-- (c) The University of Glasgow 2006


{-# LANGUAGE GeneralizedNewtypeDeriving #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE ViewPatterns #-}
{-# LANGUAGE DeriveFunctor #-}

module GHC.Data.Graph.Directed (
        Graph, graphFromEdgedVerticesOrd, graphFromEdgedVerticesUniq,
        graphFromVerticesAndAdjacency, emptyGraph,

        SCC(..), Node(..), G.flattenSCC, G.flattenSCCs,
        stronglyConnCompG,
        topologicalSortG,
        verticesG, edgesG, hasVertexG,
        reachablesG,
        transposeG, outgoingG,
        emptyG,

        findCycle,

        -- For backwards compatibility with the simpler version of Digraph
        stronglyConnCompFromEdgedVerticesOrd,
        stronglyConnCompFromEdgedVerticesOrdR,
        stronglyConnCompFromEdgedVerticesUniq,
        stronglyConnCompFromEdgedVerticesUniqR,

        -- Simple way to classify edges
        EdgeType(..), classifyEdges
        ) where

------------------------------------------------------------------------------
-- A version of the graph algorithms described in:
--
-- ``Lazy Depth-First Search and Linear IntGraph Algorithms in Haskell''
--   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.
------------------------------------------------------------------------------

import GHC.Prelude

import GHC.Utils.Misc ( sortWith, count )
import GHC.Utils.Outputable
import GHC.Utils.Panic
import GHC.Data.Maybe ( expectJust )

-- std interfaces
import Data.Maybe
import Data.Array
import Data.List ( sort )
import qualified Data.Map as Map
import qualified Data.Set as Set

import qualified Data.Graph as G
import Data.Graph ( Vertex, Bounds, SCC(..) ) -- Used in the underlying representation
import GHC.Types.Unique
import GHC.Types.Unique.FM

-- The graph internals are defined in the .Internal module so they can be
-- imported by GHC.Data.Graph.Directed.Reachability while still allowing this
-- module to export it abstractly.
import GHC.Data.Graph.Directed.Internal

{-
************************************************************************
*                                                                      *
*      Graphs and Graph Construction
*                                                                      *
************************************************************************

Note [Nodes, keys, vertices]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 * A 'node' is a big blob of client-stuff

 * Each 'node' has a unique (client) 'key', but the latter
        is in Ord and has fast comparison

 * Digraph then maps each 'key' to a Vertex (Int) which is
        arranged densely in 0.n
-}

{-| Representation for nodes of the Graph.

 * The @payload@ is user data, just carried around in this module

 * The @key@ is the node identifier.
   Key has an Ord instance for performance reasons.

 * The @[key]@ are the dependencies of the node;
   it's ok to have extra keys in the dependencies that
   are not the key of any Node in the graph
-}
data Node key payload = DigraphNode {
      forall key payload. Node key payload -> payload
node_payload :: payload, -- ^ User data
      forall key payload. Node key payload -> key
node_key :: key, -- ^ User defined node id
      forall key payload. Node key payload -> [key]
node_dependencies :: [key] -- ^ Dependencies/successors of the node
  } deriving (forall a b. (a -> b) -> Node key a -> Node key b)
-> (forall a b. a -> Node key b -> Node key a)
-> Functor (Node key)
forall a b. a -> Node key b -> Node key a
forall a b. (a -> b) -> Node key a -> Node key b
forall key a b. a -> Node key b -> Node key a
forall key a b. (a -> b) -> Node key a -> Node key b
forall (f :: * -> *).
(forall a b. (a -> b) -> f a -> f b)
-> (forall a b. a -> f b -> f a) -> Functor f
$cfmap :: forall key a b. (a -> b) -> Node key a -> Node key b
fmap :: forall a b. (a -> b) -> Node key a -> Node key b
$c<$ :: forall key a b. a -> Node key b -> Node key a
<$ :: forall a b. a -> Node key b -> Node key a
Functor


instance (Outputable a, Outputable b) => Outputable (Node a b) where
  ppr :: Node a b -> SDoc
ppr (DigraphNode b
a a
b [a]
c) = (b, a, [a]) -> SDoc
forall a. Outputable a => a -> SDoc
ppr (b
a, a
b, [a]
c)

emptyGraph :: Graph a
emptyGraph :: forall a. Graph a
emptyGraph = IntGraph -> (Vertex -> a) -> (a -> Maybe Vertex) -> Graph a
forall node.
IntGraph
-> (Vertex -> node) -> (node -> Maybe Vertex) -> Graph node
Graph ((Vertex, Vertex) -> [(Vertex, [Vertex])] -> IntGraph
forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
array (Vertex
1, Vertex
0) []) ([Char] -> Vertex -> a
forall a. HasCallStack => [Char] -> a
error [Char]
"emptyGraph") (Maybe Vertex -> a -> Maybe Vertex
forall a b. a -> b -> a
const Maybe Vertex
forall a. Maybe a
Nothing)

-- See Note [Deterministic SCC]
graphFromEdgedVertices
        :: ReduceFn key payload
        -> [Node key payload]           -- The graph; its ok for the
                                        -- out-list to contain keys which aren't
                                        -- a vertex key, they are ignored
        -> Graph (Node key payload)
graphFromEdgedVertices :: forall key payload.
ReduceFn key payload
-> [Node key payload] -> Graph (Node key payload)
graphFromEdgedVertices ReduceFn key payload
_reduceFn []            = Graph (Node key payload)
forall a. Graph a
emptyGraph
graphFromEdgedVertices ReduceFn key payload
reduceFn [Node key payload]
edged_vertices =
  IntGraph
-> (Vertex -> Node key payload)
-> (Node key payload -> Maybe Vertex)
-> Graph (Node key payload)
forall node.
IntGraph
-> (Vertex -> node) -> (node -> Maybe Vertex) -> Graph node
Graph IntGraph
graph Vertex -> Node key payload
vertex_fn (key -> Maybe Vertex
key_vertex (key -> Maybe Vertex)
-> (Node key payload -> key) -> Node key payload -> Maybe Vertex
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Node key payload -> key
forall key payload. Node key payload -> key
key_extractor)
  where key_extractor :: Node key payload -> key
key_extractor = Node key payload -> key
forall key payload. Node key payload -> key
node_key
        ((Vertex, Vertex)
bounds, Vertex -> Node key payload
vertex_fn, key -> Maybe Vertex
key_vertex, [(Vertex, Node key payload)]
numbered_nodes) =
          ReduceFn key payload
reduceFn [Node key payload]
edged_vertices Node key payload -> key
forall key payload. Node key payload -> key
key_extractor
        graph :: IntGraph
graph = (Vertex, Vertex) -> [(Vertex, [Vertex])] -> IntGraph
forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
array (Vertex, Vertex)
bounds [ (Vertex
v, [Vertex] -> [Vertex]
forall a. Ord a => [a] -> [a]
sort ([Vertex] -> [Vertex]) -> [Vertex] -> [Vertex]
forall a b. (a -> b) -> a -> b
$ (key -> Maybe Vertex) -> [key] -> [Vertex]
forall a b. (a -> Maybe b) -> [a] -> [b]
mapMaybe key -> Maybe Vertex
key_vertex [key]
ks)
                             | (Vertex
v, (Node key payload -> [key]
forall key payload. Node key payload -> [key]
node_dependencies -> [key]
ks)) <- [(Vertex, Node key payload)]
numbered_nodes]
                -- We normalize outgoing edges by sorting on node order, so
                -- that the result doesn't depend on the order of the edges

