(* 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/.
 *)

let _profiler = <:profiler<_profiler>>;;

(* $Id$ *)

open Utils;;
open Printf;;

let check_disjoint_invariant subst metasenv msg =
  if (List.exists 
        (fun (i,_,_) -> (Subst.is_in_subst i subst)) metasenv)
  then 
    begin 
      prerr_endline ("not disjoint: " ^ msg);
      assert false
    end
;;

let rec check_irl start = function
  | [] -> true
  | None::tl -> check_irl (start+1) tl
  | (Some (Cic.Rel x))::tl ->
      if x = start then check_irl (start+1) tl else false
  | _ -> false
;;

let rec is_simple_term = function
  | Cic.Appl ((Cic.Meta _)::_) -> false
  | Cic.Appl l -> List.for_all is_simple_term l
  | Cic.Meta (i, l) -> let l = [] in check_irl 1 l
  | Cic.Rel _ -> true
  | Cic.Const _ -> true
  | Cic.MutInd (_, _, []) -> true
  | Cic.MutConstruct (_, _, _, []) -> true
  | _ -> false
;;

let locked menv i =
  List.exists (fun (j,_,_) -> i = j) menv
;;

let unification_simple locked_menv metasenv context t1 t2 ugraph =
  let module C = Cic in
  let module M = CicMetaSubst in
  let module U = CicUnification in
  let lookup = Subst.lookup_subst in
  let rec occurs_check subst what where =
    match where with
    | Cic.Meta(i,_) when i = what -> true
    | C.Appl l -> List.exists (occurs_check subst what) l
    | C.Meta _ ->
        let t = lookup where subst in
        if t <> where then occurs_check subst what t else false
    | _ -> false
  in
  let rec unif subst menv s t =
    let s = match s with C.Meta _ -> lookup s subst | _ -> s
    and t = match t with C.Meta _ -> lookup t subst | _ -> t
    
    in
    match s, t with
    | s, t when s = t -> subst, menv
    (* sometimes the same meta has different local contexts; this
       could create "cyclic" substitutions *)
    | C.Meta (i, _), C.Meta (j, _) when i=j ->  subst, menv
    | C.Meta (i, _), C.Meta (j, _) 
        when (locked locked_menv i) &&(locked locked_menv j) ->
        raise
          (U.UnificationFailure (lazy "Inference.unification.unif"))
    | C.Meta (i, _), C.Meta (j, _) when (locked locked_menv i) ->          
        unif subst menv t s
    | C.Meta (i, _), C.Meta (j, _) when (i > j) && not (locked locked_menv j) ->
        unif subst menv t s
    | C.Meta (i,_), t when occurs_check subst i t ->
        raise
          (U.UnificationFailure (lazy "Inference.unification.unif"))
    | C.Meta (i, l), t when (locked locked_menv i) -> 
        raise
          (U.UnificationFailure (lazy "Inference.unification.unif"))
    | C.Meta (i, l), t -> (
        try
          let _, _, ty = CicUtil.lookup_meta i menv in
          assert (not (Subst.is_in_subst i subst));
          let subst = Subst.buildsubst i context t ty subst in
          let menv = menv in (* List.filter (fun (m, _, _) -> i <> m) menv in *)
          subst, menv
        with CicUtil.Meta_not_found m ->
          let names = names_of_context context in
          (*debug_print
            (lazy*) prerr_endline 
               (Printf.sprintf "Meta_not_found %d!: %s %s\n%s\n\n%s" m
                  (CicPp.pp t1 names) (CicPp.pp t2 names)
                  (print_metasenv menv) (print_metasenv metasenv));
          assert false
      )
    | _, C.Meta _ -> unif subst menv t s
    | C.Appl (hds::_), C.Appl (hdt::_) when hds <> hdt ->
        raise (U.UnificationFailure (lazy "Inference.unification.unif"))
    | C.Appl (hds::tls), C.Appl (hdt::tlt) -> (
        try
          List.fold_left2
            (fun (subst', menv) s t -> unif subst' menv s t)
            (subst, menv) tls tlt
        with Invalid_argument _ ->
          raise (U.UnificationFailure (lazy "Inference.unification.unif"))
      )
    | _, _ ->
        raise (U.UnificationFailure (lazy "Inference.unification.unif"))
  in
  let subst, menv = unif Subst.empty_subst metasenv t1 t2 in
  let menv = Subst.filter subst menv in
  subst, menv, ugraph
;;

