{- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 Arity and eta expansion -} {-# LANGUAGE CPP #-} {-# OPTIONS_GHC -Wno-incomplete-record-updates #-} -- | Arity and eta expansion module GHC.Core.Opt.Arity ( manifestArity, joinRhsArity, exprArity, typeArity , exprEtaExpandArity, findRhsArity , etaExpand, etaExpandAT , exprBotStrictness_maybe -- ** ArityType , ArityType(..), mkBotArityType, mkManifestArityType, expandableArityType , arityTypeArity, maxWithArity, idArityType -- ** Join points , etaExpandToJoinPoint, etaExpandToJoinPointRule -- ** Coercions and casts , pushCoArg, pushCoArgs, pushCoValArg, pushCoTyArg , pushCoercionIntoLambda, pushCoDataCon, collectBindersPushingCo ) where import GHC.Prelude import GHC.Driver.Session ( DynFlags, GeneralFlag(..), gopt ) import GHC.Core import GHC.Core.FVs import GHC.Core.Utils import GHC.Core.DataCon import GHC.Core.TyCon ( tyConArity ) import GHC.Core.TyCon.RecWalk ( initRecTc, checkRecTc ) import GHC.Core.Predicate ( isDictTy, isCallStackPredTy ) import GHC.Core.Multiplicity -- We have two sorts of substitution: -- GHC.Core.Subst.Subst, and GHC.Core.TyCo.TCvSubst -- Both have substTy, substCo Hence need for qualification import GHC.Core.Subst as Core import GHC.Core.Type as Type import GHC.Core.Coercion as Type import GHC.Types.Demand import GHC.Types.Var import GHC.Types.Var.Env import GHC.Types.Id import GHC.Types.Basic import GHC.Types.Tickish import GHC.Builtin.Uniques import GHC.Data.FastString import GHC.Data.Pair import GHC.Utils.Constants (debugIsOn) import GHC.Utils.Outputable import GHC.Utils.Panic import GHC.Utils.Panic.Plain import GHC.Utils.Trace import GHC.Utils.Misc {- ************************************************************************ * * 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) (coercionRKind co) -- See 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') <- splitForAllTyCoVar_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 and products] -- in GHC.Core.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, DmdSig) -- 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 botStrictnessArityEnv e) of Nothing -> Nothing Just ar -> Just (ar, sig ar) where sig ar = mkClosedDmdSig (replicate ar topDmd) botDiv {- 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 GHC.Iface.Tidy 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 GHC.Iface.Tidy, 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 GHC.Tc.TyCl.Instance. 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. 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 divergent 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 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 decompose 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 = 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). We use the following notation: at ::= \o1..on.div div ::= T | x | ⊥ o ::= ? | 1 And omit the \. if n = 0. Examples: \?11.T stands for @AT [NoOneShotInfo,OneShotLam,OneShotLam] topDiv@ ⊥ stands for @AT [] botDiv@ See the 'Outputable' instance for more information. It's pretty simple. Here is what the fields mean. If an arbitrary expression 'f' has ArityType 'at', then * If @at = AT [o1,..,on] botDiv@ (notation: \o1..on.⊥), 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 = in \y. error (g x y) ==> \y. let x = in error (g x y) * If @at = AT [o1,..,on] topDiv@ (notation: \o1..on.T), then expanding 'f' to @\x1..xn. f x1..xn@ loses no sharing, assuming the calls of f respect the one-shot-ness o1..on of its definition. NB 'f' is an arbitrary expression, eg @f = g e1 e2@. This 'f' can have arity type @AT oss _@, with @length oss > 0@, only if e1 e2 are themselves cheap. * In both cases, @f@, @f x1@, ... @f x1 ... x(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 = in \s(one-shot) \t(one-shot). blah 'f' has arity type \??11.T The one-shot-ness means we can, in effect, push that 'let' inside the \st. Suppose f = \xy. x+y Then f :: \??.T f v :: \?.T f :: T Note [Eta reduction in recursive RHSs] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider the following recursive function: f = \x. ....g (\y. f y).... The recursive call of f in its own RHS seems like a fine opportunity for eta-reduction because f has arity 1. And often it is! Alas, that is unsound in general if the eta-reduction happens in a tail context. Making the arity visible in the RHS allows us to eta-reduce f = \x -> f x to f = f which means we optimise terminating programs like (f `seq` ()) into non-terminating ones. Nor is this problem just for tail calls. Consider f = id (\x -> f x) where we have (for some reason) not yet inlined `id`. We must not eta-reduce to f = id f because that will then simplify to `f = f` as before. An immediate idea might be to look at whether the called function is a local loopbreaker and refrain from eta-expanding. But that doesn't work for mutually recursive function like in #21652: f = g g* x = f x Here, g* is the loopbreaker but f isn't. What can we do? Fix 1: Zap `idArity` when analysing recursive RHSs and re-attach the info when entering the let body. Has the disadvantage that other transformations which make use of arity (such as dropping of `seq`s when arity > 0) will no longer work in the RHS. Plus it requires non-trivial refactorings to both the simple optimiser (in the way `subst_opt_bndr` is used) as well as the Simplifier (in the way `simplRecBndrs` and `simplRecJoinBndrs` is used), modifying the SimplEnv's substitution twice in the process. A very complicated stop-gap. Fix 2: Pass the set of enclosing recursive binders to `tryEtaReduce`; these are the ones we should not eta-reduce. All call-site must maintain this set. Example: rec { f1 = ....rec { g = ... (\x. g x)...(\y. f2 y)... }... ; f2 = ...f1... } when eta-reducing those inner lambdas, we need to know that we are in the rec group for {f1, f2, g}. This is very much like the solution in Note [Speculative evaluation] in GHC.CoreToStg.Prep. It is a bit tiresome to maintain this info, because it means another field in SimplEnv and SimpleOptEnv. We implement Fix (2) because of it isn't as complicated to maintain as (1). Plus, it is the correct fix to begin with. After all, the arity is correct, but doing the transformation isn't. The moving parts are: * A field `scRecIds` in `SimplEnv` tracks the enclosing recursive binders * We extend the `scRecIds` set in `GHC.Core.Opt.Simplify.simplRecBind` * We consult the set in `is_eta_reduction_sound` in `tryEtaReduce` The situation is very similar to Note [Speculative evaluation] which has the same fix. -} -- | The analysis lattice of arity analysis. It is isomorphic to -- -- @ -- data ArityType' -- = AEnd Divergence -- | ALam OneShotInfo ArityType' -- @ -- -- Which is easier to display the Hasse diagram for: -- -- @ -- ALam OneShotLam at -- | -- AEnd topDiv -- | -- ALam NoOneShotInfo at -- | -- AEnd exnDiv -- | -- AEnd botDiv -- @ -- -- where the @at@ fields of @ALam@ are