{-# 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) = mapFoldlWithKey addEntry (exitLabel x) body
where addEntry :: forall a. LabelSet -> ElemOf LabelSet -> a -> LabelSet
addEntry labels label _ = 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