Revert "Refactor Digraph to use Data.Graph when possible"

This breaks the build with GHC 7.6 bootstrapping, since the Functor SCC
instance is not available.

This reverts commit c439af5f5baa2c8af3434652554135230edbf5c3.

1 files changed, 264 insertions, 36 deletions

diff --git a/compiler/utils/Digraph.hs b/compiler/utils/Digraph.hs
index 448935bea6..8f5df0ce05 100644
--- a/compiler/utils/Digraph.hs
+++ b/compiler/utils/Digraph.hs
@@ -17,6 +17,13 @@ module Digraph(
 
         -- For backwards compatability with the simpler version of Digraph
         stronglyConnCompFromEdgedVertices, stronglyConnCompFromEdgedVerticesR,
+
+        -- No friendly interface yet, not used but exported to avoid warnings
+        tabulate, preArr,
+        components, undirected,
+        back, cross, forward,
+        path,
+        bcc, do_label, bicomps, collect
     ) where
 
 #include "HsVersions.h"
@@ -28,11 +35,6 @@ module Digraph(
 --   by David King and John Launchbury
 --
 -- Also included is some additional code for printing tree structures ...
---
--- If you ever find yourself in need of algorithms for classifying edges,
--- or finding connected/biconnected components, consult the history; Sigbjorn
--- Finne contributed some implementations in 1997, although we've since
--- removed them since they were not used anywhere in GHC.
 ------------------------------------------------------------------------------
 
 
@@ -54,10 +56,6 @@ import Data.Array.ST
 import qualified Data.Map as Map
 import qualified Data.Set as Set
 
-import qualified Data.Graph as G
-import Data.Graph hiding (Graph, Edge, transposeG, reachable)
-import Data.Tree
-
 {-
 ************************************************************************
 *                                                                      *
@@ -211,6 +209,32 @@ findCycle graph
 {-
 ************************************************************************
 *                                                                      *
+*      SCC
+*                                                                      *
+************************************************************************
+-}
+
+data SCC vertex = AcyclicSCC vertex
+                | CyclicSCC  [vertex]
+
+instance Functor SCC where
+    fmap f (AcyclicSCC v) = AcyclicSCC (f v)
+    fmap f (CyclicSCC vs) = CyclicSCC (fmap f vs)
+
+flattenSCCs :: [SCC a] -> [a]
+flattenSCCs = concatMap flattenSCC
+
+flattenSCC :: SCC a -> [a]
+flattenSCC (AcyclicSCC v) = [v]
+flattenSCC (CyclicSCC vs) = vs
+
+instance Outputable a => Outputable (SCC a) where
+   ppr (AcyclicSCC v) = text "NONREC" $$ (nest 3 (ppr v))
+   ppr (CyclicSCC vs) = text "REC" $$ (nest 3 (vcat (map ppr vs)))
+
+{-
+************************************************************************
+*                                                                      *
 *      Strongly Connected Component wrappers for Graph
 *                                                                      *
 ************************************************************************
@@ -266,7 +290,7 @@ topologicalSortG graph = map (gr_vertex_to_node graph) result
 
 dfsTopSortG :: Graph node -> [[node]]
 dfsTopSortG graph =
-  map (map (gr_vertex_to_node graph) . flatten) $ dfs g (topSort g)
+  map (map (gr_vertex_to_node graph) . flattenTree) $ dfs g (topSort g)
   where
     g = gr_int_graph graph
 
@@ -292,9 +316,7 @@ edgesG graph = map (\(v1, v2) -> Edge (v2n v1) (v2n v2)) $ edges (gr_int_graph g
   where v2n = gr_vertex_to_node graph
 
 transposeG :: Graph node -> Graph node
-transposeG graph = Graph (G.transposeG (gr_int_graph graph))
-                         (gr_vertex_to_node graph)
-                         (gr_node_to_vertex graph)
+transposeG graph = Graph (transpose (gr_int_graph graph)) (gr_vertex_to_node graph) (gr_node_to_vertex graph)
 
 outdegreeG :: Graph node -> node -> Maybe Int
 outdegreeG = degreeG outdegree
@@ -302,7 +324,7 @@ outdegreeG = degreeG outdegree
 indegreeG :: Graph node -> node -> Maybe Int
 indegreeG = degreeG indegree
 