inductively subject to the same order. -- That is, @ALam os at1 < ALam os at2@ iff @at1 < at2@. -- -- Why the strange Top element? -- See Note [Combining case branches: optimistic one-shot-ness] -- -- We rely on this lattice structure for fixed-point iteration in -- 'findRhsArity'. For the semantics of 'ArityType', see Note [ArityType]. data ArityType = AT ![OneShotInfo] !Divergence -- ^ @AT oss div@ means this value can safely be eta-expanded @length oss@ -- times, provided use sites respect the 'OneShotInfo's in @oss@. -- A 'OneShotLam' annotation can come from two sources: -- * The user annotated a lambda as one-shot with 'GHC.Exts.oneShot' -- * It's from a lambda binder of a type affected by `-fstate-hack`. -- See 'idStateHackOneShotInfo'. -- In both cases, 'OneShotLam' should win over 'NoOneShotInfo', see -- Note [Combining case branches]. -- -- If @div@ is dead-ending ('isDeadEndDiv'), then application to -- @length os@ arguments will surely diverge, similar to the situation -- with 'DmdType'. deriving Eq -- | This is the BNF of the generated output: -- -- @ -- @ -- -- We format -- @AT [o1,..,on] topDiv@ as @\o1..on.T@ and -- @AT [o1,..,on] botDiv@ as @\o1..on.⊥@, respectively. -- More concretely, @AT [NOI,OS,OS] topDiv@ is formatted as @\?11.T@. -- If the one-shot info is empty, we omit the leading @\.@. instance Outputable ArityType where ppr (AT oss div) | null oss = pp_div div | otherwise = char '\\' <> hcat (map pp_os oss) <> dot <> pp_div div where pp_div Diverges = char '⊥' pp_div ExnOrDiv = char 'x' pp_div Dunno = char 'T' pp_os OneShotLam = char '1' pp_os NoOneShotInfo = char '?' mkBotArityType :: [OneShotInfo] -> ArityType mkBotArityType oss = AT oss botDiv botArityType :: ArityType botArityType = mkBotArityType [] mkManifestArityType :: [Var] -> CoreExpr -> ArityType mkManifestArityType bndrs body = AT oss div where oss = [idOneShotInfo bndr | bndr <- bndrs, isId bndr] div | exprIsDeadEnd body = botDiv | otherwise = topDiv topArityType :: ArityType topArityType = AT [] topDiv -- | The number of value args for the arity type arityTypeArity :: ArityType -> Arity arityTypeArity (AT oss _) = length oss -- | True <=> eta-expansion will add at least one lambda expandableArityType :: ArityType -> Bool expandableArityType at = arityTypeArity at > 0 -- | See Note [Dead ends] in "GHC.Types.Demand". -- Bottom implies a dead end. isDeadEndArityType :: ArityType -> Bool isDeadEndArityType (AT _ div) = isDeadEndDiv div -- | Expand a non-bottoming arity type so that it has at least the given arity. maxWithArity :: ArityType -> Arity -> ArityType maxWithArity at@(AT oss div) !ar | isDeadEndArityType at = at | oss `lengthAtLeast` ar = at | otherwise = AT (take ar $ oss ++ repeat NoOneShotInfo) div -- | Trim an arity type so that it has at most the given arity. -- Any excess 'OneShotInfo's are truncated to 'topDiv', even if they end in -- 'ABot'. minWithArity :: ArityType -> Arity -> ArityType minWithArity at@(AT oss _) ar | oss `lengthAtMost` ar = at | otherwise = AT (take ar oss) topDiv takeWhileOneShot :: ArityType -> ArityType takeWhileOneShot (AT oss div) | isDeadEndDiv div = AT (takeWhile isOneShotInfo oss) topDiv | otherwise = AT (takeWhile isOneShotInfo oss) div -- | The Arity returned is the number of value args the -- expression can be applied to without doing much work exprEtaExpandArity :: DynFlags -> CoreExpr -> ArityType -- exprEtaExpandArity is used when eta expanding -- e ==> \xy -> e x y exprEtaExpandArity dflags e = arityType (findRhsArityEnv dflags) e getBotArity :: ArityType -> Maybe Arity -- Arity of a divergent function getBotArity (AT oss div) | isDeadEndDiv div = Just $ length oss | otherwise = Nothing ---------------------- findRhsArity :: DynFlags -> Id -> CoreExpr -> Arity -> ArityType -- 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 (\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 0 botArityType -- We always do one step, but usually that produces a result equal to -- old_arity, and then we stop right away, because old_arity is assumed -- to be sound. In other words, arities should never decrease. -- Result: the common case is that there is just one iteration where go :: Int -> ArityType -> ArityType go !n cur_at@(AT oss div) | not (isDeadEndDiv div) -- the "stop right away" case , length oss <= old_arity = cur_at -- from above | next_at == cur_at = cur_at | otherwise = -- Warn if more than 2 iterations. Why 2? See Note [Exciting arity] warnPprTrace (debugIsOn && n > 2) "Exciting arity" (nest 2 (ppr bndr <+> ppr cur_at <+> ppr next_at $$ ppr rhs)) $ go (n+1) next_at where next_at = step cur_at step :: ArityType -> ArityType step at = -- pprTrace "step" (ppr bndr <+> ppr at <+> ppr (arityType env rhs)) $ arityType env rhs where env = extendSigEnv (findRhsArityEnv dflags) bndr at {- 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. We do the necessary, quite simple fixed-point iteration in 'findRhsArity', which assumes for a single binding 'ABot' on the first run and iterates until it finds a stable arity type. Two wrinkles * We often have to ask (see the Case or Let case of 'arityType') whether some expression is cheap. In the case of an application, that depends on the arity of the application head! That's why we have our own version of 'exprIsCheap', 'myExprIsCheap', that will integrate the optimistic arity types we have on f and g into the cheapness check. * Consider this (#18793) go = \ds. case ds of [] -> id (x:ys) -> let acc = go ys in case blah of True -> acc False -> \ x1 -> acc (negate x1) We must propagate go's optimistically large arity to @acc@, so that the tail call to @acc@ in the True branch has sufficient arity. This is done by the 'am_sigs' field in 'FindRhsArity', and 'lookupSigEnv' in the Var case of 'arityType'. Note [Exciting arity] ~~~~~~~~~~~~~~~~~~~~~ The fixed-point iteration in 'findRhsArity' stabilises very quickly in almost all cases. To get notified of cases where we need an usual number of iterations, we emit a warning in debug mode, so that we can investigate and make sure that we really can't do better. It's a gross hack, but catches real bugs (#18870). Now, which number is "unusual"? We pick n > 2. Here's a pretty common and expected example that takes two iterations and would ruin the specificity of the warning (from T18937): f :: [Int] -> Int -> Int f [] = id f (x:xs) = let y = sum [0..x] in \z -> f xs (y + z) Fixed-point iteration starts with arity type ⊥ for f. After the first iteration, we get arity type \??.T, e.g. arity 2, because we unconditionally 'floatIn' the let-binding (see its bottom case). After the second iteration, we get arity type \?.T, e.g. arity 1, because now we are no longer allowed to floatIn the non-cheap let-binding. Which is all perfectly benign, but means we do two iterations (well, actually 3 'step's to detect we are stable) and don't want to emit the warning. 