{- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 \section[Demand]{@Demand@: A decoupled implementation of a demand domain} -} {-# LANGUAGE CPP, FlexibleInstances, TypeSynonymInstances #-} module Demand ( StrDmd, UseDmd(..), Count(..), countOnce, countMany, -- cardinality Demand, CleanDemand, getStrDmd, getUseDmd, mkProdDmd, mkOnceUsedDmd, mkManyUsedDmd, mkHeadStrict, oneifyDmd, toCleanDmd, absDmd, topDmd, botDmd, seqDmd, lubDmd, bothDmd, lazyApply1Dmd, lazyApply2Dmd, strictApply1Dmd, catchArgDmd, isTopDmd, isAbsDmd, isSeqDmd, peelUseCall, cleanUseDmd_maybe, strictenDmd, bothCleanDmd, addCaseBndrDmd, DmdType(..), dmdTypeDepth, lubDmdType, bothDmdType, nopDmdType, botDmdType, mkDmdType, addDemand, removeDmdTyArgs, BothDmdArg, mkBothDmdArg, toBothDmdArg, DmdEnv, emptyDmdEnv, peelFV, findIdDemand, DmdResult, CPRResult, isBotRes, isTopRes, topRes, botRes, exnRes, cprProdRes, vanillaCprProdRes, cprSumRes, appIsBottom, isBottomingSig, pprIfaceStrictSig, trimCPRInfo, returnsCPR_maybe, StrictSig(..), mkStrictSig, mkClosedStrictSig, nopSig, botSig, cprProdSig, isNopSig, splitStrictSig, increaseStrictSigArity, seqDemand, seqDemandList, seqDmdType, seqStrictSig, evalDmd, cleanEvalDmd, cleanEvalProdDmd, isStrictDmd, splitDmdTy, splitFVs, deferAfterIO, postProcessUnsat, postProcessDmdType, splitProdDmd_maybe, peelCallDmd, mkCallDmd, dmdTransformSig, dmdTransformDataConSig, dmdTransformDictSelSig, argOneShots, argsOneShots, trimToType, TypeShape(..), useCount, isUsedOnce, reuseEnv, killUsageDemand, killUsageSig, zapUsageDemand, strictifyDictDmd ) where #include "HsVersions.h" import DynFlags import Outputable import Var ( Var ) import VarEnv import UniqFM import Util import BasicTypes import Binary import Maybes ( orElse ) import Type ( Type, isUnliftedType ) import TyCon ( isNewTyCon, isClassTyCon ) import DataCon ( splitDataProductType_maybe ) {- ************************************************************************ * * Joint domain for Strictness and Absence * * ************************************************************************ -} data JointDmd s u = JD { sd :: s, ud :: u } deriving ( Eq, Show ) getStrDmd :: JointDmd s u -> s getStrDmd = sd getUseDmd :: JointDmd s u -> u getUseDmd = ud -- Pretty-printing instance (Outputable s, Outputable u) => Outputable (JointDmd s u) where ppr (JD {sd = s, ud = u}) = angleBrackets (ppr s <> char ',' <> ppr u) -- Well-formedness preserving constructors for the joint domain mkJointDmd :: s -> u -> JointDmd s u mkJointDmd s u = JD { sd = s, ud = u } mkJointDmds :: [s] -> [u] -> [JointDmd s u] mkJointDmds ss as = zipWithEqual "mkJointDmds" mkJointDmd ss as {- ************************************************************************ * * Strictness domain * * ************************************************************************ Lazy | ExnStr x - | HeadStr / \ SCall SProd \ / HyperStr Note [Exceptions and strictness] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Exceptions need rather careful treatment, especially because of 'catch'. See Trac #10712. There are two main pieces. * The Termination type includes ThrowsExn, meaning "under the given demand this expression either diverges or throws an exception". This is relatively uncontroversial. The primops raise# and raiseIO# both return ThrowsExn; nothing else does. * An ArgStr has an ExnStr flag to say how to process the Termination result of the argument. If the ExnStr flag is ExnStr, we squash ThrowsExn to topRes. (This is done in postProcessDmdResult.) Here is the kay example catch# (\s -> throwIO exn s) blah We analyse the argument (\s -> raiseIO# exn s) with demand Str ExnStr (SCall HeadStr) i.e. with the ExnStr flag set. - First we analyse the argument with the "clean-demand" (SCall HeadStr), getting a DmdResult of ThrowsExn from the saturated application of raiseIO#. - Then we apply the post-processing for the shell, squashing the ThrowsExn to topRes. This also applies uniformly to free variables. Consider let r = \st -> raiseIO# blah st in catch# (\s -> ...