from Data.Func import $
from StdFunc import o, flip, const, id
+import Control.Applicative
import Control.Monad
import Control.Monad.Trans
import Control.Monad.State
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)
+ $ extend "read" (Forall [] (FuncType CharType))
+ $ extend "1printchar" (Forall [] (CharType ->> VoidType))
+ $ extend "1printint" (Forall [] (IntType ->> VoidType))
+ $ extend "1printbool" (Forall [] (BoolType ->> VoidType))
zero
-sem :: AST -> Either [SemError] AST
+sem :: AST -> Either [SemError] (AST, Gamma)
sem (AST fd) = case foldM (const $ hasNoDups fd) () fd
>>| foldM (const isNiceMain) () fd
>>| hasMain fd
- >>| evalStateT (type fd) (defaultGamma, variableStream) of
+ >>| runStateT (unfoldLambda fd >>= type) (defaultGamma, variableStream) of
Left e = Left [e]
- Right (_,fds) = Right (AST fds)
+ Right ((_,fds),(gam,_)) = Right (AST fds, gam)
where
hasNoDups :: [FunDecl] FunDecl -> Either SemError ()
hasNoDups fds (FunDecl p n _ _ _ _)
_ = Left $ SanityError p "main has to return Void")
isNiceMain _ = pure ()
+
+//------------------
+// LAMBDA UNFOLDING
+//------------------
+unfoldLambda :: [FunDecl] -> Typing [FunDecl]
+unfoldLambda [] = pure []
+unfoldLambda [fd:fds] = unfoldL_ fd >>= \(gen1, fs_)->
+ unfoldLambda fds >>= \gen2->
+ pure $ gen1 ++ [fs_] ++ gen2
+
+flattenT :: [([a],b)] -> ([a],[b])
+flattenT ts = (flatten $ map fst ts, map snd ts)
+
+class unfoldL_ a :: a -> Typing ([FunDecl], a)
+
+instance unfoldL_ FunDecl where
+ unfoldL_ (FunDecl p f args mt vds stmts) =
+ flattenT <$> mapM unfoldL_ vds >>= \(fds1,vds_) ->
+ flattenT <$> mapM unfoldL_ stmts >>= \(fds2,stmts_)->
+ pure (fds1 ++ fds2, FunDecl p f args mt vds_ stmts_)
+
+instance unfoldL_ VarDecl where
+ unfoldL_ (VarDecl p mt v e) = unfoldL_ e >>= \(fds, e_)->pure (fds, VarDecl p mt v e_)
+
+instance unfoldL_ Stmt where
+ unfoldL_ (IfStmt e th el) = unfoldL_ e >>= \(fds, e_)->pure (fds, IfStmt e_ th el)
+ unfoldL_ (WhileStmt e c) = unfoldL_ e >>= \(fds, e_)->pure (fds, WhileStmt e_ c)
+ unfoldL_ (AssStmt vd e) = unfoldL_ e >>= \(fds, e_)->pure (fds, AssStmt vd e_)
+ unfoldL_ (FunStmt f es fs) = flattenT <$> mapM unfoldL_ es >>= \(fds, es_)->
+ pure (fds, FunStmt f es_ fs)
+ unfoldL_ (ReturnStmt (Just e)) = unfoldL_ e >>= \(fds, e_) ->
+ pure (fds, ReturnStmt (Just e_))
+ unfoldL_ (ReturnStmt Nothing) = pure ([], ReturnStmt Nothing)
+
+instance unfoldL_ Expr where
+ unfoldL_ (LambdaExpr p args e) =
+ fresh >>= \(IdType n) ->
+ let f = ("2lambda_"+++n) in
+ let fd = FunDecl p f args Nothing [] [ReturnStmt $ Just e] in
+ let fe = VarExpr p (VarDef f []) in
+ pure ([fd], fe)
+ unfoldL_ (FunExpr p f es fs) = flattenT <$> mapM unfoldL_ es >>= \(fds, es_)->
+ pure (fds, FunExpr p f es_ fs)
+ unfoldL_ (Op2Expr p e1 op e2) = unfoldL_ e1 >>= \(fds1, e1_)->
+ unfoldL_ e2 >>= \(fds2, e2_)->
+ pure (fds1++fds2, Op2Expr p e1_ op e2_)