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. -} arityLam :: Id -> ArityType -> ArityType arityLam id (AT oss div) = AT (idStateHackOneShotInfo id : oss) div floatIn :: Bool -> ArityType -> ArityType -- We have something like (let x = E in b), -- where b has the given arity type. floatIn cheap at | isDeadEndArityType at || cheap = at -- If E is not cheap, keep arity only for one-shots | otherwise = takeWhileOneShot at arityApp :: ArityType -> Bool -> ArityType -- Processing (fun arg) where at is the ArityType of fun, -- Knock off an argument and behave like 'let' arityApp (AT (_:oss) div) cheap = floatIn cheap (AT oss div) arityApp at _ = at -- | Least upper bound in the 'ArityType' lattice. -- See the haddocks on 'ArityType' for the lattice. -- -- Used for branches of a @case@. andArityType :: ArityEnv -> ArityType -> ArityType -> ArityType andArityType env (AT (lam1:lams1) div1) (AT (lam2:lams2) div2) | AT lams' div' <- andArityType env (AT lams1 div1) (AT lams2 div2) = AT ((lam1 `and_lam` lam2) : lams') div' where (os1) `and_lam` (os2) = ( os1 `bestOneShot` os2) -- bestOneShot: see Note [Combining case branches: optimistic one-shot-ness] andArityType env (AT [] div1) at2 = andWithTail env div1 at2 andArityType env at1 (AT [] div2) = andWithTail env div2 at1 andWithTail :: ArityEnv -> Divergence -> ArityType -> ArityType andWithTail env div1 at2 | isDeadEndDiv div1 -- case x of { T -> error; F -> \y.e } = at2 -- Note [ABot branches: max arity wins] | pedanticBottoms env -- Note [Combining case branches: andWithTail] = AT [] topDiv | otherwise -- case x of { T -> plusInt ; F -> \y.e } = takeWhileOneShot at2 -- We know div1 = topDiv -- See Note [Combining case branches: andWithTail] {- Note [ABot branches: max arity wins] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider case x of True -> \x. error "urk" False -> \xy. error "urk2" Remember: \o1..on.⊥ means "if you apply to n args, it'll definitely diverge". So we need \??.⊥ for the whole thing, the /max/ of both arities. Note [Combining case branches: optimistic one-shot-ness] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When combining the ArityTypes for two case branches (with andArityType) and both ArityTypes have ATLamInfo, then we just combine their expensive-ness and one-shot info. The tricky point is when we have case x of True -> \x{one-shot). blah1 Fale -> \y. blah2 Since one-shot-ness is about the /consumer/ not the /producer/, we optimistically assume that if either branch is one-shot, 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. Surprisingly, this means that the one-shot arity type is effectively the top element of the lattice. Hence the call to `bestOneShot` in `andArityType`. Note [Combining case branches: andWithTail] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ When combining the ArityTypes for two case branches (with andArityType) and one side or the other has run out of ATLamInfo; then we get into `andWithTail`. * If one branch is guaranteed bottom (isDeadEndDiv), we just take the other; see Note [ABot branches: max arity wins] * Otherwise, if pedantic-bottoms is on, we just have to return AT [] topDiv. E.g. if we have f x z = case x of True -> \y. blah False -> z then we can't eta-expand, because that would change the behaviour of (f False bottom(). * But if pedantic-bottoms is not on, we allow ourselves to push `z` under a lambda (much as we allow ourselves to put the `case x` under a lambda). However we know nothing about the expensiveness or one-shot-ness of `z`, so we'd better assume it looks like (Expensive, NoOneShotInfo) all the way. Remembering Note [Combining case branches: optimistic one-shot-ness], we just add work to ever ATLamInfo, keeping the one-shot-ness. Here's an example: 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 respect the one-shot annotation provided by the user and eta-expand go and go2. When combining the branches of the case we have T `andAT` \1.T and we want to get \1.T. But if the inner lambda wasn't one-shot (\?.T) we don't want to do this. (We need a usage analysis to justify that.) Unless we can conclude that **all** branches are safe to eta-expand then we must pessimisticaly conclude that we can't eta-expand. See #21694 for where this went wrong. We can do better in the long run, but for the 9.4/9.2 branches we choose to simply ignore oneshot annotations for the time being. 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? If we end in topDiv, it's easy. But we must take great care with dead ends (i.e. botDiv). Suppose the expression was (\x y. error "urk"), we'll get \??.⊥. We absolutely must not trim that to \?.⊥, 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, if we need to trim a dead-ending arity type, switch (conservatively) to topDiv. Historical note: long ago, we unconditionally switched to topDiv when we encountered a cast, but that is far too conservative: see #5475 Note [Eta expanding through CallStacks] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Just as it's good to eta-expand through dictionaries, so it is good to do so through CallStacks. #20103 is a case in point, where we got foo :: HasCallStack => Int -> Int foo = \(d::CallStack). let d2 = pushCallStack blah d in \(x:Int). blah We really want to eta-expand this! #20103 is quite convincing! We do this regardless of -fdicts-cheap; it's not really a dictionary. -} --------------------------- -- | Each of the entry-points of the analyser ('arityType') has different -- requirements. The entry-points are -- -- 1. 'exprBotStrictness_maybe' -- 2. 'exprEtaExpandArity' -- 3. 'findRhsArity' -- -- For each of the entry-points, there is a separate mode that governs -- -- 1. How pedantic we are wrt. ⊥, in 'pedanticBottoms'. -- 2. Whether we store arity signatures for non-recursive let-bindings, -- accessed in 'extendSigEnv'/'lookupSigEnv'. -- See Note [Arity analysis] why that's important. -- 3. Which expressions we consider cheap to float inside a lambda, -- in 'myExprIsCheap'. data AnalysisMode = BotStrictness -- ^ Used during 'exprBotStrictness_maybe'. | EtaExpandArity { am_ped_bot :: !Bool , am_dicts_cheap :: !Bool } -- ^ Used for finding an expression's eta-expanding arity quickly, without -- fixed-point iteration ('exprEtaExpandArity'). | FindRhsArity { am_ped_bot :: !Bool , am_dicts_cheap :: !Bool , am_sigs :: !