{- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 Arity and eta expansion -} {-# LANGUAGE CPP #-} -- | Arity and eta expansion module CoreArity ( manifestArity, joinRhsArity, exprArity, typeArity, exprEtaExpandArity, findRhsArity, etaExpand, etaExpandToJoinPoint, etaExpandToJoinPointRule, exprBotStrictness_maybe ) where #include "HsVersions.h" import GhcPrelude import CoreSyn import CoreFVs import CoreUtils import CoreSubst import Demand import Var import VarEnv import Id import Type import TyCon ( initRecTc, checkRecTc ) import Predicate ( isDictTy ) import Coercion import BasicTypes import Unique import DynFlags ( DynFlags, GeneralFlag(..), gopt ) import Outputable import FastString import Pair import Util ( debugIsOn ) {- ************************************************************************ * * 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. -} manifestArity :: CoreExpr -> Arity -- ^ manifestArity sees how many leading value lambdas there are, -- after looking through casts manifestArity (Lam v e) | isId v = 1 + manifestArity e | otherwise = manifestArity e manifestArity (Tick t e) | not (tickishIsCode t) = manifestArity e manifestArity (Cast e _) = manifestArity e manifestArity _ = 0 joinRhsArity :: CoreExpr -> JoinArity -- Join points are supposed to have manifestly-visible -- lambdas at the top: no ticks, no casts, nothing -- Moreover, type lambdas count in JoinArity joinRhsArity (Lam _ e) = 1 + joinRhsArity e joinRhsArity _ = 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 (Tick t e) | not (tickishIsCode t) = go e go (Cast e co) = trim_arity (go e) (pSnd (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] -- NB: coercions count as a value argument go _ = 0 trim_arity :: Arity -> Type -> Arity trim_arity arity ty = arity `min` length (typeArity ty) --------------- typeArity :: Type -> [OneShotInfo] -- How many value arrows are visible in the type? -- We look through foralls, and newtypes -- See Note [exprArity invariant] typeArity ty = go initRecTc ty where go rec_nts ty | Just (_, ty') <- splitForAllTy_maybe ty = go rec_nts ty' | Just (arg,res) <- splitFunTy_maybe ty = typeOneShot arg : go rec_nts res | Just (tc,tys) <- splitTyConApp_maybe ty , Just (ty', _) <- instNewTyCon_maybe tc tys , Just rec_nts' <- checkRecTc rec_nts tc -- See Note [Expanding newtypes] -- in TyCon -- , not (isClassTyCon tc) -- Do not eta-expand through newtype classes -- -- See Note [Newtype classes and eta expansion] -- (no longer required) = go rec_nts' 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! -- -- AND through a layer of recursive newtypes -- e.g. newtype Stream m a b = Stream (m (Either b (a, Stream m a b))) | 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 env e) of Nothing -> Nothing Just ar -> Just (ar, sig ar) where env = AE { ae_ped_bot = True, ae_cheap_fn = \ _ _ -> False } sig ar = mkClosedStrictSig (replicate ar topDmd) botRes {- Note [exprArity invariant] ~~~~~~~~~~~~~~~~~~~~~~~~~~ exprArity has the following invariants: (1) 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 (2) exprArity e <= typeArity (exprType e) (3) 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] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ NB: this nasty special case is no longer required, because for newtype classes we don't use the class-op rule mechanism at all. See Note [Single-method classes] in TcInstDcls. SLPJ May 2013 -------- Old out of date comments, just for interest ----------- 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 = $copList dCInt But with eta-expansion 'blah' might (and in #3772, which is slightly more complicated, does) turn into blah = op (\eta. ($dfList dCInt |> sym co) eta) and now it is *much* harder for the op/$dfList rule to fire, because 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. -------- End of old out of date comments, just for interest ----------- 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. <f-body> 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 ************************************************************************ * * Computing the "arity" of an expression * * ************************************************************************ Note [Definition of arity] ~~~~~~~~~~~~~~~~~~~~~~~~~~ The "arity" of an expression 'e' is n if applying 'e' to *fewer* than n *value* arguments converges rapidly Or, to put it another way there is no work lost in duplicating the partial application (e x1 .. x(n-1)) In the divegent case, no work is lost by duplicating because if the thing is evaluated once, that's the end of the program. Or, to put it another way, in any context C C[ (\x1 .. xn. e x1 .. xn) ] is as efficient as C[ e ] It's all a bit more subtle than it looks: Note [One-shot lambdas] ~~~~~~~~~~~~~~~~~~~~~~~ Consider one-shot lambdas let x = expensive in \y z -> E We want this to have arity 1 if the \y-abstraction is a 1-shot lambda. Note [Dealing with bottom] ~~~~~~~~~~~~~~~~~~~~~~~~~~ A Big Deal with computing arities is expressions like f = \x -> case x of True -> \s -> e1 False -> \s -> e2 This happens all the time when f :: Bool -> IO () In this case we do eta-expand, in order to get that \s to the top, and give f arity 2. This isn't really right in the presence of seq. Consider (f bot) `seq` 1 This should diverge! But if we eta-expand, it won't. We ignore this "problem" (unless -fpedantic-bottoms is on), because being scrupulous would lose an important transformation for many programs. (See #5587 for an example.) Consider also f = \x -> error "foo" Here, arity 1 is fine. But if it is f = \x -> case x of True -> error "foo" False -> \y -> x+y then we want to get arity 2. Technically, this isn't quite right, because (f True) `seq` 1 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. So these two transformations aren't always the Right Thing, and we have several tickets reporting unexpected behaviour resulting from this transformation. So we try to limit it as much as possible: (1) Do NOT move a lambda outside a known-bottom case expression case undefined of { (a,b) -> \y -> e } This showed up in #5557 (2) Do NOT move a lambda outside a case if all the branches of the case are known to return bottom. case x of { (a,b) -> \y -> error "urk" } This case is less important, but the idea is that if the fn is going to diverge eventually anyway then getting the best arity isn't an issue, so we might as well play safe (3) Do NOT move a lambda outside a case unless (a) The scrutinee is ok-for-speculation, or (b) more liberally: the scrutinee is cheap (e.g. a variable), and -fpedantic-bottoms is not enforced (see #2915 for an example) Of course both (1) and (2) are readily defeated by disguising the bottoms. 4. Note [Newtype arity] ~~~~~~~~~~~~~~~~~~~~~~~~ Non-recursive newtypes are transparent, and should not get in the way. We do (currently) eta-expand recursive newtypes too. So if we have, say newtype T = MkT ([T] -> Int) Suppose we have e = coerce T f where f has arity 1. Then: etaExpandArity e = 1; that is, etaExpandArity looks through the coerce. When we eta-expand e to arity 1: eta_expand 1 e T we want to get: coerce T (\x::[T] -> (coerce ([T]->Int) e) x) HOWEVER, note that if you use coerce bogusly you can ge coerce Int negate And since negate has arity 2, you might try to eta expand. But you can't decopose Int to a function type. Hence the final case in eta_expand. Note [The state-transformer hack] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have f = e where e has arity n. Then, if we know from the context that f has a usage type like t1 -> ... -> tn -1-> t(n+1) -1-> ... -1-> tm -> ... then we can expand the arity to m. This usage type says that any application (x e1 .. en) will be applied to uniquely to (m-n) more args Consider f = \x. let y = <expensive> in case x of True -> foo False -> \(s:RealWorld) -> e where foo has arity 1. Then we want the state hack to apply to foo too, so we can eta expand the case. 