-- See Note [Deterministic SCC]
-- See Note [reduceNodesIntoVertices implementations]
graphFromEdgedVerticesOrd
        :: Ord key
        => [Node key payload]           -- The graph; its ok for the
                                        -- out-list to contain keys which aren't
                                        -- a vertex key, they are ignored
        -> Graph (Node key payload)
graphFromEdgedVerticesOrd :: forall key payload.
Ord key =>
[Node key payload] -> Graph (Node key payload)
graphFromEdgedVerticesOrd = ReduceFn key payload
-> [Node key payload] -> Graph (Node key payload)
forall key payload.
ReduceFn key payload
-> [Node key payload] -> Graph (Node key payload)
graphFromEdgedVertices ReduceFn key payload
forall key payload. Ord key => ReduceFn key payload
reduceNodesIntoVerticesOrd

-- See Note [Deterministic SCC]
-- See Note [reduceNodesIntoVertices implementations]
graphFromEdgedVerticesUniq
        :: Uniquable key
        => [Node key payload]           -- The graph; its ok for the
                                        -- out-list to contain keys which aren't
                                        -- a vertex key, they are ignored
        -> Graph (Node key payload)
graphFromEdgedVerticesUniq :: forall key payload.
Uniquable key =>
[Node key payload] -> Graph (Node key payload)
graphFromEdgedVerticesUniq = ReduceFn key payload
-> [Node key payload] -> Graph (Node key payload)
forall key payload.
ReduceFn key payload
-> [Node key payload] -> Graph (Node key payload)
graphFromEdgedVertices ReduceFn key payload
forall key payload. Uniquable key => ReduceFn key payload
reduceNodesIntoVerticesUniq

type ReduceFn key payload =
  [Node key payload] -> (Node key payload -> key) ->
    (Bounds, Vertex -> Node key payload
    , key -> Maybe Vertex, [(Vertex, Node key payload)])

{-
Note [reduceNodesIntoVertices implementations]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
reduceNodesIntoVertices is parameterized by the container type.
This is to accommodate key types that don't have an Ord instance
and hence preclude the use of Data.Map. An example of such type
would be Unique, there's no way to implement Ord Unique
deterministically.

For such types, there's a version with a Uniquable constraint.
This leaves us with two versions of every function that depends on
reduceNodesIntoVertices, one with Ord constraint and the other with
Uniquable constraint.
For example: graphFromEdgedVerticesOrd and graphFromEdgedVerticesUniq.

The Uniq version should be a tiny bit more efficient since it uses
Data.IntMap internally.
-}
reduceNodesIntoVertices
  :: ([(key, Vertex)] -> m)
  -> (key -> m -> Maybe Vertex)
  -> ReduceFn key payload
reduceNodesIntoVertices :: forall key m payload.
([(key, Vertex)] -> m)
-> (key -> m -> Maybe Vertex) -> ReduceFn key payload
reduceNodesIntoVertices [(key, Vertex)] -> m
fromList key -> m -> Maybe Vertex
lookup [Node key payload]
nodes Node key payload -> key
key_extractor =
  ((Vertex, Vertex)
bounds, Array Vertex (Node key payload) -> Vertex -> Node key payload
forall i e. Ix i => Array i e -> i -> e
(!) Array Vertex (Node key payload)
vertex_map, key -> Maybe Vertex
key_vertex, [(Vertex, Node key payload)]
numbered_nodes)
  where
    max_v :: Vertex
max_v           = [Node key payload] -> Vertex
forall a. [a] -> Vertex
forall (t :: * -> *) a. Foldable t => t a -> Vertex
length [Node key payload]
nodes Vertex -> Vertex -> Vertex
forall a. Num a => a -> a -> a
- Vertex
1
    bounds :: (Vertex, Vertex)
bounds          = (Vertex
0, Vertex
max_v) :: (Vertex, Vertex)

    -- Keep the order intact to make the result depend on input order
    -- instead of key order
    numbered_nodes :: [(Vertex, Node key payload)]
numbered_nodes  = [Vertex] -> [Node key payload] -> [(Vertex, Node key payload)]
forall a b. [a] -> [b] -> [(a, b)]
zip [Vertex
0..] [Node key payload]
nodes
    vertex_map :: Array Vertex (Node key payload)
vertex_map      = (Vertex, Vertex)
-> [(Vertex, Node key payload)] -> Array Vertex (Node key payload)
forall i e. Ix i => (i, i) -> [(i, e)] -> Array i e
array (Vertex, Vertex)
bounds [(Vertex, Node key payload)]
numbered_nodes

    key_map :: m
key_map = [(key, Vertex)] -> m
fromList
      [ (Node key payload -> key
key_extractor Node key payload
node, Vertex
v) | (Vertex
v, Node key payload
node) <- [(Vertex, Node key payload)]
numbered_nodes ]
    key_vertex :: key -> Maybe Vertex
key_vertex key
k = key -> m -> Maybe Vertex
lookup key
k m
key_map