(IdEnv ArityType) } -- ^ Used for regular, fixed-point arity analysis ('findRhsArity'). -- See Note [Arity analysis] for details about fixed-point iteration. -- INVARIANT: Disjoint with 'ae_joins'. data ArityEnv = AE { ae_mode :: !AnalysisMode -- ^ The analysis mode. See 'AnalysisMode'. } -- | The @ArityEnv@ used by 'exprBotStrictness_maybe'. Pedantic about bottoms -- and no application is ever considered cheap. botStrictnessArityEnv :: ArityEnv botStrictnessArityEnv = AE { ae_mode = BotStrictness } {- -- | The @ArityEnv@ used by 'exprEtaExpandArity'. etaExpandArityEnv :: DynFlags -> ArityEnv etaExpandArityEnv dflags = AE { ae_mode = EtaExpandArity { am_ped_bot = gopt Opt_PedanticBottoms dflags , am_dicts_cheap = gopt Opt_DictsCheap dflags } , ae_joins = emptyVarSet } -} -- | The @ArityEnv@ used by 'findRhsArity'. findRhsArityEnv :: DynFlags -> ArityEnv findRhsArityEnv dflags = AE { ae_mode = FindRhsArity { am_ped_bot = gopt Opt_PedanticBottoms dflags , am_dicts_cheap = gopt Opt_DictsCheap dflags , am_sigs = emptyVarEnv } } isFindRhsArity :: ArityEnv -> Bool isFindRhsArity (AE { ae_mode = FindRhsArity {} }) = True isFindRhsArity _ = False -- First some internal functions in snake_case for deleting in certain VarEnvs -- of the ArityType. Don't call these; call delInScope* instead! modifySigEnv :: (IdEnv ArityType -> IdEnv ArityType) -> ArityEnv -> ArityEnv modifySigEnv f env@AE { ae_mode = am@FindRhsArity{am_sigs = sigs} } = env { ae_mode = am { am_sigs = f sigs } } modifySigEnv _ env = env {-# INLINE modifySigEnv #-} del_sig_env :: Id -> ArityEnv -> ArityEnv -- internal! del_sig_env id = modifySigEnv (\sigs -> delVarEnv sigs id) {-# INLINE del_sig_env #-} del_sig_env_list :: [Id] -> ArityEnv -> ArityEnv -- internal! del_sig_env_list ids = modifySigEnv (\sigs -> delVarEnvList sigs ids) {-# INLINE del_sig_env_list #-} -- end of internal deletion functions extendSigEnv :: ArityEnv -> Id -> ArityType -> ArityEnv extendSigEnv env id ar_ty = modifySigEnv (\sigs -> extendVarEnv sigs id ar_ty) env delInScope :: ArityEnv -> Id -> ArityEnv delInScope env id = del_sig_env id env delInScopeList :: ArityEnv -> [Id] -> ArityEnv delInScopeList env ids = del_sig_env_list ids env lookupSigEnv :: ArityEnv -> Id -> Maybe ArityType lookupSigEnv AE{ ae_mode = mode } id = case mode of BotStrictness -> Nothing EtaExpandArity{} -> Nothing FindRhsArity{ am_sigs = sigs } -> lookupVarEnv sigs id -- | Whether the analysis should be pedantic about bottoms. -- 'exprBotStrictness_maybe' always is. pedanticBottoms :: ArityEnv -> Bool pedanticBottoms AE{ ae_mode = mode } = case mode of BotStrictness -> True EtaExpandArity{ am_ped_bot = ped_bot } -> ped_bot FindRhsArity{ am_ped_bot = ped_bot } -> ped_bot -- | A version of 'exprIsCheap' that considers results from arity analysis -- and optionally the expression's type. -- Under 'exprBotStrictness_maybe', no expressions are cheap. myExprIsCheap :: ArityEnv -> CoreExpr -> Maybe Type -> Bool myExprIsCheap AE{ae_mode = mode} e mb_ty = case mode of BotStrictness -> False _ -> cheap_dict || cheap_fun e where cheap_dict = case mb_ty of Nothing -> False Just ty -> (am_dicts_cheap mode && isDictTy ty) || isCallStackPredTy ty -- See Note [Eta expanding through dictionaries] -- See Note [Eta expanding through CallStacks] cheap_fun e = case mode of #if __GLASGOW_HASKELL__ <= 900 BotStrictness -> panic "impossible" #endif EtaExpandArity{} -> exprIsCheap e FindRhsArity{am_sigs = sigs} -> exprIsCheapX (myIsCheapApp sigs) e -- | A version of 'isCheapApp' that considers results from arity analysis. -- See Note [Arity analysis] for what's in the signature environment and why -- it's important. myIsCheapApp :: IdEnv ArityType -> CheapAppFun myIsCheapApp sigs fn n_val_args = case lookupVarEnv sigs fn of -- Nothing means not a local function, fall back to regular -- 'GHC.Core.Utils.isCheapApp' Nothing -> isCheapApp fn n_val_args -- `Just at` means local function with `at` as current SafeArityType. -- NB the SafeArityType bit: that means we can ignore the cost flags -- in 'lams', and just consider the length -- Roughly approximate what 'isCheapApp' is doing. Just (AT oss div) | isDeadEndDiv div -> True -- See Note [isCheapApp: bottoming functions] in GHC.Core.Utils | n_val_args < length oss -> True -- Essentially isWorkFreeApp | otherwise -> False ---------------- arityType :: HasDebugCallStack => ArityEnv -> CoreExpr -> ArityType -- Precondition: all the free join points of the expression -- are bound by the ArityEnv -- See Note [No free join points in arityType] arityType env (Cast e co) = minWithArity (arityType env e) co_arity -- See Note [Arity trimming] where co_arity = length (typeArity (coercionRKind 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 arityType env (Var v) | Just at <- lookupSigEnv env v -- Local binding = at | otherwise = assertPpr (not (isFindRhsArity env && isJoinId v)) (ppr v) $ -- All join-point should be in the ae_sigs -- See Note [No free join points in arityType] idArityType v -- Lambdas; increase arity arityType env (Lam x e) | isId x = arityLam x (arityType env' e) | otherwise = arityType env' e where env' = delInScope env x -- Applications; decrease arity, except for types arityType env (App fun (Type _)) = arityType env fun arityType env (App fun arg ) = arityApp (arityType env fun) (myExprIsCheap 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 bndr _ alts) | exprIsDeadEnd scrut || null alts = botArityType -- Do not eta expand. See (1) in Note [Dealing with bottom] | not (pedanticBottoms env) -- See (2) in Note [Dealing with bottom] , myExprIsCheap env scrut (Just (idType bndr)) = alts_type | exprOkForSpeculation scrut = alts_type | otherwise -- In the remaining cases we may not push = takeWhileOneShot alts_type -- evaluation of the scrutinee in where env' = delInScope env bndr arity_type_alt (Alt _con bndrs rhs) = arityType (delInScopeList env' bndrs) rhs alts_type = foldr1 (andArityType env) (map arity_type_alt alts) arityType env (Let (NonRec b r) e) = -- See Note [arityType for let-bindings] floatIn cheap_rhs (arityType env' e) where cheap_rhs = myExprIsCheap env r (Just (idType b)) env' = extendSigEnv env b (arityType env r) arityType env (Let (Rec prs) e) = floatIn (all is_cheap prs) (arityType env' e) where is_cheap (b,e) = myExprIsCheap env' e (Just (idType b)) env' = foldl extend_rec env prs extend_rec :: ArityEnv -> (Id,CoreExpr) -> ArityEnv extend_rec env (b,e) = extendSigEnv env b $ mkManifestArityType bndrs body where (bndrs, body) = collectBinders e -- We can't call arityType on the RHS, because it might mention -- join points bound in this very letrec, and we don't want to -- do a fixpoint calculation here. So we make do with the -- manifest arity arityType env (Tick t e) | not (tickishIsCode t) = arityType env e arityType _ _ = topArityType {- Note [No free join points in arityType] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we call arityType on this expression (EX1) \x . case x of True -> \y. e False -> $j 3 where $j is a join point. It really makes no sense to talk of the arity of this expression, because it has a free join point. In particular, we can't eta-expand the expression because we'd have do the same thing to the binding of $j, and we can't see that binding. If we had (EX2) \x. join $j y = blah case x of True -> \y. e False -> $j 3 then it would make perfect sense: we can determine $j's ArityType, and propagate it to the usage site as usual. But how can we get (EX1)? It doesn't make much sense, because $j can't be a join point under the \x anyway. So we make it a precondition of arityType that the