import AST
-
:: 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
+defaultGamma :: Gamma //includes all default functions
+defaultGamma = extend "print" (Forall ["a"] ((IdType "a") ->> VoidType))
+ $ extend "isEmpty" (Forall ["a"] ((ListType (IdType "a")) ->> BoolType))
+ $ extend "read" (Forall [] CharType)
+ zero
+
+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) (defaultGamma, 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
_ = Left $ SanityError p "main has to return Void")
isNiceMain _ = pure ()
-instance toString Scheme where
- toString (Forall x t) =
- concat ["Forall ": map ((+++) "\n") x] +++ toString t
-
-instance toString Gamma where
- toString mp =
- concat [concat [k, ": ", toString v, "\n"]\\(k, v)<-'Map'.toList mp]
-
-instance toString SemError where
- toString (SanityError p e) = concat [toString p,
- "SemError: SanityError: ", e]
- toString se = "SemError: "
-
class Typeable a where
ftv :: a -> [TVar]
subst :: Substitution a -> a
ftv gamma = concatMap id $ map ftv ('Map'.elems gamma)
subst s gamma = Mapmap (subst s) gamma
+extend :: String Scheme Gamma -> Gamma
+extend k t g = 'Map'.put k t g
+
//// ------------------------
//// algorithm U, Unification
//// ------------------------
compose :: Substitution Substitution -> Substitution
compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1
-//Note: unlike function composition, compose is left biased!
+//Note: just like function compositon compose does snd first
occurs :: TVar a -> Bool | Typeable a
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 ()
putGamma g = modify (appFst $ const g) >>| pure ()
-withGamma :: (Gamma -> Gamma) -> Typing ()
-withGamma f = modify (appFst f) >>| pure ()
+changeGamma :: (Gamma -> Gamma) -> Typing Gamma
+changeGamma f = modify (appFst f) >>| gamma
+withGamma :: (Gamma -> a) -> Typing a
+withGamma f = f <$> gamma
fresh :: Typing Type
fresh = gets snd >>= \vars->
modify (appSnd $ const $ tail vars) >>|
pure (IdType (head vars))
+lift :: (Either SemError a) -> Typing a
+lift (Left e) = liftT $ Left e
+lift (Right v) = pure v
+
//instantiate maps a schemes type variables to variables with fresh names
//and drops the quantification: i.e. forall a,b.a->[b] becomes c->[d]
instantiate :: Scheme -> Typing Type
mapM (const fresh) bound >>= \newVars->
let s = 'Map'.fromList (zip (bound,newVars)) in
pure (subst s t)
+
//generalize quentifies all free type variables in a type which are not
//in the gamma
generalize :: Type -> Typing Scheme
generalize t = gamma >>= \g-> pure $ Forall (difference (ftv t) (ftv g)) t
+lookup :: String -> Typing Type
+lookup k = gamma >>= \g-> case 'Map'.member k g of
+ False = liftT (Left $ UndeclaredVariableError zero k)
+ True = instantiate $ 'Map'.find k g
+
+//The inference class
+//When tying it all together we will treat the program is a big
+//let x=e1 in let y=e2 in ....
+class infer a :: a -> Typing (Substitution, Type)
+
+////---- Inference for Expressions ----
+
+instance infer Expr where
+ infer e = case e of
+ VarExpr _ (VarDef k fs) = lookup k >>= \t ->
+ foldM foldFieldSelectors t fs >>= \finalT ->
+ pure (zero, finalT)
+
+ Op2Expr _ e1 op e2 =
+ infer e1 >>= \(s1, t1) ->
+ infer e2 >>= \(s2, t2) ->
+ fresh >>= \tv ->
+ let given = t1 ->> t2 ->> tv in
+ op2Type op >>= \expected ->
+ lift (unify expected given) >>= \s3 ->
+ pure ((compose s3 $ compose s2 s1), subst s3 tv)
+
+ Op1Expr _ op e1 =
+ infer e1 >>= \(s1, t1) ->
+ fresh >>= \tv ->
+ let given = t1 ->> tv in
+ op1Type op >>= \expected ->
+ lift (unify expected given) >>= \s2 ->
+ pure (compose s2 s1, subst s2 tv)
+
+ EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
+
+ TupleExpr _ (e1, e2) =
+ infer e1 >>= \(s1, t1) ->
+ infer e2 >>= \(s2, t2) ->
+ pure (compose s2 s1, TupleType (t1,t2))
+
+ FunExpr _ f args fs = //todo: fieldselectors
+ lookup f >>= \expected ->
+ let accST = (\(s,ts) e->infer e >>= \(s_,et)->pure (compose s_ s,ts++[et])) in
+ foldM accST (zero,[]) args >>= \(s1, argTs)->
+ fresh >>= \tv->
+ let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ let fReturnType = subst s2 tv in
+ foldM foldFieldSelectors fReturnType fs >>= \returnType ->
+ pure (compose s2 s1, returnType)
+
+ IntExpr _ _ = pure $ (zero, IntType)
+ BoolExpr _ _ = pure $ (zero, BoolType)
+ CharExpr _ _ = pure $ (zero, CharType)
+
+foldFieldSelectors :: Type FieldSelector -> Typing Type
+foldFieldSelectors (ListType t) (FieldHd) = pure t
+foldFieldSelectors t=:(ListType _) (FieldTl) = pure t
+foldFieldSelectors (TupleType (t1, _)) (FieldFst) = pure t1
+foldFieldSelectors (TupleType (_, t2)) (FieldSnd) = pure t2
+foldFieldSelectors t fs = liftT $ Left $ FieldSelectorError zero t fs
+
+op2Type :: Op2 -> Typing 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 -> Typing Type
+op1Type UnNegation = pure $ (BoolType ->> BoolType)
+op1Type UnMinus = pure $ (IntType ->> IntType)
+
+////----- Inference for Statements -----
+applySubst :: Substitution -> Typing Gamma
+applySubst s = changeGamma (subst s)
+
+instance infer Stmt where
+ infer s = case s of
+ IfStmt e th el =
+ infer e >>= \(s1, et)->
+ lift (unify et BoolType) >>= \s2 ->
+ applySubst (compose s2 s1) >>|
+ infer th >>= \(s3, tht)->
+ applySubst s3 >>|
+ infer el >>= \(s4, elt)->
+ applySubst s4 >>|
+ lift (unify tht elt) >>= \s5->
+ 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 s2 s1, subst s3 wht)
+
+ AssStmt (VarDef k fs) e =
+ lookup k >>= \expected ->
+ infer e >>= \(s1, given)->
+ foldM reverseFs given (reverse fs) >>= \varType->
+ lift (unify expected varType) >>= \s2->
+ let s = compose s2 s1 in
+ applySubst s >>|
+ changeGamma (extend k (Forall [] (subst s varType))) >>|
+ pure (s, VoidType)
+
+ FunStmt f es _ = pure (zero, VoidType)
+
+ ReturnStmt Nothing = pure (zero, VoidType)
+ ReturnStmt (Just e) = infer e
+
+reverseFs :: Type FieldSelector -> Typing Type
+reverseFs t FieldHd = pure $ ListType t
+reverseFs t FieldTl = pure $ ListType t
+reverseFs t FieldFst = fresh >>= \tv -> pure $ TupleType (t, tv)
+reverseFs t FieldSnd = fresh >>= \tv -> pure $ TupleType (tv, t)
+
+//The type of a list of statements is either an encountered
+//return, or VoidType
+instance infer [a] | infer a where
+ 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_])
+
+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 ": 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 (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)
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)
-
-//// ------------------------
-//// 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
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