-- See Note [reduceNodesIntoVertices implementations]
reduceNodesIntoVerticesOrd :: Ord key => ReduceFn key payload
reduceNodesIntoVerticesOrd :: forall key payload. Ord key => ReduceFn key payload
reduceNodesIntoVerticesOrd = ([(key, Vertex)] -> Map key Vertex)
-> (key -> Map key Vertex -> Maybe Vertex) -> ReduceFn key payload
forall key m payload.
([(key, Vertex)] -> m)
-> (key -> m -> Maybe Vertex) -> ReduceFn key payload
reduceNodesIntoVertices [(key, Vertex)] -> Map key Vertex
forall k a. Ord k => [(k, a)] -> Map k a
Map.fromList key -> Map key Vertex -> Maybe Vertex
forall k a. Ord k => k -> Map k a -> Maybe a
Map.lookup

-- See Note [reduceNodesIntoVertices implementations]
reduceNodesIntoVerticesUniq :: Uniquable key => ReduceFn key payload
reduceNodesIntoVerticesUniq :: forall key payload. Uniquable key => ReduceFn key payload
reduceNodesIntoVerticesUniq = ([(key, Vertex)] -> UniqFM key Vertex)
-> (key -> UniqFM key Vertex -> Maybe Vertex)
-> ReduceFn key payload
forall key m payload.
([(key, Vertex)] -> m)
-> (key -> m -> Maybe Vertex) -> ReduceFn key payload
reduceNodesIntoVertices [(key, Vertex)] -> UniqFM key Vertex
forall key elt. Uniquable key => [(key, elt)] -> UniqFM key elt
listToUFM ((UniqFM key Vertex -> key -> Maybe Vertex)
-> key -> UniqFM key Vertex -> Maybe Vertex
forall a b c. (a -> b -> c) -> b -> a -> c
flip UniqFM key Vertex -> key -> Maybe Vertex
forall key elt. Uniquable key => UniqFM key elt -> key -> Maybe elt
lookupUFM)

{-
************************************************************************
*                                                                      *
*      SCC
*                                                                      *
************************************************************************
-}

type WorkItem key payload
  = (Node key payload,  -- Tip of the path
     [payload])         -- Rest of the path;
                        --  [a,b,c] means c depends on b, b depends on a

-- | Find a reasonably short cycle a->b->c->a, in a graph
-- The graph might not necessarily be strongly connected.
findCycle :: forall payload key. Ord key
          => [Node key payload]     -- The nodes.  The dependencies can
                                    -- contain extra keys, which are ignored
          -> Maybe [payload]        -- A cycle, starting with node
                                    -- so each depends on the next
findCycle :: forall payload key.
Ord key =>
[Node key payload] -> Maybe [payload]
findCycle [Node key payload]
graph
  = [Node key payload] -> Maybe [payload]
goRoots [Node key payload]
plausible_roots
  where
    env :: Map.Map key (Node key payload)
    env :: Map key (Node key payload)
env = [(key, Node key payload)] -> Map key (Node key payload)
forall k a. Ord k => [(k, a)] -> Map k a
Map.fromList [ (Node key payload -> key
forall key payload. Node key payload -> key
node_key Node key payload
node, Node key payload
node) | Node key payload
node <- [Node key payload]
graph ]

    goRoots :: [Node key payload] -> Maybe [payload]
goRoots [] = Maybe [payload]
forall a. Maybe a
Nothing
    goRoots (Node key payload
root:[Node key payload]
xs) =
        case Set key
-> [WorkItem key payload]
-> [WorkItem key payload]
-> Maybe [payload]
go Set key
forall a. Set a
Set.empty ([key] -> [payload] -> [WorkItem key payload]
new_work [key]
root_deps []) [] of
          Maybe [payload]
Nothing -> [Node key payload] -> Maybe [payload]
goRoots [Node key payload]
xs
          Just [payload]
res -> [payload] -> Maybe [payload]
forall a. a -> Maybe a
Just [payload]
res
      where
        DigraphNode payload
root_payload key
root_key [key]
root_deps = Node key payload
root
        -- 'go' implements Dijkstra's algorithm, more or less
        go :: Set.Set key   -- Visited
           -> [WorkItem key payload]        -- Work list, items length n
           -> [WorkItem key payload]        -- Work list, items length n+1
           -> Maybe [payload]               -- Returned cycle
           -- Invariant: in a call (go visited ps qs),
           --            visited = union (map tail (ps ++ qs))

        go :: Set key
-> [WorkItem key payload]
-> [WorkItem key payload]
-> Maybe [payload]
go Set key
_       [] [] = Maybe [payload]
forall a. Maybe a
Nothing  -- No cycles
        go Set key
visited [] [WorkItem key payload]
qs = Set key
-> [WorkItem key payload]
-> [WorkItem key payload]
-> Maybe [payload]
go Set key
visited [WorkItem key payload]
qs []
        go Set key
visited (((DigraphNode payload
payload key
key [key]
deps), [payload]
path) : [WorkItem key payload]
ps) [WorkItem key payload]
qs
           | key
key key -> key -> Bool
forall a. Eq a => a -> a -> Bool
== key
root_key           = [payload] -> Maybe [payload]
forall a. a -> Maybe a
Just (payload
root_payload payload -> [payload] -> [payload]
forall a. a -> [a] -> [a]
: [payload] -> [payload]
forall a. [a] -> [a]
reverse [payload]
path)
           | key
key key -> Set key -> Bool
forall a. Ord a => a -> Set a -> Bool
`Set.member` Set key
visited  = Set key
-> [WorkItem key payload]
-> [WorkItem key payload]
-> Maybe [payload]
go Set key
visited [WorkItem key payload]
ps [WorkItem key payload]
qs
           | key
key key -> Map key (Node key payload) -> Bool
forall k a. Ord k => k -> Map k a -> Bool
`Map.notMember` Map key (Node key payload)
env   = Set key
-> [WorkItem key payload]
-> [WorkItem key payload]
-> Maybe [payload]
go Set key
visited [WorkItem key payload]
ps [WorkItem key payload]
qs
           | Bool
otherwise                 = Set key
-> [WorkItem key payload]
-> [WorkItem key payload]
-> Maybe [payload]
go (key -> Set key -> Set key
forall a. Ord a => a -> Set a -> Set a
Set.insert key
key Set key
visited)
                                            [WorkItem key payload]
ps ([WorkItem key payload]
new_qs [WorkItem key payload]
-> [WorkItem key payload] -> [WorkItem key payload]
forall a. [a] -> [a] -> [a]
++ [WorkItem key payload]
qs)
           where
             new_qs :: [WorkItem key payload]
new_qs = [key] -> [payload] -> [WorkItem key payload]
new_work [key]
deps (payload
payload payload -> [payload] -> [payload]
forall a. a -> [a] -> [a]
: [payload]
path)