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. Note [State hack and bottoming functions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It's a terrible idea to use the state hack on a bottoming function. Here's what happens (#2861): f :: String -> IO T f = \p. error "..." Eta-expand, using the state hack: f = \p. (\s. ((error "...") |> g1) s) |> g2 g1 :: IO T ~ (S -> (S,T)) g2 :: (S -> (S,T)) ~ IO T Extrude the g2 f' = \p. \s. ((error "...") |> g1) s f = f' |> (String -> g2) Discard args for bottomming function f' = \p. \s. ((error "...") |> g1 |> g3 g3 :: (S -> (S,T)) ~ (S,T) Extrude g1.g3 f'' = \p. \s. (error "...") f' = f'' |> (String -> S -> 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 #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 exprEtaExpandArity). Here is what the fields mean. If an arbitrary expression 'f' has ArityType 'at', then * If at = ABot n, then (f x1..xn) definitely diverges. Partial applications to fewer than n args may *or may not* diverge. We allow ourselves to eta-expand bottoming functions, even if doing so may lose some `seq` sharing, let x = <expensive> in \y. error (g x y) ==> \y. let x = <expensive> in error (g x y) * If at = ATop as, and n=length as, then expanding 'f' to (\x1..xn. f x1 .. xn) loses no sharing, assuming the calls of f respect the one-shot-ness of its definition. NB 'f' is an arbitrary expression, eg (f = g e1 e2). This 'f' can have ArityType as ATop, with length as > 0, only if e1 e2 are themselves. * In both cases, f, (f x1), ... (f x1 ... f(n-1)) are definitely really functions, or bottom, but *not* casts from a data type, in at least one case branch. (If it's a function in one case branch but an unsafe cast from a data type in another, the program is bogus.) So eta expansion is dynamically ok; see Note [State hack and bottoming functions], the part about catch# Example: f = \x\y. let v = <expensive> in \s(one-shot) \t(one-shot). blah 'f' has ArityType [ManyShot,ManyShot,OneShot,OneShot] The one-shot-ness means we can, in effect, push that 'let' inside the \st. Suppose f = \xy. x+y Then f :: AT [False,False] ATop f v :: AT [False] ATop f <expensive> :: AT [] ATop -------------------- Main arity code ---------------------------- -} -- See Note [ArityType] data ArityType = ATop [OneShotInfo] | ABot Arity -- There is always an explicit lambda -- to justify the [OneShot], or the Arity instance Outputable ArityType where ppr (ATop os) = text "ATop" <> parens (ppr (length os)) ppr (ABot n) = text "ABot" <> parens (ppr n) 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 :: DynFlags -> CoreExpr -> Arity -- exprEtaExpandArity is used when eta expanding -- e ==> \xy -> e x y exprEtaExpandArity dflags e = case (arityType env e) of ATop oss -> length oss ABot n -> n where env = AE { ae_cheap_fn = mk_cheap_fn dflags isCheapApp , ae_ped_bot = gopt Opt_PedanticBottoms dflags } getBotArity :: ArityType -> Maybe Arity -- Arity of a divergent function getBotArity (ABot n) = Just n getBotArity _ = Nothing mk_cheap_fn :: DynFlags -> CheapAppFun -> CheapFun mk_cheap_fn dflags cheap_app | not (gopt Opt_DictsCheap dflags) = \e _ -> exprIsCheapX cheap_app e | otherwise = \e mb_ty -> exprIsCheapX cheap_app e || case mb_ty of Nothing -> False Just ty -> isDictTy ty ---------------------- findRhsArity :: DynFlags -> Id -> CoreExpr -> Arity -> (Arity, Bool) -- This implements the fixpoint loop for arity analysis -- See Note [Arity analysis] -- If findRhsArity e = (n, is_bot) then -- (a) any application of e to <n arguments will not do much work, -- so it is safe to expand e ==> (\x1..xn. e x1 .. xn) -- (b) if is_bot=True, then e applied to n args is guaranteed bottom findRhsArity dflags bndr rhs old_arity = go (get_arity init_cheap_app) -- We always call exprEtaExpandArity once, but usually -- that produces a result equal to old_arity, and then -- we stop right away (since arities should not decrease) -- Result: the common case is that there is just one iteration where is_lam = has_lam rhs has_lam (Tick _ e) = has_lam e has_lam (Lam b e) = isId b || has_lam e has_lam _ = False init_cheap_app :: CheapAppFun init_cheap_app fn n_val_args | fn == bndr = True -- On the first pass, this binder