{-# LANGUAGE FlexibleInstances #-} {-# LANGUAGE GADTs #-} {-# LANGUAGE RankNTypes #-} {-# LANGUAGE ScopedTypeVariables #-} {-# LANGUAGE TypeFamilies #-} module Hoopl.Graph ( Body , Graph , Graph'(..) , NonLocal(..) , addBlock , bodyList , emptyBody , labelsDefined , mapGraph , mapGraphBlocks , postorder_dfs_from ) where import GhcPrelude import Hoopl.Label import Hoopl.Block import Hoopl.Collections -- | A (possibly empty) collection of closed/closed blocks type Body n = LabelMap (Block n C C) -- | @Body@ abstracted over @block@ type Body' block (n :: * -> * -> *) = LabelMap (block n C C) ------------------------------- -- | Gives access to the anchor points for -- nonlocal edges as well as the edges themselves class NonLocal thing where entryLabel :: thing C x -> Label -- ^ The label of a first node or block successors :: thing e C -> [Label] -- ^ Gives control-flow successors instance NonLocal n => NonLocal (Block n) where entryLabel (BlockCO f _) = entryLabel f entryLabel (BlockCC f _ _) = entryLabel f successors (BlockOC _ n) = successors n successors (BlockCC _ _ n) = successors n emptyBody :: Body' block n emptyBody = mapEmpty bodyList :: Body' block n -> [(Label,block n C C)] bodyList body = mapToList body addBlock :: NonLocal thing => thing C C -> LabelMap (thing C C) -> LabelMap (thing C C) addBlock b body | mapMember lbl body = error $ "duplicate label " ++ show lbl ++ " in graph" | otherwise = mapInsert lbl b body where lbl = entryLabel b -- --------------------------------------------------------------------------- -- Graph -- | A control-flow graph, which may take any of four shapes (O/O, -- O/C, C/O, C/C). A graph open at the entry has a single, -- distinguished, anonymous entry point; if a graph is closed at the -- entry, its entry point(s) are supplied by a context. type Graph = Graph' Block -- | @Graph'@ is abstracted over the block type, so that we can build -- graphs of annotated blocks for example (Compiler.Hoopl.Dataflow -- needs this). data Graph' block (n :: * -> * -> *) e x where GNil :: Graph' block n O O GUnit :: block n O O -> Graph' block n O O GMany :: MaybeO e (block n O C) -> Body' block n -> MaybeO x (block n C O) -> Graph' block n e x -- ----------------------------------------------------------------------------- -- Mapping over graphs -- | Maps over all nodes in a graph. mapGraph :: (forall e x. n e x -> n' e x) -> Graph n e x -> Graph n' e x mapGraph f = mapGraphBlocks (mapBlock f) -- | Function 'mapGraphBlocks' enables a change of representation of blocks, -- nodes, or both. It lifts a polymorphic block transform into a polymorphic -- graph transform. When the block representation stabilizes, a similar -- function should be provided for blocks. mapGraphBlocks :: forall block n block' n' e x . (forall e x . block n e x -> block' n' e x) -> (Graph' block n e x -> Graph' block' n' e x) mapGraphBlocks f = map where map :: Graph' block n e x -> Graph' block' n' e x map GNil = GNil map (GUnit b) = GUnit (f b) map (GMany e b x) = GMany (fmap f e) (mapMap f b) (fmap f x) -- ----------------------------------------------------------------------------- -- Extracting Labels from graphs labelsDefined :: forall block n e x . NonLocal (block n) => Graph' block n e x -> LabelSet labelsDefined GNil = setEmpty labelsDefined (GUnit{}) = setEmpty labelsDefined (GMany _ body x) = mapFoldWithKey addEntry (exitLabel x) body where addEntry :: forall a. ElemOf LabelSet -> a -> LabelSet -> LabelSet addEntry label _ labels = setInsert label labels exitLabel :: MaybeO x (block n C O) -> LabelSet exitLabel NothingO = setEmpty exitLabel (JustO b) = setSingleton (entryLabel b) ---------------------------------------------------------------- class LabelsPtr l where targetLabels :: l -> [Label] instance NonLocal n => LabelsPtr (n e C) where targetLabels n = successors n instance LabelsPtr Label where targetLabels l = [l] instance LabelsPtr LabelSet where targetLabels = setElems instance LabelsPtr l => LabelsPtr [l] where targetLabels = concatMap targetLabels -- | This is the most important traversal over this data structure. It drops -- unreachable code and puts blocks in an order that is good for solving forward -- dataflow problems quickly. The reverse order is good for solving backward -- dataflow problems quickly. The forward order is also reasonably good for -- emitting instructions, except that it will not usually exploit Forrest -- Baskett's trick of eliminating the unconditional branch from a loop. For -- that you would need a more serious analysis, probably based on dominators, to -- identify loop headers. -- -- The ubiquity of 'postorder_dfs' is one reason for the ubiquity of the 'LGraph' -- representation, when for most purposes the plain 'Graph' representation is -- more mathematically elegant (but results in more complicated code). -- -- Here's an easy way to go wrong! Consider -- @ -- A -> [B,C] -- B -> D -- C -> D -- @ -- Then ordinary dfs would give [A,B,D,C] which has a back ref from C to D. -- Better to get [A,B,C,D] -- | Traversal: 'postorder_dfs' returns a list of blocks reachable -- from the entry of enterable graph. The entry and exit are *not* included. -- The list has the following property: -- -- Say a "back reference" exists if one of a block's -- control-flow successors precedes it in the output list -- -- Then there are as few back references as possible -- -- The output is suitable for use in -- a forward dataflow problem. For a backward problem, simply reverse -- the list. ('postorder_dfs' is sufficiently tricky to implement that -- one doesn't want to try and maintain both forward and backward -- versions.) postorder_dfs_from_except :: forall block e . (NonLocal block, LabelsPtr e) => LabelMap (block C C) -> e -> LabelSet -> [block C C] postorder_dfs_from_except blocks b visited = vchildren (get_children b) (\acc _visited -> acc) [] visited where vnode :: block C C -> ([block C C] -> LabelSet -> a) -> [block C C] -> LabelSet -> a vnode block cont acc visited = if setMember id visited then cont acc visited else let cont' acc visited = cont (block:acc) visited in vchildren (get_children block) cont' acc (setInsert id visited) where id = entryLabel block vchildren :: forall a. [block C C] -> ([block C C] -> LabelSet -> a) -> [block C C] -> LabelSet -> a vchildren bs cont acc visited = next bs acc visited where next children acc visited = case children of [] -> cont acc visited (b:bs) -> vnode b (next bs) acc visited get_children :: forall l. LabelsPtr l => l -> [block C C] get_children block = foldr add_id [] $ targetLabels block add_id id rst = case lookupFact id blocks of Just b -> b : rst Nothing -> rst postorder_dfs_from :: (NonLocal block, LabelsPtr b) => LabelMap (block C C) -> b -> [block C C] postorder_dfs_from blocks b = postorder_dfs_from_except blocks b setEmpty