{-# LANGUAGE RankNTypes, ScopedTypeVariables, GADTs, EmptyDataDecls, PatternGuards, TypeFamilies, MultiParamTypeClasses #-} module Compiler.Hoopl.Dataflow ( DataflowLattice(..), JoinFun, OldFact(..), NewFact(..), Fact, mkFactBase , ChangeFlag(..), changeIf , FwdPass(..), FwdTransfer, mkFTransfer, mkFTransfer3, getFTransfer3 -- * Respecting Fuel -- $fuel , FwdRewrite, mkFRewrite, mkFRewrite3, getFRewrite3, noFwdRewrite , wrapFR, wrapFR2 , BwdPass(..), BwdTransfer, mkBTransfer, mkBTransfer3, getBTransfer3 , wrapBR, wrapBR2 , BwdRewrite, mkBRewrite, mkBRewrite3, getBRewrite3, noBwdRewrite , analyzeAndRewriteFwd, analyzeAndRewriteBwd ) where import Control.Monad import Data.Maybe import Compiler.Hoopl.Checkpoint import Compiler.Hoopl.Collections import Compiler.Hoopl.Fuel import Compiler.Hoopl.Graph hiding (Graph) -- hiding so we can redefine -- and include definition in paper import qualified Compiler.Hoopl.GraphUtil as U import Compiler.Hoopl.Label import Compiler.Hoopl.Util ----------------------------------------------------------------------------- -- DataflowLattice ----------------------------------------------------------------------------- data DataflowLattice a = DataflowLattice { fact_name :: String -- Documentation , fact_bot :: a -- Lattice bottom element , fact_join :: JoinFun a -- Lattice join plus change flag -- (changes iff result > old fact) } -- ^ A transfer function might want to use the logging flag -- to control debugging, as in for example, it updates just one element -- in a big finite map. We don't want Hoopl to show the whole fact, -- and only the transfer function knows exactly what changed. type JoinFun a = Label -> OldFact a -> NewFact a -> (ChangeFlag, a) -- the label argument is for debugging purposes only newtype OldFact a = OldFact a newtype NewFact a = NewFact a data ChangeFlag = NoChange | SomeChange deriving (Eq, Ord) changeIf :: Bool -> ChangeFlag changeIf changed = if changed then SomeChange else NoChange -- | 'mkFactBase' creates a 'FactBase' from a list of ('Label', fact) -- pairs. If the same label appears more than once, the relevant facts -- are joined. mkFactBase :: DataflowLattice f -> [(Label, f)] -> FactBase f mkFactBase lattice = foldl add mapEmpty where add map (lbl, f) = mapInsert lbl newFact map where newFact = case mapLookup lbl map of Nothing -> f Just f' -> snd $ join lbl (OldFact f') (NewFact f) join = fact_join lattice ----------------------------------------------------------------------------- -- Analyze and rewrite forward: the interface ----------------------------------------------------------------------------- data FwdPass m n f = FwdPass { fp_lattice :: DataflowLattice f , fp_transfer :: FwdTransfer n f , fp_rewrite :: FwdRewrite m n f } newtype FwdTransfer n f = FwdTransfer3 { getFTransfer3 :: ( n C O -> f -> f , n O O -> f -> f , n O C -> f -> FactBase f ) } newtype FwdRewrite m n f -- see Note [Respects Fuel] = FwdRewrite3 { getFRewrite3 :: ( n C O -> f -> m (Maybe (Graph n C O, FwdRewrite m n f)) , n O O -> f -> m (Maybe (Graph n O O, FwdRewrite m n f)) , n O C -> f -> m (Maybe (Graph n O C, FwdRewrite m n f)) ) } wrapFR :: (forall e x. (n e x -> f -> m (Maybe (Graph n e x, FwdRewrite m n f ))) -> (n' e x -> f' -> m' (Maybe (Graph n' e x, FwdRewrite m' n' f'))) ) -- ^ This argument may assume that any function passed to it -- respects fuel, and it must return a result that respects fuel. -> FwdRewrite m n f -> FwdRewrite m' n' f' -- see Note [Respects Fuel] wrapFR wrap (FwdRewrite3 (f, m, l)) = FwdRewrite3 (wrap f, wrap m, wrap l) wrapFR2 :: (forall e x . (n1 e x -> f1 -> m1 (Maybe (Graph n1 e x, FwdRewrite