X-Git-Url: http://git.megacz.com/?p=ghc-hetmet.git;a=blobdiff_plain;f=compiler%2FcoreSyn%2FCoreArity.lhs;h=d0092b26c52d5fbcdeaa24a1a67c2726f51c3c00;hp=28732b31983eca9e2e75ed595f37da315a79b815;hb=66413c79385a5b30a668e91789b8a334f6977ca9;hpb=703ca1542c8e0983cc9d8eebce6e9f3dd3fd71e2 diff --git a/compiler/coreSyn/CoreArity.lhs b/compiler/coreSyn/CoreArity.lhs index 28732b3..d0092b2 100644 --- a/compiler/coreSyn/CoreArity.lhs +++ b/compiler/coreSyn/CoreArity.lhs @@ -8,7 +8,7 @@ \begin{code} -- | Arit and eta expansion module CoreArity ( - manifestArity, exprArity, + manifestArity, exprArity, exprBotStrictness_maybe, exprEtaExpandArity, etaExpand ) where @@ -17,22 +17,19 @@ module CoreArity ( import CoreSyn import CoreFVs import CoreUtils -import NewDemand -import TyCon ( isRecursiveTyCon ) -import qualified CoreSubst -import CoreSubst ( Subst, substBndr, substBndrs, substExpr - , mkEmptySubst, isEmptySubst ) +import CoreSubst +import Demand import Var import VarEnv import Id import Type +import TyCon ( isRecursiveTyCon, isClassTyCon ) import TcType ( isDictLikeTy ) import Coercion import BasicTypes import Unique import Outputable import DynFlags -import StaticFlags ( opt_NoStateHack ) import FastString \end{code} @@ -69,10 +66,19 @@ should have arity 3, regardless of f's arity. Note [exprArity invariant] ~~~~~~~~~~~~~~~~~~~~~~~~~~ exprArity has the following invariant: - (exprArity e) = n, then manifestArity (etaExpand e n) = n -That is, if exprArity says "the arity is n" then etaExpand really can get -"n" manifest lambdas to the top. + * If typeArity (exprType e) = n, + then manifestArity (etaExpand e n) = n + + That is, etaExpand can always expand as much as typeArity says + So the case analysis in etaExpand and in typeArity must match + + * exprArity e <= typeArity (exprType e) + + * Hence if (exprArity e) = n, then manifestArity (etaExpand e n) = n + + That is, if exprArity says "the arity is n" then etaExpand really + can get "n" manifest lambdas to the top. Why is this important? Because - In TidyPgm we use exprArity to fix the *final arity* of @@ -89,39 +95,113 @@ in exprArity. That is a less local change, so I'm going to leave it for today! \begin{code} manifestArity :: CoreExpr -> Arity -- ^ manifestArity sees how many leading value lambdas there are -manifestArity (Lam v e) | isId v = 1 + manifestArity e - | otherwise = manifestArity e -manifestArity (Note _ e) = manifestArity e -manifestArity (Cast e _) = manifestArity e -manifestArity _ = 0 +manifestArity (Lam v e) | isId v = 1 + manifestArity e + | otherwise = manifestArity e +manifestArity (Note n e) | notSccNote n = manifestArity e +manifestArity (Cast e _) = manifestArity e +manifestArity _ = 0 exprArity :: CoreExpr -> Arity -- ^ An approximate, fast, version of 'exprEtaExpandArity' exprArity e = go e where - go (Var v) = idArity v - go (Lam x e) | isId x = go e + 1 - | otherwise = go e - go (Note _ e) = go e - go (Cast e co) = trim_arity (go e) 0 (snd (coercionKind co)) - go (App e (Type _)) = go e - go (App f a) | exprIsCheap a = (go f - 1) `max` 0 - -- NB: exprIsCheap a! - -- f (fac x) does not have arity 2, - -- even if f has arity 3! - -- NB: `max 0`! (\x y -> f x) has arity 2, even if f is - -- unknown, hence arity 0 + go (Var v) = idArity v + go (Lam x e) | isId x = go e + 1 + | otherwise = go e + go (Note n e) | notSccNote n = go e + go (Cast e co) = go e `min` length (typeArity (snd (coercionKind co))) + -- Note [exprArity invariant] + go (App e (Type _)) = go e + go (App f a) | exprIsTrivial a = (go f - 1) `max` 0 + -- See Note [exprArity for applications] go _ = 0 - -- Note [exprArity invariant] - trim_arity n a ty - | n==a = a - | Just (_, ty') <- splitForAllTy_maybe ty = trim_arity n a ty' - | Just (_, ty') <- splitFunTy_maybe ty = trim_arity n (a+1) ty' - | Just (ty',_) <- splitNewTypeRepCo_maybe ty = trim_arity n a ty' - | otherwise = a + +typeArity :: Type -> [OneShot] +-- How many value arrows are visible in the type? +-- We look through foralls, and newtypes +-- See Note [exprArity invariant] +typeArity ty + | Just (_, ty') <- splitForAllTy_maybe ty + = typeArity ty' + + | Just (arg,res) <- splitFunTy_maybe ty + = isStateHackType arg : typeArity res + + | Just (tc,tys) <- splitTyConApp_maybe ty + , Just (ty', _) <- instNewTyCon_maybe tc tys + , not (isRecursiveTyCon tc) + , not (isClassTyCon tc) -- Do not eta-expand through newtype classes + -- See Note [Newtype classes and eta expansion] + = typeArity ty' + -- Important to look through non-recursive newtypes, so that, eg + -- (f x) where f has arity 2, f :: Int -> IO () + -- Here we want to get arity 1 for the result! + + | otherwise + = [] \end{code} +Note [Newtype classes and eta expansion] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +We have to be careful when eta-expanding through newtypes. In general +it's a good idea, but annoyingly it interacts badly with the class-op +rule mechanism. Consider + + class C a where { op :: a -> a } + instance C b => C [b] where + op x = ... + +These translate to + + co :: forall a. (a->a) ~ C a + + $copList :: C b -> [b] -> [b] + $copList d x = ... + + $dfList :: C b -> C [b] + {-# DFunUnfolding = [$copList] #-} + $dfList d = $copList d |> co@[b] + +Now suppose we have: + + dCInt :: C Int + + blah :: [Int] -> [Int] + blah = op ($dfList dCInt) + +Now we want the built-in op/$dfList rule will fire to give + blah = $copList dCInt + +But with eta-expansion 'blah' might (and in Trac #3772, which is +slightly more complicated, does) turn into + + blah = op (\eta. ($dfList dCInt |> sym co) eta) + +and now it is *much* harder for the op/$dfList rule to fire, becuase +exprIsConApp_maybe won't hold of the argument to op. I considered +trying to *make* it hold, but it's tricky and I gave up. + +The test simplCore/should_compile/T3722 is an excellent example. + + +Note [exprArity for applications] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +When we come to an application we check that the arg is trivial. + eg f (fac x) does not have arity 2, + even if f has arity 3! + +* We require that is trivial rather merely cheap. Suppose f has arity 2. + Then f (Just y) + has arity 0, because if we gave it arity 1 and then inlined f we'd get + let v = Just y in \w. + which has arity 0. And we try to maintain the invariant that we don't + have arity decreases. + +* The `max 0` is important! (\x y -> f x) has arity 2, even if f is + unknown, hence arity 0 + + %************************************************************************ %* * Eta expansion @@ -129,15 +209,14 @@ exprArity e = go e %************************************************************************ \begin{code} --- ^ The Arity returned is the number of value args the --- expression can be applied to without doing much work -exprEtaExpandArity :: DynFlags -> CoreExpr -> Arity --- exprEtaExpandArity is used when eta expanding --- e ==> \xy -> e x y -exprEtaExpandArity dflags e - = applyStateHack e (arityType dicts_cheap e) - where - dicts_cheap = dopt Opt_DictsCheap dflags +exprBotStrictness_maybe :: CoreExpr -> Maybe (Arity, StrictSig) +-- A cheap and cheerful function that identifies bottoming functions +-- and gives them a suitable strictness signatures. It's used during +-- float-out +exprBotStrictness_maybe e + = case getBotArity (arityType False e) of + Nothing -> Nothing + Just ar -> Just (ar, mkStrictSig (mkTopDmdType (replicate ar topDmd) BotRes)) \end{code} Note [Definition of arity] @@ -160,7 +239,6 @@ Or, to put it another way, in any context C is as efficient as C[ e ] - It's all a bit more subtle than it looks: Note [Arity of case expressions] @@ -182,7 +260,6 @@ This should diverge! But if we eta-expand, it won't. Again, we ignore this "problem", because being scrupulous would lose an important transformation for many programs. - 1. Note [One-shot lambdas] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider one-shot lambdas @@ -203,7 +280,6 @@ should diverge, but it'll converge if we eta-expand f. Nevertheless, we do so; it improves some programs significantly, and increasing convergence isn't a bad thing. Hence the ABot/ATop in ArityType. - 4. Note [Newtype arity] ~~~~~~~~~~~~~~~~~~~~~~~~ Non-recursive newtypes are transparent, and should not get in the way. @@ -244,38 +320,6 @@ Then we expect that if f is applied to one arg, it'll be applied to two (that's the hack -- we don't really know, and sometimes it's false) See also Id.isOneShotBndr. -\begin{code} -applyStateHack :: CoreExpr -> ArityType -> Arity -applyStateHack e (AT orig_arity is_bot) - | opt_NoStateHack = orig_arity - | ABot <- is_bot = orig_arity -- Note [State hack and bottoming functions] - | otherwise = go orig_ty orig_arity - where -- Note [The state-transformer hack] - orig_ty = exprType e - go :: Type -> Arity -> Arity - go ty arity -- This case analysis should match that in eta_expand - | Just (_, ty') <- splitForAllTy_maybe ty = go ty' arity - - | Just (tc,tys) <- splitTyConApp_maybe ty - , Just (ty', _) <- instNewTyCon_maybe tc tys - , not (isRecursiveTyCon tc) = go ty' arity - -- Important to look through non-recursive newtypes, so that, eg - -- (f x) where f has arity 2, f :: Int -> IO () - -- Here we want to get arity 1 for the result! - - | Just (arg,res) <- splitFunTy_maybe ty - , arity > 0 || isStateHackType arg = 1 + go res (arity-1) -{- - = if arity > 0 then 1 + go res (arity-1) - else if isStateHackType arg then - pprTrace "applystatehack" (vcat [ppr orig_arity, ppr orig_ty, - ppr ty, ppr res, ppr e]) $ - 1 + go res (arity-1) - else WARN( arity > 0, ppr arity ) 0 --} - | otherwise = WARN( arity > 0, ppr arity ) 0 -\end{code} - Note [State hack and bottoming functions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It's a terrible idea to use the state hack on a bottoming function. @@ -308,67 +352,169 @@ Extrude g1.g3 And now we can repeat the whole loop. Aargh! The bug is in applying the state hack to a function which then swallows the argument. +This arose in another guise in Trac #3959. Here we had + + catch# (throw exn >> return ()) + +Note that (throw :: forall a e. Exn e => e -> a) is called with [a = IO ()]. +After inlining (>>) we get + + catch# (\_. throw {IO ()} exn) + +We must *not* eta-expand to + + catch# (\_ _. throw {...} exn) + +because 'catch#' expects to get a (# _,_ #) after applying its argument to +a State#, not another function! + +In short, we use the state hack to allow us to push let inside a lambda, +but not to introduce a new lambda. + + +Note [ArityType] +~~~~~~~~~~~~~~~~ +ArityType is the result of a compositional analysis on expressions, +from which we can decide the real arity of the expression (extracted +with function getArity). + +Here is what the fields mean. If e has ArityType + (AT as r), where n = length as, +then + + * If r is ABot then (e x1..xn) definitely diverges + Partial applications may or may not diverge + + * If r is ACheap then (e x1..x(n-1)) is cheap, + including any nested sub-expressions inside e + (say e is (f e1 e2) then e1,e2 are cheap