gets infinite arity | otherwise = isCheapApp fn n_val_args go :: (Arity, Bool) -> (Arity, Bool) go cur_info@(cur_arity, _) | cur_arity <= old_arity = cur_info | new_arity == cur_arity = cur_info | otherwise = ASSERT( new_arity < cur_arity ) #if defined(DEBUG) pprTrace "Exciting arity" (vcat [ ppr bndr <+> ppr cur_arity <+> ppr new_arity , ppr rhs]) #endif go new_info where new_info@(new_arity, _) = get_arity cheap_app cheap_app :: CheapAppFun cheap_app fn n_val_args | fn == bndr = n_val_args < cur_arity | otherwise = isCheapApp fn n_val_args get_arity :: CheapAppFun -> (Arity, Bool) get_arity cheap_app = case (arityType env rhs) of ABot n -> (n, True) ATop (os:oss) | isOneShotInfo os || is_lam -> (1 + length oss, False) -- Don't expand PAPs/thunks ATop _ -> (0, False) -- Note [Eta expanding thunks] where env = AE { ae_cheap_fn = mk_cheap_fn dflags cheap_app , ae_ped_bot = gopt Opt_PedanticBottoms dflags } {- Note [Arity analysis] ~~~~~~~~~~~~~~~~~~~~~ The motivating example for arity analysis is this: f = \x. let g = f (x+1) in \y. ...g... What arity does f have? Really it should have arity 2, but a naive look at the RHS won't see that. You need a fixpoint analysis which says it has arity "infinity" the first time round. This example happens a lot; it first showed up in Andy Gill's thesis, fifteen years ago! It also shows up in the code for 'rnf' on lists in #4138. The analysis is easy to achieve because exprEtaExpandArity takes an argument type CheapFun = CoreExpr -> Maybe Type -> Bool used to decide if an expression is cheap enough to push inside a lambda. And exprIsCheapX in turn takes an argument type CheapAppFun = Id -> Int -> Bool which tells when an application is cheap. This makes it easy to write the analysis loop. The analysis is cheap-and-cheerful because it doesn't deal with mutual recursion. But the self-recursive case is the important one. Note [Eta expanding through dictionaries] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If the experimental -fdicts-cheap flag is on, we eta-expand through dictionary bindings. This improves arities. Thereby, it also means that full laziness is less prone to floating out the application of a function to its dictionary arguments, which can thereby lose opportunities for fusion. Example: foo :: Ord a => a -> ... foo = /\a \(d:Ord a). let d' = ...d... in \(x:a). .... -- So foo has arity 1 f = \x. foo dInt $ bar x The (foo DInt) is floated out, and makes ineffective a RULE foo (bar x) = ... One could go further and make exprIsCheap reply True to any dictionary-typed expression, but that's more work. Note [Eta expanding thunks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ We don't eta-expand * Trivial RHSs x = y * PAPs x = map g * Thunks f = case y of p -> \x -> blah 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 saturated" so we don't want to be too gung-ho about saturating! -} arityLam :: Id -> ArityType -> ArityType arityLam id (ATop as) = ATop (idStateHackOneShotInfo 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 isOneShotInfo 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 `max` n2) -- Note [ABot branches: use max] 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 `bestOneShot` b) : combine as bs combine [] bs = takeWhile isOneShotInfo bs combine as [] = takeWhile isOneShotInfo as {- Note [ABot branches: use max] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider case x of True -> \x. error "urk" False -> \xy. error "urk2" Remember: ABot n means "if you apply to n args, it'll definitely diverge". So we need (ABot 2) for the whole thing, the /max/ of the ABot arities. 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 branches of the case we have ATop [] `andAT` ATop [OneShotLam] and we want to get ATop [OneShotLam]. 