m1 n1 f1))) -> (n2 e x -> f2 -> m2 (Maybe (Graph n2 e x, FwdRewrite m2 n2 f2))) -> (n3 e x -> f3 -> m3 (Maybe (Graph n3 e x, FwdRewrite m3 n3 f3))) ) -- ^ This argument may assume that any function passed to it -- respects fuel, and it must return a result that respects fuel. -> FwdRewrite m1 n1 f1 -> FwdRewrite m2 n2 f2 -> FwdRewrite m3 n3 f3 -- see Note [Respects Fuel] wrapFR2 wrap2 (FwdRewrite3 (f1, m1, l1)) (FwdRewrite3 (f2, m2, l2)) = FwdRewrite3 (wrap2 f1 f2, wrap2 m1 m2, wrap2 l1 l2) mkFTransfer3 :: (n C O -> f -> f) -> (n O O -> f -> f) -> (n O C -> f -> FactBase f) -> FwdTransfer n f mkFTransfer3 f m l = FwdTransfer3 (f, m, l) mkFTransfer :: (forall e x . n e x -> f -> Fact x f) -> FwdTransfer n f mkFTransfer f = FwdTransfer3 (f, f, f) -- | Functions passed to 'mkFRewrite3' should not be aware of the fuel supply. -- The result returned by 'mkFRewrite3' respects fuel. mkFRewrite3 :: FuelMonad m => (n C O -> f -> m (Maybe (Graph n C O))) -> (n O O -> f -> m (Maybe (Graph n O O))) -> (n O C -> f -> m (Maybe (Graph n O C))) -> FwdRewrite m n f mkFRewrite3 f m l = FwdRewrite3 (lift f, lift m, lift l) where lift rw node fact = liftM (liftM asRew) (withFuel =<< rw node fact) asRew g = (g, noFwdRewrite) noFwdRewrite :: Monad m => FwdRewrite m n f noFwdRewrite = FwdRewrite3 (noRewrite, noRewrite, noRewrite) noRewrite :: Monad m => a -> b -> m (Maybe c) noRewrite _ _ = return Nothing -- | Functions passed to 'mkFRewrite' should not be aware of the fuel supply. -- The result returned by 'mkFRewrite' respects fuel. mkFRewrite :: FuelMonad m => (forall e x . n e x -> f -> m (Maybe (Graph n e x))) -> FwdRewrite m n f mkFRewrite f = mkFRewrite3 f f f type family Fact x f :: * type instance Fact C f = FactBase f type instance Fact O f = f -- | if the graph being analyzed is open at the entry, there must -- be no other entry point, or all goes horribly wrong... analyzeAndRewriteFwd :: forall m n f e x entries. (CheckpointMonad m, NonLocal n, LabelsPtr entries) => FwdPass m n f -> MaybeC e entries -> Graph n e x -> Fact e f -> m (Graph n e x, FactBase f, MaybeO x f) analyzeAndRewriteFwd pass entries g f = do (rg, fout) <- arfGraph pass (fmap targetLabels entries) g f let (g', fb) = normalizeGraph rg return (g', fb, distinguishedExitFact g' fout) distinguishedExitFact :: forall n e x f . Graph n e x -> Fact x f -> MaybeO x f distinguishedExitFact g f = maybe g where maybe :: Graph n e x -> MaybeO x f maybe GNil = JustO f maybe (GUnit {}) = JustO f maybe (GMany _ _ x) = case x of NothingO -> NothingO JustO _ -> JustO f ---------------------------------------------------------------- -- Forward Implementation ---------------------------------------------------------------- type Entries e = MaybeC e [Label] arfGraph :: forall m n f e x . (NonLocal n, CheckpointMonad m) => FwdPass m n f -> Entries e -> Graph n e x -> Fact e f -> m (DG f n e x, Fact x f) arfGraph pass entries = graph where {- nested type synonyms would be so lovely here type ARF thing = forall e x . thing e x -> f -> m (DG f n e x, Fact x f) type ARFX thing = forall e x . thing e x -> Fact e f -> m (DG f n e x, Fact x f) -} graph :: Graph n e x -> Fact e f -> m (DG f n e x, Fact x f) -- @ start block.tex -2 block :: forall e x . Block n e x -> f -> m (DG f n e x, Fact x f) -- @ end block.tex -- @ start node.tex -4 node :: forall e x . (ShapeLifter e x) => n e x -> f -> m (DG f n e x, Fact x f) -- @ end node.tex -- @ start bodyfun.tex body :: [Label] -> LabelMap (Block n C C) -> Fact C f -> m (DG f n C C, Fact C f) -- @ end bodyfun.tex -- Outgoing factbase is restricted to Labels *not* in -- in the Body; the