too) + + * e, (e x1), ... (e x1 ... x(n-1)) are definitely really + functions, or bottom, not casts from a data type + So eta expansion is dynamically ok; + see Note [State hack and bottoming functions], + the part about catch# + +We regard ABot as stronger than ACheap; ie if ABot holds +we don't bother about ACheap + +Suppose f = \xy. x+y +Then f :: AT [False,False] ACheap + f v :: AT [False] ACheap + f :: AT [False] ATop +Note the ArityRes flag tells whether the whole expression is cheap. +Note also that having a non-empty 'as' doesn't mean it has that +arity; see (f ) which does not have arity 1! + +The key function getArity extracts the arity (which in turn guides +eta-expansion) from ArityType. + * If the term is cheap or diverges we can certainly eta expand it + e.g. (f x) where x has arity 2 + + * If its a function whose first arg is one-shot (probably via the + state hack) we can eta expand it + e.g. (getChar ) -------------------- Main arity code ---------------------------- \begin{code} --- If e has ArityType (AT n r), then the term 'e' --- * Must be applied to at least n *value* args --- before doing any significant work --- * It will not diverge before being applied to n --- value arguments --- * If 'r' is ABot, then it guarantees to diverge if --- applied to n arguments (or more) - -data ArityType = AT Arity ArityRes -data ArityRes = ATop -- Know nothing - | ABot -- Diverges +-- See Note [ArityType] +data ArityType = AT [OneShot] ArityRes + -- There is always an explicit lambda + -- to justify the [OneShot] + +type OneShot = Bool -- False <=> Know nothing + -- True <=> Can definitely float inside this lambda + -- The 'True' case can arise either because a binder + -- is marked one-shot, or because it's a state lambda + -- and we have the state hack on + +data ArityRes = ATop | ACheap | ABot vanillaArityType :: ArityType -vanillaArityType = AT 0 ATop -- Totally uninformative +vanillaArityType = AT [] ATop -- Totally uninformative + +-- ^ The Arity returned is the number of value args the [_$_] +-- expression can be applied to without doing much work +exprEtaExpandArity :: DynFlags -> CoreExpr -> Arity +-- exprEtaExpandArity is used when eta expanding +-- e ==> \xy -> e x y +exprEtaExpandArity dflags e + = case (arityType dicts_cheap e) of + AT (a:as) res | want_eta a res -> 1 + length as + _ -> 0 + where + want_eta one_shot ATop = one_shot + want_eta _ _ = True + + dicts_cheap = dopt Opt_DictsCheap dflags + +getBotArity :: ArityType -> Maybe Arity +-- Arity of a divergent function +getBotArity (AT as ABot) = Just (length as) +getBotArity _ = Nothing + +arityLam :: Id -> ArityType -> ArityType +arityLam id (AT as r) = AT (isOneShotBndr id : as) r -incArity :: ArityType -> ArityType -incArity (AT a r) = AT (a+1) r +floatIn :: Bool -> ArityType -> ArityType +-- We have something like (let x = E in b), +-- where b has the given arity type. +floatIn c (AT as r) = AT as (extendArityRes r c) -decArity :: ArityType -> ArityType -decArity (AT 0 r) = AT 0 r -decArity (AT a r) = AT (a-1) r +arityApp :: ArityType -> CoreExpr -> ArityType +-- Processing (fun arg) where at is the ArityType of fun, +arityApp (AT [] r) arg = AT [] (extendArityRes r (exprIsCheap arg)) +arityApp (AT (_:as) r) arg = AT as (extendArityRes r (exprIsCheap arg)) + +extendArityRes :: ArityRes -> Bool -> ArityRes +extendArityRes ABot _ = ABot +extendArityRes ACheap True = ACheap +extendArityRes _ _ = ATop andArityType :: ArityType -> ArityType -> ArityType -- Used for branches of a 'case' -andArityType (AT a1 ATop) (AT a2 ATop) = AT (a1 `min` a2) ATop -andArityType (AT _ ABot) (AT a2 ATop) = AT a2 ATop -andArityType (AT a1 ATop) (AT _ ABot) = AT