argument has no free join-point Ids. (This is checked with an assesrt in the Var case of arityType.) BUT the invariant risks being invalidated by one very narrow special case: runRW# join $j y = blah runRW# (\s. case x of True -> \y. e False -> $j x) We have special magic in OccurAnal, and Simplify to allow continuations to move into the body of a runRW# call. So we are careful never to attempt to eta-expand the (\s.blah) in the argument to runRW#, at least not when there is a literal lambda there, so that OccurAnal has seen it and allowed join points bound outside. See Note [No eta-expansion in runRW#] in GHC.Core.Opt.Simplify.Iteration. Note [arityType for let-bindings] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ For non-recursive let-bindings, we just get the arityType of the RHS, and extend the environment. That works nicely for things like this (#18793): go = \ ds. case ds_a2CF of { [] -> id : y ys -> case y of { GHC.Types.I# x -> let acc = go ys in case x ># 42# of { __DEFAULT -> acc 1# -> \x1. acc (negate x2) Here we want to get a good arity for `acc`, based on the ArityType of `go`. All this is particularly important for join points. Consider this (#18328) f x = join j y = case y of True -> \a. blah False -> \b. blah in case x of A -> j True B -> \c. blah C -> j False and suppose the join point is too big to inline. Now, what is the arity of f? If we inlined the join point, we'd definitely say "arity 2" because we are prepared to push case-scrutinisation inside a lambda. It's important that we extend the envt with j's ArityType, so that we can use that information in the A/C branch of the case. For /recursive/ bindings it's more difficult, to call arityType, because we don't have an ArityType to put in the envt for the recursively bound Ids. So for non-join-point bindings we satisfy ourselves with mkManifestArityType. Typically we'll have eta-expanded the binding (based on an earlier fixpoint calculation in findRhsArity), so the manifest arity is good. But for /recursive join points/ things are not so good. See Note [Arity type for recursive join bindings] See Note [Arity type for recursive join bindings] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider f x = joinrec j 0 = \ a b c -> (a,x,b) j n = j (n-1) in j 20 Obviously `f` should get arity 4. But the manifest arity of `j` is 1. Remember, we don't eta-expand join points; see GHC.Core.Opt.Simplify.Utils Note [Do not eta-expand join points]. And the ArityInfo on `j` will be just 1 too; see GHC.Core Note [Invariants on join points], item (2b). So using Note [ArityType for let-bindings] won't work well. We could do a fixpoint iteration, but that's a heavy hammer to use in arityType. So we take advantage of it being a join point: * Extend the ArityEnv to bind each of the recursive binders (all join points) to `botArityType`. This means that any jump to the join point will return botArityType, which is unit for `andArityType`: botAritType `andArityType` at = at So it's almost as if those "jump" branches didn't exist. * In this extended env, find the ArityType of each of the RHS, after stripping off the join-point binders. * Use andArityType to combine all these RHS ArityTypes. * Find the ArityType of the body, also in this strange extended environment * And combine that into the result with andArityType. In our example, the jump (j 20) will yield Bot, as will the jump (j (n-1)). We'll 'and' those the ArityType of (\abc. blah). Good! In effect we are treating the RHSs as alternative bodies (like in a case), and ignoring all jumps. In this way we don't need to take a fixpoint. Tricky! NB: we treat /non-recursive/ join points in the same way, but actually it works fine to treat them uniformly with normal let-bindings, and that takes less code. -} idArityType :: Id -> ArityType idArityType v | strict_sig <- idDmdSig v , not $ isTopSig strict_sig , (ds, div) <- splitDmdSig strict_sig , let arity = length ds -- Every strictness signature admits an arity signature! = AT (take arity one_shots) div | otherwise = AT (take (idArity v) one_shots) topDiv where one_shots :: [OneShotInfo] -- One-shot-ness derived from the type one_shots = typeArity (idType v) {- %************************************************************************ %* * 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 alternative, 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. Note [Eta expansion with ArityType] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The etaExpandAT function takes an ArityType (not just an Arity) to guide eta-expansion. Why? Because we want to preserve one-shot info. Consider foo = \x. case x of True -> (\s{os}. blah) |> co False -> wubble We'll get an ArityType for foo of \?1.T. Then we want to eta-expand to foo = \x. (\eta{os}. (case x of ...as before...) eta) |> some_co That 'eta' binder is fresh, and we really want it to have the one-shot flag from the inner \s{os}. By expanding with the ArityType gotten from analysing the RHS, we achieve this neatly. This makes a big difference to the one-shot monad trick; see Note [The one-shot state monad trick] in GHC.Utils.Monad. -} -- | @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 -> CoreExpr -> CoreExpr etaExpand n orig_expr = eta_expand in_scope (replicate n NoOneShotInfo) orig_expr where in_scope = {-#SCC "eta_expand:in-scopeX" #-} mkInScopeSet (exprFreeVars orig_expr) etaExpandAT :: InScopeSet -> ArityType -> CoreExpr -> CoreExpr -- See Note [Eta expansion with ArityType] -- -- We pass in the InScopeSet from the simplifier to avoid recomputing -- it here, which can be jolly expensive if the casts are big -- In #18223 it took 10% of compile time just to do the exprFreeVars! etaExpandAT in_scope (AT oss _) orig_expr = eta_expand in_scope oss orig_expr -- etaExpand arity e = res -- Then 'res' has at least 'arity' lambdas at the top -- possibly with a cast wrapped around the outside -- See Note [Eta expansion with ArityType] -- -- etaExpand deals with for-alls. For example: -- etaExpand 1 E -- where E :: forall a. a -> a -- would return -- (/\b. \y::a -> E b y) eta_expand :: InScopeSet -> [OneShotInfo] -> CoreExpr -> CoreExpr eta_expand in_scope one_shots (Cast expr co) = Cast (eta_expand in_scope one_shots expr) co eta_expand in_scope one_shots orig_expr = go in_scope one_shots [] orig_expr where -- Strip off existing lambdas and casts before handing off to mkEtaWW -- This is mainly to avoid spending time cloning binders and substituting -- when there is actually nothing to do. It's slightly awkward to deal -- with casts here, apart from the topmost one, and they are rare, so -- if we find one we just hand off to mkEtaWW anyway -- Note [Eta expansion and SCCs] go _ [] _ _ = orig_expr -- Already has the specified arity; no-op go in_scope oss@(_:oss1) vs (Lam v body) | isTyVar v = go (in_scope `extendInScopeSet` v) oss (v:vs) body | otherwise = go (in_scope `extendInScopeSet` v) oss1 (v:vs) body go in_scope