facts for Labels *in* -- the Body are in the 'DG f n C C' -- @ start cat.tex -2 cat :: forall e a x f1 f2 f3. (f1 -> m (DG f n e a, f2)) -> (f2 -> m (DG f n a x, f3)) -> (f1 -> m (DG f n e x, f3)) -- @ end cat.tex graph GNil = \f -> return (dgnil, f) graph (GUnit blk) = block blk graph (GMany e bdy x) = (e `ebcat` bdy) `cat` exit x where ebcat :: MaybeO e (Block n O C) -> Body n -> Fact e f -> m (DG f n e C, Fact C f) exit :: MaybeO x (Block n C O) -> Fact C f -> m (DG f n C x, Fact x f) exit (JustO blk) = arfx block blk exit NothingO = \fb -> return (dgnilC, fb) ebcat entry bdy = c entries entry where c :: MaybeC e [Label] -> MaybeO e (Block n O C) -> Fact e f -> m (DG f n e C, Fact C f) c NothingC (JustO entry) = block entry `cat` body (successors entry) bdy c (JustC entries) NothingO = body entries bdy c _ _ = error "bogus GADT pattern match failure" -- Lift from nodes to blocks -- @ start block.tex -2 block (BFirst n) = node n block (BMiddle n) = node n block (BLast n) = node n block (BCat b1 b2) = block b1 `cat` block b2 -- @ end block.tex block (BHead h n) = block h `cat` node n block (BTail n t) = node n `cat` block t block (BClosed h t)= block h `cat` block t -- @ start node.tex -4 node n f = do { grw <- frewrite pass n f ; case grw of Nothing -> return ( singletonDG f n , ftransfer pass n f ) Just (g, rw) -> let pass' = pass { fp_rewrite = rw } f' = fwdEntryFact n f in arfGraph pass' (fwdEntryLabel n) g f' } -- @ end node.tex -- | Compose fact transformers and concatenate the resulting -- rewritten graphs. {-# INLINE cat #-} -- @ start cat.tex -2 cat ft1 ft2 f = do { (g1,f1) <- ft1 f ; (g2,f2) <- ft2 f1 ; return (g1 `dgSplice` g2, f2) } -- @ end cat.tex arfx :: forall thing x . NonLocal thing => (thing C x -> f -> m (DG f n C x, Fact x f)) -> (thing C x -> Fact C f -> m (DG f n C x, Fact x f)) arfx arf thing fb = arf thing $ fromJust $ lookupFact (entryLabel thing) $ joinInFacts lattice fb where lattice = fp_lattice pass -- joinInFacts adds debugging information -- Outgoing factbase is restricted to Labels *not* in -- in the Body; the facts for Labels *in* -- the Body are in the 'DG f n C C' -- @ start bodyfun.tex body entries blockmap init_fbase = fixpoint Fwd lattice do_block blocks init_fbase where blocks = forwardBlockList entries blockmap lattice = fp_lattice pass do_block b fb = block b entryFact where entryFact = getFact lattice (entryLabel b) fb -- @ end bodyfun.tex -- Join all the incoming facts with bottom. -- We know the results _shouldn't change_, but the transfer -- functions might, for example, generate some debugging traces. joinInFacts :: DataflowLattice f -> FactBase f -> FactBase f joinInFacts (lattice @ DataflowLattice {fact_bot = bot, fact_join = fj}) fb = mkFactBase lattice $ map botJoin $ mapToList fb where botJoin (l, f) = (l, snd $ fj l (OldFact bot) (NewFact f)) forwardBlockList :: (NonLocal n, LabelsPtr entry) => entry -> Body n -> [Block n C C] -- This produces a list of blocks in order suitable for forward analysis, -- along with the list of Labels it may depend on for facts. forwardBlockList entries blks = postorder_dfs_from blks entries ----------------------------------------------------------------------------- -- Backward analysis and rewriting: the interface ----------------------------------------------------------------------------- data BwdPass m n f = BwdPass { bp_lattice :: DataflowLattice f , bp_transfer :: BwdTransfer n f , bp_rewrite :: BwdRewrite m n f } newtype BwdTransfer n f = BwdTransfer3 { getBTransfer3 :: ( n C O -> f -> f , n O O -> f -> f , n O C -> FactBase f -> f ) } newtype BwdRewrite m n f = BwdRewrite3 { getBRewrite3 :: ( n C O -> f -> m (Maybe (Graph n C O, BwdRewrite m n f)) , n O O -> f -> m (Maybe (Graph n O O, BwdRewrite m n f)) , n O C -> FactBase f -> m (Maybe (Graph n O C, BwdRewrite m n f)) ) } wrapBR :: (forall e x . Shape x -> (n e x -> Fact x f -> m (Maybe (Graph n e x, BwdRewrite m n f ))) -> (n' e x -> Fact x f' -> m' (Maybe (Graph n' e x, BwdRewrite m' n' f'))) ) -- ^ This argument may assume that any function passed to it -- respects fuel, and it must return a result that respects fuel. -> BwdRewrite m n f -> BwdRewrite m' n' f' -- see Note [Respects Fuel] wrapBR wrap (BwdRewrite3 (f, m, l)) = BwdRewrite3 (wrap Open f, wrap Open m, wrap Closed l) wrapBR2 :: (forall e x . Shape x -> (n1 e x -> Fact x f1 -> m1 (Maybe (Graph n1 e x, BwdRewrite m1 n1 f1))) -> (n2 e x -> Fact x f2 -> m2 (Maybe (Graph n2 e x, BwdRewrite m2 n2 f2))) -> (n3 e x -> Fact x f3 -> m3 (Maybe (Graph n3 e x, BwdRewrite m3 n3 f3)))) -- ^ This argument may assume that any function passed to it -- respects fuel, and it must return a result that respects fuel. -> BwdRewrite m1 n1 f1 -> BwdRewrite m2 n2 f2 -> BwdRewrite m3 n3 f3 -- see Note [Respects Fuel] wrapBR2 wrap2 (BwdRewrite3 (f1, m1, l1)) (BwdRewrite3 (f2, m2, l2)) = BwdRewrite3 (wrap2 Open f1 f2, wrap2 Open m1 m2, wrap2 Closed l1 l2) mkBTransfer3 :: (n C O -> f -> f) -> (n O O -> f -> f) -> (n O C -> FactBase f -> f) -> BwdTransfer n f mkBTransfer3 f m l = BwdTransfer3 (f, m, l) mkBTransfer :: (forall e x . n e x -> Fact x f -> f) -> BwdTransfer n f mkBTransfer f = BwdTransfer3 (f, f, f) -- | Functions passed to 'mkBRewrite3' should not be aware of the fuel supply. -- The result returned by 'mkBRewrite3' respects fuel. mkBRewrite3 :: FuelMonad m => (n C O -> f -> m (Maybe (Graph n C O))) -> (n O O -> f -> m (Maybe (Graph n O O))) -> (n O C -> FactBase f -> m (Maybe (Graph n O C))) -> BwdRewrite m n f mkBRewrite3 f m l = BwdRewrite3 (lift f, lift m, lift l) where lift rw node fact = liftM (liftM asRew) (withFuel =<< rw node fact) asRew g = (g, noBwdRewrite) noBwdRewrite :: Monad m => BwdRewrite m n f noBwdRewrite = BwdRewrite3 (noRewrite, noRewrite, noRewrite) -- | Functions passed to 'mkBRewrite' should not be aware of the fuel supply. -- The result returned by 'mkBRewrite' respects fuel. mkBRewrite :: FuelMonad m => (forall e x . n e x -> Fact x f -> m (Maybe (Graph n e x))) -> BwdRewrite m n f mkBRewrite f = mkBRewrite3 f f f ----------------------------------------------------------------------------- -- Backward implementation ----------------------------------------------------------------------------- arbGraph :: forall m n f e x . (NonLocal n, CheckpointMonad m) => BwdPass m n f -> Entries e -> Graph n e x -> Fact x f -> m (DG f n e x, Fact e f) arbGraph pass entries = graph where {- nested type synonyms would be so lovely here type ARB thing = forall e x . thing e x -> Fact x f -> m (DG f n e x, f) type ARBX thing = forall e x . thing e x -> Fact x f -> m (DG f n e x, Fact e f) -} graph :: Graph n e x -> Fact x f -> m (DG f n e x, Fact e f) block :: forall e x . Block n e x -> Fact x f -> m (DG f n e x, f) node :: forall e x . (ShapeLifter e x) => n e x -> Fact x f -> m (DG f n e x, f) body :: [Label] -> Body n -> Fact C f -> m (DG f n C C, Fact C f) cat :: forall e a x info info' info''. (info' -> m (DG f n e a, info'')) -> (info -> m (DG f n a x, info')) -> (info -> m (DG f n e x, info'')) graph GNil = \f -> return (dgnil, f) graph (GUnit blk) = block blk graph (GMany e bdy x) = (e `ebcat` bdy) `cat` exit x where ebcat :: MaybeO e (Block n O C) -> Body n -> Fact C f -> m (DG f n e C, Fact e f) exit :: MaybeO x (Block n C O) -> Fact x f -> m (DG f n C x, Fact C f) exit (JustO blk) = arbx block blk exit NothingO = \fb -> return (dgnilC, fb) ebcat entry bdy = c entries entry where c :: MaybeC e [Label] -> MaybeO e (Block n O C) -> Fact C f -> m (DG f n e C, Fact e f) c NothingC (JustO entry) = block entry `cat` body (successors entry) bdy c (JustC entries) NothingO = body entries bdy c _ _ = error "bogus GADT pattern match failure" -- Lift from nodes to blocks block (BFirst n) = node n block (BMiddle n) = node n block (BLast n) = node n block (BCat b1 b2) = block b1 `cat` block b2 block (BHead h n) = block h `cat` node n block (BTail n t) = node n `cat` block t block (BClosed h t)= block h `cat` block t node n f = do { bwdres <- brewrite pass n f ; case bwdres of Nothing -> return (singletonDG entry_f n, entry_f) where entry_f = btransfer pass n f Just (g, rw) -> do { let pass' = pass { bp_rewrite = rw } ; (g, f) <- arbGraph pass' (fwdEntryLabel n) g f ; return (g, bwdEntryFact (bp_lattice pass) n f)} } -- | Compose fact transformers and concatenate the resulting -- rewritten graphs. {-# INLINE cat #-} cat ft1 ft2 f = do { (g2,f2) <- ft2 f ; (g1,f1) <- ft1 f2 ; return (g1 `dgSplice` g2, f1) } arbx :: forall thing x . NonLocal thing => (thing C x -> Fact x f -> m (DG f n C x, f)) -> (thing C x -> Fact x f -> m (DG f n C x, Fact C f)) arbx arb thing f = do { (rg, f) <- arb thing f ; let fb = joinInFacts (bp_lattice pass) $ mapSingleton (entryLabel thing) f ; return (rg, fb) } -- joinInFacts adds debugging information -- Outgoing factbase is restricted to Labels *not* in -- in the Body; the facts for Labels *in* -- the Body are in the 'DG f n C C' body entries blockmap init_fbase = fixpoint Bwd (bp_lattice pass) do_block blocks init_fbase where blocks = backwardBlockList entries blockmap do_block b f = do (g, f) <- block b f return (g, mapSingleton (entryLabel b) f) backwardBlockList :: (LabelsPtr entries, NonLocal n) => entries -> Body n -> [Block n C C] -- This produces a list of blocks in order suitable for backward analysis, -- along with the list of Labels it may depend on for facts. backwardBlockList entries body = reverse $ forwardBlockList entries body {- The forward and backward cases are not dual. In the forward case, the entry points are known, and one simply traverses the body blocks from those points. In the backward case, something is known about the exit points, but this information is essentially useless, because we don't actually have a dual graph (that is, one with edges reversed) to compute with. (Even if we did have a dual graph, it would not avail us---a backward analysis must include reachable blocks that don't reach the exit, as in a procedure that loops forever and has side effects.) -} -- | if the graph being analyzed is open at the exit, I don't -- quite understand the implications of possible other exits analyzeAndRewriteBwd :: (CheckpointMonad m, NonLocal n, LabelsPtr entries) => BwdPass m n f -> MaybeC e entries -> Graph n e x -> Fact x f -> m (Graph n e x, FactBase f, MaybeO e f) analyzeAndRewriteBwd pass entries g f = do (rg, fout) <- arbGraph pass (fmap targetLabels entries) g f let (g', fb) = normalizeGraph rg return (g', fb, distinguishedEntryFact g' fout) distinguishedEntryFact :: forall n e x f . Graph n e x -> Fact e f -> MaybeO e f distinguishedEntryFact g f = maybe g where maybe :: Graph n e x -> MaybeO e f maybe GNil = JustO f maybe (GUnit {}) = JustO f maybe (GMany e _ _) = case e of NothingO -> NothingO JustO _ -> JustO f ----------------------------------------------------------------------------- -- fixpoint: finding fixed points ----------------------------------------------------------------------------- -- @ start txfb.tex data TxFactBase n f = TxFB { tfb_fbase :: FactBase f , tfb_rg :: DG f n C C -- Transformed blocks , tfb_cha :: ChangeFlag , tfb_lbls :: LabelSet } -- @ end txfb.tex -- See Note [TxFactBase invariants] -- @ start update.tex updateFact :: DataflowLattice f -> LabelSet -> Label -> f -> (ChangeFlag, FactBase f) -> (ChangeFlag, FactBase f) -- See Note [TxFactBase change flag] updateFact lat lbls lbl new_fact (cha, fbase) | NoChange <- cha2 = (cha, fbase) | lbl `setMember` lbls = (SomeChange, new_fbase) | otherwise = (cha, new_fbase) where (cha2, res_fact) -- Note [Unreachable blocks] = case lookupFact lbl fbase of Nothing -> (SomeChange, new_fact_debug) -- Note [Unreachable blocks] Just old_fact -> join old_fact where join old_fact = fact_join lat lbl (OldFact old_fact) (NewFact new_fact) (_, new_fact_debug) = join (fact_bot lat) new_fbase = mapInsert lbl res_fact fbase -- @ end update.tex {- -- this doesn't work because it can't be implemented class Monad m => FixpointMonad m where observeChangedFactBase :: m (Maybe (FactBase f)) -> Maybe (FactBase f) -} -- @ start fptype.tex data Direction = Fwd | Bwd fixpoint :: forall m n f. (CheckpointMonad m, NonLocal n) => Direction -> DataflowLattice f -> (Block n C C -> Fact C f -> m (DG f n C C, Fact C f)) -> [Block n C C] -> (Fact C f -> m (DG f n C C, Fact C f)) -- @ end fptype.tex -- @ start fpimp.tex fixpoint direction lat do_block blocks init_fbase = do { tx_fb <- loop init_fbase ; return (tfb_rg tx_fb, map (fst . fst) tagged_blocks `mapDeleteList` tfb_fbase tx_fb ) } -- The successors of the Graph are the the Labels -- for which we have facts and which are *not* in -- the blocks of the graph where tagged_blocks = map tag blocks is_fwd = case direction of { Fwd -> True; Bwd -> False } tag b = ((entryLabel b, b), if is_fwd then [entryLabel b] else successors b) -- 'tag' adds the in-labels of the block; -- see Note [TxFactBase invairants] tx_blocks :: [((Label, Block n C C), [Label])] -- I do not understand this type -> TxFactBase n f -> m (TxFactBase n f) tx_blocks [] tx_fb = return tx_fb tx_blocks (((lbl,blk), in_lbls):bs) tx_fb = tx_block lbl blk in_lbls tx_fb >>= tx_blocks bs -- "in_lbls" == Labels the block may -- _depend_ upon for facts tx_block :: Label -> Block n C C -> [Label] -> TxFactBase n f -> m (TxFactBase n f) tx_block lbl blk in_lbls tx_fb@(TxFB { tfb_fbase = fbase, tfb_lbls = lbls , tfb_rg = blks, tfb_cha = cha }) | is_fwd && not (lbl `mapMember` fbase) = return (tx_fb {tfb_lbls = lbls'}) -- Note [Unreachable blocks] | otherwise = do { (rg, out_facts) <- do_block blk fbase ; let (cha', fbase') = mapFoldWithKey (updateFact lat lbls) (cha,fbase) out_facts ; return $ TxFB { tfb_lbls = lbls' , tfb_rg = rg `dgSplice` blks , tfb_fbase = fbase' , tfb_cha = cha' } } where lbls' = lbls `setUnion` setFromList in_lbls loop :: FactBase f -> m (TxFactBase n f) loop fbase = do { s <- checkpoint ; let init_tx = TxFB { tfb_fbase = fbase , tfb_cha = NoChange , tfb_rg = dgnilC , tfb_lbls = setEmpty } ; tx_fb <- tx_blocks tagged_blocks init_tx ; case tfb_cha tx_fb of NoChange -> return tx_fb SomeChange -> do { restart s ; loop (tfb_fbase tx_fb) } } -- @ end fpimp.tex {- Note [TxFactBase invariants] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ The TxFactBase is used only during a fixpoint iteration (or "sweep"), and accumulates facts (and the transformed code) during the fixpoint iteration. * tfb_fbase increases monotonically, across all sweeps * At the beginning of each sweep tfb_cha = NoChange tfb_lbls = {} * During each sweep