(* Copyright (C) 2005, HELM Team.
 * 
 * This file is part of HELM, an Hypertextual, Electronic
 * Library of Mathematics, developed at the Computer Science
 * Department, University of Bologna, Italy.
 * 
 * HELM is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License
 * as published by the Free Software Foundation; either version 2
 * of the License, or (at your option) any later version.
 * 
 * HELM is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with HELM; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
 * MA  02111-1307, USA.
 * 
 * For details, see the HELM World-Wide-Web page,
 * http://cs.unibo.it/helm/.
 *)

type equality =
    int *                (* weight *)
    proof *              (* proof *)
    (Cic.term *          (* type *)
     Cic.term *          (* left side *)
     Cic.term *          (* right side *)
     Utils.comparison) * (* ordering *)  
    Cic.metasenv *       (* environment for metas *)
    Cic.term list        (* arguments *)

and proof =
  | NoProof
  | BasicProof of Cic.term (* already a proof of a goal *)
  | ProofBlock of (* proof of a rewrite step *)
      Cic.substitution * UriManager.uri * (* eq_ind or eq_ind_r *)
        (Cic.name * Cic.term) * Cic.term * (Utils.pos * equality) * proof
  | ProofGoalBlock of proof * proof
      (* proof of the new meta, proof of the goal from which this comes *)
  | ProofSymBlock of Cic.term list * proof (* expl.named subst, proof *)
  | SubProof of Cic.term * int * proof
      (* parent proof, subgoal, proof of the subgoal *)

type environment = Cic.metasenv * Cic.context * CicUniv.universe_graph

(** builds the Cic.term encoded by proof *)
val build_proof_term: proof -> Cic.term

val string_of_proof: proof -> string

exception MatchingFailure

(** matching between two terms. Can raise MatchingFailure *)
val matching:
  Cic.metasenv -> Cic.context -> Cic.term -> Cic.term ->
  CicUniv.universe_graph ->
  Cic.substitution * Cic.metasenv * CicUniv.universe_graph

(**
   special unification that checks if the two terms are "simple", and in
   such case should be significantly faster than CicUnification.fo_unif
*)
val unification:
  Cic.metasenv -> Cic.context -> Cic.term -> Cic.term ->
  CicUniv.universe_graph ->
  Cic.substitution * Cic.metasenv * CicUniv.universe_graph

    
(**
   scans the context to find all Declarations "left = right"; returns a
   list of tuples (proof, (type, left, right), newmetas). Uses
   PrimitiveTactics.new_metasenv_for_apply to replace bound variables with
   fresh metas...
*)
val find_equalities:
  Cic.context -> ProofEngineTypes.proof -> int list * equality list * int

(**
   searches the library for equalities that can be applied to the current goal
*)
val find_library_equalities:
  HMysql.dbd -> Cic.context -> ProofEngineTypes.status -> int ->
  UriManager.UriSet.t * equality list * int

(**
   searches the library for theorems that are not equalities (returned by the
   function above)
*)
val find_library_theorems:
  HMysql.dbd -> environment -> ProofEngineTypes.status -> UriManager.UriSet.t ->
  (Cic.term * Cic.term * Cic.metasenv) list

(**
   searches the context for hypotheses that are not equalities
*)
val find_context_hypotheses:
  environment -> int list -> (Cic.term * Cic.term * Cic.metasenv) list


exception TermIsNotAnEquality;;

(**
   raises TermIsNotAnEquality if term is not an equation.
   The first Cic.term is a proof of the equation
*)
val equality_of_term: Cic.term -> Cic.term -> equality

val term_is_equality: Cic.term -> bool

(** tests a sort of alpha-convertibility between the two terms, but on the
    metavariables *)
val meta_convertibility: Cic.term -> Cic.term -> bool

(** meta convertibility between two equations *)
val meta_convertibility_eq: equality -> equality -> bool

val is_identity: environment -> equality -> bool

val string_of_equality: ?env:environment -> equality -> string

val metas_of_term: Cic.term -> int list

(** ensures that metavariables in equality are unique *)
val fix_metas: int -> equality -> int * equality