a1 ATop -andArityType (AT a1 ABot) (AT a2 ABot) = AT (a1 `max` a2) ABot - -trimArity :: Bool -> ArityType -> ArityType --- We have something like (let x = E in b), where b has the given --- arity type. Then --- * If E is cheap we can push it inside as far as we like --- * If b eventually diverges, we allow ourselves to push inside --- arbitrarily, even though that is not quite right -trimArity _cheap (AT a ABot) = AT a ABot -trimArity True (AT a ATop) = AT a ATop -trimArity False (AT _ ATop) = AT 0 ATop -- Bale out +andArityType (AT as1 r1) (AT as2 r2) + = AT (go_as as1 as2) (go_r r1 r2) + where + go_r ABot ABot = ABot + go_r ABot ACheap = ACheap + go_r ACheap ABot = ACheap + go_r ACheap ACheap = ACheap + go_r _ _ = ATop + + go_as (os1:as1) (os2:as2) = (os1 || os2) : go_as as1 as2 + go_as [] as2 = as2 + go_as as1 [] = as1 +\end{code} + +\begin{code} --------------------------- arityType :: Bool -> CoreExpr -> ArityType arityType _ (Var v) - | Just strict_sig <- idNewStrictness_maybe v + | Just strict_sig <- idStrictness_maybe v , (ds, res) <- splitStrictSig strict_sig - , isBotRes res - = AT (length ds) ABot -- Function diverges + = mk_arity (length ds) res | otherwise - = AT (idArity v) ATop + = mk_arity (idArity v) TopRes + + where + mk_arity id_arity res + | isBotRes res = AT (take id_arity one_shots) ABot + | id_arity>0 = AT (take id_arity one_shots) ACheap + | otherwise = AT [] ATop + + one_shots = typeArity (idType v) -- Lambdas; increase arity arityType dicts_cheap (Lam x e) - | isId x = incArity (arityType dicts_cheap e) + | isId x = arityLam x (arityType dicts_cheap e) | otherwise = arityType dicts_cheap e -- Applications; decrease arity arityType dicts_cheap (App fun (Type _)) = arityType dicts_cheap fun arityType dicts_cheap (App fun arg ) - = trimArity (exprIsCheap arg) (decArity (arityType dicts_cheap fun)) + = arityApp (arityType dicts_cheap fun) arg -- Case/Let; keep arity if either the expression is cheap -- or it's a 1-shot lambda @@ -378,11 +524,11 @@ arityType dicts_cheap (App fun arg ) -- f x y = case x of { (a,b) -> e } -- The difference is observable using 'seq' arityType dicts_cheap (Case scrut _ _ alts) - = trimArity (exprIsCheap scrut) + = floatIn (exprIsCheap scrut) (foldr1 andArityType [arityType dicts_cheap rhs | (_,_,rhs) <- alts]) arityType dicts_cheap (Let b e) - = trimArity (cheap_bind b) (arityType dicts_cheap e) + = floatIn (cheap_bind b) (arityType dicts_cheap e) where cheap_bind (NonRec b e) = is_cheap (b,e) cheap_bind (Rec prs) = all is_cheap prs @@ -408,7 +554,8 @@ arityType dicts_cheap (Let b e) -- See Note [Dictionary-like types] in TcType.lhs for why we use -- isDictLikeTy here rather than isDictTy -arityType dicts_cheap (Note _ e) = arityType dicts_cheap e +arityType dicts_cheap (Note n e) + | notSccNote n = arityType dicts_cheap e arityType dicts_cheap (Cast e _) = arityType dicts_cheap e arityType _ _ = vanillaArityType \end{code} @@ -430,6 +577,13 @@ simplification but it's not too hard. The alernative, of relying on a subsequent clean-up phase of the Simplifier to de-crapify the result, means you can't really use it in CorePrep, which is painful. +Note [Eta expansion and SCCs] +~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ +Note that SCCs are not treated specially by etaExpand. If we have + etaExpand 2 (\x -> scc "foo" e) + = (\xy -> (scc "foo" e) y) +So the costs of evaluating 'e' (not 'e y') are attributed to "foo" + \begin{code} -- | @etaExpand n us e ty@ returns an expression with -- the same meaning as @e@, but with arity @n@. @@ -444,11 +598,6 @@ means you can't really use it in CorePrep, which is painful. etaExpand :: Arity -- ^ Result should have