we process each block in turn. Processing a block is done thus: 1. Read from tfb_fbase the facts for its entry label (forward) or successors labels (backward) 2. Transform those facts into new facts for its successors (forward) or entry label (backward) 3. Augment tfb_fbase with that info We call the labels read in step (1) the "in-labels" of the sweep * The field tfb_lbls is the set of in-labels of all blocks that have been processed so far this sweep, including the block that is currently being processed. tfb_lbls is initialised to {}. It is a subset of the Labels of the *original* (not transformed) blocks. * The tfb_cha field is set to SomeChange iff we decide we need to perform another iteration of the fixpoint loop. It is initialsed to NoChange. Specifically, we set tfb_cha to SomeChange in step (3) iff (a) The fact in tfb_fbase for a block L changes (b) L is in tfb_lbls Reason: until a label enters the in-labels its accumuated fact in tfb_fbase has not been read, hence cannot affect the outcome Note [Unreachable blocks] ~~~~~~~~~~~~~~~~~~~~~~~~~ A block that is not in the domain of tfb_fbase is "currently unreachable". A currently-unreachable block is not even analyzed. Reason: consider constant prop and this graph, with entry point L1: L1: x:=3; goto L4 L2: x:=4; goto L4 L4: if x>3 goto L2 else goto L5 Here L2 is actually unreachable, but if we process it with bottom input fact, we'll propagate (x=4) to L4, and nuke the otherwise-good rewriting of L4. * If a currently-unreachable block is not analyzed, then its rewritten graph will not be accumulated in tfb_rg. And that is good: unreachable blocks simply do not appear in the output. * Note that clients must be careful to provide a fact (even if bottom) for each entry point. Otherwise useful blocks may be garbage collected. * Note that updateFact must set the change-flag if a label goes from not-in-fbase to in-fbase, even if its fact is bottom. In effect the real fact lattice is UNR bottom the points above bottom * Even if the fact is going from UNR to bottom, we still call the client's fact_join function because it might give the client some useful debugging information. * All of this only applies for *forward* fixpoints. For the backward case we must treat every block as reachable; it might finish with a 'return', and therefore have no successors, for example. -} ----------------------------------------------------------------------------- -- DG: an internal data type for 'decorated graphs' -- TOTALLY internal to Hoopl; each block is decorated with a fact ----------------------------------------------------------------------------- -- @ start dg.tex type Graph = Graph' Block type DG f = Graph' (DBlock f) data DBlock f n e x = DBlock f (Block n e x) -- ^ block decorated with fact -- @ end dg.tex instance NonLocal n => NonLocal (DBlock f n) where entryLabel (DBlock _ b) = entryLabel b successors (DBlock _ b) = successors b --- constructors dgnil :: DG f n O O dgnilC :: DG f n C C dgSplice :: NonLocal n => DG f n e a -> DG f n a x -> DG f n e x ---- observers type GraphWithFacts n f e x = (Graph n e x, FactBase f) -- A Graph together with the facts for that graph -- The domains of the two maps should be identical normalizeGraph :: forall n f e x . NonLocal n => DG f n e x -> GraphWithFacts n f e x normalizeGraph g = (graphMapBlocks dropFact g, facts g) where dropFact (DBlock _ b) = b facts :: DG f n e x -> FactBase f facts GNil = noFacts facts (GUnit _) = noFacts facts (GMany _ body exit) = bodyFacts body `mapUnion` exitFacts exit exitFacts :: MaybeO x (DBlock f n C O) -> FactBase f exitFacts NothingO = noFacts