-- | This module tests Haggle by comparing its results to those of FGL.
-- This assumes that FGL is reasonably correct.
--
-- The arbitrary instance for GraphPair generates a list of edges and
-- then constructs equivalent FGL and Haggle graphs.  The quickcheck
-- properties for each operation try to ensure that the two implementations
-- return the same results.
module Main ( main ) where

import Test.Framework ( defaultMain, testGroup, Test )
import Test.Framework.Providers.QuickCheck2 ( testProperty )
import Test.QuickCheck

import Control.Arrow ( first, second )
import Control.Monad ( replicateM )
import qualified Data.Foldable as F
import Data.Maybe ( isNothing )
import qualified Data.Set as S

import qualified Data.Graph.Inductive as FGL
import qualified Data.Graph.Haggle as HGL
import qualified Data.Graph.Haggle.VertexLabelAdapter as HGL
import qualified Data.Graph.Haggle.SimpleBiDigraph as HGL
import qualified Data.Graph.Haggle.Algorithms.DFS as HGL
import qualified Data.Graph.Haggle.Algorithms.Dominators as HGL

-- import Debug.Trace
-- debug = flip trace

type BaseGraph = FGL.Gr Int ()
type TestGraph = HGL.VertexLabeledGraph HGL.SimpleBiDigraph Int

data GraphPair = GP [(Int, Int)] BaseGraph TestGraph

instance Arbitrary GraphPair where
  arbitrary = sized mkGraphPair

instance Show GraphPair where
  show (GP es _ _) = show es

newtype NodeId = NID Int
  deriving (Show)
instance Arbitrary NodeId where
  arbitrary = sized mkNodeId
    where
      mkNodeId n = do
        i <- choose (0, n)
        return (NID i)

mkGraphPair :: Int -> Gen GraphPair
mkGraphPair sz = do
  nEdges <- choose (2, 2 * sz)
  srcs <- replicateM nEdges (choose (0, sz))
  dsts <- replicateM nEdges (choose (0, sz))
  let edges = unique $ zip srcs dsts
      nids = unique (srcs ++ dsts)
      ns = zip nids nids
      bg = FGL.mkGraph ns (map (\(s, d) -> (s, d, ())) edges)
      (tg, _) = HGL.fromEdgeList HGL.newMSimpleBiDigraph edges
  return $! GP edges bg tg

main :: IO ()
main = defaultMain tests

tests :: [Test]
tests = [ testProperty "prop_sameVertexCount" prop_sameVertexCount
        , testProperty "prop_sameEdgeCount" prop_sameEdgeCount
        , testProperty "prop_sameSuccessorsAtLabel" prop_sameSuccessorsAtLabel
        , testProperty "prop_samePredecessorsAtLabel" prop_samePredecessorsAtLabel
        , testProperty "prop_dfsSame" prop_dfsSame
        , testProperty "prop_sameComponents" prop_sameComponents
        , testProperty "prop_sameNoComponents" prop_sameNoComponents
        , testProperty "prop_immDominatorsSame" prop_immDominatorsSame
        , testProperty "prop_dominatorsSame" prop_dominatorsSame
        ]

prop_sameVertexCount :: GraphPair -> Bool
prop_sameVertexCount (GP _ bg tg) =
  length (FGL.nodes bg) == length (HGL.vertices tg)

prop_sameEdgeCount :: GraphPair -> Bool
prop_sameEdgeCount (GP _ bg tg) =
  length (FGL.edges bg) == length (HGL.edges tg)

prop_sameSuccessorsAtLabel :: (NodeId, GraphPair) -> Bool
prop_sameSuccessorsAtLabel (NID nid, GP _ bg tg)
  | not (FGL.gelem nid bg) && isNothing (vertexFromLabel tg nid) = True
  | otherwise = bss == tss
  where
    bss = S.fromList $ fmap Just $ FGL.suc bg nid
    ts = maybe [] (map (HGL.vertexLabel tg) . HGL.successors tg) (vertexFromLabel tg nid)
    tss = S.fromList ts

prop_samePredecessorsAtLabel :: (NodeId, GraphPair) -> Bool
prop_samePredecessorsAtLabel (NID nid, GP _ bg tg)
  | not (FGL.gelem nid bg) && isNothing (vertexFromLabel tg nid) = True
  | otherwise = bss == tss
  where
    bss = S.fromList $ fmap Just $ FGL.pre bg nid
    ts = maybe [] (map (HGL.vertexLabel tg) . HGL.predecessors tg) (vertexFromLabel tg nid)
    tss = S.fromList ts

-- Note that this is only checking the *set* of vertices reached.  Unfortunately,
-- verifying the *order* is difficult because there are many valid DFS orders
-- (depending on the order edges are stored).  A test using the DFS number
-- (derived from the depth in the depth-first tree) would be a good complement
-- to this.
prop_dfsSame :: (NodeId, GraphPair) -> Bool
prop_dfsSame (NID root, GP _ bg tg) =
  S.fromList bres == S.fromList tres
  where
    bres = map Just $ FGL.dfs [root] bg
    v = vertexFromLabel tg root
    tres = maybe [] (map (HGL.vertexLabel tg) . HGL.dfs tg . (:[])) v

prop_immDominatorsSame :: (NodeId, GraphPair) -> Bool
prop_immDominatorsSame (NID root, GP _ bg tg)
  | not (FGL.gelem root bg) && isNothing (vertexFromLabel tg root) = True
  | otherwise = S.fromList bdoms == S.fromList tdoms
  where
    bdoms = FGL.iDom bg root
    toLabs (v1, v2) =
      let Just v1l = HGL.vertexLabel tg v1
          Just v2l = HGL.vertexLabel tg v2
      in (v1l, v2l)
    tdoms = maybe [] (map toLabs . HGL.immediateDominators tg) (vertexFromLabel tg root)

prop_dominatorsSame :: (NodeId, GraphPair) -> Bool
prop_dominatorsSame (NID root, GP _ bg tg)
  | not (FGL.gelem root bg) && isNothing (vertexFromLabel tg root) = True
  | otherwise = S.fromList (map (first Just) bdoms) == S.fromList (map (first (HGL.vertexLabel tg)) tdoms)
  where
    bdoms = map (second (S.fromList . map Just)) $ FGL.dom bg root
    Just rv = vertexFromLabel tg root
    tdoms = map (second (S.fromList . map (HGL.vertexLabel tg))) $ HGL.dominators tg rv

prop_sameComponents :: GraphPair -> Bool
prop_sameComponents (GP _ bg tg) = bcs == tcs
  where
    bcs = S.map (S.fromList . map Just) $ S.fromList $ FGL.components bg
    tcs = S.map (S.fromList . map (HGL.vertexLabel tg)) $ S.fromList $ HGL.components tg

prop_sameNoComponents :: GraphPair -> Bool
prop_sameNoComponents (GP _ bg tg) =
  FGL.noComponents bg == HGL.noComponents tg

-- Helpers

vertexFromLabel :: TestGraph -> Int -> Maybe HGL.Vertex
vertexFromLabel g lbl = F.find labelMatch (HGL.vertices g)
  where
    labelMatch v = Just lbl == (HGL.vertexLabel g v)

unique :: (Ord a) => [a] -> [a]
unique = S.toList . S.fromList