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.) So we combine the best of the two branches, on the (slightly dodgy) basis that if we know one branch is one-shot, then they all must be. Note [Arity trimming] ~~~~~~~~~~~~~~~~~~~~~ Consider ((\x y. blah) |> co), where co :: (Int->Int->Int) ~ (Int -> F a) , and F is some type family. Because of Note [exprArity invariant], item (2), we must return with arity at most 1, because typeArity (Int -> F a) = 1. So we have to trim the result of calling arityType on (\x y. blah). Failing to do so, and hence breaking the exprArity invariant, led to #5441. How to trim? For ATop, it's easy. But we must take great care with ABot. Suppose the expression was (\x y. error "urk"), we'll get (ABot 2). We absolutely must not trim that to (ABot 1), because that claims that ((\x y. error "urk") |> co) diverges when given one argument, which it absolutely does not. And Bad Things happen if we think something returns bottom when it doesn't (#16066). So, do not reduce the 'n' in (ABot n); rather, switch (conservatively) to ATop. Historical note: long ago, we unconditionally switched to ATop when we encountered a cast, but that is far too conservative: see #5475 -} --------------------------- 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" data ArityEnv = AE { ae_cheap_fn :: CheapFun , ae_ped_bot :: Bool -- True <=> be pedantic about bottoms } arityType :: ArityEnv -> CoreExpr -> ArityType arityType env (Cast e co) = case arityType env e of ATop os -> ATop (take co_arity os) -- See Note [Arity trimming] ABot n | co_arity < n -> ATop (replicate co_arity noOneShotInfo) | otherwise -> ABot n where co_arity = length (typeArity (pSnd (coercionKind co))) -- See Note [exprArity invariant] (2); must be true of -- arityType too, since that is how we compute the arity -- of variables, and they in turn affect result of exprArity -- #5441 is a nice demo -- However, do make sure that ATop -> ATop and ABot -> ABot! -- Casts don't affect that part. Getting this wrong provoked #5475 arityType _ (Var v) | strict_sig <- idStrictness v , not $ isTopSig strict_sig , (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 :: [OneShotInfo] -- One-shot-ness derived from the type one_shots = typeArity (idType v) -- Lambdas; increase arity arityType env (Lam x e) | isId x = arityLam x (arityType env e) | otherwise = arityType env e -- Applications; decrease arity, except for types arityType env (App fun (Type _)) = arityType env fun arityType env (App fun arg ) = arityApp (arityType env fun) (ae_cheap_fn env 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 env (Case scrut _ _ alts) | exprIsBottom scrut || null alts = ABot 0 -- Do not eta expand -- See Note [Dealing with bottom (1)] | otherwise = case alts_type of ABot n | n>0 -> ATop [] -- Don't eta expand | otherwise -> ABot 0 -- if RHS is bottomming -- See Note [Dealing with bottom (2)] ATop as | not (ae_ped_bot env) -- See Note [Dealing with bottom (3)] , ae_cheap_fn env scrut Nothing -> ATop as | exprOkForSpeculation scrut -> ATop as | otherwise -> ATop (takeWhile isOneShotInfo as) where alts_type = foldr1 andArityType [arityType env rhs | (_,_,rhs) <- alts] arityType env (Let b e) = floatIn (cheap_bind b) (arityType env e) where cheap_bind (NonRec b e) = is_cheap (b,e) cheap_bind (Rec prs) = all is_cheap prs is_cheap (b,e) = ae_cheap_fn env e (Just (idType b)) arityType env (Tick t e) | not (tickishIsCode t) = arityType env e arityType _ _ = vanillaArityType {- %************************************************************************ %* * 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 example 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 for join points] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The no-crap rule is very tiresome to guarantee when we have join points. Consider eta-expanding let j :: Int -> Int -> Bool j x = e in b The simple way is \(y::Int). (let j x = e in b) y The no-crap way is \(y::Int). let j' :: Int -> Bool j' x = e y in b[j'/j] y where I have written to stress that j's type has changed. Note that (of course!) we have to push the application inside the RHS of the join as well as into the body. AND if j has an unfolding we have to push it into there too. AND j might be recursive... So for now I'm abandoning the no-crap rule in this case. I think that for the use in CorePrep it really doesn't matter; and if it does, then CoreToStg.myCollectArgs will fall over. (Moreover, I think that casts can make the no-crap rule fail too.) 