exitFacts (JustO (DBlock f b)) = mapSingleton (entryLabel b) f bodyFacts :: LabelMap (DBlock f n C C) -> FactBase f bodyFacts body = mapFold f noFacts body where f (DBlock f b) fb = mapInsert (entryLabel b) f fb --- implementation of the constructors (boring) dgnil = GNil dgnilC = GMany NothingO emptyBody NothingO dgSplice = U.splice fzCat where fzCat (DBlock f b1) (DBlock _ b2) = DBlock f (b1 `U.cat` b2) ---------------------------------------------------------------- -- Utilities ---------------------------------------------------------------- -- Lifting based on shape: -- - from nodes to blocks -- - from facts to fact-like things -- Lowering back: -- - from fact-like things to facts -- Note that the latter two functions depend only on the entry shape. -- @ start node.tex class ShapeLifter e x where singletonDG :: f -> n e x -> DG f n e x fwdEntryFact :: NonLocal n => n e x -> f -> Fact e f fwdEntryLabel :: NonLocal n => n e x -> MaybeC e [Label] ftransfer :: FwdPass m n f -> n e x -> f -> Fact x f frewrite :: FwdPass m n f -> n e x -> f -> m (Maybe (Graph n e x, FwdRewrite m n f)) -- @ end node.tex bwdEntryFact :: NonLocal n => DataflowLattice f -> n e x -> Fact e f -> f btransfer :: BwdPass m n f -> n e x -> Fact x f -> f brewrite :: BwdPass m n f -> n e x -> Fact x f -> m (Maybe (Graph n e x, BwdRewrite m n f)) instance ShapeLifter C O where singletonDG f = gUnitCO . DBlock f . BFirst fwdEntryFact n f = mapSingleton (entryLabel n) f bwdEntryFact lat n fb = getFact lat (entryLabel n) fb ftransfer (FwdPass {fp_transfer = FwdTransfer3 (ft, _, _)}) n f = ft n f btransfer (BwdPass {bp_transfer = BwdTransfer3 (bt, _, _)}) n f = bt n f frewrite (FwdPass {fp_rewrite = FwdRewrite3 (fr, _, _)}) n f = fr n f brewrite (BwdPass {bp_rewrite = BwdRewrite3 (br, _, _)}) n f = br n f fwdEntryLabel n = JustC [entryLabel n] instance ShapeLifter O O where singletonDG f = gUnitOO . DBlock f . BMiddle fwdEntryFact _ f = f bwdEntryFact _ _ f = f ftransfer (FwdPass {fp_transfer = FwdTransfer3 (_, ft, _)}) n f = ft n f btransfer (BwdPass {bp_transfer = BwdTransfer3 (_, bt, _)}) n f = bt n f frewrite (FwdPass {fp_rewrite = FwdRewrite3 (_, fr, _)}) n f = fr n f brewrite (BwdPass {bp_rewrite = BwdRewrite3 (_, br, _)}) n f = br n f fwdEntryLabel _ = NothingC instance ShapeLifter O C where singletonDG f = gUnitOC . DBlock f . BLast fwdEntryFact _ f = f bwdEntryFact _ _ f = f ftransfer (FwdPass {fp_transfer = FwdTransfer3 (_, _, ft)}) n f = ft n f btransfer (BwdPass {bp_transfer = BwdTransfer3 (_, _, bt)}) n f = bt n f frewrite (FwdPass {fp_rewrite = FwdRewrite3 (_, _, fr)}) n f = fr n f brewrite (BwdPass {bp_rewrite = BwdRewrite3 (_, _, br)}) n f = br n f fwdEntryLabel _ = NothingC -- Fact lookup: the fact `orelse` bottom getFact :: DataflowLattice f -> Label -> FactBase f -> f getFact lat l fb = case lookupFact l fb of Just f -> f Nothing -> fact_bot lat {- Note [Respects fuel] ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -} -- $fuel -- A value of type 'FwdRewrite' or 'BwdRewrite' /respects fuel/ if -- any function contained within the value satisfies the following properties: -- -- * When fuel is exhausted, it always returns 'Nothing'. -- -- * When it returns @Just g rw@, it consumes /exactly/ one unit -- of fuel, and new rewrite 'rw' also respects fuel. -- -- Provided that functions passed to 'mkFRewrite', 'mkFRewrite3', -- 'mkBRewrite', and 'mkBRewrite3' are not aware of the fuel supply, -- the results respect fuel. -- -- It is an /unchecked/ run-time error for the argument passed to 'wrapFR', -- 'wrapFR2', 'wrapBR', or 'warpBR2' to return a function that does not respect fuel.