+ unfoldL_ (Op1Expr p op e1) = unfoldL_ e1 >>= \(fds, e1_)->pure (fds, Op1Expr p op e1_)
+ unfoldL_ (TupleExpr p (e1, e2)) = unfoldL_ e1 >>= \(fds1, e1_)->
+ unfoldL_ e2 >>= \(fds2, e2_)->
+ pure (fds1++fds2, TupleExpr p (e1_, e2_))
+ unfoldL_ e = pure ([], e)
+
+//------------
+//------------
+// TYPING
+//------------
+//------------
+
class Typeable a where
ftv :: a -> [TVar]
subst :: Substitution a -> a
ftv (TupleType (t1, t2)) = ftv t1 ++ ftv t2
ftv (ListType t) = ftv t
ftv (IdType tvar) = [tvar]
+ ftv (FuncType t) = ftv t
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 (FuncType t) = FuncType (subst s t)
subst s (t1 ->> t2) = (subst s t1) ->> (subst s t2)
subst s t1=:(IdType tvar) = 'Map'.findWithDefault t1 tvar s
subst s t = t
| 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 (subst s1 ta2) (subst s1 tb2) >>= \s2->
+ Right $ compose s2 s1
unify (TupleType (ta1,ta2)) (TupleType (tb1,tb2)) = unify ta1 tb1 >>= \s1->
- unify ta2 tb2 >>= \s2->
- Right $ compose s1 s2
+ unify (subst s1 ta2) (subst s1 tb2) >>= \s2->
+ Right $ compose s2 s1
unify (ListType t1) (ListType t2) = unify t1 t2
+unify (FuncType t1) (FuncType t2) = unify t1 t2
unify t1 t2 | t1 == t2 = Right zero
| otherwise = Left $ UnifyError zero t1 t2
//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)
+class infer a :: a -> Typing (Substitution, Type, a)
////---- Inference for Expressions ----
infer e = case e of
VarExpr _ (VarDef k fs) = lookup k >>= \t ->
foldM foldFieldSelectors t fs >>= \finalT ->
- pure (zero, finalT)
+ pure (zero, finalT, e)
- Op2Expr _ e1 op e2 =
- infer e1 >>= \(s1, t1) ->
- infer e2 >>= \(s2, t2) ->
+ Op2Expr p e1 op e2 =
+ infer e1 >>= \(s1, t1, e1_) ->
+ applySubst s1 >>|
+ infer e2 >>= \(s2, t2, e2_) ->
+ applySubst s2 >>|
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)
+ applySubst s3 >>|
+ pure ((compose s3 $ compose s2 s1), subst s3 tv, Op2Expr p e1_ op e2_)
- Op1Expr _ op e1 =
- infer e1 >>= \(s1, t1) ->
+ Op1Expr p op e1 =
+ infer e1 >>= \(s1, t1, e1_) ->
+ applySubst s1 >>|
fresh >>= \tv ->
let given = t1 ->> tv in
op1Type op >>= \expected ->
lift (unify expected given) >>= \s2 ->
- pure (compose s2 s1, subst s2 tv)
+ applySubst s2 >>|
+ pure (compose s2 s1, subst s2 tv, Op1Expr p op e1)
- EmptyListExpr _ = (\tv->(zero,tv)) <$> fresh
+ EmptyListExpr _ = (\tv->(zero,ListType tv,e)) <$> fresh
- TupleExpr _ (e1, e2) =
- infer e1 >>= \(s1, t1) ->
- infer e2 >>= \(s2, t2) ->
- pure (compose s2 s1, TupleType (t1,t2))
+ TupleExpr p (e1, e2) =
+ infer e1 >>= \(s1, t1, e1_) ->
+ applySubst s1 >>|
+ infer e2 >>= \(s2, t2, e2_) ->
+ applySubst s2 >>|
+ pure (compose s2 s1, TupleType (t1,t2), TupleExpr p (e1_,e2_))
- 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)
+ LambdaExpr _ _ _ = liftT $ Left $ Error "PANIC: lambdas should be Unfolded"
- IntExpr _ _ = pure $ (zero, IntType)
- BoolExpr _ _ = pure $ (zero, BoolType)
- CharExpr _ _ = pure $ (zero, CharType)