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" Note [Eta expansion and source notes] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ CorePrep puts floatable ticks outside of value applications, but not type applications. As a result we might be trying to eta-expand an expression like (src<...> v) @a which we want to lead to code like \x -> src<...> v @a x This means that we need to look through type applications and be ready to re-add floats on the top. -} -- | @etaExpand n e@ returns an expression with -- the same meaning as @e@, but with arity @n@. -- -- Given: -- -- > e' = etaExpand n e -- -- 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 arity e = res -- Then 'res' has at least 'arity' lambdas at the top -- -- 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) | isTyVar 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]) $ retick $ etaInfoAbs etas (etaInfoApp subst' sexpr etas) where in_scope = mkInScopeSet (exprFreeVars expr) (in_scope', etas) = mkEtaWW n orig_expr in_scope (exprType expr) subst' = mkEmptySubst in_scope' -- Find ticks behind type apps. -- See Note [Eta expansion and source notes] (expr', args) = collectArgs expr (ticks, expr'') = stripTicksTop tickishFloatable expr' sexpr = foldl' App expr'' args retick expr = foldr mkTick expr ticks -- Abstraction Application -------------- data EtaInfo = EtaVar Var -- /\a. [] [] a -- \x. [] [] x | EtaCo Coercion -- [] |> sym co [] |> co instance Outputable EtaInfo where ppr (EtaVar v) = text "EtaVar" <+> ppr v ppr (EtaCo co) = text "EtaCo" <+> ppr co pushCoercion :: Coercion -> [EtaInfo] -> [EtaInfo] pushCoercion co1 (EtaCo co2 : eis) | isReflCo co = eis | otherwise = EtaCo co : eis where co = co1 `mkTransCo` 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) (mkSymCo 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 (CoreSubst.extendSubstWithVar subst v1 v2) e eis etaInfoApp subst (Cast e co1) eis = etaInfoApp subst e (pushCoercion co' eis) where co' = CoreSubst.substCo subst co1 etaInfoApp subst (Case e b ty alts) eis = Case (subst_expr subst e) b1 ty' alts' where (subst1, b1) = substBndr subst b alts' = map subst_alt alts ty' = etaInfoAppTy (CoreSubst.substTy subst ty) eis subst_alt (con, bs, rhs) = (con, bs', etaInfoApp subst2 rhs eis) where (subst2,bs') = substBndrs subst1 bs etaInfoApp subst (Let b e) eis | not (isJoinBind b) -- See Note [Eta expansion for join points] = Let b' (etaInfoApp subst' e eis) where (subst', b') = substBindSC subst b etaInfoApp subst (Tick t e) eis = Tick (substTickish subst t) (etaInfoApp subst e eis) etaInfoApp subst expr _ | (Var fun, _) <- collectArgs expr , Var fun' <- lookupIdSubst (text "etaInfoApp" <+> ppr fun) subst fun , isJoinId fun' = subst_expr subst expr 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 -------------- etaInfoAppTy :: Type -> [EtaInfo] -> Type -- If e :: ty -- then etaInfoApp e eis :: etaInfoApp ty eis etaInfoAppTy ty [] = ty etaInfoAppTy ty (EtaVar v : eis) = etaInfoAppTy (applyTypeToArg ty (varToCoreExpr v)) eis etaInfoAppTy _ (EtaCo co : eis) = etaInfoAppTy (pSnd (coercionKind co)) eis -------------- mkEtaWW :: Arity -> CoreExpr -> 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 orig_expr in_scope orig_ty = go orig_n empty_subst orig_ty [] where empty_subst = mkEmptyTCvSubst in_scope go :: Arity -- Number of value args to expand to -> TCvSubst -> Type -- We are really looking at subst(ty) -> [EtaInfo] -- Accumulating parameter -> (InScopeSet, [EtaInfo]) go n subst ty eis -- See Note [exprArity invariant] ----------- Done! No more expansion needed | n == 0 = (getTCvInScope subst, reverse eis) ----------- Forall types (forall a. ty) | Just (tcv,ty') <- splitForAllTy_maybe ty , let (subst', tcv') = Type.substVarBndr subst tcv = let ((n_subst, n_tcv), n_n) -- We want to have at least 'n' lambdas at the top. -- If tcv is a tyvar, it corresponds