bfs: use a Set for visited nodes

Logic/Graph.hs

@@ -1,7 +1,9 @@
 module Logic.Graph where
 
-bfs :: Eq a => a -> a -> (a -> [(edge, a)]) -> Maybe [edge]
-bfs goal start getEdges = reverse <$> aux [([], start)] []
+import Data.Set (Set, insert)
+
+bfs :: (Eq a, Ord a) => a -> a -> (a -> [(edge, a)]) -> Maybe [edge]
+bfs goal start getEdges = reverse <$> aux [([], start)] mempty
   where
     aux [] _ = Nothing
     aux ((path, vertex):queue) visited
@@ -12,7 +14,7 @@ bfs goal start getEdges = reverse <$> aux [([], start)] []
           case filter (\(_, v) -> v == goal) new of
             [] ->
               let queue' = queue ++ map (\(edge, next) -> (edge:path, next)) new
-              in aux queue' (vertex:visited)
+              in aux queue' $ insert vertex visited
             ((edge, _):_) -> Just (edge:path)
 
     getUnvisitedAdjacent vertex visited =

Logic/Statement.hs

@@ -9,7 +9,7 @@ data Statement
   | Or Statement Statement
   | Implies Statement Statement
   | Iff Statement Statement
-  deriving (Show, Eq)
+  deriving (Eq, Ord, Show)
 
 atoms :: Statement -> [String]
 atoms = toAscList . mkSet