(r s')..) handler st If we give the first argument of catch a strict signature, we'll get a demand 'C(S)' for 'r'; that is, 'r' is definitely called with one argument, which indeed it is. But when we post-process the free-var demands on catch#'s argument (in postProcessDmdEnv), we'll give 'r' a demand of (Str ExnStr (SCall HeadStr)); and if we feed that into r's RHS (which would be reasonable) we'll squash the exception just as if we'd inlined 'r'. -} -- Vanilla strictness domain data StrDmd = HyperStr -- Hyper-strict -- Bottom of the lattice -- Note [HyperStr and Use demands] | SCall StrDmd -- Call demand -- Used only for values of function type | SProd [ArgStr] -- Product -- Used only for values of product type -- Invariant: not all components are HyperStr (use HyperStr) -- not all components are Lazy (use HeadStr) | HeadStr -- Head-Strict -- A polymorphic demand: used for values of all types, -- including a type variable deriving ( Eq, Show ) type ArgStr = Str StrDmd data Str s = Lazy -- Lazy -- Top of the lattice | Str ExnStr s deriving ( Eq, Show ) data ExnStr -- See Note [Exceptions and strictness] = VanStr -- "Vanilla" case, ordinary strictness | ExnStr -- (Str ExnStr d) means be strict like 'd' but then degrade -- the Termination info ThrowsExn to Dunno deriving( Eq, Show ) -- Well-formedness preserving constructors for the Strictness domain strBot, strTop :: ArgStr strBot = Str VanStr HyperStr strTop = Lazy mkSCall :: StrDmd -> StrDmd mkSCall HyperStr = HyperStr mkSCall s = SCall s mkSProd :: [ArgStr] -> StrDmd mkSProd sx | any isHyperStr sx = HyperStr | all isLazy sx = HeadStr | otherwise = SProd sx isLazy :: ArgStr -> Bool isLazy Lazy = True isLazy (Str {}) = False isHyperStr :: ArgStr -> Bool isHyperStr (Str _ HyperStr) = True isHyperStr _ = False -- Pretty-printing instance Outputable StrDmd where ppr HyperStr = char 'B' ppr (SCall s) = char 'C' <> parens (ppr s) ppr HeadStr = char 'S' ppr (SProd sx) = char 'S' <> parens (hcat (map ppr sx)) instance Outputable ArgStr where ppr (Str x s) = (case x of VanStr -> empty; ExnStr -> char 'x') <> ppr s ppr Lazy = char 'L' lubArgStr :: ArgStr -> ArgStr -> ArgStr lubArgStr Lazy _ = Lazy lubArgStr _ Lazy = Lazy lubArgStr (Str x1 s1) (Str x2 s2) = Str (x1 `lubExnStr` x2) (s1 `lubStr` s2) lubExnStr :: ExnStr -> ExnStr -> ExnStr lubExnStr VanStr VanStr = VanStr lubExnStr _ _ = ExnStr -- ExnStr is lazier lubStr :: StrDmd -> StrDmd -> StrDmd lubStr HyperStr s = s lubStr (SCall s1) HyperStr = SCall s1 lubStr (SCall _) HeadStr = HeadStr lubStr (SCall s1) (SCall s2) = SCall (s1 `lubStr` s2) lubStr (SCall _) (SProd _) = HeadStr lubStr (SProd sx) HyperStr = SProd sx lubStr (SProd _) HeadStr = HeadStr lubStr (SProd s1) (SProd s2) | length s1 == length s2 = mkSProd (zipWith lubArgStr s1 s2) | otherwise = HeadStr lubStr (SProd _) (SCall _) = HeadStr lubStr HeadStr _ = HeadStr bothArgStr :: ArgStr -> ArgStr -> ArgStr bothArgStr Lazy s = s bothArgStr s Lazy = s bothArgStr (Str x1 s1) (Str x2 s2) = Str (x1 `bothExnStr` x2) (s1 `bothStr` s2) bothExnStr :: ExnStr -> ExnStr -> ExnStr bothExnStr ExnStr ExnStr = ExnStr bothExnStr _ _ = VanStr bothStr :: StrDmd -> StrDmd -> StrDmd bothStr HyperStr _ = HyperStr bothStr HeadStr s = s bothStr (SCall _) HyperStr = HyperStr bothStr (SCall s1) HeadStr = SCall s1 bothStr (SCall s1) (SCall s2) = SCall (s1 `bothStr` s2) bothStr (SCall _) (SProd _) = HyperStr -- Weird bothStr (SProd _) HyperStr = HyperStr bothStr (SProd s1) HeadStr = SProd s1 bothStr (SProd s1) (SProd s2) | length s1 == length s2 = mkSProd (zipWith bothArgStr s1 s2) | otherwise = HyperStr -- Weird bothStr (SProd _) (SCall _) = HyperStr -- utility functions to deal with memory leaks seqStrDmd :: StrDmd -> () seqStrDmd (SProd ds) = seqStrDmdList ds seqStrDmd (SCall s) = s `seq` () seqStrDmd _ = () seqStrDmdList :: [ArgStr] -> () seqStrDmdList [] = () seqStrDmdList (d:ds) = seqArgStr d `seq` seqStrDmdList ds seqArgStr :: ArgStr -> () seqArgStr Lazy = () seqArgStr (Str x s) = x `seq` seqStrDmd s -- Splitting polymorphic demands splitArgStrProdDmd :: Int -> ArgStr -> Maybe [ArgStr] splitArgStrProdDmd n Lazy = Just (replicate n Lazy) splitArgStrProdDmd n (Str _ s) = splitStrProdDmd n s splitStrProdDmd :: Int -> StrDmd -> Maybe [ArgStr] splitStrProdDmd n HyperStr = Just (replicate n strBot) splitStrProdDmd n HeadStr = Just (replicate n strTop) splitStrProdDmd n (SProd ds) = ASSERT( ds `lengthIs` n) Just ds splitStrProdDmd _ (SCall {}) = Nothing -- This can happen when the programmer uses unsafeCoerce, -- and we don't then want to crash the compiler (Trac #9208) {- ************************************************************************ * * Absence domain * * ************************************************************************ Used / \ UCall UProd \ / UHead | Count x - | Abs -} -- Domain for genuine usage data UseDmd = UCall Count UseDmd -- Call demand for absence -- Used only for values of function type | UProd [ArgUse] -- Product -- Used only for values of product type -- See Note [Don't optimise UProd(Used) to Used] -- [Invariant] Not all components are Abs -- (in that case, use UHead) | UHead -- May be used; but its sub-components are -- definitely *not* used. Roughly U(AAA) -- Eg the usage of x in x `seq` e -- A polymorphic demand: used for values of all types, -- including a type variable -- Since (UCall _ Abs) is ill-typed, UHead doesn't -- make sense for lambdas | Used -- May be used; and its sub-components may be used -- Top of the lattice deriving ( Eq, Show ) -- Extended usage demand for absence and counting type ArgUse = Use UseDmd data Use u = Abs -- Definitely unused -- Bottom of the lattice | Use Count u -- May be used with some cardinality deriving ( Eq, Show ) -- Abstract counting of usages data Count = One | Many deriving ( Eq, Show ) -- Pretty-printing instance Outputable ArgUse where ppr Abs = char 'A' ppr (Use Many a) = ppr a ppr (Use One a) = char '1' <> char '*' <> ppr a instance Outputable UseDmd where ppr Used = char 'U' ppr (UCall c a) = char 'C' <> ppr c <> parens (ppr a) ppr UHead = char 'H' ppr (UProd as) = char 'U' <> parens (hcat (punctuate (char ',') (map ppr as))) instance Outputable Count where ppr One = char '1' ppr Many = text "" -- Well-formedness preserving constructors for the Absence domain countOnce, countMany :: Count countOnce = One countMany = Many useBot, useTop :: ArgUse useBot = Abs useTop = Use Many Used mkUCall :: Count -> UseDmd -> UseDmd --mkUCall c Used = Used c mkUCall c a = UCall c a mkUProd :: [ArgUse] -> UseDmd mkUProd ux | all (== Abs) ux = UHead | otherwise = UProd ux lubCount :: Count -> Count -> Count lubCount _ Many = Many lubCount Many _ = Many lubCount x _ = x lubArgUse :: ArgUse -> ArgUse -> ArgUse lubArgUse Abs x = x lubArgUse x Abs = x lubArgUse (Use c1 a1) (Use c2 a2) = Use (lubCount c1 c2) (lubUse a1 a2) lubUse :: UseDmd -> UseDmd -> UseDmd lubUse UHead u = u lubUse (UCall c u) UHead = UCall c u lubUse (UCall c1 u1) (UCall c2 u2) = UCall (lubCount c1 c2) (lubUse u1 u2) lubUse (UCall _ _) _ = Used lubUse (UProd ux) UHead = UProd ux lubUse (UProd ux1) (UProd ux2) | length ux1 == length ux2 = UProd $ zipWith lubArgUse ux1 ux2 | otherwise = Used lubUse (UProd {}) (UCall {}) = Used -- lubUse (UProd {}) Used = Used lubUse (UProd ux) Used = UProd (map (`lubArgUse` useTop) ux) lubUse Used (UProd ux) = UProd (map (`lubArgUse` useTop) ux) lubUse Used _ = Used -- Note [Used should win] -- `both` is different from `lub` in its treatment of counting; if -- `both` is computed for two used, the result always has -- cardinality `Many` (except for the inner demands of UCall demand -- [TODO] explain). -- Also, x `bothUse` x /= x (for anything but Abs). bothArgUse :: ArgUse -> ArgUse -> ArgUse bothArgUse Abs x = x bothArgUse x Abs = x bothArgUse (Use _ a1) (Use _ a2) = Use Many (bothUse a1 a2) bothUse :: UseDmd -> UseDmd -> UseDmd bothUse UHead u = u bothUse (UCall c u) UHead = UCall c u -- Exciting special treatment of inner demand for call demands: -- use `lubUse` instead of `bothUse`! bothUse (UCall _ u1) (UCall _ u2) = UCall Many (u1 `lubUse` u2) bothUse (UCall {}) _ = Used bothUse (UProd ux) UHead = UProd ux bothUse (UProd ux1) (UProd ux2) | length ux1 == length ux2 = UProd $ zipWith bothArgUse ux1 ux2 | otherwise = Used bothUse (UProd {}) (UCall {}) = Used -- bothUse (UProd {}) Used = Used -- Note [Used should win] bothUse Used (UProd ux) = UProd (map (`bothArgUse` useTop) ux) bothUse (UProd ux) Used = UProd (map (`bothArgUse` useTop) ux) bothUse Used _ = Used -- Note [Used should win] peelUseCall :: UseDmd -> Maybe (Count, UseDmd) peelUseCall (UCall c u) = Just (c,u) peelUseCall _ = Nothing addCaseBndrDmd :: Demand -- On the case binder -> [Demand] -- On the components of the constructor -> [Demand] -- Final demands for the components of the constructor -- See Note [Demand on case-alternative binders] addCaseBndrDmd (JD { sd = ms, ud = mu }) alt_dmds = case mu of Abs -> alt_dmds Use _ u -> zipWith bothDmd alt_dmds (mkJointDmds ss us) where Just ss = splitArgStrProdDmd arity ms -- Guaranteed not to be a call Just us = splitUseProdDmd arity u -- Ditto where arity = length alt_dmds {- Note [Demand on case-alternative binders] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The demand on a binder in a case alternative comes (a) From the demand on the binder itself (b) From the demand on the case binder Forgetting (b) led directly to Trac #10148. Example. Source code: f x@(p,_) = if p then foo x else True foo (p,True) = True foo (p,q) = foo (q,p) After strictness analysis: f = \ (x_an1 [Dmd=<S(SL),1*U(U,1*U)>] :: (Bool, Bool)) -> case x_an1 of wild_X7 [Dmd=<L,1*U(1*U,1*U)>] { (p_an2 [Dmd=<S,1*U>], ds_dnz [Dmd=<L,A>]) -> case p_an2 of _ { False -> GHC.Types.True; True -> foo wild_X7 } It's true that ds_dnz is *itself* absent, but the use of wild_X7 means that it is very much alive and demanded. See Trac #10148 for how the consequences play out. This is needed even for non-product types, in case the case-binder is used but the components of