(* 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 constructor_tac ~n ~status:(proof, goal) =
  let module C = Cic in
  let module R = CicReduction in
   let (_,metasenv,_,_) = proof in
    let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
     match (R.whd context ty) with  
        (C.MutInd (uri, typeno, exp_named_subst))
      | (C.Appl ((C.MutInd (uri, typeno, exp_named_subst))::_)) ->
         PrimitiveTactics.apply_tac ~status:(proof, goal)
          ~term: (C.MutConstruct (uri, typeno, n, exp_named_subst))
      | _ -> raise (ProofEngineTypes.Fail "Constructor failed")
;;


let exists_tac ~status =
  constructor_tac ~n:1 ~status
;;


let split_tac ~status =
  constructor_tac ~n:1 ~status
;;


let left_tac ~status =
  constructor_tac ~n:1 ~status
;;


let right_tac ~status =
  constructor_tac ~n:2 ~status
;;


let reflexivity_tac =
  constructor_tac ~n:1
;;


let symmetry_tac ~status:(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 = List.find (function (m,_,_) -> m=goal) metasenv in
     match (R.whd context ty) with 
        (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
         PrimitiveTactics.apply_tac ~status:(proof,goal)
          ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/sym_eq.con", []))

      | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
         PrimitiveTactics.apply_tac ~status:(proof,goal)
          ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/sym_eqT.con", []))

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


let transitivity_tac ~term ~status:((proof, goal) as status) =
  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 = List.find (function (m,_,_) -> m=goal) metasenv in
     match (R.whd context ty) with 
        (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind")) ->
         T.thens
          ~start:(PrimitiveTactics.apply_tac
            ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic/trans_eq.con", [])))
          ~continuations:
            [T.id_tac ; T.id_tac ; PrimitiveTactics.exact_tac ~term]
          ~status

      | (C.Appl [(C.MutInd (uri, 0, [])); _; _; _]) when (uri = (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind")) ->
         T.thens 
          ~start:(PrimitiveTactics.apply_tac
            ~term: (C.Const (U.uri_of_string "cic:/Coq/Init/Logic_Type/trans_eqT.con", [])))
          ~continuations:
            [T.id_tac ; T.id_tac ; PrimitiveTactics.exact_tac ~term]
          ~status

      | _ -> raise (ProofEngineTypes.Fail "Transitivity failed")
;;


(* TODO se ce n'e' piu' di una, prende la prima che trova... sarebbe meglio chiedere *)

let assumption_tac ~status:((proof,goal) as status) =
  let module C = Cic in
  let module R = CicReduction in
  let module S = CicSubstitution in
   let _,metasenv,_,_ = proof in
    let _,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
     let rec find n = function 
        hd::tl -> 
         (match hd with
             (Some (_, C.Decl t)) when
               (R.are_convertible context (S.lift n t) ty) -> n
           | (Some (_, C.Def t)) when
               (R.are_convertible context
                (CicTypeChecker.type_of_aux' metasenv context (S.lift n t)) ty) -> n 
           | _ -> find (n+1) tl
         )
      | [] -> raise (ProofEngineTypes.Fail "Assumption: No such assumption")
     in PrimitiveTactics.apply_tac ~status ~term:(C.Rel (find 1 context))
;;

(* Questa invece era in fourierR.ml 
let assumption_tac ~status:(proof,goal)=
  let curi,metasenv,pbo,pty = proof in
  let metano,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
  let num = ref 0 in
  let tac_list = List.map
        ( fun x -> num := !num + 1;
                match x with
                  Some(Cic.Name(nm),t) -> (nm,exact ~term:(Cic.Rel(!num)))
                  | _ -> ("fake",tcl_fail 1)
        )
        context
  in
  Tacticals.try_tactics ~tactics:tac_list ~status:(proof,goal)
;;
*)


