(* Copyright (C) 2002, 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/.
 *)
 

let rewrite ~term:equality ?where ?(direction=`Left) (proof,goal) =
(*
  let module C = Cic in
  let module U = UriManager in
  let module PET = ProofEngineTypes in
  let module PER = ProofEngineReduction in
  let module PEH = ProofEngineHelpers in
  let module PT = PrimitiveTactics in
  let module HLO = HelmLibraryObjects in
  let if_left a b = 
    match direction with
    | `Right -> b
    | `Left -> a
  in
  let curi, metasenv, pbo, pty = proof in
  let metano, context, gty = CicUtil.lookup_meta goal metasenv in
  let eq_uri = HLO.Logic.eq_URI in
  let ty_eq,_ = 
    CicTypeChecker.type_of_aux' metasenv context equality 
      CicUniv.empty_ugraph
  in 
  let eq_ind, ty, t1, t2 =
    match ty_eq with
    | C.Appl [C.MutInd (uri, 0, []); ty; t1; t2] when U.eq uri eq_uri ->
        let eq_ind = 
          C.Const (if_left HLO.Logic.eq_ind_URI HLO.Logic.eq_ind_r_URI,[])
        in
        if_left (eq_ind, ty, t2, t1) (eq_ind, ty, t1, t2)
    | _ -> raise (PET.Fail "Rewrite: argument is not a proof of an equality")
  in
  (* now we always do as if direction was `Left *)
  let gty' = CicSubstitution.lift 1 gty in
  let t1' = CicSubstitution.lift 1 t1 in
  let eq_kind, what = 
    match where with
    | None  
    | Some ([], None) ->   
        PER.alpha_equivalence, [t1']
    | Some (hp_paths, goal_path) -> 
        assert (hp_paths = []); 
        match goal_path with
        | None -> assert false (* (==), [t1'] *)
        | Some path -> 
            let roots = ProofEngineHelpers.select ~term:gty' ~pattern:path in
            let subterms = 
              List.fold_left (
                fun acc (i, r) -> 
                  let wanted = CicSubstitution.lift (List.length i) t1' in
                  PEH.find_subterms ~eq:PER.alpha_equivalence ~wanted r @ acc
            ) [] roots
            in
            (==), subterms
  in
  let with_what = 
    let rec aux = function 
      | 0 -> []
      | n -> C.Rel 1 :: aux (n-1)
    in
    aux (List.length what)
  in
  let gty'' =
   ProofEngineReduction.replace_lifting_csc 0
    ~equality:eq_kind ~what ~with_what ~where:gty'
  in
  let gty_red = CicSubstitution.subst t2 gty'' in
  let fresh_meta = ProofEngineHelpers.new_meta_of_proof proof in
  let irl =CicMkImplicit.identity_relocation_list_for_metavariable context in
  let metasenv' = (fresh_meta,context,gty_red)::metasenv in
  let fresh_name = 
    FreshNamesGenerator.mk_fresh_name 
    ~subst:[] metasenv context C.Anonymous ~typ:ty
  in
  let pred = C.Lambda (fresh_name, ty, gty'') in
  let exact_proof = 
    C.Appl [eq_ind ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality]
  in
  let (proof',goals) =
    PET.apply_tactic 
      (PT.exact_tac ~term:exact_proof) ((curi,metasenv',pbo,pty),goal)
  in
  assert (List.length goals = 0) ;
  (proof',[fresh_meta])
*) assert false
  
 
let rewrite_tac ?where ~term () =
  let rewrite_tac ?where ~term status =
    rewrite ?where ~term ~direction:`Right status
  in
  ProofEngineTypes.mk_tactic (rewrite_tac ?where ~term)

let rewrite_simpl_tac ?where ~term () =
 let rewrite_simpl_tac ?where ~term status =
  ProofEngineTypes.apply_tactic
  (Tacticals.then_ 
   ~start:(rewrite_tac ?where ~term ())
   ~continuation:
     (ReductionTactics.simpl_tac
       ~pattern:(ProofEngineTypes.conclusion_pattern None)))
   status
 in
   ProofEngineTypes.mk_tactic (rewrite_simpl_tac ~term)
;;