oss rev_vs expr = -- pprTrace "ee" (vcat [ppr in_scope', ppr top_bndrs, ppr eis]) $ retick $ etaInfoAbs top_eis $ etaInfoApp in_scope' sexpr eis where (in_scope', eis@(EI eta_bndrs mco)) = mkEtaWW oss (ppr orig_expr) in_scope (exprType expr) top_bndrs = reverse rev_vs top_eis = EI (top_bndrs ++ eta_bndrs) (mkPiMCos top_bndrs mco) -- Find ticks behind type apps. -- See Note [Eta expansion and source notes] -- I don't really understand this code SLPJ May 21 (expr', args) = collectArgs expr (ticks, expr'') = stripTicksTop tickishFloatable expr' sexpr = mkApps expr'' args retick expr = foldr mkTick expr ticks {- ********************************************************************* * * The EtaInfo mechanism mkEtaWW, etaInfoAbs, etaInfoApp * * ********************************************************************* -} {- Note [The EtaInfo mechanism] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have (e :: ty) and we want to eta-expand it to arity N. This what eta_expand does. We do it in two steps: 1. mkEtaWW: from 'ty' and 'N' build a EtaInfo which describes the shape of the expansion necessary to expand to arity N. 2. Build the term \ v1..vn. e v1 .. vn where those abstractions and applications are described by the same EtaInfo. Specifically we build the term etaInfoAbs etas (etaInfoApp in_scope e etas) where etas :: EtaInfo etaInfoAbs builds the lambdas etaInfoApp builds the applictions Note that the /same/ EtaInfo drives both etaInfoAbs and etaInfoApp To a first approximation EtaInfo is just [Var]. But casts complicate the question. If we have newtype N a = MkN (S -> a) axN :: N a ~ S -> a and e :: N (N Int) then the eta-expansion should look like (\(x::S) (y::S) -> e |> co x y) |> sym co where co :: N (N Int) ~ S -> S -> Int co = axN @(N Int) ; (S -> axN @Int) We want to get one cast, at the top, to account for all those nested newtypes. This is expressed by the EtaInfo type: data EtaInfo = EI [Var] MCoercionR Note [Check for reflexive casts in eta expansion] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ It turns out that the casts created by teh above mechanism are often Refl. When casts are very deeply nested (as happens in #18223), the repetition of types can make the overall term very large. So there is a big payoff in cancelling out casts aggressively wherever possible. (See also Note [No crap in eta-expanded code].) This matters particularly in etaInfoApp, where we * Do beta-reduction on the fly * Use getArg_maybe to get a cast out of the way, so that we can do beta reduction Together this makes a big difference. Consider when e is case x of True -> (\x -> e1) |> c1 False -> (\p -> e2) |> c2 When we eta-expand this to arity 1, say, etaInfoAbs will wrap a (\eta) around the outside and use etaInfoApp to apply each alternative to 'eta'. We want to beta-reduce all that junk away. #18223 was a dramatic example in which the intermediate term was grotesquely huge, even though the next Simplifier iteration squashed it. Better to kill it at birth. The crucial spots in etaInfoApp are: * `checkReflexiveMCo` in the (Cast e co) case of `go` * `checkReflexiveMCo` in `pushCoArg` * Less important: checkReflexiveMCo in the final case of `go` Collectively these make a factor-of-5 difference to the total allocation of T18223, so take care if you change this stuff! Example: newtype N = MkN (Y->Z) f :: X -> N f = \(x::X). ((\(y::Y). blah) |> fco) where fco :: (Y->Z) ~ N mkEtaWW makes an EtaInfo of (EI [(eta1:X), (eta2:Y)] eta_co where eta_co :: (X->N) ~ (X->Y->Z) eta_co = ( -> nco) nco :: N ~ (Y->Z) -- Comes from topNormaliseNewType_maybe Now, when we push that eta_co inward in etaInfoApp: * In the (Cast e co) case, the 'fco' and 'nco' will meet, and should cancel. * When we meet the (\y.e) we want no cast on the y. -} -------------- data EtaInfo = EI [Var] MCoercionR -- (EI bs co) describes a particular eta-expansion, as follows: -- Abstraction: (\b1 b2 .. bn. []) |> sym co -- Application: ([] |> co) b1 b2 .. bn -- -- e :: T co :: T ~ (t1 -> t2 -> .. -> tn -> tr) -- e = (\b1 b2 ... bn. (e |> co) b1 b2 .. bn) |> sym co instance Outputable EtaInfo where ppr (EI vs mco) = text "EI" <+> ppr vs <+> parens (ppr mco) etaInfoApp :: InScopeSet -> CoreExpr -> EtaInfo -> CoreExpr -- (etaInfoApp s e (EI bs mco) returns something equivalent to -- ((substExpr s e) |> mco b1 .. bn) -- See Note [The EtaInfo mechanism] -- -- NB: With very deeply nested casts, this function can be expensive -- In T18223, this function alone costs 15% of allocation, all -- spent in the calls to substExprSC and substBindSC etaInfoApp in_scope expr eis = go (mkEmptySubst in_scope) expr eis where go :: Subst -> CoreExpr -> EtaInfo -> CoreExpr -- 'go' pushed down the eta-infos into the branch of a case -- and the body of a let; and does beta-reduction if possible -- go subst fun co [b1,..,bn] returns (subst(fun) |> co) b1 .. bn go subst (Tick t e) eis = Tick (substTickish subst t) (go subst e eis) go subst (Cast e co) (EI bs mco) = go subst e (EI bs mco') where mco' = checkReflexiveMCo (Core.substCo subst co `mkTransMCoR` mco) -- See Note [Check for reflexive casts in eta expansion] go subst (Case e b ty alts) eis = Case (Core.substExprSC subst e) b1 ty' alts' where (subst1, b1) = Core.substBndr subst b alts' = map subst_alt alts ty' = etaInfoAppTy (Core.substTy subst ty) eis subst_alt (Alt con bs rhs) = Alt con bs' (go subst2 rhs eis) where (subst2,bs') = Core.substBndrs subst1 bs go subst (Let b e) eis | not (isJoinBind b) -- See Note [Eta expansion for join points] = Let b' (go subst' e eis) where (subst', b') = Core.substBindSC subst b -- Beta-reduction if possible, pushing any intervening casts past -- the argument. See Note [The EtaInfo mechanism] go subst (Lam v e) (EI (b:bs) mco) | Just (arg,mco') <- pushMCoArg mco (varToCoreExpr b) = go (Core.extendSubst subst v arg) e (EI bs mco') -- Stop pushing down; just wrap the expression up -- See Note [Check for reflexive casts in eta expansion] go subst e (EI bs mco) = Core.substExprSC subst e `mkCastMCo` checkReflexiveMCo mco `mkVarApps` bs -------------- etaInfoAppTy :: Type -> EtaInfo -> Type -- If e :: ty -- then etaInfoApp e eis :: etaInfoApp ty eis etaInfoAppTy ty (EI bs mco) = applyTypeToArgs (text "etaInfoAppTy") ty1 (map varToCoreExpr bs) where ty1 = case mco of MRefl -> ty MCo co -> coercionRKind co -------------- etaInfoAbs :: EtaInfo -> CoreExpr -> CoreExpr -- See Note [The EtaInfo mechanism] etaInfoAbs (EI bs mco) expr = (mkLams bs expr) `mkCastMCo` mkSymMCo mco -------------- -- | @mkEtaWW n _ fvs ty@ will compute the 'EtaInfo' necessary for eta-expanding -- an expression @e :: ty@ to take @n@ value arguments, where @fvs@ are the -- free variables of @e@. -- -- Note that this function is entirely unconcerned about cost centres and other -- semantically-irrelevant source annotations, so call sites must take care to -- preserve that info. See Note [Eta expansion and SCCs]. mkEtaWW :: [OneShotInfo] -- ^ How