-degreeG :: (G.Graph -> Table Int) -> Graph node -> node -> Maybe Int
+degreeG :: (IntGraph -> Table Int) -> Graph node -> node -> Maybe Int
 degreeG degree graph node = let table = degree (gr_int_graph graph)
                             in fmap ((!) table) $ gr_node_to_vertex graph node
 
@@ -314,8 +336,7 @@ emptyG :: Graph node -> Bool
 emptyG g = graphEmpty (gr_int_graph g)
 
 componentsG :: Graph node -> [[node]]
-componentsG graph = map (map (gr_vertex_to_node graph) . flatten)
-                  $ components (gr_int_graph graph)
+componentsG graph = map (map (gr_vertex_to_node graph) . flattenTree) $ components (gr_int_graph graph)
 
 {-
 ************************************************************************
@@ -334,43 +355,261 @@ instance Outputable node => Outputable (Graph node) where
 instance Outputable node => Outputable (Edge node) where
     ppr (Edge from to) = ppr from <+> text "->" <+> ppr to
 
-graphEmpty :: G.Graph -> Bool
+{-
+************************************************************************
+*                                                                      *
+*      IntGraphs
+*                                                                      *
+************************************************************************
+-}
+
+type Vertex  = Int
+type Table a = Array Vertex a
+type IntGraph   = Table [Vertex]
+type Bounds  = (Vertex, Vertex)
+type IntEdge    = (Vertex, Vertex)
+
+vertices :: IntGraph -> [Vertex]
+vertices  = indices
+
+edges    :: IntGraph -> [IntEdge]
+edges g   = [ (v, w) | v <- vertices g, w <- g!v ]
+
+mapT    :: (Vertex -> a -> b) -> Table a -> Table b
+mapT f t = array (bounds t) [ (v, f v (t ! v)) | v <- indices t ]
+
+buildG :: Bounds -> [IntEdge] -> IntGraph
+buildG bounds edges = accumArray (flip (:)) [] bounds edges
+
+transpose  :: IntGraph -> IntGraph
+transpose g = buildG (bounds g) (reverseE g)
+
+reverseE    :: IntGraph -> [IntEdge]
+reverseE g   = [ (w, v) | (v, w) <- edges g ]
+
+outdegree :: IntGraph -> Table Int
+outdegree  = mapT numEdges
+             where numEdges _ ws = length ws
+
+indegree :: IntGraph -> Table Int
+indegree  = outdegree . transpose
+
+graphEmpty :: IntGraph -> Bool
 graphEmpty g = lo > hi
   where (lo, hi) = bounds g
 
 {-
 ************************************************************************
 *                                                                      *
-*      IntGraphs
+*      Trees and forests
 *                                                                      *
 ************************************************************************
 -}
 
-type IntGraph = G.Graph
+data Tree a   = Node a (Forest a)
+type Forest a = [Tree a]
+
+mapTree              :: (a -> b) -> (Tree a -> Tree b)
+mapTree f (Node x ts) = Node (f x) (map (mapTree f) ts)
+
+flattenTree :: Tree a -> [a]
+flattenTree (Node x ts) = x : concatMap flattenTree ts
+
+instance Show a => Show (Tree a) where
+  showsPrec _ t s = showTree t ++ s
+
+showTree :: Show a => Tree a -> String
+showTree  = drawTree . mapTree show
+
+drawTree        :: Tree String -> String
+drawTree         = unlines . draw
+
+draw :: Tree String -> [String]
+draw (Node x ts) = grp this (space (length this)) (stLoop ts)
+ where this          = s1 ++ x ++ " "
+
+       space n       = replicate n ' '
+
+       stLoop []     = [""]
+       stLoop [t]    = grp s2 "  " (draw t)
+       stLoop (t:ts) = grp s3 s4 (draw t) ++ [s4] ++ rsLoop ts
+
+       rsLoop []     = []
+       rsLoop [t]    = grp s5 "  " (draw t)
+       rsLoop (t:ts) = grp s6 s4 (draw t) ++ [s4] ++ rsLoop ts
+
+       grp fst rst   = zipWith (++) (fst:repeat rst)
+
+       [s1,s2,s3,s4,s5,s6] = ["- ", "--", "-+", " |", " `", " +"]
 