    -- Find the nodes with fewest dependencies among the SCC modules
    -- This is just a heuristic to find some plausible root module
    plausible_roots :: [Node key payload]
    plausible_roots :: [Node key payload]
plausible_roots = ((Node key payload, Vertex) -> Node key payload)
-> [(Node key payload, Vertex)] -> [Node key payload]
forall a b. (a -> b) -> [a] -> [b]
map (Node key payload, Vertex) -> Node key payload
forall a b. (a, b) -> a
fst (((Node key payload, Vertex) -> Vertex)
-> [(Node key payload, Vertex)] -> [(Node key payload, Vertex)]
forall b a. Ord b => (a -> b) -> [a] -> [a]
sortWith (Node key payload, Vertex) -> Vertex
forall a b. (a, b) -> b
snd [ (Node key payload
node, (key -> Bool) -> [key] -> Vertex
forall a. (a -> Bool) -> [a] -> Vertex
count (key -> Map key (Node key payload) -> Bool
forall k a. Ord k => k -> Map k a -> Bool
`Map.member` Map key (Node key payload)
env) (Node key payload -> [key]
forall key payload. Node key payload -> [key]
node_dependencies Node key payload
node))
                                            | Node key payload
node <- [Node key payload]
graph ])


    new_work :: [key] -> [payload] -> [WorkItem key payload]
    new_work :: [key] -> [payload] -> [WorkItem key payload]
new_work [key]
deps [payload]
path = [ (Node key payload
n, [payload]
path) | Just Node key payload
n <- (key -> Maybe (Node key payload))
-> [key] -> [Maybe (Node key payload)]
forall a b. (a -> b) -> [a] -> [b]
map (key -> Map key (Node key payload) -> Maybe (Node key payload)
forall k a. Ord k => k -> Map k a -> Maybe a
`Map.lookup` Map key (Node key payload)
env) [key]
deps ]

{-
************************************************************************
*                                                                      *
*      Strongly Connected Component wrappers for Graph
*                                                                      *
************************************************************************

Note: the components are returned topologically sorted: later components
depend on earlier ones, but not vice versa i.e. later components only have
edges going from them to earlier ones.
-}

