verify graph path search

Logic/Graph.hs

@@ -35,3 +35,21 @@ 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"]
 -}
+
+data VerifyPathError vertex edge
+  = NoSuchEdge vertex edge
+
+verifyPath
+  :: (Eq vertex, Ord vertex, Eq edge)
+  => GetEdges vertex edge
+  -> vertex
+  -> vertex
+  -> [edge]
+  -> Either (VerifyPathError vertex edge) Bool
+verifyPath getEdges goal start path =
+  case path of
+    [] -> Right $ start == goal
+    (thisEdge:nextEdges) ->
+      case map fst $ filter (\(next, realEdge) -> realEdge == thisEdge) $ getEdges start of
+        [] -> Left $ NoSuchEdge start thisEdge
+        (next:_) -> verifyPath getEdges goal next nextEdges