{-# LANGUAGE ViewPatterns #-} {-# LANGUAGE BinaryLiterals #-} {-# LANGUAGE PatternSynonyms #-} {-# OPTIONS_GHC -Wno-incomplete-uni-patterns #-} {- (c) The University of Glasgow 2006 (c) The GRASP/AQUA Project, Glasgow University, 1992-1998 -} -- | A language to express the evaluation context of an expression as a -- 'Demand' and track how an expression evaluates free variables and arguments -- in turn as a 'DmdType'. -- -- Lays out the abstract domain for "GHC.Core.Opt.DmdAnal". module GHC.Types.Demand ( -- * Demands Boxity(..), Card(C_00, C_01, C_0N, C_10, C_11, C_1N), CardNonAbs, CardNonOnce, Demand(AbsDmd, BotDmd, (:*)), SubDemand(Prod, Poly), mkProd, viewProd, -- ** Algebra absDmd, topDmd, botDmd, seqDmd, topSubDmd, -- *** Least upper bound lubCard, lubDmd, lubSubDmd, -- *** Plus plusCard, plusDmd, plusSubDmd, -- *** Multiply multCard, multDmd, multSubDmd, -- ** Predicates on @Card@inalities and @Demand@s isAbs, isUsedOnce, isStrict, isAbsDmd, isUsedOnceDmd, isStrUsedDmd, isStrictDmd, isTopDmd, isWeakDmd, onlyBoxedArguments, -- ** Special demands evalDmd, -- *** Demands used in PrimOp signatures lazyApply1Dmd, lazyApply2Dmd, strictOnceApply1Dmd, strictManyApply1Dmd, -- ** Other @Demand@ operations oneifyCard, oneifyDmd, strictifyDmd, strictifyDictDmd, lazifyDmd, peelCallDmd, peelManyCalls, mkCalledOnceDmd, mkCalledOnceDmds, mkWorkerDemand, -- ** Extracting one-shot information argOneShots, argsOneShots, saturatedByOneShots, -- ** Manipulating Boxity of a Demand unboxDeeplyDmd, -- * Demand environments DmdEnv, emptyDmdEnv, keepAliveDmdEnv, reuseEnv, -- * Divergence Divergence(..), topDiv, botDiv, exnDiv, lubDivergence, isDeadEndDiv, -- * Demand types DmdType(..), dmdTypeDepth, -- ** Algebra nopDmdType, botDmdType, lubDmdType, plusDmdType, multDmdType, -- *** PlusDmdArg PlusDmdArg, mkPlusDmdArg, toPlusDmdArg, -- ** Other operations peelFV, findIdDemand, addDemand, splitDmdTy, deferAfterPreciseException, keepAliveDmdType, -- * Demand signatures DmdSig(..), mkDmdSigForArity, mkClosedDmdSig, splitDmdSig, dmdSigDmdEnv, hasDemandEnvSig, nopSig, botSig, isTopSig, isDeadEndSig, isDeadEndAppSig, trimBoxityDmdSig, -- ** Handling arity adjustments prependArgsDmdSig, etaConvertDmdSig, -- * Demand transformers from demand signatures DmdTransformer, dmdTransformSig, dmdTransformDataConSig, dmdTransformDictSelSig, -- * Trim to a type shape TypeShape(..), trimToType, trimBoxity, -- * @seq@ing stuff seqDemand, seqDemandList, seqDmdType, seqDmdSig, -- * Zapping usage information zapUsageDemand, zapDmdEnvSig, zapUsedOnceDemand, zapUsedOnceSig ) where import GHC.Prelude import GHC.Types.Var ( Var, Id ) import GHC.Types.Var.Env import GHC.Types.Var.Set import GHC.Types.Unique.FM import GHC.Types.Basic import GHC.Data.Maybe ( orElse ) import GHC.Core.Type ( Type ) import GHC.Core.TyCon ( isNewTyCon, isClassTyCon ) import GHC.Core.DataCon ( splitDataProductType_maybe, StrictnessMark, isMarkedStrict ) import GHC.Core.Multiplicity ( scaledThing ) import GHC.Utils.Binary import GHC.Utils.Misc import GHC.Utils.Outputable import GHC.Utils.Panic import GHC.Utils.Panic.Plain import Data.Coerce (coerce) import Data.Function import GHC.Utils.Trace _ = pprTrace -- Tired of commenting out the import all the time {- ************************************************************************ * * Boxity: Whether the box of something is used * * ************************************************************************ -} {- Note [Strictness and Unboxing] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ If an argument is used strictly by the function body, we may use use call-by-value instead of call-by-need for that argument. What's more, we may unbox an argument that is used strictly, discarding the box at the call site. This can reduce allocations of the program drastically if the box really isn't needed in the function body. Here's an example: ``` even :: Int -> Bool even (I# 0) = True even (I# 1) = False even (I# n) = even (I# (n -# 2)) ``` All three code paths of 'even' are (a) strict in the argument, and (b) immediately discard the boxed 'Int'. Now if we have a call site like `even (I# 42)`, then it would be terrible to allocate the 'I#' box for the argument only to tear it apart immediately in the body of 'even'! Hence, worker/wrapper will allocate a wrapper for 'even' that not only uses call-by-value for the argument (e.g., `case I# 42 of b { $weven b }`), but also *unboxes* the argument, resulting in ``` even :: Int -> Bool even (I# n) = $weven n $weven :: Int# -> Bool $weven 0 = True $weven 1 = False $weven n = $weven (n -# 2) ``` And now the box in `even (I# 42)` will cancel away after inlining the wrapper. As far as the permission to unbox is concerned, *evaluatedness* of the argument is the important trait. Unboxing implies eager evaluation of an argument and we don't want to change the termination properties of the function. One way to ensure that is to unbox strict arguments only, but strictness is only a sufficient condition for evaluatedness. See Note [Unboxing evaluated arguments] in "GHC.Core.Opt.DmdAnal", where we manage to unbox *strict fields* of unboxed arguments that the function is not actually strict in, simply by realising that those fields have to be evaluated. Note [Boxity analysis] ~~~~~~~~~~~~~~~~~~~~~~ Alas, we don't want to unbox *every* strict argument (as Note [Strictness and Unboxing] might suggest). Here's an example (from T19871): ``` data Huge = H Bool Bool ... Bool ann :: Huge -> (Bool, Huge) ann h@(Huge True _ ... _) = (False, h) ann h = (True, h) ``` Unboxing 'h' yields ``` $wann :: Bool -> Bool -> ... -> Bool -> (Bool, Huge) $wann True b2 ... bn = (False, Huge True b2 ... bn) $wann b1 b2 ... bn = (True, Huge b1 b2 ... bn) ``` The pair constructor really needs its fields boxed. But '$wann' doesn't get passed 'h' anymore, only its components! Ergo it has to reallocate the 'Huge' box, in a process called "reboxing". After w/w, call sites like `case ... of Just h -> ann h` pay for the allocation of the additional box. In earlier versions of GHC we simply accepted that reboxing would sometimes happen, but we found some cases where it made a big difference: #19407, for example. We therefore perform a simple syntactic boxity analysis that piggy-backs on demand analysis in order to determine whether the box of a strict argument is always discarded in the function body, in which case we can pass it unboxed without risking regressions such as in 'ann' above. But as soon as one use needs the box, we want Boxed to win over any Unboxed uses. The demand signature (cf. Note [Demand notation]) will say whether it uses its arguments boxed or unboxed. Indeed it does so for every sub-component of the argument demand. Here's an example: ``` f :: (Int, Int) -> Bool f (a, b) = even (a + b) -- demand signature: <1!P(1!L,1!L)> ``` The '!' indicates places where we want to unbox, the lack thereof indicates the box is used by the function. Boxity flags are part of the 'Poly' and 'Prod' 'SubDemand's, see Note [Why Boxity in SubDemand and not in Demand?]. The given demand signature says "Unbox the pair and then nestedly unbox its two fields". By contrast, the demand signature of 'ann' above would look like <1P(1L,L,...,L)>, lacking any '!'. A demand signature like <1P(1!L)> -- Boxed outside but Unboxed in the field -- doesn't make a lot of sense, as we can never unbox the field without unboxing the containing record. See Note [Finalising boxity for demand signatures] in "GHC.Core.Opt.DmdAnal" for how we avoid to spread this and other kinds of misinformed boxities. Due to various practical reasons, Boxity Analysis is not conservative at times. Here are reasons for too much optimism: * Note [Function body boxity and call sites] is an observation about when it is beneficial to unbox a parameter that is returned from a function. Note [Unboxed demand on function bodies returning small products] derives a heuristic from the former Note, pretending that all call sites of a function need returned small products Unboxed. * Note [Boxity for bottoming functions] in DmdAnal makes all bottoming functions unbox their arguments, incurring reboxing in code paths that will diverge anyway. In turn we get more unboxing in hot code paths. Boxity analysis fixes a number of issues: #19871, #19407, #4267, #16859, #18907, #13331 Note [Function body boxity and call sites] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider (from T5949) ``` f n p = case n of 0 -> p :: (a, b) _ -> f (n-1) p -- Worker/wrapper split if we decide to unbox: $wf n x y = case n of 0 -> (# x, y #) _ -> $wf (n-1) x y f n (x,y) = case $wf n x y of (# r, s #) -> (r,s) ``` When is it better to /not/ to unbox 'p'? That depends on the callers of 'f'! If all call sites 1. Wouldn't need to allocate fresh boxes for 'p', and 2. Needed the result pair of 'f' boxed Only then we'd see an increase in allocation resulting from unboxing. But as soon as only one of (1) or (2) holds, it really doesn't matter if 'f' unboxes 'p' (and its result, it's important that CPR follows suit). For example ``` res = ... case f m (field t) of (r1,r2) -> ... -- (1) holds arg = ... [ f m (x,y) ] ... -- (2) holds ``` Because one of the boxes in the call site can cancel away: ``` res = ... case field1 t of (x1,x2) -> case field2 t of (y1,y2) -> case $wf x1 x2 y1 y2 of (#r1,r2#) -> ... arg = ... [ case $wf x1 x2 y1 y2 of (#r1,r2#) -> (r1,r2) ] ... ``` And when call sites neither have arg boxes (1) nor need the result boxed (2), then hesitating to unbox means /more/ allocation in the call site because of the need for fresh argument boxes. Summary: If call sites that satisfy both (1) and (2) occur more often than call sites that satisfy neither condition, then it's best /not/ to unbox 'p'. Note [Unboxed demand on function bodies returning small products] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Note [Boxity analysis] achieves its biggest wins when we avoid reboxing huge records. But when we return small products from a function, we often get faster programs by pretending that the caller unboxes the result. Long version: Observation: Big record arguments (e.g., DynFlags) tend to be modified much less frequently than small records (e.g., Int). Result: Big records tend to be passed around boxed (unmodified) much more frequently than small records. Consequnce: The larger the record, the more likely conditions (1) and (2) from Note [Function body boxity and call sites] are met, in which case unboxing returned parameters leads to reboxing. So we put an Unboxed demand on function bodies returning small products and a Boxed demand on the others. What is regarded a small product is controlled by the -fdmd-unbox-width flag. This also manages to unbox functions like ``` sum z [] = z sum (I# n) ((I# x):xs) = sum (I# (n +# x)) xs ``` where we can unbox 'z' on the grounds that it's but a small box anyway. That in turn means that the I# allocation in the recursive call site can cancel away and we get a non-allocating loop, nice and tight. Note that this is the typical case in "Observation" above: A small box is unboxed, modified, the result reboxed for the recursive call. Originally, this came up in binary-trees' check' function and #4267 which (similarly) features a strict fold over a tree. We'd also regress in join004 and join007 if we didn't assume an optimistic Unboxed demand on the function body. T17932 features a (non-recursive) function that returns a large record, e.g., ``` flags (Options f x) = `seq` f ``` and here we won't unbox 'f' because it has 5 fields (which is larger than the default -fdmd-unbox-width threshold). Why not focus on putting Unboxed demands on *all recursive* function? Then we'd unbox ``` flags 0 (Options f x) = `seq` f flags n o = flags (n-1) o ``` and that seems hardly useful. (NB: Similar to 'f' from Note [Preserving Boxity of results is rarely a win], but there we only had 2 fields.) What about the Boxity of *fields* of a small, returned box? Consider ``` sumIO :: Int -> Int -> IO Int sumIO 0 !z = return z -- What DmdAnal sees: sumIO 0 z s = z `seq` (# s, z #) sumIO n !z = sumIO (n-1) (z+n) ``` We really want 'z' to unbox here. Yet its use in the returned unboxed pair is fundamentally a Boxed one! CPR would manage to unbox it, but DmdAnal runs before that. There is an Unboxed use in the recursive call to 'go' though. But 'IO Int' returns a small product, and 'Int' is