{-
Note [Deterministic SCC]
~~~~~~~~~~~~~~~~~~~~~~~~
stronglyConnCompFromEdgedVerticesUniq,
stronglyConnCompFromEdgedVerticesUniqR,
stronglyConnCompFromEdgedVerticesOrd and
stronglyConnCompFromEdgedVerticesOrdR
provide a following guarantee:
Given a deterministically ordered list of nodes it returns a deterministically
ordered list of strongly connected components, where the list of vertices
in an SCC is also deterministically ordered.
Note that the order of edges doesn't need to be deterministic for this to work.
We use the order of nodes to normalize the order of edges.
-}

stronglyConnCompG :: Graph node -> [SCC node]
stronglyConnCompG :: forall node. Graph node -> [SCC node]
stronglyConnCompG Graph node
graph = Graph node -> [SCC Vertex] -> [SCC node]
forall node. Graph node -> [SCC Vertex] -> [SCC node]
decodeSccs Graph node
graph ([SCC Vertex] -> [SCC node]) -> [SCC Vertex] -> [SCC node]
forall a b. (a -> b) -> a -> b
$ IntGraph -> [SCC Vertex]
scc (Graph node -> IntGraph
forall node. Graph node -> IntGraph
gr_int_graph Graph node
graph)

decodeSccs :: Graph node -> [SCC Vertex] -> [SCC node]
decodeSccs :: forall node. Graph node -> [SCC Vertex] -> [SCC node]
decodeSccs Graph { gr_vertex_to_node :: forall node. Graph node -> Vertex -> node
gr_vertex_to_node = Vertex -> node
vertex_fn }
  = (SCC Vertex -> SCC node) -> [SCC Vertex] -> [SCC node]
forall a b. (a -> b) -> [a] -> [b]
map ((Vertex -> node) -> SCC Vertex -> SCC node
forall a b. (a -> b) -> SCC a -> SCC b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Vertex -> node
vertex_fn)

-- The following two versions are provided for backwards compatibility:
-- See Note [Deterministic SCC]
-- See Note [reduceNodesIntoVertices implementations]
stronglyConnCompFromEdgedVerticesOrd
        :: Ord key
        => [Node key payload]
        -> [SCC payload]
stronglyConnCompFromEdgedVerticesOrd :: forall key payload. Ord key => [Node key payload] -> [SCC payload]
stronglyConnCompFromEdgedVerticesOrd
  = (SCC (Node key payload) -> SCC payload)
-> [SCC (Node key payload)] -> [SCC payload]
forall a b. (a -> b) -> [a] -> [b]
map ((Node key payload -> payload)
-> SCC (Node key payload) -> SCC payload
forall a b. (a -> b) -> SCC a -> SCC b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Node key payload -> payload
forall key payload. Node key payload -> payload
node_payload) ([SCC (Node key payload)] -> [SCC payload])
-> ([Node key payload] -> [SCC (Node key payload)])
-> [Node key payload]
-> [SCC payload]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Node key payload] -> [SCC (Node key payload)]
forall key payload.
Ord key =>
[Node key payload] -> [SCC (Node key payload)]
stronglyConnCompFromEdgedVerticesOrdR

-- The following two versions are provided for backwards compatibility:
-- See Note [Deterministic SCC]
-- See Note [reduceNodesIntoVertices implementations]
stronglyConnCompFromEdgedVerticesUniq
        :: Uniquable key
        => [Node key payload]
        -> [SCC payload]
stronglyConnCompFromEdgedVerticesUniq :: forall key payload.
Uniquable key =>
[Node key payload] -> [SCC payload]
stronglyConnCompFromEdgedVerticesUniq
  = (SCC (Node key payload) -> SCC payload)
-> [SCC (Node key payload)] -> [SCC payload]
forall a b. (a -> b) -> [a] -> [b]
map ((Node key payload -> payload)
-> SCC (Node key payload) -> SCC payload
forall a b. (a -> b) -> SCC a -> SCC b
forall (f :: * -> *) a b. Functor f => (a -> b) -> f a -> f b
fmap Node key payload -> payload
forall key payload. Node key payload -> payload
node_payload) ([SCC (Node key payload)] -> [SCC payload])
-> ([Node key payload] -> [SCC (Node key payload)])
-> [Node key payload]
-> [SCC payload]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Node key payload] -> [SCC (Node key payload)]
forall key payload.
Uniquable key =>
[Node key payload] -> [SCC (Node key payload)]
stronglyConnCompFromEdgedVerticesUniqR

-- The "R" interface is used when you expect to apply SCC to
-- (some of) the result of SCC, so you don't want to lose the dependency info
-- See Note [Deterministic SCC]
-- See Note [reduceNodesIntoVertices implementations]
stronglyConnCompFromEdgedVerticesOrdR
        :: Ord key
        => [Node key payload]
        -> [SCC (Node key payload)]
stronglyConnCompFromEdgedVerticesOrdR :: forall key payload.
Ord key =>
[Node key payload] -> [SCC (Node key payload)]
stronglyConnCompFromEdgedVerticesOrdR =
  Graph (Node key payload) -> [SCC (Node key payload)]
forall node. Graph node -> [SCC node]
stronglyConnCompG (Graph (Node key payload) -> [SCC (Node key payload)])
-> ([Node key payload] -> Graph (Node key payload))
-> [Node key payload]
-> [SCC (Node key payload)]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Node key payload] -> Graph (Node key payload)
forall key payload.
Ord key =>
[Node key payload] -> Graph (Node key payload)
graphFromEdgedVerticesOrd

-- The "R" interface is used when you expect to apply SCC to
-- (some of) the result of SCC, so you don't want to lose the dependency info
-- See Note [Deterministic SCC]
-- See Note [reduceNodesIntoVertices implementations]
stronglyConnCompFromEdgedVerticesUniqR
        :: Uniquable key
        => [Node key payload]
        -> [SCC (Node key payload)]
stronglyConnCompFromEdgedVerticesUniqR :: forall key payload.
Uniquable key =>
[Node key payload] -> [SCC (Node key payload)]
stronglyConnCompFromEdgedVerticesUniqR =
  Graph (Node key payload) -> [SCC (Node key payload)]
forall node. Graph node -> [SCC node]
stronglyConnCompG (Graph (Node key payload) -> [SCC (Node key payload)])
-> ([Node key payload] -> Graph (Node key payload))
-> [Node key payload]
-> [SCC (Node key payload)]
forall b c a. (b -> c) -> (a -> b) -> a -> c
. [Node key payload] -> Graph (Node key payload)
forall key payload.
Uniquable key =>
[Node key payload] -> Graph (Node key payload)
graphFromEdgedVerticesUniq

{-