the case alternative are not. Note [Don't optimise UProd(Used) to Used] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ These two UseDmds: UProd [Used, Used] and Used are semantically equivalent, but we do not turn the former into the latter, for a regrettable-subtle reason. Suppose we did. then f (x,y) = (y,x) would get StrDmd = Str = SProd [Lazy, Lazy] UseDmd = Used = UProd [Used, Used] But with the joint demand of <Str, Used> doesn't convey any clue that there is a product involved, and so the worthSplittingFun will not fire. (We'd need to use the type as well to make it fire.) Moreover, consider g h p@(_,_) = h p This too would get <Str, Used>, but this time there really isn't any point in w/w since the components of the pair are not used at all. So the solution is: don't aggressively collapse UProd [Used,Used] to Used; intead leave it as-is. In effect we are using the UseDmd to do a little bit of boxity analysis. Not very nice. Note [Used should win] ~~~~~~~~~~~~~~~~~~~~~~ Both in lubUse and bothUse we want (Used `both` UProd us) to be Used. Why? Because Used carries the implication the whole thing is used, box and all, so we don't want to w/w it. If we use it both boxed and unboxed, then we are definitely using the box, and so we are quite likely to pay a reboxing cost. So we make Used win here. Example is in the Buffer argument of GHC.IO.Handle.Internals.writeCharBuffer Baseline: (A) Not making Used win (UProd wins) Compare with: (B) making Used win for lub and both Min -0.3% -5.6% -10.7% -11.0% -33.3% Max +0.3% +45.6% +11.5% +11.5% +6.9% Geometric Mean -0.0% +0.5% +0.3% +0.2% -0.8% Baseline: (B) Making Used win for both lub and both Compare with: (C) making Used win for both, but UProd win for lub Min -0.1% -0.3% -7.9% -8.0% -6.5% Max +0.1% +1.0% +21.0% +21.0% +0.5% Geometric Mean +0.0% +0.0% -0.0% -0.1% -0.1% -} -- If a demand is used multiple times (i.e. reused), than any use-once -- mentioned there, that is not protected by a UCall, can happen many times. markReusedDmd :: ArgUse -> ArgUse markReusedDmd Abs = Abs markReusedDmd (Use _ a) = Use Many (markReused a) markReused :: UseDmd -> UseDmd markReused (UCall _ u) = UCall Many u -- No need to recurse here markReused (UProd ux) = UProd (map markReusedDmd ux) markReused u = u isUsedMU :: ArgUse -> Bool -- True <=> markReusedDmd d = d isUsedMU Abs = True isUsedMU (Use One _) = False isUsedMU (Use Many u) = isUsedU u isUsedU :: UseDmd -> Bool -- True <=> markReused d = d isUsedU Used = True isUsedU UHead = True isUsedU (UProd us) = all isUsedMU us isUsedU (UCall One _) = False isUsedU (UCall Many _) = True -- No need to recurse -- Squashing usage demand demands seqUseDmd :: UseDmd -> () seqUseDmd (UProd ds) = seqArgUseList ds seqUseDmd (UCall c d) = c `seq` seqUseDmd d seqUseDmd _ = () seqArgUseList :: [ArgUse] -> () seqArgUseList [] = () seqArgUseList (d:ds) = seqArgUse d `seq` seqArgUseList ds seqArgUse :: ArgUse -> () seqArgUse (Use c u) = c `seq` seqUseDmd u seqArgUse _ = () -- Splitting polymorphic Maybe-Used demands splitUseProdDmd :: Int -> UseDmd -> Maybe [ArgUse] splitUseProdDmd n Used = Just (replicate n useTop) splitUseProdDmd n UHead = Just (replicate n Abs) splitUseProdDmd n (UProd ds) = ASSERT2( ds `lengthIs` n, text "splitUseProdDmd" $$ ppr n $$ ppr ds ) Just ds splitUseProdDmd _ (UCall _ _) = Nothing -- This can happen when the programmer uses unsafeCoerce, -- and we don't then want to crash the compiler (Trac #9208) useCount :: Use u -> Count useCount Abs = One useCount (Use One _) = One useCount _ = Many {- ************************************************************************ * * Clean demand for Strictness and Usage * * ************************************************************************ This domain differst from JointDemand in the sence that pure absence is taken away, i.e., we deal *only* with non-absent demands. Note [Strict demands] ~~~~~~~~~~~~~~~~~~~~~ isStrictDmd returns true only of demands that are both strict and used In particular, it is False for <HyperStr, Abs>, which can and does arise in, say (Trac #7319) f x = raise# <some exception> Then 'x' is not used, so f gets strictness <HyperStr,Abs> -> . Now the w/w generates fx = let x <HyperStr,Abs> = absentError "unused" in raise <some exception> At this point we really don't want to convert to fx = case absentError "unused" of x -> raise <some exception> Since the program is going to diverge, this swaps one error for another, but it's really a bad idea to *ever* evaluate an absent argument. In Trac #7319 we get T7319.exe: Oops! Entered absent arg w_s1Hd{v} [lid] [base:GHC.Base.String{tc 36u}] Note [Dealing with call