(* ANCORA DA DEBUGGARE *)


let elim_type_tac ~term ~status =
  let module C = Cic in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
   T.thens 
    ~start: (P.cut_tac ~term) 
    ~continuations:[ P.elim_intros_simpl_tac ~term:(C.Rel 1) ; T.id_tac ]
    ~status
;;

let absurd_tac ~term ~status:((proof,goal) as status) =
  let module C = Cic in
  let module U = UriManager in
  let module P = PrimitiveTactics in
   let _,metasenv,_,_ = proof in
    let _,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
     if ((CicTypeChecker.type_of_aux' metasenv context term) = (C.Sort C.Prop)) 
      then P.apply_tac ~term:(C.Appl [(C.Const ((U.uri_of_string "cic:/Coq/Init/Logic/absurd.con") , [] )) ; term ; ty]) ~status
      else raise (ProofEngineTypes.Fail "Absurd: Not a Proposition") 
;;


let contradiction_tac ~status =
  let module C = Cic in
  let module U = UriManager in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
   T.then_ 
      ~start:P.intros_tac
      ~continuation:(
        T.then_ 
           ~start: (elim_type_tac ~term:(C.MutInd (U.uri_of_string "cic:/Coq/Init/Logic/False.ind") 0 [] )) 
           ~continuation: assumption_tac)
    ~status
;;

(* Questa era in fourierR.ml 
(* !!!!! fix !!!!!!!!!! *)
let contradiction_tac ~status:(proof,goal)=
        Tacticals.then_
                ~start:(PrimitiveTactics.intros_tac ~name:"bo?" ) (*inutile sia questo che quello prima  della chiamata*)
                ~continuation:(Tacticals.then_
                        ~start:(VariousTactics.elim_type_tac ~term:_False)
                        ~continuation:(assumption_tac))
        ~status:(proof,goal)
;;
*)


(* IN FASE DI IMPLEMENTAZIONE *)


let generalize_tac ~term ~status:((proof,goal) as status) =
  let module C = Cic in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
  let struct_equality t a = (t == a) in
   let _,metasenv,_,_ = proof in
    let _,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
     T.thens 
      ~start:(P.cut_tac 
       ~term:(
         C.Lambda (
          (C.Name "dummy_for_gen"), 
          (CicTypeChecker.type_of_aux' metasenv context term), 
          (ProofEngineReduction.replace 
            ~equality:(==) 
            ~with_what:(C.Rel 1)(* (C.Name "dummy_for_gen") *) 
            ~what:term 
            ~where:ty))))	 (* dove?? nel goal va bene?*)
      ~continuations: 
       [(P.apply_tac ~term:(C.Appl [(C.Rel 1); term])) ; T.id_tac]	(* in quest'ordine o viceversa? provare *)
      ~status
;;

(* PROVE DI DECOMPOSE

(* in realta' non so bene cosa contiene la lista what, io ho supposto contenga dei term (Const uri) *)
let decompose_tac ~what ~where ~status:((proof,goal) as status) =  
  let module C = Cic in
  let module R = CicReduction in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
  let module S = ProofEngineStructuralRules in

   let rec decomposing ty what = 
    match (what) with 
       [] -> C.Implicit (* qui mi servirebbe un termine per cui elim_simpl_intros fallisce *)
     | hd::tl as what ->
        match ty with
           (C.Appl (hd::_)) -> hd
         | _ -> decomposing ty tl
    in

   let (_,metasenv,_,_) = proof in
    let _,context,_ = List.find (function (m,_,_) -> m=goal) metasenv in
     T.repeat_tactic 
       ~tactic:(T.then_ 
                   ~start:(P.elim_simpl_intros_tac ~term:(decomposing (R.whd context where) what))
                   ~continuation:(S.clear ~hyp:(Some ((C.Name "name"), (C.Decl where)))) 		(* ma che ipotesi sto cancellando??? *) 
               )
       ~status 
;;


let decompose_tac ~clist ~status:((proof,goal) as status) =
  let module C = Cic in
  let module R = CicReduction in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
  let module S = ProofEngineStructuralRules in
   let (_,metasenv,_,_) = proof in
    let _,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in