************************************************************************
*                                                                      *
*      Misc wrappers for Graph
*                                                                      *
************************************************************************
-}

topologicalSortG :: Graph node -> [node]
topologicalSortG :: forall node. Graph node -> [node]
topologicalSortG Graph node
graph = (Vertex -> node) -> [Vertex] -> [node]
forall a b. (a -> b) -> [a] -> [b]
map (Graph node -> Vertex -> node
forall node. Graph node -> Vertex -> node
gr_vertex_to_node Graph node
graph) [Vertex]
result
  where result :: [Vertex]
result = {-# SCC "Digraph.topSort" #-} IntGraph -> [Vertex]
G.topSort (Graph node -> IntGraph
forall node. Graph node -> IntGraph
gr_int_graph Graph node
graph)

outgoingG :: Graph node -> node -> [node]
outgoingG :: forall node. Graph node -> node -> [node]
outgoingG Graph node
graph node
from = (Vertex -> node) -> [Vertex] -> [node]
forall a b. (a -> b) -> [a] -> [b]
map (Graph node -> Vertex -> node
forall node. Graph node -> Vertex -> node
gr_vertex_to_node Graph node
graph) [Vertex]
result
  where from_vertex :: Vertex
from_vertex = [Char] -> Maybe Vertex -> Vertex
forall a. HasDebugCallStack => [Char] -> Maybe a -> a
expectJust [Char]
"outgoingG" (Graph node -> node -> Maybe Vertex
forall node. Graph node -> node -> Maybe Vertex
gr_node_to_vertex Graph node
graph node
from)
        result :: [Vertex]
result = Graph node -> IntGraph
forall node. Graph node -> IntGraph
gr_int_graph Graph node
graph IntGraph -> Vertex -> [Vertex]
forall i e. Ix i => Array i e -> i -> e
! Vertex
from_vertex

-- | Given a list of roots, return all reachable nodes in topological order.
-- Implemented using a depth-first traversal.
reachablesG :: Graph node -> [node] -> [node]
reachablesG :: forall node. Graph node -> [node] -> [node]
reachablesG Graph node
graph [node]
froms = (Vertex -> node) -> [Vertex] -> [node]
forall a b. (a -> b) -> [a] -> [b]
map (Graph node -> Vertex -> node
forall node. Graph node -> Vertex -> node
gr_vertex_to_node Graph node
graph) [Vertex]
result
  where result :: [Vertex]
result = {-# SCC "Digraph.reachable" #-}
                 IntGraph -> [Vertex] -> [Vertex]
reachable (Graph node -> IntGraph
forall node. Graph node -> IntGraph
gr_int_graph Graph node
graph) [Vertex]
vs
        vs :: [Vertex]
vs = [ Vertex
v | Just Vertex
v <- (node -> Maybe Vertex) -> [node] -> [Maybe Vertex]
forall a b. (a -> b) -> [a] -> [b]
map (Graph node -> node -> Maybe Vertex
forall node. Graph node -> node -> Maybe Vertex
gr_node_to_vertex Graph node
graph) [node]
froms ]

hasVertexG :: Graph node -> node -> Bool
hasVertexG :: forall node. Graph node -> node -> Bool
hasVertexG Graph node
graph node
node = Maybe Vertex -> Bool
forall a. Maybe a -> Bool
isJust (Maybe Vertex -> Bool) -> Maybe Vertex -> Bool
forall a b. (a -> b) -> a -> b
$ Graph node -> node -> Maybe Vertex
forall node. Graph node -> node -> Maybe Vertex
gr_node_to_vertex Graph node
graph node
node

transposeG :: Graph node -> Graph node
transposeG :: forall node. Graph node -> Graph node
transposeG Graph node
graph = IntGraph
-> (Vertex -> node) -> (node -> Maybe Vertex) -> Graph node
forall node.
IntGraph
-> (Vertex -> node) -> (node -> Maybe Vertex) -> Graph node
Graph (IntGraph -> IntGraph
G.transposeG (Graph node -> IntGraph
forall node. Graph node -> IntGraph
gr_int_graph Graph node
graph))
                         (Graph node -> Vertex -> node
forall node. Graph node -> Vertex -> node
gr_vertex_to_node Graph node
graph)
                         (Graph node -> node -> Maybe Vertex
forall node. Graph node -> node -> Maybe Vertex
gr_node_to_vertex Graph node
graph)

emptyG :: Graph node -> Bool
emptyG :: forall node. Graph node -> Bool
emptyG Graph node
g = IntGraph -> Bool
graphEmpty (Graph node -> IntGraph
forall node. Graph node -> IntGraph
gr_int_graph Graph node
g)

graphEmpty :: G.Graph -> Bool
graphEmpty :: IntGraph -> Bool
graphEmpty IntGraph
g = Vertex
lo Vertex -> Vertex -> Bool
forall a. Ord a => a -> a -> Bool
> Vertex
hi
  where (Vertex
lo, Vertex
hi) = IntGraph -> (Vertex, Vertex)
forall i e. Array i e -> (i, i)
bounds IntGraph
g


{-
************************************************************************
*                                                                      *
*                         Classify Edge Types
*                                                                      *
************************************************************************
-}

-- Remark: While we could generalize this algorithm this comes at a runtime
-- cost and with no advantages. If you find yourself using this with graphs
-- not easily represented using Int nodes please consider rewriting this
-- using the more general Graph type.

-- | Edge direction based on DFS Classification
data EdgeType
  = Forward
  | Cross
  | Backward -- ^ Loop back towards the root node.
             -- Eg backjumps in loops
  | SelfLoop -- ^ v -> v
   deriving (EdgeType -> EdgeType -> Bool
(EdgeType -> EdgeType -> Bool)
-> (EdgeType -> EdgeType -> Bool) -> Eq EdgeType
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: EdgeType -> EdgeType -> Bool
== :: EdgeType -> EdgeType -> Bool
$c/= :: EdgeType -> EdgeType -> Bool
/= :: EdgeType -> EdgeType -> Bool
Eq,Eq EdgeType
Eq EdgeType =>
(EdgeType -> EdgeType -> Ordering)
-> (EdgeType -> EdgeType -> Bool)
-> (EdgeType -> EdgeType -> Bool)
-> (EdgeType -> EdgeType -> Bool)
-> (EdgeType -> EdgeType -> Bool)
-> (EdgeType -> EdgeType -> EdgeType)
-> (EdgeType -> EdgeType -> EdgeType)
-> Ord EdgeType
EdgeType -> EdgeType -> Bool
EdgeType -> EdgeType -> Ordering
EdgeType -> EdgeType -> EdgeType
forall a.
Eq a =>
(a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
$ccompare :: EdgeType -> EdgeType -> Ordering
compare :: EdgeType -> EdgeType -> Ordering
$c< :: EdgeType -> EdgeType -> Bool
