    {-# 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