demands] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Call demands are constructed and deconstructed coherently for strictness and absence. For instance, the strictness signature for the following function f :: (Int -> (Int, Int)) -> (Int, Bool) f g = (snd (g 3), True) should be: <L,C(U(AU))>m -} type CleanDemand = JointDmd StrDmd UseDmd -- A demand that is at least head-strict bothCleanDmd :: CleanDemand -> CleanDemand -> CleanDemand bothCleanDmd (JD { sd = s1, ud = a1}) (JD { sd = s2, ud = a2}) = JD { sd = s1 `bothStr` s2, ud = a1 `bothUse` a2 } mkHeadStrict :: CleanDemand -> CleanDemand mkHeadStrict cd = cd { sd = HeadStr } mkOnceUsedDmd, mkManyUsedDmd :: CleanDemand -> Demand mkOnceUsedDmd (JD {sd = s,ud = a}) = JD { sd = Str VanStr s, ud = Use One a } mkManyUsedDmd (JD {sd = s,ud = a}) = JD { sd = Str VanStr s, ud = Use Many a } evalDmd :: Demand -- Evaluated strictly, and used arbitrarily deeply evalDmd = JD { sd = Str VanStr HeadStr, ud = useTop } mkProdDmd :: [Demand] -> CleanDemand mkProdDmd dx = JD { sd = mkSProd $ map getStrDmd dx , ud = mkUProd $ map getUseDmd dx } mkCallDmd :: CleanDemand -> CleanDemand mkCallDmd (JD {sd = d, ud = u}) = JD { sd = mkSCall d, ud = mkUCall One u } cleanEvalDmd :: CleanDemand cleanEvalDmd = JD { sd = HeadStr, ud = Used } cleanEvalProdDmd :: Arity -> CleanDemand cleanEvalProdDmd n = JD { sd = HeadStr, ud = UProd (replicate n useTop) } {- ************************************************************************ * * Demand: combining stricness and usage * * ************************************************************************ -} type Demand = JointDmd ArgStr ArgUse lubDmd :: Demand -> Demand -> Demand lubDmd (JD {sd = s1, ud = a1}) (JD {sd = s2, ud = a2}) = JD { sd = s1 `lubArgStr` s2 , ud = a1 `lubArgUse` a2 } bothDmd :: Demand -> Demand -> Demand bothDmd (JD {sd = s1, ud = a1}) (JD {sd = s2, ud = a2}) = JD { sd = s1 `bothArgStr` s2 , ud = a1 `bothArgUse` a2 } lazyApply1Dmd, lazyApply2Dmd, strictApply1Dmd, catchArgDmd :: Demand strictApply1Dmd = JD { sd = Str VanStr (SCall HeadStr) , ud = Use Many (UCall One Used) } -- First argument of catch#: -- uses its arg once, applies it once -- and catches exceptions (the ExnStr) part catchArgDmd = JD { sd = Str ExnStr (SCall HeadStr) , ud = Use One (UCall One Used) } lazyApply1Dmd = JD { sd = Lazy , ud = Use One (UCall One Used) } -- Second argument of catch#: -- uses its arg at most once, applies it once -- but is lazy (might not be called at all) lazyApply2Dmd = JD { sd = Lazy , ud = Use One (UCall One (UCall One Used)) } absDmd :: Demand absDmd = JD { sd = Lazy, ud = Abs } topDmd :: Demand topDmd = JD { sd = Lazy, ud = useTop } botDmd :: Demand botDmd = JD { sd = strBot, ud = useBot } seqDmd :: Demand seqDmd = JD { sd = Str VanStr HeadStr, ud = Use One UHead } oneifyDmd :: Demand -> Demand oneifyDmd (JD { sd = s, ud = Use _ a }) = JD { sd = s, ud = Use One a } oneifyDmd jd = jd isTopDmd :: Demand -> Bool -- Used to suppress pretty-printing of an uninformative demand isTopDmd (JD {sd = Lazy, ud = Use Many Used}) = True isTopDmd _ = False isAbsDmd :: Demand -> Bool isAbsDmd (JD {ud = Abs}) = True -- The strictness part can be HyperStr isAbsDmd _ = False -- for a bottom demand isSeqDmd :: Demand -> Bool isSeqDmd (JD {sd = Str VanStr HeadStr, ud = Use _ UHead}) = True isSeqDmd _ = False isUsedOnce :: Demand -> Bool isUsedOnce (JD { ud = a }) = case useCount a of One -> True Many -> False -- More utility functions for strictness seqDemand :: Demand -> () seqDemand (JD {sd = s, ud = u}) = seqArgStr s `seq` seqArgUse u seqDemandList :: [Demand] -> () seqDemandList [] = () seqDemandList (d:ds) = seqDemand d `seq` seqDemandList ds isStrictDmd :: Demand -> Bool -- See Note [Strict demands] isStrictDmd (JD {ud = Abs}) = False isStrictDmd (JD {sd = Lazy}) = False isStrictDmd _ = True isWeakDmd :: Demand -> Bool isWeakDmd (JD {sd = s, ud = a}) = isLazy s && isUsedMU a cleanUseDmd_maybe :: Demand -> Maybe UseDmd cleanUseDmd_maybe (JD { ud = Use _ u }) = Just u cleanUseDmd_maybe _ = Nothing splitFVs :: Bool -- Thunk -> DmdEnv -> (DmdEnv, DmdEnv) splitFVs is_thunk rhs_fvs | is_thunk = foldUFM_Directly add (emptyVarEnv, emptyVarEnv) rhs_fvs | otherwise = partitionVarEnv isWeakDmd rhs_fvs where add uniq dmd@(JD { sd = s, ud = u }) (lazy_fv, sig_fv) | Lazy <- s = (addToUFM_Directly lazy_fv uniq dmd, sig_fv) | otherwise = ( addToUFM_Directly lazy_fv uniq (JD { sd = Lazy, ud = u }) , addToUFM_Directly sig_fv uniq (JD { sd = s, ud = Abs }) ) data TypeShape = TsFun TypeShape | TsProd [TypeShape] | TsUnk instance Outputable TypeShape where ppr TsUnk = text "TsUnk" ppr (TsFun ts) = text "TsFun" <> parens (ppr ts) ppr (TsProd tss) = parens (hsep $ punctuate