many value arguments to eta-expand -> SDoc -- ^ The pretty-printed original expression, for warnings. -> InScopeSet -- ^ A super-set of the free vars of the expression to eta-expand. -> Type -> (InScopeSet, EtaInfo) -- ^ The variables in 'EtaInfo' are fresh wrt. to the incoming 'InScopeSet'. -- The outgoing 'InScopeSet' extends the incoming 'InScopeSet' with the -- fresh variables in 'EtaInfo'. mkEtaWW orig_oss ppr_orig_expr in_scope orig_ty = go 0 orig_oss empty_subst orig_ty where empty_subst = mkEmptyTCvSubst in_scope go :: Int -- For fresh names -> [OneShotInfo] -- Number of value args to expand to -> TCvSubst -> Type -- We are really looking at subst(ty) -> (InScopeSet, EtaInfo) -- (go [o1,..,on] subst ty) = (in_scope, EI [b1,..,bn] co) -- co :: subst(ty) ~ b1_ty -> ... -> bn_ty -> tr go _ [] subst _ -- See Note [exprArity invariant] ----------- Done! No more expansion needed = (getTCvInScope subst, EI [] MRefl) go n oss@(one_shot:oss1) subst ty -- See Note [exprArity invariant] ----------- Forall types (forall a. ty) | Just (tcv,ty') <- splitForAllTyCoVar_maybe ty , (subst', tcv') <- Type.substVarBndr subst tcv , let oss' | isTyVar tcv = oss | otherwise = oss1 -- A forall can bind a CoVar, in which case -- we consume one of the [OneShotInfo] , (in_scope, EI bs mco) <- go n oss' subst' ty' = (in_scope, EI (tcv' : bs) (mkHomoForAllMCo tcv' mco)) ----------- Function types (t1 -> t2) | Just (mult, arg_ty, res_ty) <- splitFunTy_maybe ty , typeHasFixedRuntimeRep arg_ty -- See Note [Representation polymorphism invariants] in GHC.Core -- See also test case typecheck/should_run/EtaExpandLevPoly , (subst', eta_id) <- freshEtaId n subst (Scaled mult arg_ty) -- Avoid free vars of the original expression , let eta_id' = eta_id `setIdOneShotInfo` one_shot , (in_scope, EI bs mco) <- go (n+1) oss1 subst' res_ty = (in_scope, EI (eta_id' : bs) (mkFunResMCo (idScaledType eta_id') mco)) ----------- 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 , -- co :: ty ~ ty' let co' = Type.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) , (in_scope, EI bs mco) <- go n oss subst ty' -- mco :: subst(ty') ~ b1_ty -> ... -> bn_ty -> tr = (in_scope, EI bs (mkTransMCoR co' mco)) | otherwise -- We have an expression of arity > 0, -- but its type isn't a function, or a binder -- does not have a fixed runtime representation = warnPprTrace True "mkEtaWW" ((ppr orig_oss <+> ppr orig_ty) $$ ppr_orig_expr) (getTCvInScope subst, EI [] MRefl) -- This *can* legitimately 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 {- ********************************************************************* * * The "push rules" * * ************************************************************************ Here we implement the "push rules" from FC papers: * The push-argument rules, where we can move a coercion past an argument. We have (fun |> co) arg and we want to transform it to (fun arg') |> co' for some suitable co' and transformed arg'. * The PushK rule for data constructors. We have (K e1 .. en) |> co and we want to transform to (K e1' .. en') by pushing the coercion into the arguments -} pushCoArgs :: CoercionR -> [CoreArg] -> Maybe ([CoreArg], MCoercion) pushCoArgs co [] = return ([], MCo co) pushCoArgs co (arg:args) = do { (arg', m_co1) <- pushCoArg co arg ; case m_co1 of MCo co1 -> do { (args', m_co2) <- pushCoArgs co1 args ; return (arg':args', m_co2) } MRefl -> return (arg':args, MRefl) } pushMCoArg :: MCoercionR -> CoreArg -> Maybe (CoreArg, MCoercion) pushMCoArg MRefl arg = Just (arg, MRefl) pushMCoArg (MCo co) arg = pushCoArg co arg pushCoArg :: CoercionR -> CoreArg -> Maybe (CoreArg, MCoercion) -- We have (fun |> co) arg, and we want to transform it to -- (fun arg) |> co -- This may fail, e.g. if (fun :: N) where N is a newtype -- C.f. simplCast in GHC.Core.Opt.Simplify -- 'co' is always Representational pushCoArg co arg | Type ty <- arg = do { (ty', m_co') <- pushCoTyArg co ty ; return (Type ty', m_co') } | otherwise = do { (arg_mco, m_co') <- pushCoValArg co ; let arg_mco' = checkReflexiveMCo arg_mco -- checkReflexiveMCo: see Note [Check for reflexive casts in eta expansion] -- The coercion is very often (arg_co -> res_co), but without -- the argument coercion actually being ReflCo ; return (arg `mkCastMCo` arg_mco', m_co') } pushCoTyArg :: CoercionR -> Type -> Maybe (Type, MCoercionR) -- We have (fun |> co) @ty -- Push the coercion through to return -- (fun @ty') |> co' -- 'co' is always Representational -- If the returned coercion is Nothing, then it would have been reflexive; -- it's faster not to compute it, though. pushCoTyArg co ty -- The following is inefficient - don't do `eqType` here, the coercion -- optimizer will take care of it. See #14737. -- -- | tyL `eqType` tyR -- -- = Just (ty, Nothing) | isReflCo co = Just (ty, MRefl) | isForAllTy_ty tyL = assertPpr (isForAllTy_ty tyR) (ppr co $$ ppr ty) $ Just (ty `mkCastTy` co1, MCo co2) | otherwise = Nothing where Pair tyL tyR = coercionKind co -- co :: tyL ~ tyR -- tyL = forall (a1 :: k1). ty1 -- tyR = forall (a2 :: k2). ty2 co1 = mkSymCo (mkNthCo Nominal 0 co) -- co1 :: k2 ~N k1 -- Note that NthCo can extract a Nominal equality between the -- kinds of the types related by a coercion between forall-types. -- See the NthCo case in GHC.Core.Lint. co2 = mkInstCo co (mkGReflLeftCo Nominal ty co1) -- co2 :: ty1[ (ty|>co1)/a1 ] ~ ty2[ ty/a2 ] -- Arg of mkInstCo is always nominal, hence mkNomReflCo pushCoValArg :: CoercionR -> Maybe (MCoercionR, MCoercionR) -- We have (fun |> co) arg -- Push the coercion through to return -- (fun (arg |> co_arg)) |> co_res -- 'co' is always Representational -- If the second returned Coercion is actually Nothing, then no cast is necessary; -- the returned coercion would have been reflexive. pushCoValArg co -- The following is inefficient - don't do `eqType` here, the coercion -- optimizer will take care of it. See #14737. -- -- | tyL `eqType` tyR -- -- = Just (mkRepReflCo arg, Nothing) | isReflCo co = Just (MRefl, MRefl) | isFunTy tyL , (co_mult, co1, co2) <- decomposeFunCo Representational co , isReflexiveCo co_mult -- We can't push the coercion in the case where co_mult isn't reflexivity: -- it could be an unsafe axiom, and losing this information could yield -- ill-typed terms. For instance (fun x ::(1) Int -> (fun _ -> () |> co) x) -- with co :: (Int -> ()) ~ (Int %1 -> ()), would reduce to (fun x ::(1) Int -- -> (fun _ ::(Many) Int -> ()) x) which is ill-typed -- If co :: (tyL1 -> tyL2) ~ (tyR1 -> tyR2) -- then co1 :: tyL1 ~ tyR1 -- co2 :: tyL2 ~ tyR2 = assertPpr (isFunTy tyR) (ppr co $$ ppr arg) $ Just (coToMCo (mkSymCo co1), coToMCo co2) -- Critically, coToMCo to checks for ReflCo; the whole coercion may not -- be reflexive, but either of its components might be -- We could use isReflexiveCo, but it's not clear if the benefit -- is worth the cost, and it makes no difference in #18223 | otherwise = Nothing where arg = funArgTy tyR Pair tyL tyR = coercionKind