module Logic.Graph where

bfs :: Eq a => a -> a -> (a -> [(edge, a)]) -> Maybe [edge]
bfs goal start getEdges = reverse <$> aux [([], start)] []
  where
    aux [] _ = Nothing
    aux ((path, vertex):queue) visited
      | vertex == goal = Just path
      | otherwise =
        let new = getUnvisitedAdjacent vertex visited
        in
          case filter (\(_, v) -> v == goal) new of
            [] ->
              let queue' = queue ++ map (\(edge, next) -> (edge:path, next)) new
              in aux queue' (vertex:visited)
            ((edge, _):_) -> Just (edge:path)

    getUnvisitedAdjacent vertex visited =
      filter (\(edge, next) -> not $ next `elem` visited) $
      getEdges vertex

{-
ghci> bfs 10 0 (\x -> [("pred", x-1), ("succ", x+1)])
Just ["succ","succ","succ","succ","succ","succ","succ","succ","succ","succ"]
ghci> bfs 13 0 (\x -> [("double", x+x), ("add", x+1)])
Just ["add","double","add","double","double","add"]
-}