{-# LANGUAGE RankNTypes, ScopedTypeVariables, GADTs, EmptyDataDecls, PatternGuards, TypeFamilies #-} {-# OPTIONS_GHC -fno-warn-incomplete-patterns #-} -- bug in GHC {- Notes about the genesis of Hoopl7 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Hoopl7 has the following major chages a) GMany has symmetric entry and exit b) GMany closed-entry does not record a BlockId c) GMany open-exit does not record a BlockId d) The body of a GMany is called Body e) A Body is just a list of blocks, not a map. I've argued elsewhere that this is consistent with (c) A consequence is that Graph is no longer an instance of Edges, but nevertheless I managed to keep the ARF and ARB signatures nice and uniform. This was made possible by * FwdTransfer looks like this: type FwdTransfer n f = forall e x. n e x -> Fact e f -> Fact x f type family Fact x f :: * type instance Fact C f = FactBase f type instance Fact O f = f Note that the incoming fact is a Fact (not just 'f' as in Hoopl5,6). It's up to the *transfer function* to look up the appropriate fact in the FactBase for a closed-entry node. Example: constProp (Label l) fb = lookupFact fb l That is how Hoopl can avoid having to know the block-id for the first node: it defers to the client. [Side note: that means the client must know about bottom, in case the looupFact returns Nothing] * Note also that FwdTransfer *returns* a Fact too; that is, the types in both directions are symmetrical. Previously we returned a [(BlockId,f)] but I could not see how to make everything line up if we do this. Indeed, the main shortcoming of Hoopl7 is that we are more or less forced into this uniform representation of the facts flowing into or out of a closed node/block/graph, whereas previously we had more flexibility. In exchange the code is neater, with fewer distinct types. And morally a FactBase is equivalent to [(BlockId,f)] and nearly equivalent to (BlockId -> f). * I've realised that forwardBlockList and backwardBlockList both need (Edges n), and that goes everywhere. * I renamed BlockId to Label -} module Compiler.Hoopl.Dataflow ( DataflowLattice(..), JoinFun, OldFact(..), NewFact(..) , ChangeFlag(..), changeIf , FwdPass(..), FwdTransfer, FwdRewrite, FwdRes(..) , BwdPass(..), BwdTransfer, BwdRewrite, BwdRes(..) , Fact , analyzeAndRewriteFwd, analyzeAndRewriteBwd , analyzeAndRewriteFwd', analyzeAndRewriteBwd' ) where import Compiler.Hoopl.Fuel import Compiler.Hoopl.Graph import qualified Compiler.Hoopl.GraphUtil as U import Compiler.Hoopl.Label import Compiler.Hoopl.MkGraph (AGraph, graphOfAGraph) import Compiler.Hoopl.Util ----------------------------------------------------------------------------- -- DataflowLattice ----------------------------------------------------------------------------- data DataflowLattice a = DataflowLattice { fact_name :: String -- Documentation , fact_bot :: a -- Lattice bottom element , fact_extend :: JoinFun a -- Lattice join plus change flag -- (changes iff result > old fact) , fact_do_logging :: Bool -- log changes } 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 ----------------------------------------------------------------------------- -- Analyze and rewrite forward: the interface ----------------------------------------------------------------------------- data FwdPass n f = FwdPass { fp_lattice :: DataflowLattice f , fp_transfer :: FwdTransfer n f , fp_rewrite :: FwdRewrite n f } type FwdTransfer n f = forall e x. n e x -> Fact e f -> Fact x f type FwdRewrite n f = forall e x. n e x -> Fact e f -> Maybe (FwdRes n f e x) data FwdRes n f e x = FwdRes (AGraph n e x) (FwdRewrite n f) -- result of a rewrite is a new graph and a (possibly) new rewrite function type family Fact x f :: * type instance Fact C f = FactBase f type instance Fact O f = f analyzeAndRewriteFwd :: forall n f. Edges n => FwdPass n f -> Body n -> FactBase f -> FuelMonad (Body n, FactBase f) analyzeAndRewriteFwd pass body facts = do { (rg, _) <- arfBody pass body facts ; return (normaliseBody rg) } -- | if the graph being analyzed is open at the entry, there must -- be no other entry point, or all goes horribly wrong... analyzeAndRewriteFwd' :: forall