src/Provers/trancl.ML

 
 fun transpose eq_comp g =
   let
    (* Compute list of reversed edges for each adjacency list *)
    fun flip (u,(v,l)::el) = (v,(u,l)) :: flip (u,el)
-     | flip (_,nil) = nil
+     | flip (_,[]) = []
 
    (* Compute adjacency list for node u from the list of edges
       and return a likewise reduced list of edges.  The list of edges
       is searches for edges starting from u, and these edges are removed. *)
    fun gather (u,(v,w)::el) =

      val (adj,edges) = gather (u,el)
     in
      if eq_comp (u, v) then (w::adj,edges)
      else (adj,(v,w)::edges)
     end
-   | gather (_,nil) = (nil,nil)
+   | gather (_,[]) = ([],[])
 
    (* For every node in the input graph, call gather to find all reachable
       nodes in the list of edges *)
    fun assemble ((u,_)::el) edges =
        let val (adj,edges) = gather (u,edges)
        in (u,adj) :: assemble el edges
        end
-     | assemble nil _ = nil
+     | assemble [] _ = []
 
    (* Compute, for each adjacency list, the list with reversed edges,
       and concatenate these lists. *)
-   val flipped = List.foldr (op @) nil (map flip g)
+   val flipped = maps flip g
 
  in assemble g flipped end
 
 (* *********************************************************************** *)
 (*                                                                         *)

 (* *********************************************************************** *)
 
 fun dfs_reachable eq_comp g u =
  let
   (* List of vertices which have been visited. *)
-  val visited  = Unsynchronized.ref nil;
+  val visited  = Unsynchronized.ref [];
 
   fun been_visited v = exists (fn w => eq_comp (w, v)) (!visited)
 
   fun dfs_visit g u  =
       let
    val _ = visited := u :: !visited
    val descendents =
        List.foldr (fn ((v,l),ds) => if been_visited v then ds
             else v :: dfs_visit g v @ ds)
-        nil (adjacent eq_comp g u)
+        [] (adjacent eq_comp g u)
    in  descendents end
 
  in u :: dfs_visit g u end;
 
 (* *********************************************************************** *)