let rewrite_back_tac ?where ~term () =
  let rewrite_back_tac ?where ~term status =
    rewrite ?where ~term ~direction:`Left status
  in
  ProofEngineTypes.mk_tactic (rewrite_back_tac ?where ~term)

let rewrite_back_simpl_tac ?where ~term () =
 let rewrite_back_simpl_tac ?where ~term status =
  ProofEngineTypes.apply_tactic
   (Tacticals.then_ 
    ~start:(rewrite_back_tac ?where ~term ())
    ~continuation:
     (ReductionTactics.simpl_tac
       ~pattern:(ProofEngineTypes.conclusion_pattern None)))
   status
 in
  ProofEngineTypes.mk_tactic (rewrite_back_simpl_tac ~term)
;;

let replace_tac ~pattern ~with_what =
(*
 let replace_tac ~pattern ~with_what status =
  let (proof, goal) = status in
  let module C = Cic in
  let module U = UriManager in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
  let _,metasenv,_,_ = proof in
  let _,context,_ = CicUtil.lookup_meta goal metasenv in
  let wty,u = (* TASSI: FIXME *)
    CicTypeChecker.type_of_aux' metasenv context what CicUniv.empty_ugraph in
  let wwty,_ = CicTypeChecker.type_of_aux' metasenv context with_what u in
    try
      if (wty = wwty) then
        ProofEngineTypes.apply_tactic
          (T.thens
             ~start:(
               P.cut_tac 
		       (C.Appl [
			  (C.MutInd (HelmLibraryObjects.Logic.eq_URI, 0, [])) ;
			  wty ; 
			  what ; 
			  with_what]))
             ~continuations:[            
	       
	       T.then_ 	   ~start:(rewrite_simpl_tac ~term:(C.Rel 1) ())
			   ~continuation:(
				 ProofEngineStructuralRules.clear
						~hyp:(List.hd context)) ;
               T.id_tac])
          status
      else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
    with (Failure "hd") -> 
      raise (ProofEngineTypes.Fail "Replace: empty context")
 in
   ProofEngineTypes.mk_tactic (replace_tac ~what ~with_what)
*) assert false
;;


(* All these tacs do is applying the right constructor/theorem *)

let reflexivity_tac =
  IntroductionTactics.constructor_tac ~n:1
;;

let symmetry_tac =
 let symmetry_tac (proof, goal) =
  let module C = Cic in
  let module R = CicReduction in
  let module U = UriManager in
   let (_,metasenv,_,_) = proof in
    let metano,context,ty = CicUtil.lookup_meta goal metasenv in
     match (R.whd context ty) with
        (C.Appl [(C.MutInd (uri, 0, [])); _; _; _])
	 when (U.eq uri HelmLibraryObjects.Logic.eq_URI) ->
	  ProofEngineTypes.apply_tactic 
           (PrimitiveTactics.apply_tac 
	    ~term: (C.Const (HelmLibraryObjects.Logic.sym_eq_URI, []))) 
	   (proof,goal)

      | _ -> raise (ProofEngineTypes.Fail "Symmetry failed")
 in
  ProofEngineTypes.mk_tactic symmetry_tac
;;

let transitivity_tac ~term =
 let transitivity_tac ~term status =
  let (proof, goal) = status in
  let module C = Cic in
  let module R = CicReduction in
  let module U = UriManager in
  let module T = Tacticals in
   let (_,metasenv,_,_) = proof in
    let metano,context,ty = CicUtil.lookup_meta goal metasenv in
     match (R.whd context ty) with
        (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) 
	when (uri = HelmLibraryObjects.Logic.eq_URI) ->
         ProofEngineTypes.apply_tactic 
	 (T.thens
          ~start:(PrimitiveTactics.apply_tac
            ~term: (C.Const (HelmLibraryObjects.Logic.trans_eq_URI, [])))
          ~continuations:
            [PrimitiveTactics.exact_tac ~term ; T.id_tac ; T.id_tac])
          status

      | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
 in
  ProofEngineTypes.mk_tactic (transitivity_tac ~term)
;;