 {-
+************************************************************************
+*                                                                      *
+*      Depth first search
+*                                                                      *
+************************************************************************
+-}
+
+type Set s    = STArray s Vertex Bool
+
+mkEmpty      :: Bounds -> ST s (Set s)
+mkEmpty bnds  = newArray bnds False
+
+contains     :: Set s -> Vertex -> ST s Bool
+contains m v  = readArray m v
+
+include      :: Set s -> Vertex -> ST s ()
+include m v   = writeArray m v True
+
+dff          :: IntGraph -> Forest Vertex
+dff g         = dfs g (vertices g)
+
+dfs          :: IntGraph -> [Vertex] -> Forest Vertex
+dfs g vs      = prune (bounds g) (map (generate g) vs)
+
+generate     :: IntGraph -> Vertex -> Tree Vertex
+generate g v  = Node v (map (generate g) (g!v))
+
+prune        :: Bounds -> Forest Vertex -> Forest Vertex
+prune bnds ts = runST (mkEmpty bnds  >>= \m ->
+                       chop m ts)
+
+chop         :: Set s -> Forest Vertex -> ST s (Forest Vertex)
+chop _ []     = return []
+chop m (Node v ts : us)
+              = contains m v >>= \visited ->
+                if visited then
+                  chop m us
+                else
+                  include m v >>= \_  ->
+                  chop m ts   >>= \as ->
+                  chop m us   >>= \bs ->
+                  return (Node v as : bs)
+
+{-
+************************************************************************
+*                                                                      *
+*      Algorithms
+*                                                                      *
+************************************************************************
+
 ------------------------------------------------------------
--- Depth first search numbering
+-- Algorithm 1: depth first search numbering
 ------------------------------------------------------------
 -}
 
--- Data.Tree has flatten for Tree, but nothing for Forest
+preorder            :: Tree a -> [a]
+preorder (Node a ts) = a : preorderF ts
+
 preorderF           :: Forest a -> [a]
-preorderF ts         = concat (map flatten ts)
+preorderF ts         = concat (map preorder ts)
+
+tabulate        :: Bounds -> [Vertex] -> Table Int
+tabulate bnds vs = array bnds (zip vs [1..])
+
+preArr          :: Bounds -> Forest Vertex -> Table Int
+preArr bnds      = tabulate bnds . preorderF
+
+{-
+------------------------------------------------------------
+-- Algorithm 2: topological sorting
+------------------------------------------------------------
+-}
+
+postorder :: Tree a -> [a] -> [a]
+postorder (Node a ts) = postorderF ts . (a :)
+
+postorderF   :: Forest a -> [a] -> [a]
+postorderF ts = foldr (.) id $ map postorder ts
+
+postOrd :: IntGraph -> [Vertex]
+postOrd g = postorderF (dff g) []
+
+topSort :: IntGraph -> [Vertex]
+topSort = reverse . postOrd
+
+{-
+------------------------------------------------------------
+-- Algorithm 3: connected components
+------------------------------------------------------------
+-}
+
+components   :: IntGraph -> Forest Vertex
+components    = dff . undirected
+
+undirected   :: IntGraph -> IntGraph
+undirected g  = buildG (bounds g) (edges g ++ reverseE g)
 
