz k v ml mr) = 'Map'.Bin sz k (f v)
+ (Mapmap f ml)
+ (Mapmap f mr)
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