< :: EdgeType -> EdgeType -> Bool
$c<= :: EdgeType -> EdgeType -> Bool
<= :: EdgeType -> EdgeType -> Bool
$c> :: EdgeType -> EdgeType -> Bool
> :: EdgeType -> EdgeType -> Bool
$c>= :: EdgeType -> EdgeType -> Bool
>= :: EdgeType -> EdgeType -> Bool
$cmax :: EdgeType -> EdgeType -> EdgeType
max :: EdgeType -> EdgeType -> EdgeType
$cmin :: EdgeType -> EdgeType -> EdgeType
min :: EdgeType -> EdgeType -> EdgeType
Ord)

instance Outputable EdgeType where
  ppr :: EdgeType -> SDoc
ppr EdgeType
Forward = [Char] -> SDoc
forall doc. IsLine doc => [Char] -> doc
text [Char]
"Forward"
  ppr EdgeType
Cross = [Char] -> SDoc
forall doc. IsLine doc => [Char] -> doc
text [Char]
"Cross"
  ppr EdgeType
Backward = [Char] -> SDoc
forall doc. IsLine doc => [Char] -> doc
text [Char]
"Backward"
  ppr EdgeType
SelfLoop = [Char] -> SDoc
forall doc. IsLine doc => [Char] -> doc
text [Char]
"SelfLoop"

newtype Time = Time Int deriving (Time -> Time -> Bool
(Time -> Time -> Bool) -> (Time -> Time -> Bool) -> Eq Time
forall a. (a -> a -> Bool) -> (a -> a -> Bool) -> Eq a
$c== :: Time -> Time -> Bool
== :: Time -> Time -> Bool
$c/= :: Time -> Time -> Bool
/= :: Time -> Time -> Bool
Eq,Eq Time
Eq Time =>
(Time -> Time -> Ordering)
-> (Time -> Time -> Bool)
-> (Time -> Time -> Bool)
-> (Time -> Time -> Bool)
-> (Time -> Time -> Bool)
-> (Time -> Time -> Time)
-> (Time -> Time -> Time)
-> Ord Time
Time -> Time -> Bool
Time -> Time -> Ordering
Time -> Time -> Time
forall a.
Eq a =>
(a -> a -> Ordering)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> Bool)
-> (a -> a -> a)
-> (a -> a -> a)
-> Ord a
$ccompare :: Time -> Time -> Ordering
compare :: Time -> Time -> Ordering
$c< :: Time -> Time -> Bool
< :: Time -> Time -> Bool
$c<= :: Time -> Time -> Bool
<= :: Time -> Time -> Bool
$c> :: Time -> Time -> Bool
> :: Time -> Time -> Bool
$c>= :: Time -> Time -> Bool
>= :: Time -> Time -> Bool
$cmax :: Time -> Time -> Time
max :: Time -> Time -> Time
$cmin :: Time -> Time -> Time
min :: Time -> Time -> Time
Ord,Integer -> Time
Time -> Time
Time -> Time -> Time
(Time -> Time -> Time)
-> (Time -> Time -> Time)
-> (Time -> Time -> Time)
-> (Time -> Time)
-> (Time -> Time)
-> (Time -> Time)
-> (Integer -> Time)
-> Num Time
forall a.
(a -> a -> a)
-> (a -> a -> a)
-> (a -> a -> a)
-> (a -> a)
-> (a -> a)
-> (a -> a)
-> (Integer -> a)
-> Num a
$c+ :: Time -> Time -> Time
+ :: Time -> Time -> Time
$c- :: Time -> Time -> Time
- :: Time -> Time -> Time
$c* :: Time -> Time -> Time
* :: Time -> Time -> Time
$cnegate :: Time -> Time
negate :: Time -> Time
$cabs :: Time -> Time
abs :: Time -> Time
$csignum :: Time -> Time
signum :: Time -> Time
$cfromInteger :: Integer -> Time
fromInteger :: Integer -> Time
Num,Time -> SDoc
(Time -> SDoc) -> Outputable Time
forall a. (a -> SDoc) -> Outputable a
$cppr :: Time -> SDoc
ppr :: Time -> SDoc
Outputable)

--Allow for specialization
{-# INLINEABLE classifyEdges #-}

-- | Given a start vertex, a way to get successors from a node
-- and a list of (directed) edges classify the types of edges.
classifyEdges :: forall key. Uniquable key => key -> (key -> [key])
              -> [(key,key)] -> [((key, key), EdgeType)]
classifyEdges :: forall key.
Uniquable key =>
key -> (key -> [key]) -> [(key, key)] -> [((key, key), EdgeType)]
classifyEdges key
root key -> [key]
getSucc [(key, key)]
edges =
    --let uqe (from,to) = (getUnique from, getUnique to)
    --in pprTrace "Edges:" (ppr $ map uqe edges) $
    [(key, key)] -> [EdgeType] -> [((key, key), EdgeType)]
forall a b. [a] -> [b] -> [(a, b)]
zip [(key, key)]
edges ([EdgeType] -> [((key, key), EdgeType)])
-> [EdgeType] -> [((key, key), EdgeType)]
forall a b. (a -> b) -> a -> b
$ ((key, key) -> EdgeType) -> [(key, key)] -> [EdgeType]
forall a b. (a -> b) -> [a] -> [b]
map (key, key) -> EdgeType
classify [(key, key)]
edges
  where
    (Time
_time, UniqFM key Time
starts, UniqFM key Time
ends) = (Time, UniqFM key Time, UniqFM key Time)
-> key -> (Time, UniqFM key Time, UniqFM key Time)
addTimes (Time
0,UniqFM key Time
forall {k} (key :: k) elt. UniqFM key elt
emptyUFM,UniqFM key Time
forall {k} (key :: k) elt. UniqFM key elt
emptyUFM) key
root
    classify :: (key,key) -> EdgeType
    classify :: (key, key) -> EdgeType
classify (key
from,key
to)
      | Time
startFrom Time -> Time -> Bool
forall a. Ord a => a -> a -> Bool
< Time
startTo
      , Time
endFrom   Time -> Time -> Bool
forall a. Ord a => a -> a -> Bool
> Time
endTo
      = EdgeType
Forward
      | Time
startFrom Time -> Time -> Bool
forall a. Ord a => a -> a -> Bool
> Time
startTo
      , Time
endFrom   Time -> Time -> Bool
forall a. Ord a => a -> a -> Bool
< Time
endTo
      = EdgeType
Backward
      | Time
startFrom Time -> Time -> Bool
forall a. Ord a => a -> a -> Bool
> Time
startTo
      , Time
endFrom   Time -> Time -> Bool
forall a. Ord a => a -> a -> Bool
> Time
endTo
      = EdgeType
Cross
      | key -> Unique
forall a. Uniquable a => a -> Unique
getUnique key
from Unique -> Unique -> Bool
forall a. Eq a => a -> a -> Bool
== key -> Unique
forall a. Uniquable a => a -> Unique
getUnique key
to
      = EdgeType
SelfLoop
      | Bool
otherwise
      = [Char] -> SDoc -> EdgeType
forall a. HasCallStack => [Char] -> SDoc -> a
pprPanic [Char]
"Failed to classify edge of Graph"
                 ((Unique, Unique) -> SDoc
forall a. Outputable a => a -> SDoc
ppr (key -> Unique
forall a. Uniquable a => a -> Unique
getUnique key
from, key -> Unique
forall a. Uniquable a => a -> Unique
getUnique key
to))

      where
        getTime :: UniqFM key Time -> key -> Time
getTime UniqFM key Time
event key
node
          | Just Time
time <- UniqFM key Time -> key -> Maybe Time
forall key elt. Uniquable key => UniqFM key elt -> key -> Maybe elt
lookupUFM UniqFM key Time
event key
node
          = Time
time
          | Bool
otherwise
          = [Char] -> SDoc -> Time
forall a. HasCallStack => [Char] -> SDoc -> a
pprPanic [Char]