comma $ map ppr tss) trimToType :: Demand -> TypeShape -> Demand -- See Note [Trimming a demand to a type] trimToType (JD { sd = ms, ud = mu }) ts = JD (go_ms ms ts) (go_mu mu ts) where go_ms :: ArgStr -> TypeShape -> ArgStr go_ms Lazy _ = Lazy go_ms (Str x s) ts = Str x (go_s s ts) go_s :: StrDmd -> TypeShape -> StrDmd go_s HyperStr _ = HyperStr go_s (SCall s) (TsFun ts) = SCall (go_s s ts) go_s (SProd mss) (TsProd tss) | equalLength mss tss = SProd (zipWith go_ms mss tss) go_s _ _ = HeadStr go_mu :: ArgUse -> TypeShape -> ArgUse go_mu Abs _ = Abs go_mu (Use c u) ts = Use c (go_u u ts) go_u :: UseDmd -> TypeShape -> UseDmd go_u UHead _ = UHead go_u (UCall c u) (TsFun ts) = UCall c (go_u u ts) go_u (UProd mus) (TsProd tss) | equalLength mus tss = UProd (zipWith go_mu mus tss) go_u _ _ = Used {- Note [Trimming a demand to a type] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider this: f :: a -> Bool f x = case ... of A g1 -> case (x |> g1) of (p,q) -> ... B -> error "urk" where A,B are the constructors of a GADT. We'll get a U(U,U) demand on x from the A branch, but that's a stupid demand for x itself, which has type 'a'. Indeed we get ASSERTs going off (notably in splitUseProdDmd, Trac #8569). Bottom line: we really don't want to have a binder whose demand is more deeply-nested than its type. There are various ways to tackle this. When processing (x |> g1), we could "trim" the incoming demand U(U,U) to match x's type. But I'm currently doing so just at the moment when we pin a demand on a binder, in DmdAnal.findBndrDmd. Note [Threshold demands] ~~~~~~~~~~~~~~~~~~~~~~~~ Threshold usage demand is generated to figure out if cardinality-instrumented demands of a binding's free variables should be unleashed. See also [Aggregated demand for cardinality]. Note [Replicating polymorphic demands] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Some demands can be considered as polymorphic. Generally, it is applicable to such beasts as tops, bottoms as well as Head-Used adn Head-stricts demands. For instance, S ~ S(L, ..., L) Also, when top or bottom is occurred as a result demand, it in fact can be expanded to saturate a callee's arity. -} splitProdDmd_maybe :: Demand -> Maybe [Demand] -- Split a product into its components, iff there is any -- useful information to be extracted thereby -- The demand is not necessarily strict! splitProdDmd_maybe (JD { sd = s, ud = u }) = case (s,u) of (Str _ (SProd sx), Use _ u) | Just ux <- splitUseProdDmd (length sx) u -> Just (mkJointDmds sx ux) (Str _ s, Use _ (UProd ux)) | Just sx <- splitStrProdDmd (length ux) s -> Just (mkJointDmds sx ux) (Lazy, Use _ (UProd ux)) -> Just (mkJointDmds (replicate (length ux) Lazy) ux) _ -> Nothing {- ************************************************************************ * * Demand results * * ************************************************************************ DmdResult: Dunno CPRResult / ThrowsExn / Diverges CPRResult: NoCPR / \ RetProd RetSum ConTag Product contructors return (Dunno (RetProd rs)) In a fixpoint iteration, start from Diverges We have lubs, but not glbs; but that is ok. -} ------------------------------------------------------------------------ -- Constructed Product Result ------------------------------------------------------------------------ data Termination r = Diverges -- Definitely diverges | ThrowsExn -- Definitely throws an exception or diverges | Dunno r -- Might diverge or converge deriving( Eq, Show ) type DmdResult = Termination CPRResult data CPRResult = NoCPR -- Top of the lattice | RetProd -- Returns a constructor from a product type | RetSum ConTag -- Returns a constructor from a data type deriving( Eq, Show ) lubCPR :: CPRResult -> CPRResult -> CPRResult lubCPR (RetSum t1) (RetSum t2) | t1 == t2 = RetSum t1 lubCPR RetProd RetProd = RetProd lubCPR _ _ = NoCPR lubDmdResult :: DmdResult -> DmdResult -> DmdResult lubDmdResult Diverges r = r lubDmdResult ThrowsExn Diverges = ThrowsExn lubDmdResult ThrowsExn r = r lubDmdResult (Dunno c1) Diverges = Dunno c1 lubDmdResult (Dunno c1) ThrowsExn = Dunno c1 lubDmdResult (Dunno c1) (Dunno c2) = Dunno (c1 `lubCPR` c2) -- This needs to commute with defaultDmd, i.e. -- defaultDmd (r1 `lubDmdResult` r2) = defaultDmd r1 `lubDmd` defaultDmd r2 -- (See Note [Default demand on free variables] for why) bothDmdResult :: DmdResult -> Termination () -> DmdResult -- See Note [Asymmetry of 'both' for DmdType and DmdResult] bothDmdResult _ Diverges = Diverges bothDmdResult r ThrowsExn = case r of { Diverges -> r; _ -> ThrowsExn } bothDmdResult r (Dunno {}) = r -- This needs to commute with defaultDmd, i.e. -- defaultDmd (r1 `bothDmdResult` r2) = defaultDmd r1 `bothDmd` defaultDmd r2 -- (See Note [Default demand on free variables] for why) instance Outputable r => Outputable (Termination r) where ppr Diverges = char 'b' ppr ThrowsExn = char 'x' ppr (Dunno c) = ppr c instance Outputable CPRResult where ppr NoCPR = empty ppr (RetSum n) = char 'm' <> int n ppr RetProd = char 'm' seqDmdResult :: DmdResult -> () seqDmdResult Diverges = () seqDmdResult ThrowsExn = () seqDmdResult (Dunno c) = seqCPRResult c seqCPRResult :: CPRResult -> () seqCPRResult NoCPR = () seqCPRResult (RetSum n) = n `seq` () seqCPRResult RetProd = () ------------------------------------------------------------------------ -- Combined demand result -- ------------------------------------------------------------------------ -- [cprRes] lets us switch off CPR analysis -- by making sure that everything uses TopRes topRes, exnRes, botRes :: DmdResult topRes = Dunno NoCPR exnRes = ThrowsExn botRes = Diverges cprSumRes :: ConTag -> DmdResult cprSumRes tag = Dunno $ RetSum tag cprProdRes :: [DmdType] -> DmdResult cprProdRes _arg_tys = Dunno $ RetProd vanillaCprProdRes :: Arity -> DmdResult vanillaCprProdRes _arity = Dunno $ RetProd isTopRes :: DmdResult -> Bool isTopRes (Dunno NoCPR) = True isTopRes _ = False isBotRes :: DmdResult -> Bool -- True if the result diverges or throws an exception isBotRes Diverges = True isBotRes ThrowsExn = True isBotRes (Dunno {}) = False trimCPRInfo :: Bool -> Bool -> DmdResult -> DmdResult trimCPRInfo trim_all trim_sums res = trimR res where trimR (Dunno c) = Dunno (trimC c) trimR res = res trimC (RetSum n) | trim_all || trim_sums = NoCPR | otherwise = RetSum n trimC RetProd | trim_all = NoCPR | otherwise = RetProd trimC NoCPR = NoCPR returnsCPR_maybe :: DmdResult -> Maybe ConTag returnsCPR_maybe (Dunno c) = retCPR_maybe c returnsCPR_maybe _ = Nothing retCPR_maybe :: CPRResult -> Maybe ConTag retCPR_maybe (RetSum t) = Just t retCPR_maybe RetProd = Just fIRST_TAG retCPR_maybe NoCPR = Nothing -- See Notes [Default demand on free variables] -- and [defaultDmd vs. resTypeArgDmd] defaultDmd :: Termination r -> Demand defaultDmd (Dunno {}) = absDmd defaultDmd _ = botDmd -- Diverges or ThrowsExn resTypeArgDmd :: Termination r -> Demand -- TopRes and BotRes are polymorphic, so that -- BotRes === (Bot -> BotRes) === ... -- TopRes === (Top -> TopRes) === ... -- This function makes that concrete -- Also see Note [defaultDmd vs. resTypeArgDmd] resTypeArgDmd (Dunno _) = topDmd resTypeArgDmd _ = botDmd -- Diverges or ThrowsExn {- Note [defaultDmd and resTypeArgDmd] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ These functions are similar: They express the demand on something not explicitly mentioned in the environment resp. the argument list. Yet they are different: * Variables not mentioned in the free variables environment are definitely unused, so we can use absDmd there. * Further arguments *can* be used, of course. Hence topDmd is used. Note [Worthy functions for Worker-Wrapper split] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ For non-bottoming functions a worker-wrapper transformation takes into account several possibilities to decide if the function is worthy for splitting: 1. The result is of product type and the function is strict in some (or even all) of its arguments. The check that the argument is used is more of sanity nature, since strictness implies usage. Example: f :: (Int, Int) -> Int f p = (case p of (a,b) -> a) + 1 should be splitted to f :: (Int, Int) -> Int f p = case p of (a,b) -> $wf a $wf :: Int -> Int $wf a = a + 1 2. Sometimes it also makes sense to perform a WW split if the strictness analysis cannot say for sure if the function is strict in components of its argument. Then we reason according to the inferred usage information: if the function uses its product argument's components, the WW split can be beneficial. Example: g :: Bool -> (Int, Int) -> Int g c p = case p of (a,b) -> if c then a else b The function g is strict in is argument p and lazy in its components. However, both components are used in the RHS. The idea is since some of the components (both in this case) are used in the right-hand side, the product must presumable be taken apart. Therefore, the WW transform splits the function g to g :: Bool -> (Int, Int) -> Int g c p = case p of (a,b) -> $wg c a b $wg :: Bool -> Int -> Int -> Int $wg c a b = if c then a else b 3. If an argument is absent, it would be silly to pass it to a function, hence the worker with reduced arity is generated. Note [Worker-wrapper for bottoming functions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We used not to split if the result is bottom. [Justification: there's no efficiency