(**************************************************************************)
(*     Sail                                                               *)
(*                                                                        *)
(*  Copyright (c) 2013-2017                                               *)
(*    Kathyrn Gray                                                        *)
(*    Shaked Flur                                                         *)
(*    Stephen Kell                                                        *)
(*    Gabriel Kerneis                                                     *)
(*    Robert Norton-Wright                                                *)
(*    Christopher Pulte                                                   *)
(*    Peter Sewell                                                        *)
(*    Alasdair Armstrong                                                  *)
(*    Brian Campbell                                                      *)
(*    Thomas Bauereiss                                                    *)
(*    Anthony Fox                                                         *)
(*    Jon French                                                          *)
(*    Dominic Mulligan                                                    *)
(*    Stephen Kell                                                        *)
(*    Mark Wassell                                                        *)
(*                                                                        *)
(*  All rights reserved.                                                  *)
(*                                                                        *)
(*  This software was developed by the University of Cambridge Computer   *)
(*  Laboratory as part of the Rigorous Engineering of Mainstream Systems  *)
(*  (REMS) project, funded by EPSRC grant EP/K008528/1.                   *)
(*                                                                        *)
(*  Redistribution and use in source and binary forms, with or without    *)
(*  modification, are permitted provided that the following conditions    *)
(*  are met:                                                              *)
(*  1. Redistributions of source code must retain the above copyright     *)
(*     notice, this list of conditions and the following disclaimer.      *)
(*  2. Redistributions in binary form must reproduce the above copyright  *)
(*     notice, this list of conditions and the following disclaimer in    *)
(*     the documentation and/or other materials provided with the         *)
(*     distribution.                                                      *)
(*                                                                        *)
(*  THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS''    *)
(*  AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED     *)
(*  TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A       *)
(*  PARTICULAR PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR   *)
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(*  SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT      *)
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(*  SUCH DAMAGE.                                                          *)
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(** Generic graph type based on OCaml Set and Map *)

module type OrderedType =
  sig
    type t
    val compare : t -> t -> int
  end

module type S =
  sig
    type node
    type graph
    type node_set

    val leaves : graph -> node_set

    val empty : graph

    (** Add an edge from the first node to the second node, creating
       the nodes if they do not exist. *)
    val add_edge : node -> node -> graph -> graph
    val add_edges : node -> node list -> graph -> graph

    val children : graph -> node -> node list

    (** Return the set of nodes that are reachable from the first set
       of nodes (roots), without passing through the second set of
       nodes (cuts). *)
    val reachable : node_set -> node_set -> graph -> node_set

    (** Prune a graph from roots to cuts. *)
    val prune : node_set -> node_set -> graph -> graph

    val remove_self_loops : graph -> graph

    val reverse : graph -> graph

    exception Not_a_DAG of node * graph;;

    (** Topologically sort a graph. Throws Not_a_DAG if the graph is
       not directed acyclic. *)
    val topsort : graph -> node list

    (** Find strongly connected components using Tarjan's algorithm.
        This algorithm also returns a topological sorting of the graph
        components. *)
    val scc : ?original_order:(node list) -> graph -> node list list

    val make_dot : (node -> string) -> (node -> node -> string) -> (node -> string) -> out_channel -> graph -> unit
  end

module Make(Ord: OrderedType) : S
       with type node = Ord.t
        and type node_set = Set.Make(Ord).t
        and type graph = Set.Make(Ord).t Map.Make(Ord).t