this number of value args -> CoreExpr -- ^ Expression to expand -> CoreExpr --- Note that SCCs are not treated specially. If we have --- etaExpand 2 (\x -> scc "foo" e) --- = (\xy -> (scc "foo" e) y) --- So the costs of evaluating 'e' (not 'e y') are attributed to "foo" - -- etaExpand deals with for-alls. For example: -- etaExpand 1 E -- where E :: forall a. a -> a @@ -459,16 +608,13 @@ etaExpand :: Arity -- ^ Result should have this number of value args -- so perhaps the extra code isn't worth it etaExpand n orig_expr - | manifestArity orig_expr >= n = orig_expr -- The no-op case - | otherwise = go n orig_expr where - -- Strip off existing lambdas + -- Strip off existing lambdas and casts -- Note [Eta expansion and SCCs] go 0 expr = expr - go n (Lam v body) | isTyVar v = Lam v (go n body) + go n (Lam v body) | isTyCoVar v = Lam v (go n body) | otherwise = Lam v (go (n-1) body) - go n (Note InlineMe expr) = Note InlineMe (go n expr) go n (Cast expr co) = Cast (go n expr) co go n expr = -- pprTrace "ee" (vcat [ppr orig_expr, ppr expr, ppr etas]) $ etaInfoAbs etas (etaInfoApp subst' expr etas) @@ -510,7 +656,7 @@ etaInfoApp :: Subst -> CoreExpr -> [EtaInfo] -> CoreExpr etaInfoApp subst (Lam v1 e) (EtaVar v2 : eis) = etaInfoApp subst' e eis where - subst' | isTyVar v1 = CoreSubst.extendTvSubst subst v1 (mkTyVarTy v2) + subst' | isTyCoVar v1 = CoreSubst.extendTvSubst subst v1 (mkTyVarTy v2) | otherwise = CoreSubst.extendIdSubst subst v1 (Var v2) etaInfoApp subst (Cast e co1) eis @@ -550,12 +696,12 @@ mkEtaWW :: Arity -> InScopeSet -> Type -- Outgoing InScopeSet includes the EtaInfo vars -- and the original free vars -mkEtaWW n in_scope ty - = go n empty_subst ty [] +mkEtaWW orig_n in_scope orig_ty + = go orig_n empty_subst orig_ty [] where empty_subst = mkTvSubst in_scope emptyTvSubstEnv - go n subst ty eis + go n subst ty eis -- See Note [exprArity invariant] | n == 0 = (getTvInScope subst, reverse eis) @@ -576,10 +722,12 @@ mkEtaWW n in_scope ty -- eta_expand 1 e T -- We want to get -- coerce T (\x::[T] -> (coerce ([T]->Int) e) x) - go n subst ty' (EtaCo (substTy subst co) : eis) + go n subst ty' (EtaCo (Type.substTy subst co) : eis) - | otherwise -- We have an expression of arity > 0, - = (getTvInScope subst, reverse eis) -- but its type isn't a function. + | otherwise -- We have an expression of arity > 0, + -- but its type isn't a function. + = WARN( True, ppr orig_n <+> ppr orig_ty ) + (getTvInScope subst, reverse eis) -- This *can* legitmately happen: -- e.g. coerce Int (\x. x) Essentially the programmer is -- playing fast and loose with types (Happy does this a lot). @@ -588,22 +736,13 @@ mkEtaWW n in_scope ty -------------- --- Avoiding unnecessary substitution +-- Avoiding unnecessary substitution; use short-cutting versions subst_expr :: Subst -> CoreExpr -> CoreExpr -subst_expr s e | isEmptySubst s = e - | otherwise = substExpr s e +subst_expr = substExprSC (text "CoreArity:substExpr") subst_bind :: Subst -> CoreBind -> (Subst, CoreBind) -subst_bind subst (NonRec b r) - = (subst', NonRec b' (subst_expr subst r)) - where - (subst', b') = substBndr subst b -subst_bind subst (Rec prs) - = (subst', Rec (bs1 `zip` map (subst_expr subst') rhss)) - where - (bs, rhss) = unzip prs - (subst', bs1) = substBndrs subst bs +subst_bind = substBindSC -------------- @@ -618,9 +757,9 @@ freshEtaId :: Int -> TvSubst -> Type -> (TvSubst, Id) freshEtaId n subst ty = (subst', eta_id') where - ty' = substTy subst ty + ty' = Type.substTy subst ty eta_id' = uniqAway (getTvInScope subst) $ mkSysLocal (fsLit "eta") (mkBuiltinUnique n) ty' - subst' = extendTvInScope subst [eta_id'] + subst' = extendTvInScope subst eta_id' \end{code}