a small product itself. So we'll put the RHS of 'sumIO' under sub-demand '!P(L,L!P(L))', indicating that *if* we evaluate 'z', we don't need the box later on. And indeed the bang will evaluate `z`, so we conclude with a total demand of `1!P(L)` on `z` and unbox it. Unlike for recursive functions, where we can often speed up the loop by unboxing at the cost of a bit of reboxing in the base case, the wins for non-recursive functions quickly turn into losses when unboxing too deeply. That happens in T11545, T18109 and T18174. Therefore, we deeply unbox recursive function bodies but only shallowly unbox non-recursive function bodies (governed by the max_depth variable). The implementation is in 'GHC.Core.Opt.DmdAnal.unboxWhenSmall'. It is quite vital, guarding for regressions in test cases like #2387, #3586, #16040, #5075 and #19871. Note that this is fundamentally working around a phase problem, namely that the results of boxity analysis depend on CPR analysis (and vice versa, of course). Note [unboxedWins] ~~~~~~~~~~~~~~~~~~ We used to use '_unboxedWins' below in 'lubBoxity', which was too optimistic. While it worked around some shortcomings of the phase separation between Boxity analysis and CPR analysis, it was a gross hack which caused regressions itself that needed all kinds of fixes and workarounds. Examples (from #21119): * As #20767 says, L and B were no longer top and bottom of our lattice * In #20746 we unboxed huge Handle types that were never needed boxed in the first place. See Note [deferAfterPreciseException]. * It also caused unboxing of huge records where we better shouldn't, for example in T19871.absent. * It became impossible to work with when implementing !7599, mostly due to the chaos that results from #20767. Conclusion: We should use 'boxedWins' in 'lubBoxity', #21119. Fortunately, we could come up with a number of better mechanisms to make up for the sometimes huge regressions that would have otherwise incured: 1. A beefed up Note [Unboxed demand on function bodies returning small products] that works recursively fixes most regressions. It's a bit unsound, but pretty well-behaved. 2. We saw bottoming functions spoil boxity in some less severe cases and countered that with Note [Boxity for bottoming functions]. -} boxedWins :: Boxity -> Boxity -> Boxity boxedWins Unboxed Unboxed = Unboxed boxedWins _ !_ = Boxed _unboxedWins :: Boxity -> Boxity -> Boxity -- See Note [unboxedWins] _unboxedWins Boxed Boxed = Boxed _unboxedWins _ !_ = Unboxed lubBoxity :: Boxity -> Boxity -> Boxity -- See Note [Boxity analysis] for the lattice. lubBoxity = boxedWins plusBoxity :: Boxity -> Boxity -> Boxity plusBoxity = boxedWins {- ************************************************************************ * * Card: Combining Strictness and Usage * * ************************************************************************ -} {- Note [Evaluation cardinalities] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The demand analyser uses an (abstraction of) /evaluation cardinality/ of type Card, to specify how many times a term is evaluated. A Card C_lu represents an /interval/ of possible cardinalities [l..u], meaning * Evaluated /at least/ 'l' times (strictness). Hence 'l' is either 0 (lazy) or 1 (strict) * Evaluated /at most/ 'u' times (usage). Hence 'u' is either 0 (not used at all), or 1 (used at most once) or n (no information) Intervals describe sets, so the underlying lattice is the powerset lattice. Usually l<=u, but we also have C_10, the interval [1,0], the empty interval, denoting the empty set. This is the bottom element of the lattice. See Note [Demand notation] for the notation we use for each of the constructors. Note [Bit vector representation for Card] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ While the 6 inhabitants of Card admit an efficient representation as an enumeration, implementing operations such as lubCard, plusCard and multCard leads to unreasonably bloated code. This was the old defn for lubCard, for example: -- Handle C_10 (bot) lubCard C_10 n = n -- bot lubCard n C_10 = n -- bot -- Handle C_0N (top) lubCard C_0N _ = C_0N -- top lubCard _ C_0N = C_0N -- top -- Handle C_11 lubCard C_00 C_11 = C_01 -- {0} ∪ {1} = {0,1} lubCard C_11 C_00 = C_01 -- {0} ∪ {1} = {0,1} lubCard C_11 n = n -- {1} is a subset of all other intervals lubCard n C_11 = n -- {1} is a subset of all other intervals -- Handle C_1N lubCard C_1N C_1N = C_1N -- reflexivity lubCard _ C_1N = C_0N -- {0} ∪ {1,n} = top lubCard C_1N _ = C_0N -- {0} ∪ {1,n} = top -- Handle C_01 lubCard C_01 _ = C_01 -- {0} ∪ {0,1} = {0,1} lubCard _ C_01 = C_01 -- {0} ∪ {0,1} = {0,1} -- Handle C_00 lubCard C_00 C_00 = C_00 -- reflexivity There's a much more compact way to encode these operations if Card is represented not as distinctly denoted intervals, but as the subset of the set of all cardinalities {0,1,n} instead. We represent such a subset as a bit vector of length 3 (which fits in an Int). That's actually pretty common for such powerset lattices. There's one bit per denoted cardinality that is set iff that cardinality is part of the denoted set, with n being the most significand bit (index 2) and 0 being represented by the least significand bit (index 0). How does that help? Well, for one, lubCard just becomes lubCard (Card a) (Card b) = Card (a .|. b) The other operations, 'plusCard' and 'multCard', become significantly more tricky, but immensely more compact. It's all straight-line code with a few bit twiddling instructions now! Note [Algebraic specification for plusCard and multCard] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The representation change in Note [Bit vector representation for Card] admits very dense definitions of 'plusCard' and 'multCard' in terms of bit twiddling, but the connection to the algebraic operations they implement is lost. It's helpful to have a written specification of what 'plusCard' and 'multCard' here that says what they should compute. * plusCard: a@[l1,u1] + b@[l2,u2] = r@[l1+l2,u1+u2]. - In terms of sets, 0 ∈ r iff 0 ∈ a and 0 ∈ b. Examples: set in C_00 + C_00, C_01 + C_0N, but not in C_10 + C_00 - In terms of sets, 1 ∈ r iff 1 ∈ a or 1 ∈ b. Examples: set in C_01 + C_00, C_0N + C_0N, but not in C_10 + C_00 - In terms of sets, n ∈ r iff n ∈ a or n ∈ b, or (1 ∈ a and 1 ∈ b), so not unlike add with carry. Examples: set in C_01 + C_01, C_01 + C_0N, but not in C_10 + C_01 - Handy special cases: o 'plusCard C_10' bumps up the strictness of its argument, just like 'lubCard C_00' lazifies it, without touching upper bounds. o Similarly, 'plusCard C_0N' discards usage information (incl. absence) but leaves strictness alone. * multCard: a@[l1,u1] * b@[l2,u2] = r@[l1*l2,u1*u2]. - In terms of sets, 0 ∈ r iff 0 ∈ a or 0 ∈ b. Examples: set in C_00 * C_10, C_01 * C_1N, but not in C_10 * C_1N - In terms of sets, 1 ∈ r iff 1 ∈ a and 1 ∈ b. Examples: set in C_01 * C_01, C_01 * C_1N, but not in C_11 * C_10 - In terms of sets, n ∈ r iff 1 ∈ r and (n ∈ a or n ∈ b). Examples: set in C_1N * C_01, C_1N * C_0N, but not in C_10 * C_1N - Handy special cases: o 'multCard C_1N c' is the same as 'plusCard c c' and drops used-once info. But unlike 'plusCard C_0N', it leaves absence and strictness. o 'multCard C_01' drops strictness info, like 'lubCard C_00'. o 'multCard C_0N' does both; it discards all strictness and used-once info and retains only absence info. -} -- | Describes an interval of /evaluation cardinalities/. -- See Note [Evaluation cardinalities] -- See Note [Bit vector representation for Card] newtype Card = Card Int deriving Eq -- | A subtype of 'Card' for which the upper bound is never 0 (no 'C_00' or -- 'C_10'). The only four inhabitants are 'C_01', 'C_0N', 'C_11', 'C_1N'. -- Membership can be tested with 'isCardNonAbs'. -- See 'D' and 'Call' for use sites and explanation. type CardNonAbs = Card -- | A subtype of 'Card' for which the upper bound is never 1 (no 'C_01' or -- 'C_11'). The only four inhabitants are 'C_00', 'C_0N', 'C_10', 'C_1N'. -- Membership can be tested with 'isCardNonOnce'. -- See 'Poly' for use sites and explanation. type CardNonOnce = Card -- | Absent, {0}. Pretty-printed as A. pattern C_00 :: Card pattern C_00 = Card 0b001 -- | Bottom, {}. Pretty-printed as A. pattern C_10 :: Card pattern C_10 = Card 0b000 -- | Strict and used once, {1}. Pretty-printed as 1. pattern C_11 :: Card pattern C_11 = Card 0b010 -- | Used at most once, {0,1}. Pretty-printed as M. pattern C_01 :: Card pattern C_01 = Card 0b011 -- | Strict and used (possibly) many times, {1,n}. Pretty-printed as S. pattern C_1N :: Card pattern C_1N = Card 0b110 -- | Every possible cardinality; the top element, {0,1,n}. Pretty-printed as L. pattern C_0N :: Card pattern C_0N = Card 0b111 {-# COMPLETE C_00, C_01, C_0N, C_10, C_11, C_1N :: Card #-} _botCard, topCard :: Card _botCard = C_10 topCard = C_0N -- | True <=> lower bound is 1. isStrict :: Card -> Bool -- See Note [Bit vector representation for Card] isStrict (Card c) = c .&. 0b001 == 0 -- simply check 0 bit is not set -- | True <=> upper bound is 0. isAbs :: Card -> Bool -- See Note [Bit vector representation for Card] isAbs (Card c) = c .&. 0b110 == 0 -- simply check 1 and n bit are not set -- | True <=> upper bound is 1. isUsedOnce :: Card -> Bool -- See Note [Bit vector representation for Card] isUsedOnce (Card c) = c .&. 0b100 == 0 -- simply check n bit is not set -- | Is this a 'CardNonAbs'? isCardNonAbs :: Card -> Bool isCardNonAbs = not . isAbs -- | Is this a 'CardNonOnce'? isCardNonOnce :: Card -> Bool isCardNonOnce n = isAbs n || not (isUsedOnce n) -- | Intersect with [0,1]. oneifyCard :: Card -> Card oneifyCard C_0N = C_01 oneifyCard C_1N = C_11 oneifyCard c = c -- | Denotes '∪' on 'Card'. lubCard :: Card -> Card -> Card -- See Note [Bit vector representation for Card] lubCard (Card a) (Card b) = Card (a .|. b) -- main point of the bit-vector encoding! -- | Denotes '+' on lower and upper bounds of 'Card'. plusCard :: Card -> Card -> Card -- See Note [Algebraic specification for plusCard and multCard] plusCard (Card a) (Card b) = Card (bit0 .|. bit1 .|. bitN) where bit0 = (a .&. b) .&. 0b001 bit1 = (a .|. b) .&. 0b010 bitN = ((a .|. b) .|. shiftL (a .&. b) 1) .&. 0b100 -- | Denotes '*' on lower and upper bounds of 'Card'. multCard :: Card -> Card -> Card -- See Note [Algebraic specification for plusCard and multCard] multCard (Card a) (Card b) = Card (bit0 .|. bit1 .|. bitN) where bit0 = (a .|. b) .&. 0b001 bit1 = (a .&. b) .&. 0b010 bitN = (a .|. b) .&. shiftL bit1 1 .&. 0b100 {- ************************************************************************ * * Demand: Evaluation contexts * * ************************************************************************ -} -- | A demand describes a /scaled evaluation context/, e.g. how many times -- and how deep the denoted thing is evaluated. -- -- The "how many" component is represented by a 'Card'inality. -- The "how deep" component is represented by a 'SubDemand'. -- Examples (using Note [Demand notation]): -- -- * 'seq' puts demand @1A@ on its first argument: It evaluates the argument -- strictly (@1@), but not any deeper (@A@). -- * 'fst' puts demand @1P(1L,A)@ on its argument: It evaluates the argument -- pair strictly and the first component strictly, but no nested info -- beyond that (@L@). Its second argument is not used at all. -- * '$' puts demand @1C1(L)@ on its first argument: It calls (@C@) the -- argument function with one argument, exactly once (@1@). No info -- on how the result of that call is evaluated (@L@). -- * 'maybe' puts demand @MCM(L)@ on its second argument: It evaluates -- the argument function at most once ((M)aybe) and calls it once when -- it is evaluated. -- * @fst p + fst p@ puts demand @SP(SL,A)@ on @p@: It's @1P(1L,A)@ -- multiplied by two, so we get @S@ (used at least once, possibly multiple -- times). -- -- This data type is quite similar to @'Scaled' 'SubDemand'@, but it's scaled -- by 'Card', which is an /interval/ on 'Multiplicity', the upper bound of -- which could be used to infer uniqueness types. Also we treat 'AbsDmd' and -- 'BotDmd' specially, as the concept of a 'SubDemand' doesn't apply when there -- isn't any evaluation at all. If you don't care, simply use '(:*)'. data Demand = BotDmd -- ^ A bottoming demand, produced by a diverging function ('C_10'), hence there is no -- 'SubDemand' that describes how it was evaluated. | AbsDmd -- ^ An absent demand: Evaluated exactly 0 times ('C_00'), hence there is no -- 'SubDemand' that describes how it was evaluated. | D !CardNonAbs !SubDemand -- ^ Don't use this internal data constructor; use '(:*)' instead. -- Since BotDmd deals with 'C_10' and AbsDmd deals with 'C_00', the -- cardinality component is CardNonAbs deriving Eq -- | Only meant to be used in the pattern synonym below! viewDmdPair :: Demand -> (Card, SubDemand) viewDmdPair BotDmd = (C_10, botSubDmd) viewDmdPair AbsDmd = (C_00, seqSubDmd) viewDmdPair (D n sd) = (n, sd) -- | @c :* sd@ is a demand that says \"evaluated @c@ times, and each time it -- was evaluated, it was at least as deep as @sd@\". -- -- Matching on this pattern synonym is a complete match. -- If the matched demand was 'AbsDmd', it will match as @C_00 :* seqSubDmd@. -- If the matched demand was 'BotDmd', it will match as @C_10 :* botSubDmd@. -- The builder of this pattern synonym simply /discards/ the 'SubDemand' if the -- 'Card' was absent and returns 'AbsDmd' or 'BotDmd' instead. It will assert -- that the discarded sub-demand was 'seqSubDmd' and 'botSubDmd', respectively. -- -- Call sites should consider whether they really want to look at the -- 'SubDemand' of an absent demand and match on 'AbsDmd' and/or 'BotDmd' -- otherwise. Really, any other 'SubDemand' would be allowed and -- might work better, depending on context. pattern (:*) :: HasDebugCallStack => Card -> SubDemand -> Demand pattern n :* sd <- (viewDmdPair -> (n, sd)) where C_10 :* sd = BotDmd & assertPpr (sd == botSubDmd) (text "B /=" <+> ppr sd) C_00 :* sd = AbsDmd & assertPpr (sd == seqSubDmd) (text "A /=" <+> ppr sd) n :* sd = D n sd & assertPpr (isCardNonAbs n) (ppr n $$ ppr sd) {-# COMPLETE (:*) #-} -- | A sub-demand describes an /evaluation context/, e.g. how deep the -- denoted thing is evaluated. See 'Demand' for examples. -- -- The nested 'SubDemand' @d@ of a 'Call' @Cn(d)@ is /relative/ to a single such call. -- E.g. The expression @f 1 2 + f 3 4@ puts call demand @SCS(C1(L))@ on @f@: -- @f@ is called exactly twice (@S@), each time exactly once (@1@) with an -- additional argument. -- -- The nested 'Demand's @dn@ of a 'Prod' @P(d1,d2,...)@ apply /absolutely/: -- If @dn@ is a used once demand (cf. 'isUsedOnce'), then that means that -- the denoted sub-expression is used once in the entire evaluation context -- described by the surrounding 'Demand'. E.g., @LP(ML)@ means that the -- field of the denoted expression is used at most once, although the -- entire expression might be used many times. -- -- See Note [Call demands are relative] -- and Note [Demand notation]. -- See also Note [Why Boxity in SubDemand and not in Demand?]. data SubDemand = Poly !Boxity !CardNonOnce -- ^ Polymorphic demand, the denoted thing is evaluated arbitrarily deep, -- with the specified cardinality at every level. The 'Boxity' applies only -- to the outer evaluation context as well as all inner evaluation context. -- See Note [Boxity in Poly] for why we want it to carry 'Boxity'. -- Expands to 'Call' via 'viewCall' and to 'Prod' via 'viewProd'. -- -- @Poly b n@ is semantically equivalent to @Prod b [n :* Poly b n, ...] -- or @Call n (Poly Boxed n)@. 'viewCall' and 'viewProd' do these rewrites. -- -- In Note [Demand notation]: @L === P(L,L,...)@ and @L === CL(L)@, -- @B === P(B,B,...)@ and @B === CB(B)@, -- @!A === !P(A,A,...)@ and @!A === !CA(A)@, -- and so on. -- -- We'll only see 'Poly' with 'C_10' (B), 'C_00' (A), 'C_0N' (L) and sometimes -- 'C_1N' (S) through 'plusSubDmd', never 'C_01' (M) or 'C_11' (1) (grep the -- source code). Hence 'CardNonOnce', which is closed under 'lub' and 'plus'. | Call !CardNonAbs !SubDemand -- ^ @Call n sd@ describes the evaluation context of @n@ function -- applications, where every individual result is evaluated according to @sd@. -- @sd@ is /relative/ to a single call, see Note [Call demands are relative]. -- That Note also explains why it doesn't make sense for @n@ to be absent, -- hence we forbid it with 'CardNonAbs'. Absent call demands can still be -- expressed with 'Poly'. -- Used only for values of function type. Use the smart constructor 'mkCall' -- whenever possible! | Prod !Boxity ![Demand] -- ^ @Prod b ds@ describes the evaluation context of a case scrutinisation -- on an expression of product type, where the product components are -- evaluated according to @ds@. The 'Boxity' @b@ says whether or not the box -- of the product was used. -- | We have to respect Poly rewrites through 'viewCall' and 'viewProd'. instance Eq SubDemand where d1 == d2 = case d1 of Prod b1 ds1 | Just (b2, ds2) <- viewProd (length ds1) d2 -> b1 == b2 && ds1 == ds2 Call n1 sd1 | Just (n2, sd2) <- viewCall d2 -> n1 == n2 && sd1 == sd2 Poly b1 n1 | Poly b2 n2 <- d2 -> b1 == b2 && n1 == n2 _ -> False topSubDmd, botSubDmd, seqSubDmd :: SubDemand topSubDmd = Poly Boxed C_0N botSubDmd = Poly Unboxed C_10 seqSubDmd = Poly Unboxed C_00 -- | The uniform field demand when viewing a 'Poly' as a 'Prod', as in -- 'viewProd'. polyFieldDmd :: Boxity -> CardNonOnce -> Demand polyFieldDmd _ C_00 = AbsDmd polyFieldDmd _ C_10 = BotDmd polyFieldDmd Boxed C_0N = topDmd polyFieldDmd b n = n :* Poly b n & assertPpr (isCardNonOnce n) (ppr n) -- | A smart constructor for 'Prod', applying rewrite rules along the semantic -- equality @Prod b [n :* Poly Boxed n, ...] === Poly b n@, simplifying to -- 'Poly' 'SubDemand's when possible. Examples: -- -- * Rewrites @P(L,L)@ (e.g., arguments @Boxed@, @[L,L]@) to @L@ -- * Rewrites @!P(L!L,L!L)@ (e.g., arguments @Unboxed@, @[L!L,L!L]@) to @!L@ -- * Does not rewrite @P(1L)@, @P(L!L)@, @!P(L)@ or @P(L,A)@ -- mkProd :: Boxity -> [Demand] -> SubDemand mkProd b ds | all (== AbsDmd) ds = Poly b C_00 | all (== BotDmd) ds = Poly b C_10 | dmd@(n :* Poly b2 m):_ <- ds , n == m -- don't rewrite P(SL) to S , b == b2 -- don't rewrite P(S!S) to !S , all (== dmd) ds -- don't rewrite P(L,A) to L = Poly b n | otherwise = Prod b ds -- | @viewProd n sd@ interprets @sd@ as a 'Prod' of arity @n@, expanding 'Poly' -- demands as necessary. viewProd :: Arity -> SubDemand -> Maybe (Boxity, [Demand]) -- It's quite important that this function is optimised well; -- it is used by lubSubDmd and plusSubDmd. viewProd n (Prod b ds) | ds `lengthIs` n = Just (b, ds) -- Note the strict application to replicate: This makes sure we don't allocate -- a thunk for it, inlines it and lets case-of-case fire at call sites. viewProd n (Poly b card) | let !ds = replicate n $! polyFieldDmd b card = Just (b, ds) viewProd _ _ = Nothing {-# INLINE viewProd #-} -- we want to fuse away the replicate and the allocation -- for Arity. Otherwise, #18304 bites us. -- | A smart constructor for 'Call', applying rewrite rules along the semantic -- equality @Call n (Poly n) === Poly n@, simplifying to 'Poly' 'SubDemand's -- when possible. mkCall :: CardNonAbs -> SubDemand -> SubDemand mkCall C_1N sd@(Poly Boxed C_1N) = sd mkCall C_0N sd@(Poly Boxed C_0N) = sd mkCall n cd = assertPpr (isCardNonAbs n) (ppr n $$ ppr cd) $ Call n cd -- | @viewCall sd@ interprets @sd@ as a 'Call', expanding 'Poly' subdemands as -- necessary. viewCall :: SubDemand -> Maybe (Card, SubDemand) viewCall (Call n sd) = Just (n :: Card, sd) viewCall (Poly _ n) = Just (n :: Card, Poly Boxed n) viewCall _ = Nothing topDmd, absDmd, botDmd, seqDmd :: Demand topDmd = C_0N :* topSubDmd absDmd = AbsDmd botDmd = BotDmd seqDmd = C_11 :* seqSubDmd -- | Sets 'Boxity' to 'Unboxed' for non-'Call' sub-demands and recurses into 'Prod'. unboxDeeplySubDmd :: SubDemand -> SubDemand unboxDeeplySubDmd (Poly _ n) = Poly Unboxed n unboxDeeplySubDmd (Prod _ ds) = mkProd Unboxed (strictMap unboxDeeplyDmd ds) unboxDeeplySubDmd call@Call{} = call -- | Sets 'Boxity' to 'Unboxed' for the 'Demand', recursing into 'Prod's. unboxDeeplyDmd :: Demand -> Demand unboxDeeplyDmd AbsDmd = AbsDmd unboxDeeplyDmd BotDmd = BotDmd unboxDeeplyDmd (D n sd) = D n (unboxDeeplySubDmd sd) -- | Denotes '∪' on 'SubDemand'. lubSubDmd :: SubDemand -> SubDemand -> SubDemand -- Handle botSubDmd (just an optimisation, the general case would do the same) lubSubDmd (Poly Unboxed C_10) d2 = d2 lubSubDmd d1 (Poly Unboxed C_10) = d1 -- Handle Prod lubSubDmd (Prod b1 ds1) (Poly b2 n2) | let !d = polyFieldDmd b2 n2 = mkProd (lubBoxity b1 b2) (strictMap (lubDmd d) ds1) lubSubDmd (Prod b1 ds1) (Prod b2 ds2) | equalLength ds1 ds2 = mkProd (lubBoxity b1 b2) (strictZipWith lubDmd ds1 ds2) -- Handle Call lubSubDmd (Call n1 sd1) sd2@(Poly _ n2) -- See Note [Call demands are relative] | isAbs n2 = mkCall (lubCard n2 n1) sd1 | otherwise = mkCall (lubCard n2 n1) (lubSubDmd sd1 sd2) lubSubDmd (Call n1 d1) (Call n2 d2) | otherwise = mkCall (lubCard n1 n2) (lubSubDmd d1 d2) -- Handle Poly. Exploit reflexivity (so we'll match the Prod or Call cases again). lubSubDmd (Poly b1 n1) (Poly b2 n2) = Poly (lubBoxity b1 b2) (lubCard n1 n2) lubSubDmd sd1@Poly{} sd2 = lubSubDmd sd2 sd1 -- Otherwise (Call `lub` Prod) return Top lubSubDmd _ _ = topSubDmd -- | Denotes '∪' on 'Demand'. lubDmd :: Demand -> Demand -> Demand lubDmd (n1 :* sd1) (n2 :* sd2) = lubCard n1 n2 :* lubSubDmd sd1 sd2 multSubDmd :: Card -> SubDemand -> SubDemand multSubDmd C_11 sd = sd -- The following three equations don't have an impact on Demands, only on -- Boxity. They are needed so that we don't trigger the assertions in `:*` -- when called from `multDmd`. multSubDmd C_00 _ = seqSubDmd -- Otherwise `multSubDmd A L == A /= !A` multSubDmd C_10 (Poly _ n) = if isStrict n then botSubDmd else seqSubDmd -- Otherwise `multSubDmd B L == B /= !B` multSubDmd C_10 (Call n _) = if isStrict n then botSubDmd else seqSubDmd -- Otherwise we'd call `mkCall` with absent cardinality multSubDmd n (Poly b m) = Poly b (multCard n m) multSubDmd n (Call n' sd) = mkCall (multCard n n') sd -- See Note [Call demands are relative] multSubDmd n (Prod b ds) = mkProd b (strictMap (multDmd n) ds) multDmd :: Card -> Demand -> Demand -- The first two lines compute the same result as the last line, but won't -- trigger the assertion in `:*` for input like `multDmd B 1L`, which would call -- `B :* A`. We want to return `B` in these cases. multDmd C_10 (n :* _) = if isStrict n then BotDmd else AbsDmd multDmd n (C_10 :* _) = if isStrict n then BotDmd else AbsDmd multDmd n (m :* sd) = multCard n m :* multSubDmd n sd -- | Denotes '+' on 'SubDemand'. plusSubDmd :: SubDemand -> SubDemand -> SubDemand -- Handle seqSubDmd (just an optimisation, the general case would do the same) plusSubDmd (Poly Unboxed C_00) d2 = d2 plusSubDmd d1 (Poly Unboxed C_00) = d1 -- Handle Prod plusSubDmd (Prod b1 ds1) (Poly b2 n2) | let !d = polyFieldDmd b2 n2 = mkProd (plusBoxity b1 b2) (strictMap (plusDmd d) ds1) plusSubDmd (Prod b1 ds1) (Prod b2 ds2) | equalLength ds1 ds2 = mkProd (plusBoxity b1 b2) (strictZipWith plusDmd ds1 ds2) -- Handle Call plusSubDmd (Call n1 sd1) sd2@(Poly _ n2) -- See Note [Call demands are relative] | isAbs n2 = mkCall (plusCard n2 n1) sd1 | otherwise = mkCall (plusCard n2 n1) (lubSubDmd sd1 sd2) plusSubDmd (Call n1 sd1) (Call n2 sd2) | otherwise = mkCall (plusCard n1 n2) (lubSubDmd sd1 sd2) -- Handle Poly. Exploit reflexivity (so we'll match the Prod or Call cases again). plusSubDmd (Poly b1 n1) (Poly b2 n2) = Poly (plusBoxity b1 b2) (plusCard n1 n2) plusSubDmd sd1@Poly{} sd2 = plusSubDmd sd2 sd1 -- Otherwise (Call `lub` Prod) return Top plusSubDmd _ _ = topSubDmd -- | Denotes '+' on 'Demand'. plusDmd :: Demand -> Demand -> Demand plusDmd (n1 :* sd1) (n2 :* sd2) = plusCard n1 n2 :* plusSubDmd sd1 sd2 -- | Used to suppress pretty-printing of an uninformative demand isTopDmd :: Demand -> Bool isTopDmd dmd = dmd == topDmd isAbsDmd :: Demand -> Bool isAbsDmd (n :* _) = isAbs n -- | Contrast with isStrictUsedDmd. See Note [Strict demands] isStrictDmd :: Demand -> Bool isStrictDmd (n :* _) = isStrict n -- | Not absent and used strictly. See Note [Strict demands] isStrUsedDmd :: Demand -> Bool isStrUsedDmd (n :* _) = isStrict n && not (isAbs n) -- | Is the value used at most once? isUsedOnceDmd :: Demand -> Bool isUsedOnceDmd (n :* _) = isUsedOnce n -- | We try to avoid tracking weak free variable demands in strictness -- signatures for analysis performance reasons. -- See Note [Lazy and unleashable free variables] in "GHC.Core.Opt.DmdAnal". isWeakDmd :: Demand -> Bool isWeakDmd dmd@(n :* _) = not (isStrict n) && is_plus_idem_dmd dmd where -- @is_plus_idem_* thing@ checks whether @thing `plus` thing = thing@, -- e.g. if @thing@ is idempotent