let profiler = HExtlib.profile "P/Inference.unif_simple[flatten]"
let profiler2 = HExtlib.profile "P/Inference.unif_simple[flatten_fast]"
let profiler3 = HExtlib.profile "P/Inference.unif_simple[resolve_meta]"
let profiler4 = HExtlib.profile "P/Inference.unif_simple[filter]"

let unification_aux b metasenv1 metasenv2 context t1 t2 ugraph =
  let metasenv = 
    HExtlib.list_uniq (List.sort Pervasives.compare (metasenv1 @ metasenv2)) 
    (* metasenv1 @ metasenv2 *)
  in
  let subst, menv, ug =
    if not (is_simple_term t1) || not (is_simple_term t2) then (
      debug_print
        (lazy
           (Printf.sprintf "NOT SIMPLE TERMS: %s %s"
              (CicPp.ppterm t1) (CicPp.ppterm t2)));
      raise (CicUnification.UnificationFailure (lazy "Inference.unification.unif"))
    ) else
      if b then
        (* full unification *)
        unification_simple [] metasenv context t1 t2 ugraph
      else
        (* matching: metasenv1 is locked *)
        unification_simple metasenv1 metasenv context t1 t2 ugraph
  in
  if Utils.debug_res then
            ignore(check_disjoint_invariant subst menv "unif");
  (* let flatten subst = 
    List.map
      (fun (i, (context, term, ty)) ->
         let context = apply_subst_context subst context in
         let term = apply_subst subst term in
         let ty = apply_subst subst ty in  
           (i, (context, term, ty))) subst 
  in
  let flatten subst = profiler.HExtlib.profile flatten subst in
  let subst = flatten subst in *)
    subst, menv, ug
;;

exception MatchingFailure;;

(** matching takes in input the _disjoint_ metasenv of t1 and  t2;
it perform unification in the union metasenv, then check that
the first metasenv has not changed *)
let matching metasenv1 metasenv2 context t1 t2 ugraph = 
  try 
    unification_aux false metasenv1 metasenv2 context t1 t2 ugraph
  with
    CicUnification.UnificationFailure _ -> 
      raise MatchingFailure
;;

let unification m1 m2 c t1 t2 ug = 
  try 
    unification_aux true m1 m2 c t1 t2 ug
  with exn -> 
    raise exn
;;


let check_eq context msg eq =
  let w, proof, (eq_ty, left, right, order), metas = eq in
  if not (fst (CicReduction.are_convertible ~metasenv:metas context eq_ty
   (fst (CicTypeChecker.type_of_aux' metas context  left CicUniv.empty_ugraph))
   CicUniv.empty_ugraph))
  then
    begin
      prerr_endline msg;
      assert false;
    end
  else ()
;;

let find_equalities context proof =
  let module C = Cic in
  let module S = CicSubstitution in
  let module T = CicTypeChecker in
  let newmeta = ProofEngineHelpers.new_meta_of_proof ~proof in
  let ok_types ty menv =
    List.for_all (fun (_, _, mt) -> mt = ty) menv
  in
  let rec aux index newmeta = function
    | [] -> [], newmeta
    | (Some (_, C.Decl (term)))::tl ->
        let do_find context term =
          match term with
          | C.Prod (name, s, t) ->
              let (head, newmetas, args, newmeta) =
                ProofEngineHelpers.saturate_term newmeta []
                  context (S.lift index term) 0
              in
              let p =
                if List.length args = 0 then
                  C.Rel index
                else
                  C.Appl ((C.Rel index)::args)
              in (
                match head with
                | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
                    when (LibraryObjects.is_eq_URI uri) && 
                         (ok_types ty newmetas) ->
                    debug_print
                      (lazy
                         (Printf.sprintf "OK: %s" (CicPp.ppterm term)));
                    let o = !Utils.compare_terms t1 t2 in
                    let stat = (ty,t1,t2,o) in
                    let w = compute_equality_weight stat in
                    let proof = Equality.Exact p in
                    let e = Equality.mk_equality (w, proof, stat, newmetas) in
                    Some e, (newmeta+1)
                | _ -> None, newmeta
              )
          | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
              when LibraryObjects.is_eq_URI uri ->
              let ty = S.lift index ty in
              let t1 = S.lift index t1 in
              let t2 = S.lift index t2 in
              let o = !Utils.compare_terms t1 t2 in
              let stat = (ty,t1,t2,o) in
              let w = compute_equality_weight stat in
              let p = C.Rel index in
              let proof = Equality.Exact p in
              let e = Equality.mk_equality (w, proof,stat,[]) in
              Some e, (newmeta+1)
          | _ -> None, newmeta
        in (
          match do_find context term with
          | Some p, newmeta ->
              let tl, newmeta' = (aux (index+1) newmeta tl) in
              if newmeta' < newmeta then 
                prerr_endline "big trouble";
              (index, p)::tl, newmeta' (* max???? *)
          | None, _ ->
              aux (index+1) newmeta tl
        )
    | _::tl ->
        aux (index+1) newmeta tl
  in
  let il, maxm = aux 1 newmeta context in
  let indexes, equalities = List.split il in
  (* ignore (List.iter (check_eq context "find") equalities); *)
  indexes, equalities, maxm
;;


