(* Copyright (C) 2000, 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/.
 *)

exception CannotSubstInMeta;;
exception RelToHiddenHypothesis;;

let lift n =
 let rec liftaux k =
  let module C = Cic in
   function
      C.Rel m ->
       if m < k then
        C.Rel m
       else
        C.Rel (m + n)
    | C.Var _  as t -> t
    | C.Meta (i,l) ->
       let l' =
        List.map
         (function
             None -> None
           | Some t -> Some (liftaux k t)
         ) l
       in
        C.Meta(i,l')
    | C.Sort _ as t -> t
    | C.Implicit as t -> t
    | C.Cast (te,ty) -> C.Cast (liftaux k te, liftaux k ty)
    | C.Prod (n,s,t) -> C.Prod (n, liftaux k s, liftaux (k+1) t)
    | C.Lambda (n,s,t) -> C.Lambda (n, liftaux k s, liftaux (k+1) t)
    | C.LetIn (n,s,t) -> C.LetIn (n, liftaux k s, liftaux (k+1) t)
    | C.Appl l -> C.Appl (List.map (liftaux k) l)
    | C.Const _ as t -> t
    | C.Abst _  as t -> t
    | C.MutInd _ as t -> t
    | C.MutConstruct _ as t -> t
    | C.MutCase (sp,cookingsno,i,outty,t,pl) ->
       C.MutCase (sp, cookingsno, i, liftaux k outty, liftaux k t,
        List.map (liftaux k) pl)
    | C.Fix (i, fl) ->
       let len = List.length fl in
       let liftedfl =
        List.map
         (fun (name, i, ty, bo) -> (name, i, liftaux k ty, liftaux (k+len) bo))
          fl
       in
        C.Fix (i, liftedfl)
    | C.CoFix (i, fl) ->
       let len = List.length fl in
       let liftedfl =
        List.map
         (fun (name, ty, bo) -> (name, liftaux k ty, liftaux (k+len) bo))
          fl
       in
        C.CoFix (i, liftedfl)
 in
  if n = 0 then
   (function t -> t)
  else
   liftaux 1
;;

let subst arg =
 let rec substaux k =
  let module C = Cic in
   function
      C.Rel n as t ->
       (match n with
           n when n = k -> lift (k - 1) arg
         | n when n < k -> t
         | _            -> C.Rel (n - 1)
       )
    | C.Var _ as t  -> t
    | C.Meta (i, l) as t -> 
       let l' =
        List.map
         (function
             None -> None
           | Some t -> Some (substaux k t)
         ) l
       in
        C.Meta(i,l')
    | C.Sort _ as t -> t
    | C.Implicit as t -> t
    | C.Cast (te,ty) -> C.Cast (substaux k te, substaux k ty)
    | C.Prod (n,s,t) -> C.Prod (n, substaux k s, substaux (k + 1) t)
    | C.Lambda (n,s,t) -> C.Lambda (n, substaux k s, substaux (k + 1) t)
    | C.LetIn (n,s,t) -> C.LetIn (n, substaux k s, substaux (k + 1) t)
    | C.Appl (he::tl) ->
       (* Invariant: no Appl applied to another Appl *)
       let tl' = List.map (substaux k) tl in
        begin
         match substaux k he with
            C.Appl l -> C.Appl (l@tl')
          | _ as he' -> C.Appl (he'::tl')
        end
    | C.Appl _ -> assert false
    | C.Const _ as t -> t
    | C.Abst _ as t -> t
    | C.MutInd _ as t -> t
    | C.MutConstruct _ as t -> t
    | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
       C.MutCase (sp,cookingsno,i,substaux k outt, substaux k t,
        List.map (substaux k) pl)
    | C.Fix (i,fl) ->
       let len = List.length fl in
       let substitutedfl =
        List.map
         (fun (name,i,ty,bo) -> (name, i, substaux k ty, substaux (k+len) bo))
          fl
       in
        C.Fix (i, substitutedfl)
    | C.CoFix (i,fl) ->
       let len = List.length fl in
       let substitutedfl =
        List.map
         (fun (name,ty,bo) -> (name, substaux k ty, substaux (k+len) bo))
          fl
       in
        C.CoFix (i, substitutedfl)
 in
  substaux 1
;;

let undebrujin_inductive_def uri =
 function
    Cic.InductiveDefinition (dl,params,n_ind_params) ->
     let dl' =
      List.map
       (fun (name,inductive,arity,constructors) ->
         let constructors' =
          List.map
           (fun (name,ty,r) ->
             let ty' =
              let counter = ref (List.length dl) in
               List.fold_right
                (fun _ ->
                  decr counter ;
                  subst (Cic.MutInd (uri,0,!counter))
                ) dl ty
             in
              (name,ty',r)
           ) constructors
         in
          (name,inductive,arity,constructors')
       ) dl
      in
       Cic.InductiveDefinition (dl', params, n_ind_params)
  | obj -> obj
;;

