-- | Arit and eta expansion module CoreArity ( manifestArity, exprArity, exprBotStrictness_maybe, exprEtaExpandArity, CheapFun, etaExpand ) where #include "HsVersions.h" import CoreSyn import CoreFVs import CoreUtils import CoreSubst import Demand import Var import VarEnv import Id import Type import TyCon ( isRecursiveTyCon, isClassTyCon ) import Coercion import BasicTypes import Unique import Outputable import FastString\end{code} %************************************************************************ %* * manifestArity and exprArity %* * %************************************************************************ exprArity is a cheap-and-cheerful version of exprEtaExpandArity. It tells how many things the expression can be applied to before doing any work. It doesn't look inside cases, lets, etc. The idea is that exprEtaExpandArity will do the hard work, leaving something that's easy for exprArity to grapple with. In particular, Simplify uses exprArity to compute the ArityInfo for the Id. Originally I thought that it was enough just to look for top-level lambdas, but it isn't. I've seen this foo = PrelBase.timesInt We want foo to get arity 2 even though the eta-expander will leave it unchanged, in the expectation that it'll be inlined. But occasionally it isn't, because foo is blacklisted (used in a rule). Similarly, see the ok_note check in exprEtaExpandArity. So f = __inline_me (\x -> e) won't be eta-expanded. And in any case it seems more robust to have exprArity be a bit more intelligent. But note that (\x y z -> f x y z) should have arity 3, regardless of f's arity. \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 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 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 --------------- 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 = [] --------------- 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 is_cheap e) of Nothing -> Nothing Just ar -> Just (ar, mkStrictSig (mkTopDmdType (replicate ar topDmd) BotRes)) where is_cheap _ _ = False -- Irrelevant for this purpose\end{code} Note [exprArity invariant] ~~~~~~~~~~~~~~~~~~~~~~~~~~ exprArity has the following invariant: * 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 each top-level Id, and in - In CorePrep we use etaExpand on each rhs, so that the visible lambdas actually match that arity, which in turn means that the StgRhs has the right number of lambdas An alternative would be to do the eta-expansion in TidyPgm, at least for top-level bindings, in which case we would not need the trim_arity in exprArity. That is a less local change, so I'm going to leave it for today! 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.

-- See Note [ArityType] data ArityType = ATop [OneShot] | ABot Arity -- There is always an explicit lambda -- to justify the [OneShot], or the Arity 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 vanillaArityType :: ArityType vanillaArityType = ATop [] -- Totally uninformative -- ^ The Arity returned is the number of value args the [_$_] -- expression can be applied to without doing much work exprEtaExpandArity :: CheapFun -> CoreExpr -> Arity -- exprEtaExpandArity is used when eta expanding -- e ==> \xy -> e x y exprEtaExpandArity cheap_fun e = case (arityType cheap_fun e) of ATop (os:oss) | os || has_lam e -> 1 + length oss -- Note [Eta expanding thunks] | otherwise -> 0 ATop [] -> 0 ABot n -> n where has_lam (Note _ e) = has_lam e has_lam (Lam b e) = isId b || has_lam e has_lam _ = False getBotArity :: ArityType -> Maybe Arity -- Arity of a divergent function getBotArity (ABot n) = Just n getBotArity _ = Nothing\end{code} Note [Eta expanding thunks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ When we see f = case y of p -> \x -> blah should we eta-expand it? Well, if 'x' is a one-shot state token then 'yes' because 'f' will only be applied once. But otherwise we (conservatively) say no. My main reason is to avoid expanding PAPSs f = g d ==> f = \x. g d x because that might in turn make g inline (if it has an inline pragma), which we might not want. After all, INLINE pragmas say "inline only when saturate" so we don't want to be too gung-ho about saturating! \begin{code}