(*
let equations_blacklist =
  List.fold_left
    (fun s u -> UriManager.UriSet.add (UriManager.uri_of_string u) s)
    UriManager.UriSet.empty [
      "cic:/Coq/Init/Logic/eq.ind#xpointer(1/1/1)";
      "cic:/Coq/Init/Logic/trans_eq.con";
      "cic:/Coq/Init/Logic/f_equal.con";
      "cic:/Coq/Init/Logic/f_equal2.con";
      "cic:/Coq/Init/Logic/f_equal3.con";
      "cic:/Coq/Init/Logic/f_equal4.con";
      "cic:/Coq/Init/Logic/f_equal5.con";
      "cic:/Coq/Init/Logic/sym_eq.con";
      "cic:/Coq/Init/Logic/eq_ind.con";
      "cic:/Coq/Init/Logic/eq_ind_r.con";
      "cic:/Coq/Init/Logic/eq_rec.con";
      "cic:/Coq/Init/Logic/eq_rec_r.con";
      "cic:/Coq/Init/Logic/eq_rect.con";
      "cic:/Coq/Init/Logic/eq_rect_r.con";
      "cic:/Coq/Logic/Eqdep/UIP.con";
      "cic:/Coq/Logic/Eqdep/UIP_refl.con";
      "cic:/Coq/Logic/Eqdep_dec/eq2eqT.con";
      "cic:/Coq/ZArith/Zcompare/rename.con";
      (* ALB !!!! questo e` imbrogliare, ma x ora lo lasciamo cosi`...
         perche' questo cacchio di teorema rompe le scatole :'( *)
      "cic:/Rocq/SUBST/comparith/mult_n_2.con";

      "cic:/matita/logic/equality/eq_f.con";
      "cic:/matita/logic/equality/eq_f2.con";
      "cic:/matita/logic/equality/eq_rec.con";
      "cic:/matita/logic/equality/eq_rect.con";
    ]
;;
*)
let equations_blacklist = UriManager.UriSet.empty;;

let tty_of_u u = 
  let _ = <:start<tty_of_u>> in
  let t = CicUtil.term_of_uri u in
  let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
  let _ = <:stop<tty_of_u>> in
  t, ty
;;

let utty_of_u u =
  let t,ty = tty_of_u u in
  u, t, ty
;;