wrt. to @plus@. -- is_plus_idem_card n = plusCard n n == n is_plus_idem_card = isCardNonOnce -- is_plus_idem_dmd dmd = plusDmd dmd dmd == dmd is_plus_idem_dmd AbsDmd = True is_plus_idem_dmd BotDmd = True is_plus_idem_dmd (n :* sd) = is_plus_idem_card n && is_plus_idem_sub_dmd sd -- is_plus_idem_sub_dmd sd = plusSubDmd sd sd == sd is_plus_idem_sub_dmd (Poly _ n) = assert (isCardNonOnce n) True is_plus_idem_sub_dmd (Prod _ ds) = all is_plus_idem_dmd ds is_plus_idem_sub_dmd (Call n _) = is_plus_idem_card n -- See Note [Call demands are relative] evalDmd :: Demand evalDmd = C_1N :* topSubDmd -- | First argument of 'GHC.Exts.maskAsyncExceptions#': @1C1(L)@. -- Called exactly once. strictOnceApply1Dmd :: Demand strictOnceApply1Dmd = C_11 :* mkCall C_11 topSubDmd -- | First argument of 'GHC.Exts.atomically#': @SCS(L)@. -- Called at least once, possibly many times. strictManyApply1Dmd :: Demand strictManyApply1Dmd = C_1N :* mkCall C_1N topSubDmd -- | First argument of catch#: @MCM(L)@. -- Evaluates its arg lazily, but then applies it exactly once to one argument. lazyApply1Dmd :: Demand lazyApply1Dmd = C_01 :* mkCall C_01 topSubDmd -- | Second argument of catch#: @MCM(C1(L))@. -- Calls its arg lazily, but then applies it exactly once to an additional argument. lazyApply2Dmd :: Demand lazyApply2Dmd = C_01 :* mkCall C_01 (mkCall C_11 topSubDmd) -- | Make a 'Demand' evaluated at-most-once. oneifyDmd :: Demand -> Demand oneifyDmd AbsDmd = AbsDmd oneifyDmd BotDmd = BotDmd oneifyDmd (n :* sd) = oneifyCard n :* sd -- | Make a 'Demand' evaluated at-least-once (e.g. strict). strictifyDmd :: Demand -> Demand strictifyDmd AbsDmd = seqDmd strictifyDmd BotDmd = BotDmd strictifyDmd (n :* sd) = plusCard C_10 n :* sd -- | If the argument is a used non-newtype dictionary, give it strict demand. -- Also split the product type & demand and recur in order to similarly -- strictify the argument's contained used non-newtype superclass dictionaries. -- We use the demand as our recursive measure to guarantee termination. strictifyDictDmd :: Type -> Demand -> Demand strictifyDictDmd ty (n :* Prod b ds) | not (isAbs n) , Just field_tys <- as_non_newtype_dict ty = C_1N :* mkProd b (zipWith strictifyDictDmd field_tys ds) -- main idea: ensure it's strict where -- Return a TyCon and a list of field types if the given -- type is a non-newtype dictionary type as_non_newtype_dict ty | Just (tycon, _arg_tys, _data_con, map scaledThing -> inst_con_arg_tys) <- splitDataProductType_maybe ty , not (isNewTyCon tycon) , isClassTyCon tycon = Just inst_con_arg_tys | otherwise = Nothing strictifyDictDmd _ dmd = dmd -- | Make a 'Demand' lazy, setting all lower bounds (outside 'Call's) to 0. lazifyDmd :: Demand -> Demand lazifyDmd AbsDmd = AbsDmd lazifyDmd BotDmd = AbsDmd lazifyDmd (n :* sd) = multCard C_01 n :* lazifySubDmd sd -- | Make a 'SubDemand' lazy, setting all lower bounds (outside 'Call's) to 0. lazifySubDmd :: SubDemand -> SubDemand lazifySubDmd (Poly b n) = Poly b (multCard C_01 n) lazifySubDmd (Prod b sd) = mkProd b (strictMap lazifyDmd sd) lazifySubDmd (Call n sd) = mkCall (lubCard C_01 n) sd -- | Wraps the 'SubDemand' with a one-shot call demand: @d@ -> @C1(d)@. mkCalledOnceDmd :: SubDemand -> SubDemand mkCalledOnceDmd sd = mkCall C_11 sd -- | @mkCalledOnceDmds n d@ returns @C1(C1...(C1 d))@ where there are @n@ @C1@'s. mkCalledOnceDmds :: Arity -> SubDemand -> SubDemand mkCalledOnceDmds arity sd = iterate mkCalledOnceDmd sd !! arity -- | Peels one call level from the sub-demand, and also returns how many -- times we entered the lambda body. peelCallDmd :: SubDemand -> (Card, SubDemand) peelCallDmd sd = viewCall sd `orElse` (topCard, topSubDmd) -- Peels multiple nestings of 'Call' sub-demands and also returns -- whether it was unsaturated in the form of a 'Card'inality, denoting -- how many times the lambda body was entered. -- See Note [Demands from unsaturated function calls]. peelManyCalls :: Arity -> SubDemand -> (Card, SubDemand) peelManyCalls k sd = go k C_11 sd where go 0 !n !sd = (n, sd) go k !n (viewCall -> Just (m, sd)) = go (k-1) (n `multCard` m) sd go _ _ _ = (topCard, topSubDmd) {-# INLINE peelManyCalls #-} -- so that the pair cancels away in a `fst _` context -- See Note [Demand on the worker] in GHC.Core.Opt.WorkWrap mkWorkerDemand :: Int -> Demand mkWorkerDemand n = C_01 :* go n where go 0 = topSubDmd go n = Call C_01 $ go (n-1) argsOneShots :: DmdSig -> Arity -> [[OneShotInfo]] -- ^ See Note [Computing one-shot info] argsOneShots (DmdSig (DmdType _ arg_ds _)) n_val_args | unsaturated_call = [] | otherwise = go arg_ds where unsaturated_call = arg_ds `lengthExceeds` n_val_args go [] = [] go (arg_d : arg_ds) = argOneShots arg_d `cons` go arg_ds -- Avoid list tail like [ [], [], [] ] cons [] [] = [] cons a as = a:as argOneShots :: Demand -- ^ depending on saturation -> [OneShotInfo] -- ^ See Note [Computing one-shot info] argOneShots AbsDmd = [] -- This defn conflicts with 'saturatedByOneShots', argOneShots BotDmd = [] -- according to which we should return -- @repeat OneShotLam@ here... argOneShots (_ :* sd) = go sd -- See Note [Call demands are relative] where go (Call n sd) | isUsedOnce n = OneShotLam : go sd | otherwise = NoOneShotInfo : go sd go _ = [] -- | -- @saturatedByOneShots n CM(CM(...)) = True@ -- <=> -- There are at least n nested CM(..) calls. -- See Note [Demand on the worker] in GHC.Core.Opt.WorkWrap saturatedByOneShots :: Int -> Demand -> Bool saturatedByOneShots _ AbsDmd = True saturatedByOneShots _ BotDmd = True saturatedByOneShots n (_ :* sd) = isUsedOnce $ fst $ peelManyCalls n sd {- Note [Strict demands] ~~~~~~~~~~~~~~~~~~~~~~~~ 'isStrUsedDmd' returns true only of demands that are both strict and used In particular, it is False for (i.e. strict and not used, cardinality C_10), which can and does arise in, say (#7319) f x = raise# Then 'x' is not used, so f gets strictness -> . Now the w/w generates fx = let x = absentError "unused" in raise At this point we really don't want to convert to fx = case absentError "unused" of x -> raise 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 #7319 we get T7319.exe: Oops! Entered absent arg w_s1Hd{v} [lid] [base:GHC.Base.String{tc 36u}] Note [Call demands are relative] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The expression @if b then 0 else f 1 2 + f 3 4@ uses @f@ according to the demand @LCL(C1(P(L)))@, meaning "f is called multiple times or not at all (CL), but each time it is called, it's called with *exactly one* (C1) more argument. Whenever it is called with two arguments, we have no info on how often the field of the product result is used (L)." So the 'SubDemand' nested in a 'Call' demand is relative to exactly one call. And that extends to the information we have how its results are used in each call site. Consider (#18903) h :: Int -> Int h m = let g :: Int -> (Int,Int) g 1 = (m, 0) g n = (2 * n, 2 `div` n) {-# NOINLINE g #-} in case m of 1 -> 0 2 -> snd (g m) _ -> uncurry (+) (g m) We want to give @g@ the demand @MCM(P(MP(L),1P(L)))@, so we see that in each call site of @g@, we are strict in the second component of the returned pair. This relative cardinality leads to an otherwise unexpected call to 'lubSubDmd' in 'plusSubDmd', but if you do the math it's just the right thing. There's one more subtlety: Since the nested demand is relative to exactly one call, in the case where we have *at most zero calls* (e.g. CA(...)), the premise is hurt and we can assume that the nested demand is 'botSubDmd'. That ensures that @g@ above actually gets the @1P(L)@ demand on its second pair component, rather than the lazy @MP(L)@ if we 'lub'bed with an absent demand. Note [Computing one-shot info] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider a call f (\pqr. e1) (\xyz. e2) e3 where f has usage signature Then argsOneShots returns a [[OneShotInfo]] of [[OneShot,NoOneShotInfo,OneShot], [OneShot]] The occurrence analyser propagates this one-shot infor to the binders \pqr and \xyz; see Note [Use one-shot information] in "GHC.Core.Opt.OccurAnal". Note [Boxity in Poly] ~~~~~~~~~~~~~~~~~~~~~ To support Note [Boxity analysis], it makes sense that 'Prod' carries a 'Boxity'. But why does 'Poly' have to carry a 'Boxity', too? Shouldn't all 'Poly's be 'Boxed'? Couldn't we simply use 'Prod Unboxed' when we need to express an unboxing demand? 'botSubDmd' (B) needs to be the bottom of the lattice, so it needs to be an Unboxed demand (and deeply, at that). Similarly, 'seqSubDmd' (A) is an Unboxed demand. So why not say that Polys with absent cardinalities have Unboxed boxity? That doesn't work, because we also need the boxed equivalents. Here's an example for A (function 'absent' in T19871): ``` f _ True = 1 f a False = a `seq` 2 -- demand on a: MA, the A is short for `Poly Boxed C_00` g a = a `seq` f a True -- demand on a: SA, which is `Poly Boxed C_00` h True p = g p -- SA on p (inherited from g) h False p@(x,y) = x+y -- S!P(1!L,1!L) on p ``` If A is treated as Unboxed, we get reboxing in the call site to 'g'. So we obviously would need a Boxed variant of A. Rather than introducing a lot of special cases, we just carry the Boxity in 'Poly'. Plus, we could most likely find examples like the above for any other cardinality. Note [Why Boxity in SubDemand and not in Demand?] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In #19871, we started out by storing 'Boxity' in 'SubDemand', in the 'Prod' constructor only. But then we found that we weren't able to express the unboxing 'seqSubDmd', because that one really is a `Poly C_00` sub-demand. We then tried to store the Boxity in 'Demand' instead, for these reasons: 1. The whole boxity-of-seq business comes to a satisfying conclusion 2. Putting Boxity in the SubDemand is weird to begin with, because it describes the box and not its fields, just as the evaluation cardinality of a Demand describes how often the box is used. It makes more sense that Card and Boxity travel together. Also the alternative would have been to store Boxity with Poly, which is even weirder and more redundant. But then we regressed in T7837 (grep #19871 for boring specifics), which needed to transfer an ambient unboxed *demand* on a dictionary selector to its argument dictionary, via a 'Call' sub-demand `C1(sd)`, as Note [Demand transformer for a dictionary selector] explains. Annoyingly, the boxity info has to be stored in the *sub-demand* `sd`! There's no demand to store the boxity in. So we bit the bullet and now we store Boxity in 'SubDemand', both in 'Prod' *and* 'Poly'. See also Note [Boxity in Poly]. Note [Demand transformer for data constructors] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider the expression (x,y) with sub-demand P(SL,A). What is the demand on x,y? Obviously `x` is used strictly, and `y` not at all. So we want to decompose a product demand, and feed its components demands into the arguments. That is the job of dmdTransformDataConSig. More precisely, * it gets the demand on the data constructor itself; in the above example that is C(1,C(1,P(SL,A))) * it returns the demands on the arguments; in the above example that is [SL, A] Nasty wrinkle. Consider this code (#22475 has more realistic examples but assume this is what the demand analyser sees) data T = MkT !Int Bool get :: T -> Bool get (MkT _ b) = b foo = let v::Int = I# 7 t::T = MkT v True in get t Now `v` is unused by `get`, /but/ we can't give `v` an Absent demand, else we'll drop the binding and replace it with an error thunk. Then the code generator (more specifically GHC.Stg.InferTags.Rewrite) will add an extra eval of MkT's argument to give foo = let v::Int = error "absent" t::T = case v of v' -> MkT v' True in get t Boo! Because of this extra eval (added in STG-land), the truth is that `MkT` may (or may not) evaluate its arguments (as established in #21497). Hence the use of `bump` in dmdTransformDataConSig, which adds in a `C_01` eval. The `C_01` says "may or may not evaluate" which is absolutely faithful to what InferTags.Rewrite does. In particular it is very important /not/ to make that a `C_11` eval, see Note [Data-con worker strictness]. -} {- ********************************************************************* * * Divergence: Whether evaluation surely diverges * * ********************************************************************* -} -- | 'Divergence' characterises whether something surely diverges. -- Models a subset lattice