to one Lambda (/\). -- And we won't reduce n. -- If tcv is a covar, we could eta-expand the expr with one -- lambda \co:ty. e co. In this case we generate a new variable -- of the coercion type, update the scope, and reduce n by 1. | isTyVar tcv = ((subst', tcv'), n) | otherwise = (freshEtaId n subst' (varType tcv'), n-1) -- Avoid free vars of the original expression in go n_n n_subst ty' (EtaVar n_tcv : eis) ----------- Function types (t1 -> t2) | Just (arg_ty, res_ty) <- splitFunTy_maybe ty , not (isTypeLevPoly arg_ty) -- See Note [Levity polymorphism invariants] in CoreSyn -- See also test case typecheck/should_run/EtaExpandLevPoly , 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) ----------- Newtypes -- 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) | Just (co, ty') <- topNormaliseNewType_maybe ty , let co' = Coercion.substCo subst co -- Remember to apply the substitution to co (#16979) -- (or we could have applied to ty, but then -- we'd have had to zap it for the recursive call) = go n subst ty' (pushCoercion co' eis) | otherwise -- We have an expression of arity > 0, -- but its type isn't a function, or a binder -- is levity-polymorphic = WARN( True, (ppr orig_n <+> ppr orig_ty) $$ ppr orig_expr ) (getTCvInScope subst, reverse eis) -- This *can* legitmately happen: -- e.g. coerce Int (\x. x) Essentially the programmer is -- playing fast and loose with types (Happy does this a lot). -- So we simply decline to eta-expand. Otherwise we'd end up -- with an explicit lambda having a non-function type -------------- -- Don't use short-cutting substitution - we may be changing the types of join -- points, so applying the in-scope set is necessary -- TODO Check if we actually *are* changing any join points' types subst_expr :: Subst -> CoreExpr -> CoreExpr subst_expr = substExpr (text "CoreArity:substExpr") -------------- -- | Split an expression into the given number of binders and a body, -- eta-expanding if necessary. Counts value *and* type binders. etaExpandToJoinPoint :: JoinArity -> CoreExpr -> ([CoreBndr], CoreExpr) etaExpandToJoinPoint join_arity expr = go join_arity [] expr where go 0 rev_bs e = (reverse rev_bs, e) go n rev_bs (Lam b e) = go (n-1) (b : rev_bs) e go n rev_bs e = case etaBodyForJoinPoint n e of (bs, e') -> (reverse rev_bs ++ bs, e') etaExpandToJoinPointRule :: JoinArity -> CoreRule -> CoreRule etaExpandToJoinPointRule _ rule@(BuiltinRule {}) = WARN(True, (sep [text "Can't eta-expand built-in rule:", ppr rule])) -- How did a local binding get a built-in rule anyway? Probably a plugin. rule etaExpandToJoinPointRule join_arity rule@(Rule { ru_bndrs = bndrs, ru_rhs = rhs , ru_args = args }) | need_args == 0 = rule | need_args < 0 = pprPanic "etaExpandToJoinPointRule" (ppr join_arity $$ ppr rule) | otherwise = rule { ru_bndrs = bndrs ++ new_bndrs, ru_args = args ++ new_args , ru_rhs = new_rhs } where need_args = join_arity - length args (new_bndrs, new_rhs) = etaBodyForJoinPoint need_args rhs new_args = varsToCoreExprs new_bndrs -- Adds as many binders as asked for; assumes expr is not a lambda etaBodyForJoinPoint :: Int -> CoreExpr -> ([CoreBndr], CoreExpr) etaBodyForJoinPoint need_args body = go need_args (exprType body) (init_subst body) [] body where go 0 _ _ rev_bs e = (reverse rev_bs, e) go n ty subst rev_bs e | Just (tv, res_ty) <- splitForAllTy_maybe ty , let (subst', tv') = Type.substVarBndr subst tv = go (n-1) res_ty subst' (tv' : rev_bs) (e `App` varToCoreExpr tv') | Just (arg_ty, res_ty) <- splitFunTy_maybe ty , let (subst', b) = freshEtaId n subst arg_ty = go (n-1) res_ty subst' (b : rev_bs) (e `App` Var b) | otherwise = pprPanic "etaBodyForJoinPoint" $ int need_args $$ ppr body $$ ppr (exprType body) init_subst e = mkEmptyTCvSubst (mkInScopeSet (exprFreeVars e)) -------------- freshEtaId :: Int -> TCvSubst -> Type -> (TCvSubst, 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.substTyUnchecked subst ty eta_id' = uniqAway (getTCvInScope subst) $ mkSysLocalOrCoVar (fsLit "eta") (mkBuiltinUnique n) ty' subst' = extendTCvInScope subst eta_id'