X-Git-Url: https://git.martlubbers.net/?a=blobdiff_plain;f=sem.icl;h=0c5b55273cb8d7fb05f1fe73dc1fa069409ff49c;hb=978dc486bf8c83cf9cad0925e3128574639656e0;hp=23fb04aa5aa1778bf3c6ed436b7898b3736600b6;hpb=13a108705dbabbc75711ce9b3b29fe508262919f;p=cc1516.git diff --git a/sem.icl b/sem.icl index 23fb04a..0c5b552 100644 --- a/sem.icl +++ b/sem.icl @@ -3,114 +3,421 @@ implementation module sem import qualified Data.Map as Map from Data.Func import $ -from StdFunc import o +from StdFunc import o, flip, const, id import Control.Monad +import Control.Monad.Trans +import Control.Monad.State import Data.Either +import Data.Maybe import Data.Monoid +import Data.List +import Data.Functor +import Data.Tuple import StdString +import StdTuple import StdList import StdMisc import StdEnum -import RWST import GenEq from Text import class Text(concat), instance Text String import AST -:: Scheme = Forall [String] Type -:: Gamma :== 'Map'.Map String Scheme +:: 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)] -:: Infer a :== RWST Gamma Constraints [String] (Either SemError) a :: SemError = ParseError Pos String | UnifyError Pos Type Type + | InfiniteTypeError Pos Type | FieldSelectorError Pos Type FieldSelector | OperatorError Pos Op2 Type | UndeclaredVariableError Pos String | ArgumentMisMatchError Pos String + | SanityError Pos String | Error String -variableStream :: [String] +instance zero Gamma where + zero = 'Map'.newMap + +variableStream :: [TVar] variableStream = map toString [1..] -sem :: AST -> SemOutput -sem (AST fd) = Right (AST fd, 'Map'.newMap) +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 + >>| evalStateT (type fd) (defaultGamma, variableStream) of + Left e = Left [e] + Right (_,fds) = Right (AST fds) +where + hasNoDups :: [FunDecl] FunDecl -> Either SemError () + hasNoDups fds (FunDecl p n _ _ _ _) + # mbs = map (\(FunDecl p` n` _ _ _ _)->if (n == n`) (Just p`) Nothing) fds + = case catMaybes mbs of + [] = Left $ SanityError p "HUH THIS SHOULDN'T HAPPEN" + [x] = pure () + [_:x] = Left $ SanityError p (concat + [n, " multiply defined at ", toString p]) + + hasMain :: [FunDecl] -> Either SemError () + hasMain [(FunDecl _ "main" _ _ _ _):fd] = pure () + hasMain [_:fd] = hasMain fd + hasMain [] = Left $ SanityError zero "no main function defined" + + isNiceMain :: FunDecl -> Either SemError () + isNiceMain (FunDecl p "main" as mt _ _) = case (as, mt) of + ([_:_], _) = Left $ SanityError p "main must have arity 0" + ([], t) = (case t of + Nothing = pure () + Just VoidType = pure () + _ = Left $ SanityError p "main has to return Void") + isNiceMain _ = pure () + +class Typeable a where + ftv :: a -> [TVar] + subst :: Substitution a -> a + +instance Typeable Scheme where + ftv (Forall bound t) = difference (ftv t) bound + subst s (Forall bound t) = Forall bound $ subst s_ t + where s_ = 'Map'.filterWithKey (\k _ -> not (elem k bound)) s + +instance Typeable [a] | Typeable a where + ftv types = foldr (\t ts-> ftv t ++ ts) [] types + subst s ts = map (\t->subst s t) ts + +instance Typeable Type where + ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2 + ftv (ListType t) = ftv t + ftv (IdType tvar) = [tvar] + ftv (t1 ->> t2) = ftv t1 ++ ftv t2 + ftv _ = [] + subst s (TupleType (t1, t2))= TupleType (subst s t1, subst s t2) + subst s (ListType t1) = ListType (subst s t1) + subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2) + subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s + subst s t = t + +instance Typeable Gamma where + 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 +//// ------------------------ +instance zero Substitution where zero = 'Map'.newMap + +compose :: Substitution Substitution -> Substitution +compose s1 s2 = 'Map'.union (Mapmap (subst s1) s2) s1 +//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 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 ta2 tb2 >>= \s2-> + Right $ compose s1 s2 +unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1-> + unify ta2 tb2 >>= \s2-> + Right $ compose s1 s2 +unify (ListType t1) (ListType t2) = unify t1 t2 +unify t1 t2 | t1 == t2 = Right zero + | otherwise = Left $ UnifyError zero t1 t2 + +//// ------------------------ +//// Algorithm M, Inference and Solving +//// ------------------------ +gamma :: Typing Gamma +gamma = gets fst +putGamma :: Gamma -> Typing () +putGamma g = modify (appFst $ const g) >>| 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 +instantiate (Forall bound t) = + 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 ": map ((+++) "\n") x] +++ toString t + 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] + 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 se = "SemError: " - -uni :: Type Type -> Infer () -uni t1 t2 = tell [(t1, t2)] - -inEnv :: (String, Scheme) (Infer a) -> (Infer a) -inEnv (x, sc) m = local scope m - where - scope e = 'Map'.put x sc ('Map'.del x e ) - -class infer a :: a -> Infer Type - -instance infer Expr where - infer (VarExpr _ vd) = undef - infer (Op2Expr _ e1 op e2) = case op of - BiPlus = pure IntType - BiMinus = pure IntType - BiTimes = pure IntType - BiDivide = pure IntType - BiMod = pure IntType - BiLesser = pure IntType - BiGreater = pure IntType - BiLesserEq = pure IntType - BiGreaterEq = pure IntType - BiAnd = pure BoolType - BiOr = pure BoolType - BiEquals = infer e1 - BiUnEqual = infer e1 // maybe check e2? - BiCons = infer e1 >>= \it1->pure $ ListType it1 - infer (Op1Expr _ op e) = case op of - UnMinus = pure IntType - UnNegation = pure BoolType - infer (IntExpr _ _) = pure IntType - infer (CharExpr _ _) = pure CharType - infer (BoolExpr _ _) = pure BoolType - infer (FunExpr _ _ _ _) = undef - infer (EmptyListExpr _) = undef - 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 + 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)