of the following exhaustive set of divergence -- results: -- -- [n] nontermination (e.g. loops) -- [i] throws imprecise exception -- [p] throws precise exceTtion -- [c] converges (reduces to WHNF). -- -- The different lattice elements correspond to different subsets, indicated by -- juxtaposition of indicators (e.g. __nc__ definitely doesn't throw an -- exception, and may or may not reduce to WHNF). -- -- @ -- Dunno (nipc) -- | -- ExnOrDiv (nip) -- | -- Diverges (ni) -- @ -- -- As you can see, we don't distinguish __n__ and __i__. -- See Note [Precise exceptions and strictness analysis] for why __p__ is so -- special compared to __i__. data Divergence = Diverges -- ^ Definitely throws an imprecise exception or diverges. | ExnOrDiv -- ^ Definitely throws a *precise* exception, an imprecise -- exception or diverges. Never converges, hence 'isDeadEndDiv'! -- See scenario 1 in Note [Precise exceptions and strictness analysis]. | Dunno -- ^ Might diverge, throw any kind of exception or converge. deriving Eq lubDivergence :: Divergence -> Divergence -> Divergence lubDivergence Diverges div = div lubDivergence div Diverges = div lubDivergence ExnOrDiv ExnOrDiv = ExnOrDiv lubDivergence _ _ = Dunno -- This needs to commute with defaultFvDmd, i.e. -- defaultFvDmd (r1 `lubDivergence` r2) = defaultFvDmd r1 `lubDmd` defaultFvDmd r2 -- (See Note [Default demand on free variables and arguments] for why) -- | See Note [Asymmetry of 'plus*'], which concludes that 'plusDivergence' -- needs to be symmetric. -- Strictly speaking, we should have @plusDivergence Dunno Diverges = ExnOrDiv@. -- But that regresses in too many places (every infinite loop, basically) to be -- worth it and is only relevant in higher-order scenarios -- (e.g. Divergence of @f (throwIO blah)@). -- So 'plusDivergence' currently is 'glbDivergence', really. plusDivergence :: Divergence -> Divergence -> Divergence plusDivergence Dunno Dunno = Dunno plusDivergence Diverges _ = Diverges plusDivergence _ Diverges = Diverges plusDivergence _ _ = ExnOrDiv -- | In a non-strict scenario, we might not force the Divergence, in which case -- we might converge, hence Dunno. multDivergence :: Card -> Divergence -> Divergence multDivergence n _ | not (isStrict n) = Dunno multDivergence _ d = d topDiv, exnDiv, botDiv :: Divergence topDiv = Dunno exnDiv = ExnOrDiv botDiv = Diverges -- | True if the 'Divergence' indicates that evaluation will not return. -- See Note [Dead ends]. isDeadEndDiv :: Divergence -> Bool isDeadEndDiv Diverges = True isDeadEndDiv ExnOrDiv = True isDeadEndDiv Dunno = False -- See Notes [Default demand on free variables and arguments] -- and Scenario 1 in [Precise exceptions and strictness analysis] defaultFvDmd :: Divergence -> Demand defaultFvDmd Dunno = absDmd defaultFvDmd ExnOrDiv = absDmd -- This is the whole point of ExnOrDiv! defaultFvDmd Diverges = botDmd -- Diverges defaultArgDmd :: Divergence -> Demand -- TopRes and BotRes are polymorphic, so that -- BotRes === (Bot -> BotRes) === ... -- TopRes === (Top -> TopRes) === ... -- This function makes that concrete -- Also see Note [Default demand on free variables and arguments] defaultArgDmd Dunno = topDmd -- NB: not botDmd! We don't want to mask the precise exception by forcing the -- argument. But it is still absent. defaultArgDmd ExnOrDiv = absDmd defaultArgDmd Diverges = botDmd {- Note [Precise vs imprecise exceptions] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ An exception is considered to be /precise/ when it is thrown by the 'raiseIO#' primop. It follows that all other primops (such as 'raise#' or division-by-zero) throw /imprecise/ exceptions. Note that the actual type of the exception thrown doesn't have any impact! GHC undertakes some effort not to apply an optimisation that would mask a /precise/ exception with some other source of nontermination, such as genuine divergence or an imprecise exception, so that the user can reliably intercept the precise exception with a catch handler before and after optimisations. See also the wiki page on precise exceptions: https://gitlab.haskell.org/ghc/ghc/wikis/exceptions/precise-exceptions Section 5 of "Tackling the awkward squad" talks about semantic concerns. Imprecise exceptions are actually more interesting than precise ones (which are fairly standard) from the perspective of semantics. See the paper "A Semantics for Imprecise Exceptions" for more details. Note [Dead ends] ~~~~~~~~~~~~~~~~ We call an expression that either diverges or throws a precise or imprecise exception a "dead end". We used to call such an expression just "bottoming", but with the measures we take to preserve precise exception semantics (see Note [Precise exceptions and strictness analysis]), that is no longer accurate: 'exnDiv' is no longer the bottom of the Divergence lattice. Yet externally to demand analysis, we mostly care about being able to drop dead code etc., which is all due to the property that such an expression never returns, hence we consider throwing a precise exception to be a dead end. See also 'isDeadEndDiv'. Note [Precise exceptions and strictness analysis] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We have to take care to preserve precise exception semantics in strictness analysis (#17676). There are two scenarios that need careful treatment. The fixes were discussed at https://gitlab.haskell.org/ghc/ghc/wikis/fixing-precise-exceptions Recall that raiseIO# raises a *precise* exception, in contrast to raise# which raises an *imprecise* exception. See Note [Precise vs imprecise exceptions]. Scenario 1: Precise exceptions in case alternatives --------------------------------------------------- Unlike raise# (which returns botDiv), we want raiseIO# to return exnDiv. Here's why. Consider this example from #13380 (similarly #17676): f x y | x>0 = raiseIO# Exc | y>0 = return 1 | otherwise = return 2 Is 'f' strict in 'y'? One might be tempted to say yes! But that plays fast and loose with the precise exception; after optimisation, (f 42 (error "boom")) turns from throwing the precise Exc to throwing the imprecise user error "boom". So, the defaultFvDmd of raiseIO# should be lazy (topDmd), which can be achieved by giving it divergence exnDiv. See Note [Default demand on free variables and arguments]. Why don't we just give it topDiv instead of introducing exnDiv? Because then the simplifier will fail to discard raiseIO#'s continuation in case raiseIO# x s of { (# s', r #) -> } which we'd like to optimise to case raiseIO# x s of {} Hence we came up with exnDiv. The default FV demand of exnDiv is lazy (and its default arg dmd is absent), but otherwise (in terms of 'isDeadEndDiv') it behaves exactly as botDiv, so that dead code elimination works as expected. This is tracked by T13380b. Scenario 2: Precise exceptions in case scrutinees ------------------------------------------------- Consider (more complete examples in #148, #1592, testcase strun003) case foo x s of { (# s', r #) -> y } Is this strict in 'y'? Often not! If @foo x s@ might throw a precise exception (ultimately via raiseIO#), then we must not force 'y', which may fail to terminate or throw an imprecise exception, until we have performed @foo x s@. So we have to 'deferAfterPreciseException' (which 'lub's with 'exnDmdType' to model the exceptional control flow) when @foo x s@ may throw a precise exception. Motivated by T13380{d,e,f}. See Note [Which scrutinees may throw precise exceptions] in "GHC.Core.Opt.DmdAnal". We have to be careful not to discard dead-end Divergence from case alternatives, though (#18086): m = putStrLn "foo" >> error "bar" 'm' should still have 'exnDiv', which is why it is not sufficient to lub with 'nopDmdType' (which has 'topDiv') in 'deferAfterPreciseException'. Historical Note: This used to be called the "IO hack". But that term is rather a bad fit because 1. It's easily confused with the "State hack", which also affects IO. 2. Neither "IO" nor "hack" is a good description of what goes on here, which is deferring strictness results after possibly throwing a precise exception. The "hack" is probably not having to defer when we can prove that the expression may not throw a precise exception (increasing precision of the analysis), but that's just a favourable guess. Note [Exceptions and strictness] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ We used to smart about catching exceptions, but we aren't anymore. See #14998 for the way it's resolved at the moment. Here's a historic breakdown: Apparently, exception handling prim-ops didn't use to have any special strictness signatures, thus defaulting to nopSig, which assumes they use their arguments lazily. Joachim was the first to realise that we could provide richer information. Thus, in 0558911f91c (Dec 13), he added signatures to primops.txt.pp indicating that functions like `catch#` and `catchRetry#` call their argument, which is useful information for usage analysis. Still with a 'Lazy' strictness demand (i.e. 'lazyApply1Dmd'), though, and the world was fine. In 7c0fff4 (July 15), Simon argued that giving `catch#` et al. a 'strictApply1Dmd' leads to substantial performance gains. That was at the cost of correctness, as #10712 proved. So, back to 'lazyApply1Dmd' in 28638dfe79e (Dec 15). Motivated to reproduce the gains of 7c0fff4 without the breakage of #10712, Ben opened #11222. Simon made the demand analyser "understand catch" in 9915b656 (Jan 16) by adding a new 'catchArgDmd', which basically said to call its argument strictly, but also swallow any thrown exceptions in 'multDivergence'. This was realized by extending the 'Str' constructor of 'ArgStr' with a 'ExnStr' field, indicating that it catches the exception, and adding a 'ThrowsExn' constructor to the 'Divergence' lattice as an element between 'Dunno' and 'Diverges'. Then along came #11555 and finally #13330, so we had to revert to 'lazyApply1Dmd' again in 701256df88c (Mar 17). This left the other variants like 'catchRetry#' having 'catchArgDmd', which is where #14998 picked up. Item 1 was concerned with measuring the impact of also making `catchRetry#` and `catchSTM#` have 'lazyApply1Dmd'. The result was that there was none. We removed the last usages of 'catchArgDmd' in 00b8ecb7 (Apr 18). There was a lot of dead code resulting from that change, that we removed in ef6b283 (Jan 19): We got rid of 'ThrowsExn' and 'ExnStr' again and removed any code that was dealing with the peculiarities. Where did the speed-ups vanish to? In #14998, item 3 established that turning 'catch#' strict in its first argument didn't bring back any of the alleged performance benefits. Item 2 of that ticket finally found out that it was entirely due to 'catchException's new (since #11555) definition, which was simply catchException !io handler = catch io handler While 'catchException' is arguably the saner semantics for 'catch', it is an internal helper function in "GHC.IO". Its use in "GHC.IO.Handle.Internals.do_operation" made for the huge allocation differences: Remove the bang and you find the regressions we originally wanted to avoid with 'catchArgDmd'. See also #exceptions_and_strictness# in "GHC.IO". So history keeps telling us that the only possibly correct strictness annotation for the first argument of 'catch#' is 'lazyApply1Dmd', because 'catch#' really is not strict in its argument: Just try this in GHCi :set -XScopedTypeVariables import Control.Exception catch undefined (\(_ :: SomeException) -> putStrLn "you'll see this") Any analysis that assumes otherwise will be broken in some way or another (beyond `-fno-pendantic-bottoms`). But then #13380 and #17676 suggest (in Mar 20) that we need to re-introduce a subtly different variant of `ThrowsExn` (which we call `ExnOrDiv` now) that is only used by `raiseIO#` in order to preserve precise exceptions by strictness analysis, while not impacting the ability to eliminate dead code. See Note [Precise exceptions and strictness analysis]. Note [Default demand on free variables and arguments] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Free variables not mentioned in the environment of a 'DmdType' are demanded according to the demand type's Divergence: * In a Diverges (botDiv) context, that demand is botDmd (strict and absent). * In all other contexts, the demand is absDmd (lazy and absent). This is recorded in 'defaultFvDmd'. Similarly, we can eta-expand demand types to get demands on excess