 {-
 ------------------------------------------------------------
--- Finding reachable vertices
+-- Algorithm 4: strongly connected components
+------------------------------------------------------------
+-}
+
+scc  :: IntGraph -> Forest Vertex
+scc g = dfs g (reverse (postOrd (transpose g)))
+
+{-
+------------------------------------------------------------
+-- Algorithm 5: Classifying edges
+------------------------------------------------------------
+-}
+
+back              :: IntGraph -> Table Int -> IntGraph
+back g post        = mapT select g
+ where select v ws = [ w | w <- ws, post!v < post!w ]
+
+cross             :: IntGraph -> Table Int -> Table Int -> IntGraph
+cross g pre post   = mapT select g
+ where select v ws = [ w | w <- ws, post!v > post!w, pre!v > pre!w ]
+
+forward           :: IntGraph -> IntGraph -> Table Int -> IntGraph
+forward g tree pre = mapT select g
+ where select v ws = [ w | w <- ws, pre!v < pre!w ] \\ tree!v
+
+{-
+------------------------------------------------------------
+-- Algorithm 6: Finding reachable vertices
 ------------------------------------------------------------
 -}
 
--- This generalizes reachable which was found in Data.Graph
 reachable    :: IntGraph -> [Vertex] -> [Vertex]
 reachable g vs = preorderF (dfs g vs)
 
+path         :: IntGraph -> Vertex -> Vertex -> Bool
+path g v w    = w `elem` (reachable g [v])
+
 {-
 ------------------------------------------------------------
--- Total ordering on groups of vertices
+-- Algorithm 7: Biconnected components
+------------------------------------------------------------
+-}
+
+bcc :: IntGraph -> Forest [Vertex]
+bcc g = (concat . map bicomps . map (do_label g dnum)) forest
+ where forest = dff g
+       dnum   = preArr (bounds g) forest
+
+do_label :: IntGraph -> Table Int -> Tree Vertex -> Tree (Vertex,Int,Int)
+do_label g dnum (Node v ts) = Node (v,dnum!v,lv) us
+ where us = map (do_label g dnum) ts
+       lv = minimum ([dnum!v] ++ [dnum!w | w <- g!v]
+                     ++ [lu | Node (_,_,lu) _ <- us])
+
+bicomps :: Tree (Vertex, Int, Int) -> Forest [Vertex]
+bicomps (Node (v,_,_) ts)
+      = [ Node (v:vs) us | (_,Node vs us) <- map collect ts]
+
+collect :: Tree (Vertex, Int, Int) -> (Int, Tree [Vertex])
+collect (Node (v,dv,lv) ts) = (lv, Node (v:vs) cs)
+ where collected = map collect ts
+       vs = concat [ ws | (lw, Node ws _)  <- collected, lw<dv]
+       cs = concat [ if lw<dv then us else [Node (v:ws) us]
+                        | (lw, Node ws us) <- collected ]
+
+{-
+------------------------------------------------------------
+-- Algorithm 8: Total ordering on groups of vertices
 ------------------------------------------------------------
 
 The plan here is to extract a list of groups of elements of the graph
@@ -386,17 +625,6 @@ and their associated edges from the graph.
 This probably isn't very efficient and certainly isn't very clever.
 -}
 
-type Set s    = STArray s Vertex Bool
-
-mkEmpty      :: Bounds -> ST s (Set s)
-mkEmpty bnds  = newArray bnds False
-
-contains     :: Set s -> Vertex -> ST s Bool
-contains m v  = readArray m v
-
-include      :: Set s -> Vertex -> ST s ()
-include m v   = writeArray m v True
-
 vertexGroups :: IntGraph -> [[Vertex]]
 vertexGroups g = runST (mkEmpty (bounds g) >>= \provided -> vertexGroupsS provided g next_vertices)
   where next_vertices = noOutEdges g