+ FunExpr p f args fs =
+ lookup f >>= \expected ->
+ let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
+ foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
+ applySubst s1 >>|
+ (case f of
+ "print" = case head argTs of
+ IntType = pure "1printint"
+ CharType = pure "1printchar"
+ BoolType = pure "1printbool"
+ ListType (CharType) = pure "1printstr"
+ t = liftT $ Left $ SanityError p ("can not print " +++ toString t)
+ _ = pure f
+ ) >>= \newF->
+ fresh >>= \tv->case expected of
+ FuncType t = foldM foldFieldSelectors t fs >>= \returnType ->
+ pure (s1, returnType, (FunExpr p newF args fs))
+ _ = (let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ applySubst s2 >>|
+ let fReturnType = subst s2 tv in
+ foldM foldFieldSelectors fReturnType fs >>= \returnType ->
+ pure (compose s2 s1, returnType, FunExpr p newF args_ fs))
+
+ IntExpr _ _ = pure $ (zero, IntType, e)
+ BoolExpr _ _ = pure $ (zero, BoolType, e)
+ CharExpr _ _ = pure $ (zero, CharType, e)
foldFieldSelectors :: Type FieldSelector -> Typing Type
foldFieldSelectors (ListType t) (FieldHd) = pure t
instance infer Stmt where
infer s = case s of
IfStmt e th el =
- infer e >>= \(s1, et)->
+ infer e >>= \(s1, et, e_)->
lift (unify et BoolType) >>= \s2 ->
applySubst (compose s2 s1) >>|
- infer th >>= \(s3, tht)->
+ infer th >>= \(s3, tht, th_)->
applySubst s3 >>|
- infer el >>= \(s4, elt)->
+ infer el >>= \(s4, elt, el_)->
applySubst s4 >>|
lift (unify tht elt) >>= \s5->
- pure (compose s5 $ compose s4 $ compose s3 $ compose s2 s1, subst s5 tht)
+ let sub = compose s5 $ compose s4 $ compose s3 $ compose s2 s1 in
+ pure (sub, subst s5 tht, IfStmt e_ th_ el_)
WhileStmt e wh =
- infer e >>= \(s1, et)->
+ infer e >>= \(s1, et, e_)->
lift (unify et BoolType) >>= \s2 ->
applySubst (compose s2 s1) >>|
- infer wh >>= \(s3, wht)->
- pure (compose s3 $ compose s2 s1, subst s3 wht)
+ infer wh >>= \(s3, wht, wh_)->
+ pure (compose s3 $ compose s2 s1, subst s3 wht, WhileStmt e_ wh_)
- AssStmt (VarDef k fs) e =
+ AssStmt vd=:(VarDef k fs) e =
lookup k >>= \expected ->
- infer e >>= \(s1, given)->
+ infer e >>= \(s1, given, e_)->
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)
+ pure (s, VoidType, AssStmt vd e_)
- FunStmt f es _ = pure (zero, VoidType)
-
- ReturnStmt Nothing = pure (zero, VoidType)
- ReturnStmt (Just e) = infer e
+ FunStmt f args fs =
+ lookup f >>= \expected ->
+ let accST = (\(s,ts,es) e->infer e >>= \(s_,et,e_)-> pure (compose s_ s,ts++[et],es++[e_])) in
+ foldM accST (zero,[],[]) args >>= \(s1, argTs, args_)->
+ fresh >>= \tv->
+ let given = foldr (->>) tv argTs in
+ lift (unify expected given) >>= \s2->
+ let fReturnType = subst s2 tv in
+ foldM foldFieldSelectors fReturnType fs >>= \returnType ->
+ (case f of
+ "print" = case head argTs of
+ IntType = pure "1printint"
+ CharType = pure "1printchar"
+ BoolType = pure "1printbool"
+ ListType (CharType) = pure "1printstr"