     let rec repeat_elim ~term ~status = 		(* term -> status -> proof * (goal list) *)
      try
       let (proof, goallist) = 
        T.then_
           ~start:(P.elim_simpl_intros_tac ~term)
           ~continuation:(S.clear ~hyp:(Some ((C.Name "name"), (C.Decl ty))))                (* non so che ipotesi sto cancellando??? *)
           ~status
        in
         let rec step proof goallist =
          match goallist with
             [] -> (proof, [])
           | hd::tl ->
              let (proof', goallist') = repeat_elim ~term ~status:(proof, hd) in
               let (proof'', goallist'') = step proof' tl in
                proof'', goallist'@goallist''
          in
           step proof goallist
       with
        (Fail _) -> T.id_tac

    in
     let rec decomposing ty clist =		(* term -> (term list) -> bool *)
      match (clist) with
        [] -> false
      | hd::tl as clist ->
         match ty with
           (C.Appl (hd::_)) -> true
         | _ -> decomposing ty tl

      in
       let term = decomposing (R.whd context ty) clist in
	if (term == C.Implicit) 
         then (Fail "Decompose: nothing to decompose or no application")
         else repeat_elim ~term ~status
;; 
*)

let decompose_tac ~clist ~status =
  let module C = Cic in
  let module R = CicReduction in
  let module P = PrimitiveTactics in
  let module T = Tacticals in
  let module S = ProofEngineStructuralRules in

   let rec choose ty =
    function
       [] -> C.Implicit (* a cosa serve? *)
     | hd::tl ->
        match ty with
           (C.Appl (hd::_)) -> hd
         | _ -> choose ty tl
     in

    let decompose_one_tac ~clist ~status:((proof,goal) as status) =
     let (_,metasenv,_,_) = proof in
      let _,context,ty = List.find (function (m,_,_) -> m=goal) metasenv in
       let term = choose (R.whd context ty) clist in
        if (term == C.Implicit)
         then raise (ProofEngineTypes.Fail "Decompose: nothing to decompose or no application")
         else T.then_
                 ~start:(P.elim_intros_simpl_tac ~term)
                 ~continuation:(S.clear ~hyp:(Some ((C.Name "FOO") , (C.Decl ty))))                (* ma che ipotesi sto cancellando??? *)  
                 ~status   
     in
      T.repeat_tactic ~tactic:(decompose_one_tac ~clist) ~status
;;


let decide_equality_tac =
  Tacticals.id_tac
;;

(*
let compare_tac ~term1 ~term2 ~status:((proof, goal) as status) =
  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,gty = List.find (function (m,_,_) -> m=goal) metasenv in
     if ((CicTypeChecker.type_of_aux' metasenv context term1) = (CicTypeChecker.type_of_aux' metasenv context term2))
       (* controllo che i due termini siano comparabili *)
      then
       T.thens 
         ~start:P.cut_tac ~term:(* term1=term2->gty/\~term1=term2->gty *)
         ~continuations:[split_tac ; intros_tac ~name:"FOO"]  
      else raise (ProofEngineTypes.Fail "Compare: Comparing terms of different types") 
;;
*)


let rewrite_tac ~term:equality ~status:(proof,goal) =
 let module C = Cic in
 let module U = UriManager in
  let curi,metasenv,pbo,pty = proof in
  let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
   let eq_ind_r,ty,t1,t2 =
    match CicTypeChecker.type_of_aux' metasenv context equality with
       C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
        when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
         let eq_ind_r =
          C.Const
           (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind_r.con",[])
         in
          eq_ind_r,ty,t1,t2
     | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
        when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
         let eqT_ind_r =
          C.Const
           (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind_r.con",[])
         in
          eqT_ind_r,ty,t1,t2
     | _ ->
       raise
        (ProofEngineTypes.Fail
          "Rewrite: the argument is not a proof of an equality")
   in
    let pred =
     let gty' = CicSubstitution.lift 1 gty in
     let t1' = CicSubstitution.lift 1 t1 in
     let gty'' =
      ProofEngineReduction.replace_lifting
       ~equality:ProofEngineReduction.alpha_equivalence
       ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
     in
      C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
    in
prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
    let fresh_meta = ProofEngineHelpers.new_meta proof in
    let irl =
     ProofEngineHelpers.identity_relocation_list_for_metavariable context in
    let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in

