:: 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 a = pure a
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 []
+ Right fds = Right (AST fds)
//_ = case execRWST (constraints fd) zero variableStream of
// Left e = Left [e]
// Right (a, b) = Right b
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 ()
pure ((compose s3 $ compose s2 s1), subst s3 tv)
Op1Expr _ op e1 =
+ abort "infereing op1" >>|
infer e1 >>= \(s1, t1) ->
fresh >>= \tv ->
let given = t1 ->> tv in
lift (unify expected given) >>= \s2 ->
pure (compose s2 s1, subst s2 tv)
- EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
+ EmptyListExpr _ = abort "infereing []" >>| (\tv->(zero,tv)) <$> fresh
TupleExpr _ (e1, e2) =
+ abort "infereing (,)" >>|
infer e1 >>= \(s1, t1) ->
infer e2 >>= \(s2, t2) ->
pure (compose s2 s1, TupleType (t1,t2))
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)->
+ //abort (concat (["argsTs: "] ++ (map toString argTs))) >>|
fresh >>= \tv->
let given = foldr (->>) tv argTs in
lift (unify expected given) >>= \s2->
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)->
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
-
-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)
+ 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 a
+
+instance type VarDecl where
+ type (VarDecl p expected k e) =
+ infer e >>= \(s, given) ->
+ applySubst s >>|
+ case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given)
+ >>|
+ generalize given >>= \t ->
+ changeGamma (extend k t) >>|
+ pure (VarDecl p (Just given) k e)
+
+instance type FunDecl where
+ type (FunDecl p f args expected vds stmts) =
+ introduce f >>|
+ mapM introduce args >>= \argTs->
+ type vds >>= \tVds->
+ infer stmts >>= \(s1, result)->
+ let given = foldr (->>) result argTs in
+ applySubst s1 >>|
+ (case expected of
+ Nothing = pure zero
+ Just expected_ = lift (unify expected_ given))
+ >>= \s2 ->
+ let ftype = subst (compose s2 s1) given in
+ generalize ftype >>= \t->
+ changeGamma (extend f t) >>|
+ pure (FunDecl p f args (Just ftype) tVds stmts)
+
+instance toString (Maybe a) | toString a where
+ toString Nothing = "Nothing"
+ toString (Just e) = concat ["Just ", toString e]
+
+instance type [a] | type a where
+ type dcls = mapM type dcls
+
+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 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
//// ------------------------//
repositories / cc1516.git / blobdiff