+ t = liftT $ Left $ SanityError zero ("can not print " +++ toString t)
+ _ = pure f) >>= \newF->
+ pure (compose s2 s1, VoidType, FunStmt newF args_ fs)
+
+ ReturnStmt Nothing = pure (zero, VoidType, s)
+ //hier ook sub applyen
+ ReturnStmt (Just e) = infer e >>= \(sub, t, e_)-> pure (sub, t, ReturnStmt (Just e_))
reverseFs :: Type FieldSelector -> Typing Type
reverseFs t FieldHd = pure $ ListType t
-reverseFs t FieldTl = pure $ ListType t
+reverseFs t FieldTl = pure 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 [] = pure (zero, VoidType, [])
infer [stmt:ss] =
- infer stmt >>= \(s1, t1) ->
+ infer stmt >>= \(s1, t1, s_) ->
applySubst s1 >>|
- infer ss >>= \(s2, t2) ->
+ infer ss >>= \(s2, t2, ss_) ->
applySubst s2 >>|
case t1 of
- VoidType = pure (compose s2 s1, t2)
+ VoidType = pure (compose s2 s1, t2, [s_:ss_])
_ = case t2 of
- VoidType = pure (compose s2 s1, t1)
+ VoidType = pure (compose s2 s1, t1, [s_:ss_])
_ = lift (unify t1 t2) >>= \s3 ->
- pure (compose s3 $ compose s2 s1, t1)
+ pure (compose s3 $ compose s2 s1, t1, [s_:ss_])
//the type class inferes the type of an AST element (VarDecl or FunDecl)
//and adds it to the AST element
instance type VarDecl where
type (VarDecl p expected k e) =
- infer e >>= \(s1, given) ->
+ infer e >>= \(s1, given, e_) ->
applySubst s1 >>|
case expected of
Nothing = pure zero
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)
+ pure (compose s2 s1, VarDecl p (Just vtype) k e_)
instance type FunDecl where
- type (FunDecl p f args expected vds stmts) =
+ type fd=:(FunDecl p f args expected vds stmts) =
gamma >>= \outerScope-> //functions are infered in their own scopde
introduce f >>|
mapM introduce args >>= \argTs->
+ fresh >>= \tempTv ->
+ let temp = foldr (->>) tempTv argTs in
+ (case expected of
+ Just expected_ = lift (unify expected_ temp)
+ _ = pure zero
+ ) >>= \s0->
+ applySubst s0 >>|
type vds >>= \(s1, tVds)->
applySubst s1 >>|
- infer stmts >>= \(s2, result)->
+ infer stmts >>= \(s2, result, stmts_)->
applySubst s1 >>|
- let argTs_ = map (subst $ compose s2 s1) argTs in
- //abort (concat $ intersperse "\n" $ map toString argTs_) >>|
+ let argTs_ = map (subst $ compose s2 $ compose s1 s0) argTs in
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->
+ Just (FuncType expected_) = lift (unify expected_ given)
+ Just expected_ = lift (unify expected_ given)
+ ) >>= \s3 ->
+ let ftype = subst (compose s3 $ compose s2 $ compose s1 s0) given in
+ (case ftype of
+ _ ->> _ = pure ftype
+ _ = pure $ FuncType ftype
+ ) >>= \ftype_->
+ generalize ftype_ >>= \t->
putGamma outerScope >>|
changeGamma (extend f t) >>|
- pure (compose s3 $ compose s2 s1, FunDecl p f args (Just ftype) tVds stmts)
+ pure (compose s3 $ compose s2 $ compose s1 s0,
+ FunDecl p f args (Just ftype_) tVds stmts_)
instance type [a] | type a where
type [] = pure (zero, [])
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