co pushCoercionIntoLambda :: HasDebugCallStack => InScopeSet -> Var -> CoreExpr -> CoercionR -> Maybe (Var, CoreExpr) -- This implements the Push rule from the paper on coercions -- (\x. e) |> co -- ===> -- (\x'. e |> co') pushCoercionIntoLambda in_scope x e co | assert (not (isTyVar x) && not (isCoVar x)) True , Pair s1s2 t1t2 <- coercionKind co , Just (_, _s1,_s2) <- splitFunTy_maybe s1s2 , Just (w1, t1,_t2) <- splitFunTy_maybe t1t2 , (co_mult, co1, co2) <- decomposeFunCo Representational co , isReflexiveCo co_mult -- We can't push the coercion in the case where co_mult isn't -- reflexivity. See pushCoValArg for more details. = let -- Should we optimize the coercions here? -- Otherwise they might not match too well x' = x `setIdType` t1 `setIdMult` w1 in_scope' = in_scope `extendInScopeSet` x' subst = extendIdSubst (mkEmptySubst in_scope') x (mkCast (Var x') (mkSymCo co1)) -- We substitute x' for x, except we need to preserve types. -- The types are as follows: -- x :: s1, x' :: t1, co1 :: s1 ~# t1, -- so we extend the substitution with x |-> (x' |> sym co1). in Just (x', substExpr subst e `mkCast` co2) | otherwise -- See #21555 / #21577 for a case where this trace fired but the cause was benign = -- pprTrace "exprIsLambda_maybe: Unexpected lambda in case" (ppr (Lam x e)) Nothing pushCoDataCon :: DataCon -> [CoreExpr] -> Coercion -> Maybe (DataCon , [Type] -- Universal type args , [CoreExpr]) -- All other args incl existentials -- Implement the KPush reduction rule as described in "Down with kinds" -- The transformation applies iff we have -- (C e1 ... en) `cast` co -- where co :: (T t1 .. tn) ~ to_ty -- The left-hand one must be a T, because exprIsConApp returned True -- but the right-hand one might not be. (Though it usually will.) pushCoDataCon dc dc_args co | isReflCo co || from_ty `eqType` to_ty -- try cheap test first , let (univ_ty_args, rest_args) = splitAtList (dataConUnivTyVars dc) dc_args = Just (dc, map exprToType univ_ty_args, rest_args) | Just (to_tc, to_tc_arg_tys) <- splitTyConApp_maybe to_ty , to_tc == dataConTyCon dc -- These two tests can fail; we might see -- (C x y) `cast` (g :: T a ~ S [a]), -- where S is a type function. In fact, exprIsConApp -- will probably not be called in such circumstances, -- but there's nothing wrong with it = let tc_arity = tyConArity to_tc dc_univ_tyvars = dataConUnivTyVars dc dc_ex_tcvars = dataConExTyCoVars dc arg_tys = dataConRepArgTys dc non_univ_args = dropList dc_univ_tyvars dc_args (ex_args, val_args) = splitAtList dc_ex_tcvars non_univ_args -- Make the "Psi" from the paper omegas = decomposeCo tc_arity co (tyConRolesRepresentational to_tc) (psi_subst, to_ex_arg_tys) = liftCoSubstWithEx Representational dc_univ_tyvars omegas dc_ex_tcvars (map exprToType ex_args) -- Cast the value arguments (which include dictionaries) new_val_args = zipWith cast_arg (map scaledThing arg_tys) val_args cast_arg arg_ty arg = mkCast arg (psi_subst arg_ty) to_ex_args = map Type to_ex_arg_tys dump_doc = vcat [ppr dc, ppr dc_univ_tyvars, ppr dc_ex_tcvars, ppr arg_tys, ppr dc_args, ppr ex_args, ppr val_args, ppr co, ppr from_ty, ppr to_ty, ppr to_tc , ppr $ mkTyConApp to_tc (map exprToType $ takeList dc_univ_tyvars dc_args) ] in assertPpr (eqType from_ty (mkTyConApp to_tc (map exprToType $ takeList dc_univ_tyvars dc_args))) dump_doc $ assertPpr (equalLength val_args arg_tys) dump_doc $ Just (dc, to_tc_arg_tys, to_ex_args ++ new_val_args) | otherwise = Nothing where Pair from_ty to_ty = coercionKind co collectBindersPushingCo :: CoreExpr -> ([Var], CoreExpr) -- Collect lambda binders, pushing coercions inside if possible -- E.g. (\x.e) |> g g :: -> blah -- = (\x. e |> Nth 1 g) -- -- That is, -- -- collectBindersPushingCo ((\x.e) |> g) === ([x], e |> Nth 1 g) collectBindersPushingCo e = go [] e where -- Peel off lambdas until we hit a cast. go :: [Var] -> CoreExpr -> ([Var], CoreExpr) -- The accumulator is in reverse order go bs (Lam b e) = go (b:bs) e go bs (Cast e co) = go_c bs e co go bs e = (reverse bs, e) -- We are in a cast; peel off casts until we hit a lambda. go_c :: [Var] -> CoreExpr -> CoercionR -> ([Var], CoreExpr) -- (go_c bs e c) is same as (go bs e (e |> c)) go_c bs (Cast e co1) co2 = go_c bs e (co1 `mkTransCo` co2) go_c bs (Lam b e) co = go_lam bs b e co go_c bs e co = (reverse bs, mkCast e co) -- We are in a lambda under a cast; peel off lambdas and build a -- new coercion for the body. go_lam :: [Var] -> Var -> CoreExpr -> CoercionR -> ([Var], CoreExpr) -- (go_lam bs b e c) is same as (go_c bs (\b.e) c) go_lam bs b e co | isTyVar b , let Pair tyL tyR = coercionKind co , assert (isForAllTy_ty tyL) $ isForAllTy_ty tyR , isReflCo (mkNthCo Nominal 0 co) -- See Note [collectBindersPushingCo] = go_c (b:bs) e (mkInstCo co (mkNomReflCo (mkTyVarTy b))) | isCoVar b , let Pair tyL tyR = coercionKind co , assert (isForAllTy_co tyL) $ isForAllTy_co tyR , isReflCo (mkNthCo Nominal 0 co) -- See Note [collectBindersPushingCo] , let cov = mkCoVarCo b = go_c (b:bs) e (mkInstCo co (mkNomReflCo (mkCoercionTy cov))) | isId b , let Pair tyL tyR = coercionKind co , assert (isFunTy tyL) $ isFunTy tyR , (co_mult, co_arg, co_res) <- decomposeFunCo Representational co , isReflCo co_mult -- See Note [collectBindersPushingCo] , isReflCo co_arg -- See Note [collectBindersPushingCo] = go_c (b:bs) e co_res | otherwise = (reverse bs, mkCast (Lam b e) co) {- Note [collectBindersPushingCo] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We just look for coercions of form % w -> blah (and similarly for foralls) to keep this function simple. We could do more elaborate stuff, but it'd involve substitution etc. -} {- ********************************************************************* * * Join points * * ********************************************************************* -} ------------------- -- | 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 {}) = warnPprTrace True "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) <- splitForAllTyCoVar_maybe ty , let (subst', tv') = substVarBndr subst tv = go (n-1) res_ty subst' (tv' : rev_bs) (e `App` varToCoreExpr tv') -- The varToCoreExpr is important: `tv` might be a coercion variable | Just (mult, arg_ty, res_ty) <- splitFunTy_maybe ty , let (subst', b) = freshEtaId n subst (Scaled mult arg_ty) = go (n-1) res_ty subst' (b : rev_bs) (e `App` varToCoreExpr b) -- The varToCoreExpr is important: `b` might be a coercion variable | otherwise = pprPanic "etaBodyForJoinPoint" $ int need_args $$ ppr body $$ ppr (exprType body) init_subst e = mkEmptyTCvSubst (mkInScopeSet (exprFreeVars e)) -------------- freshEtaId :: Int -> TCvSubst -> Scaled 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 Scaled mult' ty' = Type.substScaledTyUnchecked subst ty eta_id' = uniqAway (getTCvInScope subst) $ mkSysLocalOrCoVar (fsLit "eta") (mkBuiltinUnique n) mult' ty' -- "OrCoVar" since this can be used to eta-expand -- coercion abstractions subst' = extendTCvInScope subst eta_id'