"Failed to classify edge of CFG - not not timed"
            ([Char] -> SDoc
forall doc. IsLine doc => [Char] -> doc
text [Char]
"edges" SDoc -> SDoc -> SDoc
forall doc. IsLine doc => doc -> doc -> doc
<> (Unique, Unique) -> SDoc
forall a. Outputable a => a -> SDoc
ppr (key -> Unique
forall a. Uniquable a => a -> Unique
getUnique key
from, key -> Unique
forall a. Uniquable a => a -> Unique
getUnique key
to)
                          SDoc -> SDoc -> SDoc
forall doc. IsLine doc => doc -> doc -> doc
<+> UniqFM key Time -> SDoc
forall a. Outputable a => a -> SDoc
ppr UniqFM key Time
starts SDoc -> SDoc -> SDoc
forall doc. IsLine doc => doc -> doc -> doc
<+> UniqFM key Time -> SDoc
forall a. Outputable a => a -> SDoc
ppr UniqFM key Time
ends )
        startFrom :: Time
startFrom = UniqFM key Time -> key -> Time
getTime UniqFM key Time
starts key
from
        startTo :: Time
startTo   = UniqFM key Time -> key -> Time
getTime UniqFM key Time
starts key
to
        endFrom :: Time
endFrom   = UniqFM key Time -> key -> Time
getTime UniqFM key Time
ends   key
from
        endTo :: Time
endTo     = UniqFM key Time -> key -> Time
getTime UniqFM key Time
ends   key
to

    addTimes :: (Time, UniqFM key Time, UniqFM key Time) -> key
             -> (Time, UniqFM key Time, UniqFM key Time)
    addTimes :: (Time, UniqFM key Time, UniqFM key Time)
-> key -> (Time, UniqFM key Time, UniqFM key Time)
addTimes (Time
time,UniqFM key Time
starts,UniqFM key Time
ends) key
n
      --Dont reenter nodes
      | key -> UniqFM key Time -> Bool
forall key elt. Uniquable key => key -> UniqFM key elt -> Bool
elemUFM key
n UniqFM key Time
starts
      = (Time
time,UniqFM key Time
starts,UniqFM key Time
ends)
      | Bool
otherwise =
        let
          starts' :: UniqFM key Time
starts' = UniqFM key Time -> key -> Time -> UniqFM key Time
forall key elt.
Uniquable key =>
UniqFM key elt -> key -> elt -> UniqFM key elt
addToUFM UniqFM key Time
starts key
n Time
time
          time' :: Time
time' = Time
time Time -> Time -> Time
forall a. Num a => a -> a -> a
+ Time
1
          succs :: [key]
succs = key -> [key]
getSucc key
n :: [key]
          (Time
time'',UniqFM key Time
starts'',UniqFM key Time
ends') = ((Time, UniqFM key Time, UniqFM key Time)
 -> key -> (Time, UniqFM key Time, UniqFM key Time))
-> (Time, UniqFM key Time, UniqFM key Time)
-> [key]
-> (Time, UniqFM key Time, UniqFM key Time)
forall b a. (b -> a -> b) -> b -> [a] -> b
forall (t :: * -> *) b a.
Foldable t =>
(b -> a -> b) -> b -> t a -> b
foldl' (Time, UniqFM key Time, UniqFM key Time)
-> key -> (Time, UniqFM key Time, UniqFM key Time)
addTimes (Time
time',UniqFM key Time
starts',UniqFM key Time
ends) [key]
succs
          ends'' :: UniqFM key Time
ends'' = UniqFM key Time -> key -> Time -> UniqFM key Time
forall key elt.
Uniquable key =>
UniqFM key elt -> key -> elt -> UniqFM key elt
addToUFM UniqFM key Time
ends' key
n Time
time''
        in
        (Time
time'' Time -> Time -> Time
forall a. Num a => a -> a -> a
+ Time
1, UniqFM key Time
starts'', UniqFM key Time
ends'')

graphFromVerticesAndAdjacency
        :: Ord key
        => [Node key payload]
        -> [(key, key)]  -- First component is source vertex key,
                         -- second is target vertex key (thing depended on)
                         -- Unlike the other interface I insist they correspond to
                         -- actual vertices because the alternative hides bugs. I can't
                         -- do the same thing for the other one for backcompat reasons.
        -> Graph (Node key payload)
graphFromVerticesAndAdjacency :: forall key payload.
Ord key =>
[Node key payload] -> [(key, key)] -> Graph (Node key payload)
graphFromVerticesAndAdjacency []       [(key, key)]
_     = Graph (Node key payload)
forall a. Graph a
emptyGraph
graphFromVerticesAndAdjacency [Node key payload]
vertices [(key, key)]
edges = IntGraph
-> (Vertex -> Node key payload)
-> (Node key payload -> Maybe Vertex)
-> Graph (Node key payload)
forall node.
IntGraph
-> (Vertex -> node) -> (node -> Maybe Vertex) -> Graph node
Graph IntGraph
graph Vertex -> Node key payload
vertex_node (key -> Maybe Vertex
key_vertex (key -> Maybe Vertex)
-> (Node key payload -> key) -> Node key payload -> Maybe Vertex
forall b c a. (b -> c) -> (a -> b) -> a -> c
. Node key payload -> key
forall key payload. Node key payload -> key
key_extractor)
  where key_extractor :: Node key payload -> key
key_extractor = Node key payload -> key
forall key payload. Node key payload -> key
node_key
        ((Vertex, Vertex)
bounds, Vertex -> Node key payload
vertex_node, key -> Maybe Vertex
key_vertex, [(Vertex, Node key payload)]
_) = ReduceFn key payload
forall key payload. Ord key => ReduceFn key payload
reduceNodesIntoVerticesOrd [Node key payload]
vertices Node key payload -> key
forall key payload. Node key payload -> key
key_extractor
        key_vertex_pair :: (key, key) -> (Vertex, Vertex)
key_vertex_pair (key
a, key
b) = ([Char] -> Maybe Vertex -> Vertex
forall a. HasDebugCallStack => [Char] -> Maybe a -> a
expectJust [Char]
"graphFromVerticesAndAdjacency" (Maybe Vertex -> Vertex) -> Maybe Vertex -> Vertex
forall a b. (a -> b) -> a -> b
$ key -> Maybe Vertex
key_vertex key
a,
                                  [Char] -> Maybe Vertex -> Vertex
forall a. HasDebugCallStack => [Char] -> Maybe a -> a
expectJust [Char]
"graphFromVerticesAndAdjacency" (Maybe Vertex -> Vertex) -> Maybe Vertex -> Vertex
forall a b. (a -> b) -> a -> b
$ key -> Maybe Vertex
key_vertex key
b)
        reduced_edges :: [(Vertex, Vertex)]
reduced_edges = ((key, key) -> (Vertex, Vertex))
-> [(key, key)] -> [(Vertex, Vertex)]
forall a b. (a -> b) -> [a] -> [b]
map (key, key) -> (Vertex, Vertex)
key_vertex_pair [(key, key)]
edges
        graph :: IntGraph
graph = (Vertex, Vertex) -> [(Vertex, Vertex)] -> IntGraph
G.buildG (Vertex, Vertex)
bounds [(Vertex, Vertex)]
reduced_edges