n f e x. Edges n => FwdPass n f -> Graph n e x -> Fact e f -> FuelMonad (Graph n e x, FactBase f, MaybeO x f) analyzeAndRewriteFwd' pass g f = do (rg, fout) <- arfGraph pass g f let (g', fb) = normalizeGraph g 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 normalizeGraph :: Edges n => Graph n e x -> RG n f e x -> GraphWithFacts n f e x normalizeGraph GNil = normOO normalizeGraph (GUnit {}) = normOO normalizeGraph (GMany NothingO _ NothingO) = normCC normalizeGraph (GMany (JustO _) _ NothingO) = normOC normalizeGraph (GMany NothingO _ (JustO _)) = normCO normalizeGraph (GMany (JustO _) _ (JustO _)) = normOO ---------------------------------------------------------------- -- Forward Implementation ---------------------------------------------------------------- type ARF thing n = forall f e x. FwdPass n f -> thing e x -> Fact e f -> FuelMonad (RG n f e x, Fact x f) arfNode :: Edges n => ARF n n arfNode pass node f = do { mb_g <- withFuel (fp_rewrite pass node f) ; case mb_g of Nothing -> return (RGUnit f (BUnit node), fp_transfer pass node f) Just (FwdRes ag rw) -> do { g <- graphOfAGraph ag ; let pass' = pass { fp_rewrite = rw } ; arfGraph pass' g f } } arfBlock :: Edges n => ARF (Block n) n -- Lift from nodes to blocks arfBlock pass (BUnit node) f = arfNode pass node f arfBlock pass (BCat hd mids) f = do { (g1,f1) <- arfBlock pass hd f ; (g2,f2) <- arfBlock pass mids f1 ; return (g1 `RGCatO` g2, f2) } arfBody :: Edges n => FwdPass n f -> Body n -> FactBase f -> FuelMonad (RG n f C C, FactBase f) -- Outgoing factbase is restricted to Labels *not* in -- in the Body; the facts for Labels *in* -- the Body are in the BodyWithFacts arfBody pass blocks init_fbase = fixpoint True (fp_lattice pass) (arfBlock pass) init_fbase $ forwardBlockList (factBaseLabels init_fbase) blocks arfGraph :: Edges n => ARF (Graph n) n -- Lift from blocks to graphs arfGraph _ GNil f = return (RGNil, f) arfGraph pass (GUnit blk) f = arfBlock pass blk f arfGraph pass (GMany NothingO body NothingO) f = do { (body', fb) <- arfBody pass body f ; return (body', fb) } arfGraph pass (GMany NothingO body (JustO exit)) f = do { (body', fb) <- arfBody pass body f ; (exit', fx) <- arfBlock pass exit fb ; return (body' `RGCatC` exit', fx) } arfGraph pass (GMany (JustO entry) body NothingO) f = do { (entry', fe) <- arfBlock pass entry f ; (body', fb) <- arfBody pass body fe ; return (entry' `RGCatC` body', fb) } arfGraph pass (GMany (JustO entry) body (JustO exit)) f = do { (entry', fe) <- arfBlock pass entry f ; (body', fb) <- arfBody pass body fe ; (exit', fx) <- arfBlock pass exit fb ; return (entry' `RGCatC` body' `RGCatC` exit', fx) } forwardBlockList :: (Edges 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 (bodyMap blks) entries ----------------------------------------------------------------------------- -- Backward analysis and rewriting: the interface ----------------------------------------------------------------------------- data BwdPass n f = BwdPass { bp_lattice :: DataflowLattice f , bp_transfer :: BwdTransfer n f , bp_rewrite :: BwdRewrite n f } type BwdTransfer n f = forall e x. n e x -> Fact x f -> Fact e f type BwdRewrite n f = forall e x. n e x -> Fact x f -> Maybe (BwdRes n f e x) data BwdRes n f e x = BwdRes (AGraph n e x) (BwdRewrite n f) ----------------------------------------------------------------------------- -- Backward implementation ----------------------------------------------------------------------------- type ARB thing n = forall f e x. BwdPass n f -> thing e x -> Fact x f -> FuelMonad (RG n f e x, Fact e f) arbNode :: Edges n => ARB n n -- Lifts (BwdTransfer,BwdRewrite) to ARB_Node; -- this time we do rewriting as well. -- The ARB_Graph parameters specifies what to do with the rewritten graph arbNode pass node f = do { mb_g <- withFuel (bp_rewrite pass node f) ; case mb_g of Nothing -> return (RGUnit entry_f (BUnit node), entry_f) where entry_f = bp_transfer pass node f Just (BwdRes ag rw) -> do { g <- graphOfAGraph ag ; let pass' = pass { bp_rewrite = rw } ; arbGraph pass' g f} } arbBlock :: Edges n => ARB (Block n) n -- Lift from nodes to blocks arbBlock pass (BUnit