arguments not accounted for in the type, by consulting 'defaultArgDmd': * In a Diverges (botDiv) context, that demand is again botDmd. * In a ExnOrDiv (exnDiv) context, that demand is absDmd: We surely diverge before evaluating the excess argument, but don't want to eagerly evaluate it (cf. Note [Precise exceptions and strictness analysis]). * In a Dunno context (topDiv), the demand is topDmd, because it's perfectly possible to enter the additional lambda and evaluate it in unforeseen ways (so, not absent). Note [Bottom CPR iff Dead-Ending Divergence] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Both CPR analysis and Demand analysis handle recursive functions by doing fixed-point iteration. To find the *least* (e.g., most informative) fixed-point, iteration starts with the bottom element of the semantic domain. Diverging functions generally have the bottom element as their least fixed-point. One might think that CPR analysis and Demand analysis then agree in when a function gets a bottom denotation. E.g., whenever it has 'botCpr', it should also have 'botDiv'. But that is not the case, because strictness analysis has to be careful around precise exceptions, see Note [Precise vs imprecise exceptions]. So Demand analysis gives some diverging functions 'exnDiv' (which is *not* the bottom element) when the CPR signature says 'botCpr', and that's OK. Here's an example (from #18086) where that is the case: ioTest :: IO () ioTest = do putStrLn "hi" undefined However, one can loosely say that we give a function 'botCpr' whenever its 'Divergence' is 'exnDiv' or 'botDiv', i.e., dead-ending. But that's just a consequence of fixed-point iteration, it's not important that they agree. ************************************************************************ * * Demand environments and types * * ************************************************************************ -} -- Subject to Note [Default demand on free variables and arguments] type DmdEnv = VarEnv Demand emptyDmdEnv :: DmdEnv emptyDmdEnv = emptyVarEnv multDmdEnv :: Card -> DmdEnv -> DmdEnv multDmdEnv C_11 env = env multDmdEnv C_00 _ = emptyDmdEnv multDmdEnv n env = mapVarEnv (multDmd n) env reuseEnv :: DmdEnv -> DmdEnv reuseEnv = multDmdEnv C_1N -- | @keepAliveDmdType dt vs@ makes sure that the Ids in @vs@ have -- /some/ usage in the returned demand types -- they are not Absent. -- See Note [Absence analysis for stable unfoldings and RULES] -- in "GHC.Core.Opt.DmdAnal". keepAliveDmdEnv :: DmdEnv -> IdSet -> DmdEnv keepAliveDmdEnv env vs = nonDetStrictFoldVarSet add env vs where add :: Id -> DmdEnv -> DmdEnv add v env = extendVarEnv_C add_dmd env v topDmd add_dmd :: Demand -> Demand -> Demand -- If the existing usage is Absent, make it used -- Otherwise leave it alone add_dmd dmd _ | isAbsDmd dmd = topDmd | otherwise = dmd -- | Characterises how an expression -- -- * Evaluates its free variables ('dt_env') -- * Evaluates its arguments ('dt_args') -- * Diverges on every code path or not ('dt_div') -- -- Equality is defined modulo 'defaultFvDmd's in 'dt_env'. -- See Note [Demand type Equality]. data DmdType = DmdType { dt_env :: !DmdEnv -- ^ Demand on explicitly-mentioned free variables , dt_args :: ![Demand] -- ^ Demand on arguments , dt_div :: !Divergence -- ^ Whether evaluation diverges. -- See Note [Demand type Divergence] } -- | See Note [Demand type Equality]. instance Eq DmdType where (==) (DmdType fv1 ds1 div1) (DmdType fv2 ds2 div2) = div1 == div2 && ds1 == ds2 -- cheap checks first && canonicalise div1 fv1 == canonicalise div2 fv2 where canonicalise div fv = filterUFM (/= defaultFvDmd div) fv -- | Compute the least upper bound of two 'DmdType's elicited /by the same -- incoming demand/! lubDmdType :: DmdType -> DmdType -> DmdType lubDmdType d1 d2 = DmdType lub_fv lub_ds lub_div where n = max (dmdTypeDepth d1) (dmdTypeDepth d2) (DmdType fv1 ds1 r1) = etaExpandDmdType n d1 (DmdType fv2 ds2 r2) = etaExpandDmdType n d2 -- See Note [Demand type Equality] lub_fv = plusVarEnv_CD lubDmd fv1 (defaultFvDmd r1) fv2 (defaultFvDmd r2) lub_ds = zipWithEqual "lubDmdType" lubDmd ds1 ds2 lub_div = lubDivergence r1 r2 type PlusDmdArg = (DmdEnv, Divergence) mkPlusDmdArg :: DmdEnv -> PlusDmdArg mkPlusDmdArg env = (env, topDiv) toPlusDmdArg :: DmdType -> PlusDmdArg toPlusDmdArg (DmdType fv _ r) = (fv, r) plusDmdType :: DmdType -> PlusDmdArg -> DmdType plusDmdType (DmdType fv1 ds1 r1) (fv2, t2) -- See Note [Asymmetry of 'plus*'] -- 'plus' takes the argument/result info from its *first* arg, -- using its second arg just for its free-var info. | isEmptyVarEnv fv2, defaultFvDmd t2 == absDmd = DmdType fv1 ds1 (r1 `plusDivergence` t2) -- a very common case that is much more efficient | otherwise = DmdType (plusVarEnv_CD plusDmd fv1 (defaultFvDmd r1) fv2 (defaultFvDmd t2)) ds1 (r1 `plusDivergence` t2) botDmdType :: DmdType botDmdType = DmdType emptyDmdEnv [] botDiv -- | The demand type of doing nothing (lazy, absent, no Divergence -- information). Note that it is ''not'' the top of the lattice (which would be -- "may use everything"), so it is (no longer) called topDmdType. nopDmdType :: DmdType nopDmdType = DmdType emptyDmdEnv [] topDiv isTopDmdType :: DmdType -> Bool isTopDmdType (DmdType env args div) = div == topDiv && null args && isEmptyVarEnv env -- | The demand type of an unspecified expression that is guaranteed to -- throw a (precise or imprecise) exception or diverge. exnDmdType :: DmdType exnDmdType = DmdType emptyDmdEnv [] exnDiv dmdTypeDepth :: DmdType -> Arity dmdTypeDepth = length . dt_args -- | This makes sure we can use the demand type with n arguments after eta -- expansion, where n must not be lower than the demand types depth. -- It appends the argument list with the correct 'defaultArgDmd'. etaExpandDmdType :: Arity -> DmdType -> DmdType etaExpandDmdType n d@DmdType{dt_args = ds, dt_div = div} | n == depth = d | n > depth = d{dt_args = inc_ds} | otherwise = pprPanic "etaExpandDmdType: arity decrease" (ppr n $$ ppr d) where depth = length ds -- Arity increase: -- * Demands on FVs are still valid -- * Demands on args also valid, plus we can extend with defaultArgDmd -- as appropriate for the given Divergence -- * Divergence is still valid: -- - A dead end after 2 arguments stays a dead end after 3 arguments -- - The remaining case is Dunno, which is already topDiv inc_ds = take n (ds ++ repeat (defaultArgDmd div)) -- | A conservative approximation for a given 'DmdType' in case of an arity -- decrease. Currently, it's just nopDmdType. decreaseArityDmdType :: DmdType -> DmdType decreaseArityDmdType _ = nopDmdType splitDmdTy :: DmdType -> (Demand, DmdType) -- Split off one function argument -- We already have a suitable demand on all -- free vars, so no need to add more! splitDmdTy ty@DmdType{dt_args=dmd:args} = (dmd, ty{dt_args=args}) splitDmdTy ty@DmdType{dt_div=div} = (defaultArgDmd div, ty) multDmdType :: Card -> DmdType -> DmdType multDmdType n (DmdType fv args res_ty) = -- pprTrace "multDmdType" (ppr n $$ ppr fv $$ ppr (multDmdEnv n fv)) $ DmdType (multDmdEnv n fv) (map (multDmd n) args) (multDivergence n res_ty) peelFV :: DmdType -> Var -> (DmdType, Demand) peelFV (DmdType fv ds res) id = -- pprTrace "rfv" (ppr id <+> ppr dmd $$ ppr fv) (DmdType fv' ds res, dmd) where -- Force these arguments so that old `Env` is not retained. !fv' = fv `delVarEnv` id -- See Note [Default demand on free variables and arguments] !dmd = lookupVarEnv fv id `orElse` defaultFvDmd res addDemand :: Demand -> DmdType -> DmdType addDemand dmd (DmdType fv ds res) = DmdType fv (dmd:ds) res findIdDemand :: DmdType -> Var -> Demand findIdDemand (DmdType fv _ res) id = lookupVarEnv fv id `orElse` defaultFvDmd res -- | When e is evaluated after executing an IO action that may throw a precise -- exception, we act as if there is an additional control flow path that is -- taken if e throws a precise exception. The demand type of this control flow -- path -- * is lazy and absent ('topDmd') and boxed in all free variables and arguments -- * has 'exnDiv' 'Divergence' result -- See Note [Precise exceptions and strictness analysis] -- -- So we can simply take a variant of 'nopDmdType', 'exnDmdType'. -- Why not 'nopDmdType'? Because then the result of 'e' can never be 'exnDiv'! -- That means failure to drop dead-ends, see #18086. deferAfterPreciseException :: DmdType -> DmdType deferAfterPreciseException = lubDmdType exnDmdType -- | See 'keepAliveDmdEnv'. keepAliveDmdType :: DmdType -> VarSet -> DmdType keepAliveDmdType (DmdType fvs ds res) vars = DmdType (fvs `keepAliveDmdEnv` vars) ds res {- Note [deferAfterPreciseException] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The big picture is in Note [Precise exceptions and strictness analysis] The idea is that we want to treat case of (# s', r #) -> rhs as if it was case of Just (# s', r #) -> rhs Nothing -> error That is, the I/O operation might throw an exception, so that 'rhs' never gets reached. For example, we don't want to be strict in the strict free variables of 'rhs'. So we have the simple definition deferAfterPreciseException = lubDmdType (DmdType emptyDmdEnv [] exnDiv) Historically, when we had `lubBoxity = _unboxedWins` (see Note [unboxedWins]), we had a more complicated definition for deferAfterPreciseException to make sure it preserved boxity in its argument. That was needed for code like case of (# s', r) -> f x which uses `x` *boxed*. If we `lub`bed it with `(DmdType emptyDmdEnv [] exnDiv)` we'd get an *unboxed* demand on `x` (because we let Unboxed win), which led to ticket #20746. Nowadays with `lubBoxity = boxedWins` we don't need the complicated definition. Note [Demand type Divergence] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ In contrast to DmdSigs, DmdTypes are elicited under a specific incoming demand. This is described in detail in Note [Understanding DmdType and DmdSig]. Here, we'll focus on what that means for a DmdType's Divergence in a higher-order scenario. Consider err x y = x `seq` y `seq` error (show x) this has a strictness signature of <1L><1L>b meaning that we don't know what happens when we call err in weaker contexts than C1(C1(L)), like @err `seq` ()@ (1A) and @err 1 `seq` ()@ (CS(A)). We may not unleash the botDiv, hence assume topDiv. Of course, in @err 1 2 `seq` ()@ the incoming demand CS(CS(A)) is strong enough and we see that the expression diverges. Now consider a function f g = g 1 2 with signature , and the expression f err `seq` () now f puts a strictness demand of C1(C1(L)) onto its argument, which is unleashed on err via the App rule. In contrast to weaker head strictness, this demand is strong enough to unleash err's signature and hence we see that the whole expression diverges! Note [Demand type Equality] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ What is the difference between the DmdType {x->A} and ? Answer: There is none! They have the exact same semantics, because any var that is not mentioned in 'dt_env' implicitly has demand 'defaultFvDmd', based on the divergence of the demand type 'dt_div'. Similarly, b{x->B, y->A} is the same as b{y->A}, because the default FV demand of BotDiv is B. But neither is equal to b, because y has demand B in the latter, not A as before. NB: 'dt_env' technically can't stand for its own, because it doesn't tell us the demand on FVs that don't appear in the DmdEnv. Hence 'PlusDmdArg' carries along a 'Divergence', for example. The Eq instance of DmdType must reflect that, otherwise we can get into monotonicity issues during fixed-point iteration ({x->A} /= /= {x->A} /= ...). It does so by filtering out any default FV demands prior to comparing 'dt_env'. An alternative would be to maintain an invariant that there are no default FV demands in 'dt_env' to begin with, but that seems more involved to maintain in the current implementation. Note that 'lubDmdType' maintains this kind of equality by using 'plusVarEnv_CD', involving 'defaultFvDmd' for any entries present in one 'dt_env' but not the other. Note [Asymmetry of 'plus*'] ~~~~~~~~~~~~~~~~~~~~~~~~~~~ 'plus' for DmdTypes is *asymmetrical*, because there can only one be one type contributing argument demands! 