arityLam :: Id -> ArityType -> ArityType arityLam id (ATop as) = ATop (isOneShotBndr id : as) arityLam _ (ABot n) = ABot (n+1) floatIn :: Bool -> ArityType -> ArityType -- We have something like (let x = E in b), -- where b has the given arity type. floatIn _ (ABot n) = ABot n floatIn True (ATop as) = ATop as floatIn False (ATop as) = ATop (takeWhile id as) -- If E is not cheap, keep arity only for one-shots arityApp :: ArityType -> Bool -> ArityType -- Processing (fun arg) where at is the ArityType of fun, -- Knock off an argument and behave like 'let' arityApp (ABot 0) _ = ABot 0 arityApp (ABot n) _ = ABot (n-1) arityApp (ATop []) _ = ATop [] arityApp (ATop (_:as)) cheap = floatIn cheap (ATop as) andArityType :: ArityType -> ArityType -> ArityType -- Used for branches of a 'case' andArityType (ABot n1) (ABot n2) = ABot (n1 `min` n2) andArityType (ATop as) (ABot _) = ATop as andArityType (ABot _) (ATop bs) = ATop bs andArityType (ATop as) (ATop bs) = ATop (as `combine` bs) where -- See Note [Combining case branches] combine (a:as) (b:bs) = (a && b) : combine as bs combine [] bs = take_one_shots bs combine as [] = take_one_shots as take_one_shots [] = [] take_one_shots (one_shot : as) | one_shot = True : take_one_shots as | otherwise = []\end{code} Note [Combining case branches] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider go = \x. let z = go e0 go2 = \x. case x of True -> z False -> \s(one-shot). e1 in go2 x We *really* want to eta-expand go and go2. When combining the barnches of the case we have ATop [] `andAT` ATop [True] and we want to get ATop [True]. But if the inner lambda wasn't one-shot we don't want to do this. (We need a proper arity analysis to justify that.) \begin{code}

--------------------------- type CheapFun = CoreExpr -> Maybe Type -> Bool -- How to decide if an expression is cheap -- If the Maybe is Just, the type is the type -- of the expression; Nothing means "don't know" arityType :: CheapFun -> CoreExpr -> ArityType arityType _ (Var v) | Just strict_sig <- idStrictness_maybe v , (ds, res) <- splitStrictSig strict_sig , let arity = length ds = if isBotRes res then ABot arity else ATop (take arity one_shots) | otherwise = ATop (take (idArity v) one_shots) where one_shots :: [Bool] -- One-shot-ness derived from the type one_shots = typeArity (idType v) -- Lambdas; increase arity arityType cheap_fn (Lam x e) | isId x = arityLam x (arityType cheap_fn e) | otherwise = arityType cheap_fn e -- Applications; decrease arity arityType cheap_fn (App fun (Type _)) = arityType cheap_fn fun arityType cheap_fn (App fun arg ) = arityApp (arityType cheap_fn fun) (cheap_fn arg Nothing) -- Case/Let; keep arity if either the expression is cheap -- or it's a 1-shot lambda -- The former is not really right for Haskell -- f x = case x of { (a,b) -> \y. e } -- ===> -- f x y = case x of { (a,b) -> e } -- The difference is observable using 'seq' arityType cheap_fn (Case scrut bndr _ alts) = floatIn (cheap_fn scrut (Just (idType bndr))) (foldr1 andArityType [arityType cheap_fn rhs | (_,_,rhs) <- alts]) arityType cheap_fn (Let b e) = floatIn (cheap_bind b) (arityType cheap_fn e) where cheap_bind (NonRec b e) = is_cheap (b,e) cheap_bind (Rec prs) = all is_cheap prs is_cheap (b,e) = cheap_fn e (Just (idType b)) arityType cheap_fn (Note n e) | notSccNote n = arityType cheap_fn e arityType cheap_fn (Cast e _) = arityType cheap_fn e arityType _ _ = vanillaArityType\end{code} %************************************************************************ %* * The main eta-expander %* * %************************************************************************ We go for: f = \x1..xn -> N ==> f = \x1..xn y1..ym -> N y1..ym (n >= 0) where (in both cases) * The xi can include type variables * The yi are all value variables * N is a NORMAL FORM (i.e. no redexes anywhere) wanting a suitable number of extra args. The biggest reason for doing this is for cases like f = \x -> case x of True -> \y -> e1 False -> \y -> e2 Here we want to get the lambdas together. A good exmaple is the nofib program fibheaps, which gets 25% more allocation if you don't do this eta-expansion. We may have to sandwich some coerces between the lambdas to make the types work. exprEtaExpandArity looks through coerces when computing arity; and etaExpand adds the coerces as necessary when actually computing the expansion. Note [No crap in eta-expanded code] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The eta expander is careful not to introduce "crap". In particular, given a CoreExpr satisfying the 'CpeRhs' invariant (in CorePrep), it returns a CoreExpr satisfying the same invariant. See Note [Eta expansion and the CorePrep invariants] in CorePrep. This means the eta-expander has to do a bit of on-the-fly 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@. -- -- Given: -- -- > e' = etaExpand n us e ty -- -- We should have that: -- -- > ty = exprType e = exprType e' etaExpand :: Arity -- ^ Result should have this number of value args -> CoreExpr -- ^ Expression to expand -> CoreExpr -- etaExpand deals with for-alls. For example: -- etaExpand 1 E -- where E :: forall a. a -> a -- would return -- (/\b. \y::a -> E b y) -- -- It deals with coerces too, though they are now rare -- so perhaps the extra code isn't worth it etaExpand n orig_expr = go n orig_expr where -- Strip off existing lambdas and casts -- Note [Eta expansion and SCCs] go 0 expr = expr go n (Lam v body) | isTyCoVar v = Lam v (go n body) | otherwise = Lam v (go (n-1) body) 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) where in_scope = mkInScopeSet (exprFreeVars expr) (in_scope', etas) = mkEtaWW n in_scope (exprType expr) subst' = mkEmptySubst in_scope' -- Wrapper Unwrapper -------------- data EtaInfo = EtaVar Var -- /\a. [], [] a -- \x. [], [] x | EtaCo Coercion -- [] |> co, [] |> (sym co) instance Outputable EtaInfo where ppr (EtaVar v) = ptext (sLit "EtaVar") <+> ppr v ppr (EtaCo co) = ptext (sLit "EtaCo") <+> ppr co pushCoercion :: Coercion -> [EtaInfo] -> [EtaInfo] pushCoercion co1 (EtaCo co2 : eis) | isIdentityCoercion co = eis | otherwise = EtaCo co : eis where co = co1 `mkTransCoercion` co2 pushCoercion co eis = EtaCo co : eis -------------- etaInfoAbs :: [EtaInfo] -> CoreExpr -> CoreExpr etaInfoAbs [] expr = expr etaInfoAbs (EtaVar v : eis) expr = Lam v (etaInfoAbs eis expr) etaInfoAbs (EtaCo co : eis) expr = Cast (etaInfoAbs eis expr) (mkSymCoercion co) -------------- etaInfoApp :: Subst -> CoreExpr -> [EtaInfo] -> CoreExpr -- (etaInfoApp s e eis) returns something equivalent to -- ((substExpr s e) `appliedto` eis) etaInfoApp subst (Lam v1 e) (EtaVar v2 : eis) = etaInfoApp subst' e eis where subst' | isTyCoVar v1 = CoreSubst.extendTvSubst subst v1 (mkTyVarTy v2) | otherwise = CoreSubst.extendIdSubst subst v1 (Var v2) etaInfoApp subst (Cast e co1) eis = etaInfoApp subst e (pushCoercion co' eis) where co' = CoreSubst.substTy subst co1 etaInfoApp subst (Case e b _ alts) eis = Case (subst_expr subst e) b1 (coreAltsType alts') alts' where (subst1, b1) = substBndr subst b alts' = map subst_alt alts subst_alt (con, bs, rhs) = (con, bs', etaInfoApp subst2 rhs eis) where (subst2,bs') = substBndrs subst1 bs etaInfoApp subst (Let b e) eis = Let b' (etaInfoApp subst' e eis) where (subst', b') = subst_bind subst b etaInfoApp subst (Note note e) eis = Note note (etaInfoApp subst e eis) etaInfoApp subst e eis = go (subst_expr subst e) eis where go e [] = e go e (EtaVar v : eis) = go (App e (varToCoreExpr v)) eis go e (EtaCo co : eis) = go (Cast e co) eis -------------- mkEtaWW :: Arity -> InScopeSet -> Type -> (InScopeSet, [EtaInfo]) -- EtaInfo contains fresh variables, -- not free in the incoming CoreExpr -- Outgoing InScopeSet includes the EtaInfo vars -- and the original free vars 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 -- See Note [exprArity invariant] | n == 0 = (getTvInScope subst, reverse eis) | Just (tv,ty') <- splitForAllTy_maybe ty , let (subst', tv') = substTyVarBndr subst tv -- Avoid free vars of the original expression = go n subst' ty' (EtaVar tv' : eis) | Just (arg_ty, res_ty) <- splitFunTy_maybe ty , let (subst', eta_id') = freshEtaId n subst arg_ty -- Avoid free vars of the original expression = go (n-1) subst' res_ty (EtaVar eta_id' : eis) | Just(ty',co) <- splitNewTypeRepCo_maybe ty = -- Given this: -- newtype T = MkT ([T] -> Int) -- Consider eta-expanding this -- eta_expand 1 e T -- We want to get -- coerce T (\x::[T] -> (coerce ([T]->Int) e) x) go n subst ty' (EtaCo (Type.substTy subst co) : eis) | 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). -- So we simply decline to eta-expand. Otherwise we'd end up -- with an explicit lambda having a non-function type -------------- -- Avoiding unnecessary substitution; use short-cutting versions subst_expr :: Subst -> CoreExpr -> CoreExpr subst_expr = substExprSC (text "CoreArity:substExpr") subst_bind :: Subst -> CoreBind -> (Subst, CoreBind) subst_bind = substBindSC -------------- freshEtaId :: Int -> TvSubst -> Type -> (TvSubst, Id) -- Make a fresh Id, with specified type (after applying substitution) -- It should be "fresh" in the sense that it's not in the in-scope set -- of the TvSubstEnv; and it should itself then be added to the in-scope -- set of the TvSubstEnv -- -- The Int is just a reasonable starting point for generating a unique; -- it does not necessarily have to be unique itself. freshEtaId n subst ty = (subst', eta_id') where ty' = Type.substTy subst ty eta_id' = uniqAway (getTvInScope subst) $ mkSysLocal (fsLit "eta") (mkBuiltinUnique n) ty' subst' = extendTvInScope subst eta_id'\end{code}