node) f = arbNode pass node f arbBlock pass (BCat b1 b2) f = do { (g2,f2) <- arbBlock pass b2 f ; (g1,f1) <- arbBlock pass b1 f2 ; return (g1 `RGCatO` g2, f1) } arbBody :: Edges n => BwdPass n f -> Body n -> FactBase f -> FuelMonad (RG n f C C, FactBase f) arbBody pass blocks init_fbase = fixpoint False (bp_lattice pass) (arbBlock pass) init_fbase $ backwardBlockList blocks arbGraph :: Edges n => ARB (Graph n) n arbGraph _ GNil f = return (RGNil, f) arbGraph pass (GUnit blk) f = arbBlock pass blk f arbGraph pass (GMany NothingO body NothingO) f = do { (body', fb) <- arbBody pass body f ; return (body', fb) } arbGraph pass (GMany NothingO body (JustO exit)) f = do { (exit', fx) <- arbBlock pass exit f ; (body', fb) <- arbBody pass body fx ; return (body' `RGCatC` exit', fb) } arbGraph pass (GMany (JustO entry) body NothingO) f = do { (body', fb) <- arbBody pass body f ; (entry', fe) <- arbBlock pass entry fb ; return (entry' `RGCatC` body', fe) } arbGraph pass (GMany (JustO entry) body (JustO exit)) f = do { (exit', fx) <- arbBlock pass exit f ; (body', fb) <- arbBody pass body fx ; (entry', fe) <- arbBlock pass entry fb ; return (entry' `RGCatC` body' `RGCatC` exit', fe) } backwardBlockList :: Edges n => 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 body = reachable ++ missing where reachable = reverse $ forwardBlockList entries body entries = externalEntryLabels body all = bodyList body missingLabels = mkLabelSet (map fst all) `minusLabelSet` mkLabelSet (map entryLabel reachable) missing = map snd $ filter (flip elemLabelSet missingLabels . fst) all {- The forward and backward dataflow analyses now use postorder depth-first order for faster convergence. 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.) Since in the general case, no information is available about entry points, I have put in a horrible hack. First, I assume that every label defined but not used is an entry point. Then, because an entry point might also be a loop header, I add, in arbitrary order, all the remaining "missing" blocks. Needless to say, I am not pleased. I am not satisfied. I am not Senator Morgan. Wait! I believe that the Right Thing here is to require that anyone wishing to analyze a graph closed at the entry provide a way of determining the entry points, if any, of that graph. This requirement can apply equally to forward and backward analyses; I believe that using the input FactBase to determine the entry points of a closed graph is *also* a hack. NR -} analyzeAndRewriteBwd :: forall n f. Edges n => BwdPass n f -> Body n -> FactBase f -> FuelMonad (Body n, FactBase f) analyzeAndRewriteBwd pass body facts = do { (rg, _) <- arbBody pass body facts ; return (normaliseBody rg) } -- | if the graph being analyzed is open at the exit, I don't -- quite understand the implications of possible other exits analyzeAndRewriteBwd' :: forall n f e x. Edges n => BwdPass n f -> Graph n e x -> Fact x f -> FuelMonad (Graph n e x, FactBase f, MaybeO e f) analyzeAndRewriteBwd' pass g f = do (rg, fout) <- arbGraph pass g f let (g', fb) = normalizeGraph g 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 ----------------------------------------------------------------------------- data TxFactBase n f = TxFB { tfb_fbase :: FactBase f , tfb_rg :: RG n f C C -- Transformed blocks , tfb_cha :: ChangeFlag , tfb_lbls :: LabelSet } -- Note [TxFactBase change flag] -- ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- Set the tfb_cha flag iff -- (a) the fact in tfb_fbase for or a block L changes -- (b) L is in tfb_lbls. -- The tfb_lbls are all Labels of the *original* -- (not transformed) blocks 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 `elemLabelSet` lbls = (SomeChange, new_fbase) | otherwise = (cha, new_fbase) where (cha2, res_fact) -- Note [Unreachable blocks] = case lookupFact fbase lbl of Nothing -> (SomeChange, snd $ join $ fact_bot lat) -- Note [Unreachable blocks] Just old_fact -> join old_fact where join old_fact = fact_extend lat lbl (OldFact old_fact) (NewFact new_fact) new_fbase = extendFactBase fbase lbl res_fact fixpoint :: forall n f. Edges n => Bool -- Going forwards? -> DataflowLattice