     let (proof',goals) =
      PrimitiveTactics.exact_tac
       ~term:(C.Appl
         [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
        ~status:((curi,metasenv',pbo,pty),goal)
     in
      assert (List.length goals = 0) ;
      (proof',[fresh_meta])
;;


let rewrite_simpl_tac ~term ~status =
 Tacticals.then_ ~start:(rewrite_tac ~term)
  ~continuation:
   (ReductionTactics.simpl_tac ~also_in_hypotheses:false ~term:None)
  ~status
;;


let rewrite_back_tac ~term:equality ~status:(proof,goal) = 
 let module C = Cic in
 let module U = UriManager in
  let curi,metasenv,pbo,pty = proof in
  let metano,context,gty = List.find (function (m,_,_) -> m=goal) metasenv in
   let eq_ind_r,ty,t1,t2 =
    match CicTypeChecker.type_of_aux' metasenv context equality with
       C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
        when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic/eq.ind") ->
         let eq_ind_r =
          C.Const
           (U.uri_of_string "cic:/Coq/Init/Logic/eq_ind.con",[])
         in
          eq_ind_r,ty,t1,t2
     | C.Appl [C.MutInd (uri,0,[]) ; ty ; t1 ; t2]
        when U.eq uri (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT.ind") ->
         let eqT_ind_r =
          C.Const
           (U.uri_of_string "cic:/Coq/Init/Logic_Type/eqT_ind.con",[])
         in
          eqT_ind_r,ty,t1,t2
     | _ ->
       raise
        (ProofEngineTypes.Fail
          "Rewrite: the argument is not a proof of an equality")
   in
    let pred =
     let gty' = CicSubstitution.lift 1 gty in
     let t1' = CicSubstitution.lift 1 t1 in
     let gty'' =
      ProofEngineReduction.replace_lifting
       ~equality:ProofEngineReduction.alpha_equivalence
       ~what:t1' ~with_what:(C.Rel 1) ~where:gty'
     in
      C.Lambda (C.Name "dummy_for_rewrite", ty, gty'')
    in
prerr_endline ("#### Sintetizzato: " ^ CicPp.ppterm pred);
    let fresh_meta = ProofEngineHelpers.new_meta proof in
    let irl =
     ProofEngineHelpers.identity_relocation_list_for_metavariable context in
    let metasenv' = (fresh_meta,context,C.Appl [pred ; t2])::metasenv in

     let (proof',goals) =
      PrimitiveTactics.exact_tac
       ~term:(C.Appl
         [eq_ind_r ; ty ; t2 ; pred ; C.Meta (fresh_meta,irl) ; t1 ;equality])
        ~status:((curi,metasenv',pbo,pty),goal)
     in
      assert (List.length goals = 0) ;
      (proof',[fresh_meta])

;;


let replace_tac ~what ~with_what ~status:((proof, goal) as status) =
  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,_ = List.find (function (m,_,_) -> m=goal) metasenv in
     let wty = CicTypeChecker.type_of_aux' metasenv context what in
      if (wty = (CicTypeChecker.type_of_aux' metasenv context with_what))
       then T.thens 
              ~start:(P.cut_tac ~term:(C.Appl [(C.MutInd ((U.uri_of_string "cic:/Coq/Init/Logic/eq.ind"), 0, [])) ; wty ; what ; with_what]))	
  							(* quale uguaglianza usare, eq o eqT ? *)
              ~continuations:[
                T.then_ 
                   ~start:P.intros_tac
                   ~continuation:(T.then_ 
                                     ~start:(rewrite_back_tac ~term:(C.Rel 1)) (* C.Name "dummy_for_replace" *)
                                     ~continuation:(ProofEngineStructuralRules.clear 
                                                     ~hyp:(Some((C.Name "dummy_for_replace") , (C.Def C.Implicit) (* NO!! tipo di dummy *) ))
                                                   )
                                 ) ; 
                T.id_tac]
             ~status
      else raise (ProofEngineTypes.Fail "Replace: terms not replaceable")
;;