(* l is the relocation list *)

let lift_meta l t = 
    let module C = Cic in
    if l = [] then t else 
    let rec aux k = function
      C.Rel n as t -> 
	if n <= k then t else 
         (try
           match List.nth l (n-k-1) with
              None -> raise RelToHiddenHypothesis
            | Some t -> lift k t
          with
           (Failure _) -> assert false
         )
    | C.Var _ as t  -> t
    | C.Meta (i,l) ->
       let l' =
        List.map
         (function
             None -> None
           | Some t ->
              try
               Some (aux k t)
              with
               RelToHiddenHypothesis -> None
         ) l
       in
        C.Meta(i,l')
    | C.Sort _ as t -> t
    | C.Implicit as t -> t
    | C.Cast (te,ty) -> C.Cast (aux k te, aux k ty) (*CSC ??? *)
    | C.Prod (n,s,t) -> C.Prod (n, aux k s, aux (k + 1) t)
    | C.Lambda (n,s,t) -> C.Lambda (n, aux k s, aux (k + 1) t)
    | C.LetIn (n,s,t) -> C.LetIn (n, aux k s, aux (k + 1) t)
    | C.Appl l -> C.Appl (List.map (aux k) l)
    | C.Const _ as t -> t
    | C.Abst _ as t -> t
    | C.MutInd _ as t -> t
    | C.MutConstruct _ as t -> t
    | C.MutCase (sp,cookingsno,i,outt,t,pl) ->
       C.MutCase (sp,cookingsno,i,aux k outt, aux k t,
        List.map (aux k) pl)
    | C.Fix (i,fl) ->
       let len = List.length fl in
       let substitutedfl =
        List.map
         (fun (name,i,ty,bo) -> (name, i, aux k ty, aux (k+len) bo))
          fl
       in
        C.Fix (i, substitutedfl)
    | C.CoFix (i,fl) ->
       let len = List.length fl in
       let substitutedfl =
        List.map
         (fun (name,ty,bo) -> (name, aux k ty, aux (k+len) bo))
          fl
       in
        C.CoFix (i, substitutedfl)
 in
  aux 0 t          
;;

(************************************************************************)
(*CSC: spostare in cic_unification *)

(* the delift function takes in input an ordered list of integers [n1,...,nk]
   and a term t, and relocates rel(nk) to k. Typically, the list of integers 
   is a parameter of a metavariable occurrence. *)

exception NotInTheList;;

let position n =
  let rec aux k =
   function 
       [] -> raise NotInTheList
     | (Some (Cic.Rel m))::_ when m=n -> k
     | _::tl -> aux (k+1) tl in
  aux 1
;;
 
let restrict to_be_restricted =
  let rec erase i n = 
    function
	[] -> []
      |	_::tl when List.mem (n,i) to_be_restricted ->
	  None::(erase (i+1) n tl) 
      | he::tl -> he::(erase (i+1) n tl) in
  let rec aux =
    function 
	[] -> []
      |	(n,context,t)::tl -> (n,erase 1 n context,t)::(aux tl) in
  aux
;;


let delift context metasenv l t =
 let to_be_restricted = ref [] in
 let rec deliftaux k =
  let module C = Cic in
   function
      C.Rel m -> 
        if m <=k then
         C.Rel m   (*CSC: che succede se c'e' un Def? Dovrebbe averlo gia' *)
                   (*CSC: deliftato la regola per il LetIn                 *)
        else
	 (match List.nth context (m-k-1) with
	   Some (_,C.Def t) -> deliftaux k (lift m t)
	 | Some (_,C.Decl t) ->
            (* It may augment to_be_restricted *)
            ignore (deliftaux k (lift m t)) ;
            C.Rel ((position (m-k) l) + k)
	 | None -> raise RelToHiddenHypothesis)
    | C.Var _  as t -> t
    | C.Meta (i, l1) as t -> 
       let rec deliftl j =
        function
           [] -> []
         | None::tl -> None::(deliftl (j+1) tl)
         | (Some t)::tl ->
            let l1' = (deliftl (j+1) tl) in
             try
              Some (deliftaux k t)::l1'
             with
                RelToHiddenHypothesis
              | NotInTheList ->
                 to_be_restricted := (i,j)::!to_be_restricted ; None::l1'
       in
        let l' = deliftl 1 l1 in
         C.Meta(i,l')
    | C.Sort _ as t -> t
    | C.Implicit as t -> t
    | C.Cast (te,ty) -> C.Cast (deliftaux k te, deliftaux k ty)
    | C.Prod (n,s,t) -> C.Prod (n, deliftaux k s, deliftaux (k+1) t)
    | C.Lambda (n,s,t) -> C.Lambda (n, deliftaux k s, deliftaux (k+1) t)
    | C.LetIn (n,s,t) -> C.LetIn (n, deliftaux k s, deliftaux (k+1) t)
    | C.Appl l -> C.Appl (List.map (deliftaux k) l)
    | C.Const _ as t -> t
    | C.Abst _  as t -> t
    | C.MutInd _ as t -> t
    | C.MutConstruct _ as t -> t
    | C.MutCase (sp,cookingsno,i,outty,t,pl) ->
       C.MutCase (sp, cookingsno, i, deliftaux k outty, deliftaux k t,
        List.map (deliftaux k) pl)
    | C.Fix (i, fl) ->
       let len = List.length fl in
       let liftedfl =
        List.map
         (fun (name, i, ty, bo) -> (name, i, deliftaux k ty, deliftaux (k+len) bo))
          fl
       in
        C.Fix (i, liftedfl)
    | C.CoFix (i, fl) ->
       let len = List.length fl in
       let liftedfl =
        List.map
         (fun (name, ty, bo) -> (name, deliftaux k ty, deliftaux (k+len) bo))
          fl
       in
        C.CoFix (i, liftedfl)
 in
   let res = deliftaux 0 t in
   res, restrict !to_be_restricted metasenv
;;