let find_library_equalities dbd context status maxmeta = 
  let module C = Cic in
  let module S = CicSubstitution in
  let module T = CicTypeChecker in
  let _ = <:start<equations_for_goal>> in
  let eqs = (MetadataQuery.equations_for_goal ~dbd status) in
  let _ = <:stop<equations_for_goal>> in
  let candidates =
    List.fold_left
      (fun l uri ->
        if LibraryObjects.is_eq_refl_URI uri ||
           LibraryObjects.is_sym_eq_URI uri ||
           LibraryObjects.is_trans_eq_URI uri ||
           LibraryObjects.is_eq_ind_URI uri ||
           LibraryObjects.is_eq_ind_r_URI uri 
         then 
           l
         else
           (utty_of_u uri)::l)
      [] eqs
  in
  let ok_types ty menv =
    List.for_all (fun (_, _, mt) -> mt = ty) menv
  in
  let rec has_vars = function
    | C.Meta _ | C.Rel _ | C.Const _ -> false
    | C.Var _ -> true
    | C.Appl l -> List.exists has_vars l
    | C.Prod (_, s, t) | C.Lambda (_, s, t)
    | C.LetIn (_, s, t) | C.Cast (s, t) ->
        (has_vars s) || (has_vars t)
    | _ -> false
 in
  let rec aux newmeta = function
    | [] -> [], newmeta
    | (uri, term, termty)::tl ->
        debug_print
          (lazy
             (Printf.sprintf "Examining: %s (%s)"
                (CicPp.ppterm term) (CicPp.ppterm termty)));
        let res, newmeta = 
          match termty with
          | C.Prod (name, s, t) when not (has_vars termty) ->
              let head, newmetas, args, newmeta =
                ProofEngineHelpers.saturate_term newmeta [] context termty 0
              in
              let p =
                if List.length args = 0 then
                  term
                else
                  C.Appl (term::args)
              in (
                  match head with
                    | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
                        when (LibraryObjects.is_eq_URI uri ||
                              LibraryObjects.is_eq_refl_URI uri) && 
                             (ok_types ty newmetas) ->
                    debug_print
                      (lazy
                         (Printf.sprintf "OK: %s" (CicPp.ppterm term)));
                    let o = !Utils.compare_terms t1 t2 in
                    let stat = (ty,t1,t2,o) in
                    let w = compute_equality_weight stat in
                    let proof = Equality.Exact p in
                    let e = Equality.mk_equality (w, proof, stat, newmetas) in
                    Some e, (newmeta+1)
                | _ -> None, newmeta
              )
          | C.Appl [C.MutInd (uri, _, _); ty; t1; t2]
              when 
                (LibraryObjects.is_eq_URI uri || 
                 LibraryObjects.is_eq_refl_URI uri) && 
                not (has_vars termty) ->
              let o = !Utils.compare_terms t1 t2 in
              let stat = (ty,t1,t2,o) in
              let w = compute_equality_weight stat in
              let proof = Equality.Exact term in 
              let e = Equality.mk_equality (w, proof, stat, []) in
              Some e, (newmeta+1)
          | _ -> None, newmeta
        in
        match res with
        | Some e ->
            let tl, newmeta' = aux newmeta tl in
              if newmeta' < newmeta then 
                prerr_endline "big trouble";
              (uri, e)::tl, newmeta' (* max???? *)
        | None ->
            aux newmeta tl
  in
  let found, maxm = aux maxmeta candidates in
  let uriset, eqlist = 
    let mceq = Equality.meta_convertibility_eq in
    (List.fold_left
       (fun (s, l) (u, e) ->
          if List.exists (mceq e) (List.map snd l) then (
            debug_print
              (lazy
                 (Printf.sprintf "NO!! %s already there!"
                    (Equality.string_of_equality e)));
            (UriManager.UriSet.add u s, l)
          ) else (UriManager.UriSet.add u s, (u, e)::l))
       (UriManager.UriSet.empty, []) found)
  in
  uriset, eqlist, maxm
;;


let find_library_theorems dbd env status equalities_uris =
  let module C = Cic in
  let module S = CicSubstitution in
  let module T = CicTypeChecker in
  let candidates =
    List.fold_left
      (fun l uri ->
        if LibraryObjects.is_sym_eq_URI uri ||
           LibraryObjects.is_trans_eq_URI uri ||
           LibraryObjects.is_eq_ind_URI uri ||
           LibraryObjects.is_eq_ind_r_URI uri 
         then l
         else
           (let t,ty = tty_of_u uri in t, ty, [] )::l)
      [] (MetadataQuery.signature_of_goal ~dbd status)
  in
  let refl_equal =
    let eq = 
      match LibraryObjects.eq_URI () with
      | Some u -> u
      | None -> 
          raise 
            (ProofEngineTypes.Fail 
              (lazy "No default eq defined when running find_library_theorems"))
    in
    let t = CicUtil.term_of_uri (LibraryObjects.eq_refl_URI ~eq) in
    let ty, _ = CicTypeChecker.type_of_aux' [] [] t CicUniv.empty_ugraph in
    (t, ty, [])
  in
  let res = refl_equal::candidates in
  res
;;


let find_context_hypotheses env equalities_indexes =
  let metasenv, context, ugraph = env in
  let _, res = 
    List.fold_left
      (fun (n, l) entry ->
         match entry with
         | None -> (n+1, l)
         | Some _ ->
             if List.mem n equalities_indexes then
               (n+1, l)
             else
               let t = Cic.Rel n in
               let ty, _ =
                 CicTypeChecker.type_of_aux' metasenv context t ugraph in 
               (n+1, (t, ty, [])::l))
      (1, []) context
  in
  res
;;

let get_stats () = <:show<Inference.>> ;;