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 `plusType` 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 `plusType` 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, as in plusDivergence. Since we don't use argument demands of the second argument anyway, 'plus's second argument is just a 'PlusDmdType'. But note that the argument demand types are not guaranteed to be observed in left to right order. For example, analysis of a case expression will pass the demand type for the alts as the left argument and the type for the scrutinee as the right argument. Also, it is not at all clear if there is such an order; consider the LetUp case, where the RHS might be forced at any point while evaluating the let body. Therefore, it is crucial that 'plusDivergence' is symmetric! Note [Demands from unsaturated function calls] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Consider a demand transformer d1 -> d2 -> r for f. If a sufficiently detailed demand is fed into this transformer, e.g arising from "f x1 x2" in a strict, use-once context, then d1 and d2 is precisely the demand unleashed onto x1 and x2 (similar for the free variable environment) and furthermore the result information r is the one we want to use. An anonymous lambda is also an unsaturated function all (needs one argument, none given), so this applies to that case as well. But the demand fed into f might be less than C1(C1(L)). Then we have to 'multDmdType' the announced demand type. Examples: * Not strict enough, e.g. C1(C1(L)): - We have to multiply all argument and free variable demands with C_01, zapping strictness. - We have to multiply divergence with C_01. If r says that f Diverges for sure, then this holds when the demand guarantees that two arguments are going to be passed. If the demand is lower, we may just as well converge. If we were tracking definite convergence, than that would still hold under a weaker demand than expected by the demand transformer. * Used more than once, e.g. CS(C1(L)): - Multiply with C_1N. Even if f puts a used-once demand on any of its argument or free variables, if we call f multiple times, we may evaluate this argument or free variable multiple times. In dmdTransformSig, we call peelManyCalls to find out the 'Card'inality with which we have to multiply and then call multDmdType with that. Similarly, dmdTransformDictSelSig and dmdAnal, when analyzing a Lambda, use peelCallDmd, which peels only one level, but also returns the demand put on the body of the function. -} {- ************************************************************************ * * Demand signatures * * ************************************************************************ In a let-bound Id we record its demand signature. In principle, this demand signature is a demand transformer, mapping a demand on the Id into a DmdType, which gives a) the free vars of the Id's value b) the Id's arguments c) an indication of the result of applying the Id to its arguments However, in fact we store in the Id an extremely emascuated demand transfomer, namely a single DmdType (Nevertheless we dignify DmdSig as a distinct type.) This DmdType gives the demands unleashed by the Id when it is applied to as many arguments as are given in by the arg demands in the DmdType. Also see Note [Demand type Divergence] for the meaning of a Divergence in a strictness signature. If an Id is applied to less arguments than its arity, it means that the demand on the function at a call site is weaker than the vanilla call demand, used for signature inference. Therefore we place a top demand on all arguments. Otherwise, the demand is specified by Id's signature. For example, the demand transformer described by the demand signature DmdSig (DmdType {x -> <1L>} <1P(L,L)>) says that when the function is applied to two arguments, it unleashes demand 1L on the free var x, A on the first arg, and 1P(L,L) on the second. If this same function is applied to one arg, all we can say is that it uses x with 1L, and its arg with demand 1P(L,L). Note [Understanding DmdType and DmdSig] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Demand types are sound approximations of an expression's semantics relative to the incoming demand we put the expression under. Consider the following expression: \x y -> x `seq` (y, 2*x) Here is a table with demand types resulting from different incoming demands we put that expression under. Note the monotonicity; a stronger incoming demand yields a more precise demand type: incoming demand | demand type -------------------------------- 1A | {} C1(C1(L)) | <1P(L)>{} C1(C1(1P(1P(L),A))) | <1P(A)>{} Note that in the first example, the depth of the demand type was *higher* than the arity of the incoming call demand due to the anonymous lambda. The converse is also possible and happens when we unleash demand signatures. In @f x y@, the incoming call demand on f has arity 2. But if all we have is a demand signature with depth 1 for @f@ (which we can safely unleash, see below), the demand type of @f@ under a call demand of arity 2 has a *lower* depth of 1. So: Demand types are elicited by putting an expression under an incoming (call) demand, the arity of which can be lower or higher than the depth of the resulting demand type. In contrast, a demand signature summarises a function's semantics *without* immediately specifying the incoming demand it was produced under. Despite StrSig being a newtype wrapper around DmdType, it actually encodes two things: * The threshold (i.e., minimum arity) to unleash the signature * A demand type that is sound to unleash when the minimum arity requirement is met. Here comes the subtle part: The threshold is encoded in the wrapped demand type's depth! So in mkDmdSigForArity we make sure to trim the list of argument demands to the given threshold arity. Call sites will make sure that this corresponds to the arity of the call demand that elicited the wrapped demand type. See also Note [What are demand signatures?]. -} -- | The depth of the wrapped 'DmdType' encodes the arity at which it is safe -- to unleash. Better construct this through 'mkDmdSigForArity'. -- See Note [Understanding DmdType and DmdSig] newtype DmdSig = DmdSig DmdType deriving Eq -- | Turns a 'DmdType' computed for the particular 'Arity' into a 'DmdSig' -- unleashable at that arity. See Note [Understanding DmdType and DmdSig]. mkDmdSigForArity :: Arity -> DmdType -> DmdSig mkDmdSigForArity arity dmd_ty@(DmdType fvs args div) | arity < dmdTypeDepth dmd_ty = DmdSig $ DmdType fvs (take arity args) div | otherwise = DmdSig (etaExpandDmdType arity dmd_ty) mkClosedDmdSig :: [Demand] -> Divergence -> DmdSig mkClosedDmdSig ds res = mkDmdSigForArity (length ds) (DmdType emptyDmdEnv ds res) splitDmdSig :: DmdSig -> ([Demand], Divergence) splitDmdSig (DmdSig (DmdType _ dmds res)) = (dmds, res) dmdSigDmdEnv :: DmdSig -> DmdEnv dmdSigDmdEnv (DmdSig (DmdType env _ _)) = env hasDemandEnvSig :: DmdSig -> Bool hasDemandEnvSig = not . isEmptyVarEnv . dmdSigDmdEnv botSig :: DmdSig botSig = DmdSig botDmdType nopSig :: DmdSig nopSig = DmdSig nopDmdType isTopSig :: DmdSig -> Bool isTopSig (DmdSig ty) = isTopDmdType ty -- | True if the signature diverges or throws an exception in a saturated call. -- See Note [Dead ends]. isDeadEndSig :: DmdSig -> Bool isDeadEndSig (DmdSig (DmdType _ _ res)) = isDeadEndDiv res -- | True when the signature indicates all arguments are boxed onlyBoxedArguments :: DmdSig -> Bool onlyBoxedArguments (DmdSig (DmdType _ dmds _)) = all demandIsBoxed dmds where demandIsBoxed BotDmd = True demandIsBoxed AbsDmd = True demandIsBoxed (_ :* sd) = subDemandIsboxed sd subDemandIsboxed (Poly Unboxed _) = False subDemandIsboxed (Poly _ _) = True subDemandIsboxed (Call _ sd) = subDemandIsboxed sd subDemandIsboxed (Prod Unboxed _) = False subDemandIsboxed (Prod _ ds) = all demandIsBoxed ds -- | Returns true if an application to n value args would diverge or throw an -- exception. -- -- If a function having 'botDiv' is applied to a less number of arguments than -- its syntactic arity, we cannot say for sure that it is going to diverge. -- Hence this function conservatively returns False in that case. -- See Note [Dead ends]. isDeadEndAppSig :: DmdSig -> Int -> Bool isDeadEndAppSig (DmdSig (DmdType _ ds res)) n = isDeadEndDiv res && not (lengthExceeds ds n) trimBoxityDmdType :: DmdType -> DmdType trimBoxityDmdType (DmdType fvs ds res) = DmdType (mapVarEnv trimBoxity fvs) (map trimBoxity ds) res trimBoxityDmdSig :: DmdSig -> DmdSig trimBoxityDmdSig = coerce trimBoxityDmdType prependArgsDmdSig :: Int -> DmdSig -> DmdSig -- ^ Add extra ('topDmd') arguments to a strictness signature. -- In contrast to 'etaConvertDmdSig', this /prepends/ additional argument -- demands. This is used by FloatOut. prependArgsDmdSig new_args sig@(DmdSig dmd_ty@(DmdType env dmds res)) | new_args == 0 = sig | isTopDmdType dmd_ty = sig | new_args < 0 = pprPanic "prependArgsDmdSig: negative new_args" (ppr new_args $$ ppr sig) | otherwise = DmdSig (DmdType env dmds' res) where dmds' = replicate new_args topDmd ++ dmds etaConvertDmdSig :: Arity -> DmdSig -> DmdSig -- ^ We are expanding (\x y. e) to (\x y z. e z) or reducing from the latter to -- the former (when the Simplifier identifies a new join points, for example). -- In contrast to 'prependArgsDmdSig', this /appends/ extra arg demands if -- necessary. -- This works by looking at the 'DmdType' (which was produced under a call -- demand for the old arity) and trying to transfer as many facts as we can to -- the call demand of new arity. -- An arity increase (resulting in a stronger incoming demand) can retain much -- of the info, while an arity decrease (a weakening of the incoming demand) -- must fall back to a conservative default. etaConvertDmdSig arity (DmdSig dmd_ty) | arity < dmdTypeDepth dmd_ty = DmdSig $ decreaseArityDmdType dmd_ty | otherwise = DmdSig $ etaExpandDmdType arity dmd_ty {- ************************************************************************ * * Demand transformers * * ************************************************************************ -} -- | A /demand transformer/ is a monotone function from an incoming evaluation -- context ('SubDemand') to a 'DmdType', describing how the denoted thing -- (i.e. expression, function) uses its arguments and free variables, and -- whether it diverges. -- -- See Note [Understanding DmdType and DmdSig] -- and Note [What are demand signatures?]. type DmdTransformer = SubDemand -> DmdType -- | Extrapolate a demand signature ('DmdSig') into a 'DmdTransformer'. -- -- Given a function's 'DmdSig' and a 'SubDemand' for the evaluation context, -- return how the function evaluates its free variables and arguments. dmdTransformSig :: DmdSig -> DmdTransformer dmdTransformSig (DmdSig dmd_ty@(DmdType _ arg_ds _)) sd = multDmdType (fst $ peelManyCalls (length arg_ds) sd) dmd_ty -- see Note [Demands from unsaturated function calls] -- and Note [What are demand signatures?] -- | A special 'DmdTransformer' for data constructors that feeds product -- demands into the constructor arguments. dmdTransformDataConSig :: [StrictnessMark] -> DmdTransformer -- See Note [Demand transformer for data constructors] dmdTransformDataConSig str_marks sd = case viewProd arity body_sd of Just (_, dmds) -> mk_body_ty n dmds Nothing -> nopDmdType where arity = length str_marks (n, body_sd) = peelManyCalls arity sd mk_body_ty n dmds = DmdType emptyDmdEnv (zipWith (bump n) str_marks dmds) topDiv bump n str dmd | isMarkedStrict str = multDmd n (plusDmd str_field_dmd dmd) | otherwise = multDmd n dmd str_field_dmd = C_01 :* seqSubDmd -- Why not C_11? See Note [Data-con worker strictness] -- | A special 'DmdTransformer' for dictionary selectors that feeds the demand -- on the result into the indicated dictionary component (if saturated). -- See Note [Demand transformer for a dictionary selector]. dmdTransformDictSelSig :: DmdSig -> DmdTransformer -- NB: This currently doesn't handle newtype dictionaries. -- It should simply apply call_sd directly to the dictionary, I suppose. dmdTransformDictSelSig (DmdSig (DmdType _ [_ :* prod] _)) call_sd | (n, sd') <- peelCallDmd call_sd , Prod _ sig_ds <- prod = multDmdType n $ DmdType emptyDmdEnv [C_11 :* mkProd Unboxed (map (enhance sd') sig_ds)] topDiv | otherwise = nopDmdType -- See Note [Demand transformer for a dictionary selector] where enhance _ AbsDmd = AbsDmd enhance _ BotDmd = BotDmd enhance sd _dmd_var = C_11 :* sd -- This is the one! -- C_11, because we multiply with n above dmdTransformDictSelSig sig sd = pprPanic "dmdTransformDictSelSig: no args" (ppr sig $$ ppr sd) {- Note [What are demand signatures?] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Demand analysis interprets expressions in the abstract domain of demand transformers. Given a (sub-)demand that denotes the evaluation context, the abstract transformer of an expression gives us back a demand type denoting how other things (like arguments and free vars) were used when the expression was evaluated. Here's an example: f x y = if x + expensive then \z -> z + y * ... else \z -> z * ... The abstract transformer (let's call it F_e) of the if expression (let's call it e) would transform an incoming (undersaturated!) head demand 1A into a demand type like {x-><1L>,y->}. In pictures: Demand ---F_e---> DmdType <1A> {x-><1L>,y->} Let's assume that the demand transformers we compute for an expression are correct wrt. to some concrete semantics for Core. How do demand signatures fit in? They are strange beasts, given that they come with strict rules when to it's sound to unleash them. Fortunately, we can formalise the rules with Galois connections. Consider f's strictness signature, {}<1L>. It's a single-point approximation of the actual abstract transformer of f's RHS for arity 2. So, what happens is that we abstract *once more* from the abstract domain we already are in, replacing the incoming Demand by a simple lattice with two elements denoting incoming arity: A_2 = {<2, >=2} (where '<2' is the top element and >=2 the bottom element). Here's the diagram: A_2 -----f_f----> DmdType ^ | | α γ | | v SubDemand --F_f----> DmdType With α(C1(C1(_))) = >=2 α(_) = <2 γ(ty) = ty and F_f being the abstract transformer of f's RHS and f_f being the abstracted abstract transformer computable from our demand signature simply by f_f(>=2) = {}<1L> f_f(<2) = multDmdType C_0N {}<1L> where multDmdType makes a proper top element out of the given demand type. In practice, the A_n domain is not just a simple Bool, but a Card, which is exactly the Card with which we have to multDmdType. The Card for arity n is computed by calling @peelManyCalls n@, which corresponds to α above. Note [Demand transformer for a dictionary selector] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Suppose we have a superclass selector 'sc_sel' and a class method selector 'op_sel', and a function that uses both, like this -- Strictness sig: 1P(1,A) sc_sel (x,y) = x -- Strictness sig: 1P(A,1) op_sel (p,q)= q f d v = op_sel (sc_sel d) v What do we learn about the demand on 'd'? Alas, we see only the demand from 'sc_sel', namely '1P(1,A)'. We /don't/ see that 'd' really has a nested demand '1P(1P(A,1C1(1)),A)'. On the other hand, if we inlined the two selectors we'd have f d x = case d of (x,_) -> case x of (_,q) -> q v If we analyse that, we'll get a richer, nested demand on 'd'. We want to behave /as if/ we'd inlined 'op_sel' and 'sc_sel'. We can do this easily by building a richer demand transformer for dictionary selectors than is expressible by a regular demand signature. And that is what 'dmdTransformDictSelSig' does: it transforms the demand on the result to a demand on the (single) argument. How does it do that? If we evaluate (op dict-expr) under demand 'd', then we can push the demand 'd' into the appropriate field of the dictionary. What *is* the appropriate field? We just look at the strictness signature of the class op, which will be something like: P(AAA1AAAAA). Then replace the '1' (or any other non-absent demand, really) by the demand 'd'. The '1' acts as if it was a demand variable, the whole signature really means `\d. P(AAAdAAAAA)` for any incoming demand 'd'. For single-method classes, which are represented by newtypes the signature of 'op' won't look like P(...), so matching on Prod will fail. That's fine: if we are doing strictness analysis we are also doing inlining, so we'll have inlined 'op' into a cast. So we can bale out in a conservative way, returning nopDmdType. SG: Although we then probably want to apply the eval demand 'd' directly to 'op' rather than turning it into 'topSubDmd'... It is (just.. #8329) possible to be running strictness analysis *without* having inlined class ops from single-method classes. Suppose you are using ghc --make; and the first module has a local -O0 flag. So you may load a class without interface pragmas, ie (currently) without an unfolding for the class ops. Now if a subsequent module in the --make sweep has a local -O flag you might do strictness analysis, but there is no inlining for the class op. This is weird, so I'm not worried about whether this optimises brilliantly; but it should not fall over. -} -- | Remove the demand environment from the signature. zapDmdEnvSig :: DmdSig -> DmdSig zapDmdEnvSig (DmdSig (DmdType _ ds r)) = mkClosedDmdSig ds r zapUsageDemand :: Demand -> Demand -- Remove the usage info, but not the strictness info, from the demand zapUsageDemand = kill_usage $ KillFlags { kf_abs = True , kf_used_once = True , kf_called_once = True } -- | Remove all `C_01 :*` info (but not `CM` sub-demands) from the demand zapUsedOnceDemand :: Demand -> Demand zapUsedOnceDemand = kill_usage $ KillFlags { kf_abs = False , kf_used_once = True , kf_called_once = False } -- | Remove all `C_01 :*` info (but not `CM` sub-demands) from the strictness -- signature zapUsedOnceSig :: DmdSig -> DmdSig zapUsedOnceSig (DmdSig (DmdType env ds r)) = DmdSig (DmdType env (map zapUsedOnceDemand ds) r) data KillFlags = KillFlags { kf_abs :: Bool , kf_used_once :: Bool , kf_called_once :: Bool } kill_usage_card :: KillFlags -> Card -> Card kill_usage_card kfs C_00 | kf_abs kfs = C_0N kill_usage_card kfs C_10 | kf_abs kfs = C_1N kill_usage_card kfs C_01 | kf_used_once kfs = C_0N kill_usage_card kfs C_11 | kf_used_once kfs = C_1N kill_usage_card _ n = n kill_usage :: KillFlags -> Demand -> Demand kill_usage _ AbsDmd = AbsDmd kill_usage _ BotDmd = BotDmd kill_usage kfs (n :* sd) = kill_usage_card kfs n :* kill_usage_sd kfs sd kill_usage_sd :: KillFlags -> SubDemand -> SubDemand kill_usage_sd kfs (Call n sd) | kf_called_once kfs = mkCall (lubCard C_1N n) (kill_usage_sd kfs sd) | otherwise = mkCall n (kill_usage_sd kfs sd) kill_usage_sd kfs (Prod b ds) = mkProd b (map (kill_usage kfs) ds) kill_usage_sd _ sd = sd {- ********************************************************************* * * TypeShape and demand trimming * * ********************************************************************* -} data TypeShape -- See Note [Trimming a demand to a type] -- in GHC.Core.Opt.DmdAnal = TsFun TypeShape | TsProd [TypeShape] | TsUnk trimToType :: Demand -> TypeShape -> Demand -- See Note [Trimming a demand to a type] in GHC.Core.Opt.DmdAnal trimToType AbsDmd _ = AbsDmd trimToType BotDmd _ = BotDmd trimToType (n :* sd) ts = n :* go sd ts where go (Prod b ds) (TsProd tss) | equalLength ds tss = mkProd b (zipWith trimToType ds tss) go (Call n sd) (TsFun ts) = mkCall n (go sd ts) go sd@Poly{} _ = sd go _ _ = topSubDmd -- | Drop all boxity trimBoxity :: Demand -> Demand trimBoxity AbsDmd = AbsDmd trimBoxity BotDmd = BotDmd trimBoxity (n :* sd) = n :* go sd where go (Poly _ n) = Poly Boxed n go (Prod _ ds) = mkProd Boxed (map trimBoxity ds) go (Call n sd) = mkCall n $ go sd {- ************************************************************************ * * 'seq'ing demands * * ************************************************************************ -} seqDemand :: Demand -> () seqDemand AbsDmd = () seqDemand BotDmd = () seqDemand (_ :* sd) = seqSubDemand sd seqSubDemand :: SubDemand -> () seqSubDemand (Prod _ ds) = seqDemandList ds seqSubDemand (Call _ sd) = seqSubDemand sd seqSubDemand (Poly _ _) = () seqDemandList :: [Demand] -> () seqDemandList = foldr (seq . seqDemand) () seqDmdType :: DmdType -> () seqDmdType (DmdType env ds res) = seqDmdEnv env `seq` seqDemandList ds `seq` res `seq` () seqDmdEnv :: DmdEnv -> () seqDmdEnv env = seqEltsUFM seqDemand env seqDmdSig :: DmdSig -> () seqDmdSig (DmdSig ty) = seqDmdType ty {- ************************************************************************ * * Outputable and Binary instances * * ************************************************************************ -} -- Just for debugging purposes. instance Show Card where show C_00 = "C_00" show C_01 = "C_01" show C_0N = "C_0N" show C_10 = "C_10" show C_11 = "C_11" show C_1N = "C_1N" {- Note [Demand notation] ~~~~~~~~~~~~~~~~~~~~~~~~~ This Note should be kept up to date with the documentation of `-fstrictness` in the user's guide. For pretty-printing demands, we use quite a compact notation with some abbreviations. Here's the BNF: card ::= B {} | A {0} | M {0,1} | L {0,1,n} | 1 {1} | S {1,n} box ::= ! Unboxed | Boxed d ::= card sd The :* constructor, just juxtaposition | card abbreviation: Same as "card card" sd ::= box card @Poly box card@ | box P(d,d,..) @Prod box [d1,d2,..]@ | Ccard(sd) @Call card sd@ So, L can denote a 'Card', polymorphic 'SubDemand' or polymorphic 'Demand', but it's always clear from context which "overload" is meant. It's like return-type inference of e.g. 'read'. Examples are in the haddock for 'Demand'. This is the syntax for demand signatures: div ::= topDiv | x exnDiv | b botDiv sig ::= {x->dx,y->dy,z->dz...}...div ^ ^ ^ ^ ^ ^ | | | | | | | \---+---+------/ | | | | demand on free demand on divergence variables arguments information (omitted if empty) (omitted if no information) -} -- | See Note [Demand notation] -- Current syntax was discussed in #19016. instance Outputable Card where ppr C_00 = char 'A' -- "Absent" ppr C_01 = char 'M' -- "Maybe" ppr C_0N = char 'L' -- "Lazy" ppr C_11 = char '1' -- "exactly 1" ppr C_1N = char 'S' -- "Strict" ppr C_10 = char 'B' -- "Bottom" -- | See Note [Demand notation] instance Outputable Demand where ppr AbsDmd = char 'A' ppr BotDmd = char 'B' ppr (C_0N :* Poly Boxed C_0N) = char 'L' -- Print LL as just L ppr (C_1N :* Poly Boxed C_1N) = char 'S' -- Dito SS ppr (n :* sd) = ppr n <> ppr sd -- | See Note [Demand notation] instance Outputable SubDemand where ppr (Poly b sd) = pp_boxity b <> ppr sd ppr (Call n sd) = char 'C' <> ppr n <> parens (ppr sd) ppr (Prod b ds) = pp_boxity b <> char 'P' <> parens (fields ds) where fields [] = empty fields [x] = ppr x fields (x:xs) = ppr x <> char ',' <> fields xs pp_boxity :: Boxity -> SDoc pp_boxity Unboxed = char '!' pp_boxity _ = empty instance Outputable Divergence where ppr Diverges = char 'b' -- for (b)ottom ppr ExnOrDiv = char 'x' -- for e(x)ception ppr Dunno = empty instance Outputable DmdType where ppr (DmdType fv ds res) = hsep [hcat (map (angleBrackets . ppr) ds) <> ppr res, if null fv_elts then empty else braces (fsep (map pp_elt fv_elts))] where pp_elt (uniq, dmd) = ppr uniq <> text "->" <> ppr dmd fv_elts = nonDetUFMToList fv -- It's OK to use nonDetUFMToList here because we only do it for -- pretty printing instance Outputable DmdSig where ppr (DmdSig ty) = ppr ty 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) instance Binary Card where put_ bh C_00 = putByte bh 0 put_ bh C_01 = putByte bh 1 put_ bh C_0N = putByte bh 2 put_ bh C_11 = putByte bh 3 put_ bh C_1N = putByte bh 4 put_ bh C_10 = putByte bh 5 get bh = do h <- getByte bh case h of 0 -> return C_00 1 -> return C_01 2 -> return C_0N 3 -> return C_11 4 -> return C_1N 5 -> return C_10 _ -> pprPanic "Binary:Card" (ppr (fromIntegral h :: Int)) instance Binary Demand where put_ bh (n :* sd) = put_ bh n *> case n of C_00 -> return () C_10 -> return () _ -> put_ bh sd get bh = get bh >>= \n -> case n of C_00 -> return AbsDmd C_10 -> return BotDmd _ -> (n :*) <$> get bh instance Binary SubDemand where put_ bh (Poly b sd) = putByte bh 0 *> put_ bh b *> put_ bh sd put_ bh (Call n sd) = putByte bh 1 *> put_ bh n *> put_ bh sd put_ bh (Prod b ds) = putByte bh 2 *> put_ bh b *> put_ bh ds get bh = do h <- getByte bh case h of 0 -> Poly <$> get bh <*> get bh 1 -> mkCall <$> get bh <*> get bh 2 -> Prod <$> get bh <*> get bh _ -> pprPanic "Binary:SubDemand" (ppr (fromIntegral h :: Int)) instance Binary DmdSig where put_ bh (DmdSig aa) = put_ bh aa get bh = DmdSig <$> get bh instance Binary DmdType where -- Ignore DmdEnv when spitting out the DmdType put_ bh (DmdType _ ds dr) = put_ bh ds *> put_ bh dr get bh = DmdType emptyDmdEnv <$> get bh <*> get bh instance Binary Divergence where put_ bh Dunno = putByte bh 0 put_ bh ExnOrDiv = putByte bh 1 put_ bh Diverges = putByte bh 2 get bh = do h <- getByte bh case h of 0 -> return Dunno 1 -> return ExnOrDiv 2 -> return Diverges _ -> pprPanic "Binary:Divergence" (ppr (fromIntegral h :: Int))