f -> (Block n C C -> FactBase f -> FuelMonad (RG n f C C, FactBase f)) -> FactBase f -> [Block n C C] -> FuelMonad (RG n f C C, FactBase f) fixpoint is_fwd lat do_block init_fbase untagged_blocks = do { fuel <- getFuel ; tx_fb <- loop fuel init_fbase ; return (tfb_rg tx_fb, tfb_fbase tx_fb `delFromFactBase` map fst blocks) } -- The successors of the Graph are the the Labels for which -- we have facts, that are *not* in the blocks of the graph where blocks = map tag untagged_blocks where tag b = ((entryLabel b, b), if is_fwd then [entryLabel b] else successors b) tx_blocks :: [((Label, Block n C C), [Label])] -- I do not understand this type -> TxFactBase n f -> FuelMonad (TxFactBase n f) tx_blocks [] tx_fb = return tx_fb tx_blocks (((lbl,blk), deps):bs) tx_fb = tx_block lbl blk deps tx_fb >>= tx_blocks bs -- "deps" == Labels the block may _depend_ upon for facts tx_block :: Label -> Block n C C -> [Label] -> TxFactBase n f -> FuelMonad (TxFactBase n f) tx_block lbl blk deps tx_fb@(TxFB { tfb_fbase = fbase, tfb_lbls = lbls , tfb_rg = blks, tfb_cha = cha }) | is_fwd && not (lbl `elemFactBase` fbase) = return tx_fb {tfb_lbls = lbls `unionLabelSet` mkLabelSet deps} -- Note [Unreachable blocks] | otherwise = do { (rg, out_facts) <- do_block blk fbase ; let (cha',fbase') = foldr (updateFact lat lbls) (cha,fbase) (factBaseList out_facts) lbls' = lbls `unionLabelSet` mkLabelSet deps ; return (TxFB { tfb_lbls = lbls' , tfb_rg = rg `RGCatC` blks , tfb_fbase = fbase', tfb_cha = cha' }) } loop :: Fuel -> FactBase f -> FuelMonad (TxFactBase n f) loop fuel fbase = do { let init_tx_fb = TxFB { tfb_fbase = fbase , tfb_cha = NoChange , tfb_rg = RGNil , tfb_lbls = emptyLabelSet } ; tx_fb <- tx_blocks blocks init_tx_fb ; case tfb_cha tx_fb of NoChange -> return tx_fb SomeChange -> do { setFuel fuel ; loop fuel (tfb_fbase tx_fb) } } {- 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_extend 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. -} ----------------------------------------------------------------------------- -- RG: an internal data type for graphs under construction -- TOTALLY internal to Hoopl ----------------------------------------------------------------------------- -- this type exists because we have not yet found a way to write arfNode -- to return a Graph; the invariants of Graph seem too strong data RG n f e x where RGNil :: RG n f a a RGUnit :: Fact e f -> Block n e x -> RG n f e x RGCatO :: RG n f e O -> RG n f O x -> RG n f e x RGCatC :: RG n f e C -> RG n f C x -> RG n f e x type BodyWithFacts n f = (Body n, FactBase f) 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 normaliseBody :: Edges n => RG n f C C -> BodyWithFacts n f normaliseBody rg = (body, fact_base) where (GMany _ body _, fact_base) = normCC rg normOO :: Edges n => RG n f O O -> GraphWithFacts n f O O normOO RGNil = (GNil, noFacts) normOO (RGUnit _ b) = (GUnit b, noFacts) normOO (RGCatO g1 g2) = normOO g1 `gwfCat` normOO g2 normOO (RGCatC g1 g2) = normOC g1 `gwfCat` normCO g2 normOC :: Edges n => RG n f O C -> GraphWithFacts n f O C normOC (RGUnit _ b) = (GMany (JustO b) BodyEmpty NothingO, noFacts) normOC (RGCatO g1 g2) = normOO g1 `gwfCat` normOC g2 normOC (RGCatC g1 g2) = normOC g1 `gwfCat` normCC g2 normCO :: Edges n => RG n f C O -> GraphWithFacts n f C O normCO (RGUnit f b) = (GMany NothingO BodyEmpty (JustO b), unitFact l f) where l = entryLabel b normCO (RGCatO g1 g2) = normCO g1 `gwfCat` normOO g2 normCO (RGCatC g1 g2) = normCC g1 `gwfCat` normCO g2 normCC :: Edges n => RG n f C C -> GraphWithFacts n f C C normCC RGNil = (GMany NothingO BodyEmpty NothingO, noFacts) normCC (RGUnit f b) = (GMany NothingO (BodyUnit b) NothingO, unitFact l f) where l = entryLabel b normCC (RGCatO g1 g2) = normCO g1 `gwfCat` normOC g2 normCC (RGCatC g1 g2) = normCC g1 `gwfCat` normCC g2 gwfCat :: Edges n => GraphWithFacts n f e a -> GraphWithFacts n f a x -> GraphWithFacts n f e x gwfCat (g1, fb1) (g2, fb2) = (g1 `U.gSplice` g2, fb1 `unionFactBase` fb2) {- bwfUnion :: BodyWithFacts n f -> BodyWithFacts n f -> BodyWithFacts n f bwfUnion (bg1, fb1) (bg2, fb2) = (bg1 `BodyCat` bg2, fb1 `unionFactBase` fb2) -}