to be gained.] But it's sometimes bad not to make a wrapper. Consider fw = \x# -> let x = I# x# in case e of p1 -> error_fn x p2 -> error_fn x p3 -> the real stuff The re-boxing code won't go away unless error_fn gets a wrapper too. [We don't do reboxing now, but in general it's better to pass an unboxed thing to f, and have it reboxed in the error cases....] However we *don't* want to do this when the argument is not actually taken apart in the function at all. Otherwise we risk decomposing a masssive tuple which is barely used. Example: f :: ((Int,Int) -> String) -> (Int,Int) -> a f g pr = error (g pr) main = print (f fst (1, error "no")) Here, f does not take 'pr' apart, and it's stupid to do so. Imagine that it had millions of fields. This actually happened in GHC itself where the tuple was DynFlags ************************************************************************ * * Demand environments and types * * ************************************************************************ -} type DmdEnv = VarEnv Demand -- See Note [Default demand on free variables] data DmdType = DmdType DmdEnv -- Demand on explicitly-mentioned -- free variables [Demand] -- Demand on arguments DmdResult -- See [Nature of result demand] {- Note [Nature of result demand] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ A DmdResult contains information about termination (currently distinguishing definite divergence and no information; it is possible to include definite convergence here), and CPR information about the result. The semantics of this depends on whether we are looking at a DmdType, i.e. the demand put on by an expression _under a specific incoming demand_ on its environment, or at a StrictSig describing a demand transformer. For a * DmdType, the termination information is true given the demand it was generated with, while for * a StrictSig it holds after applying enough arguments. The CPR information, though, is valid after the number of arguments mentioned in the type is given. Therefore, when forgetting the demand on arguments, as in dmdAnalRhs, this needs to be considere (via removeDmdTyArgs). Consider b2 x y = x `seq` y `seq` error (show x) this has a strictness signature of <S><S>b meaning that "b2 `seq` ()" and "b2 1 `seq` ()" might well terminate, but for "b2 1 2 `seq` ()" we get definite divergence. For comparison, b1 x = x `seq` error (show x) has a strictness signature of <S>b and "b1 1 `seq` ()" is known to terminate. Now consider a function h with signature "<C(S)>", and the expression e1 = h b1 now h puts a demand of <C(S)> onto its argument, and the demand transformer turns it into <S>b Now the DmdResult "b" does apply to us, even though "b1 `seq` ()" does not diverge, and we do not anything being passed to b. Note [Asymmetry of 'both' for DmdType and DmdResult] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 'both' for DmdTypes is *assymetrical*, because there is only one result! For example, given (e1 e2), we get a DmdType dt1 for e1, use its arg demand to analyse e2 giving dt2, and then do (dt1 `bothType` dt2). Similarly with case e of { p -> rhs } we get dt_scrut from the scrutinee and dt_rhs from the RHS, and then compute (dt_rhs `bothType` dt_scrut). We 1. combine the information on the free variables, 2. take the demand on arguments from the first argument 3. combine the termination results, but 4. take CPR info from the first argument. 3 and 4 are implementd in bothDmdResult. -} -- Equality needed for fixpoints in DmdAnal instance Eq DmdType where (==) (DmdType fv1 ds1 res1) (DmdType fv2 ds2 res2) = ufmToList fv1 == ufmToList fv2 && ds1 == ds2 && res1 == res2 lubDmdType :: DmdType -> DmdType -> DmdType lubDmdType d1 d2 = DmdType lub_fv lub_ds lub_res where n = max (dmdTypeDepth d1) (dmdTypeDepth d2) (DmdType fv1 ds1 r1) = ensureArgs n d1 (DmdType fv2 ds2 r2) = ensureArgs n d2 lub_fv = plusVarEnv_CD lubDmd fv1 (defaultDmd r1) fv2 (defaultDmd r2) lub_ds = zipWithEqual "lubDmdType" lubDmd ds1 ds2 lub_res = lubDmdResult r1 r2 {- Note [The need for BothDmdArg] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Previously, the right argument to bothDmdType, as well as the return value of dmdAnalStar via postProcessDmdType, was a DmdType. But bothDmdType only needs to know about the free variables and termination information, but nothing about the demand put on arguments, nor cpr information. So we make that explicit by only passing the relevant information. -} type BothDmdArg = (DmdEnv, Termination ()) mkBothDmdArg :: DmdEnv -> BothDmdArg mkBothDmdArg env = (env, Dunno ()) toBothDmdArg :: DmdType -> BothDmdArg toBothDmdArg (DmdType fv _ r) = (fv, go r) where go (Dunno {}) = Dunno ()