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+(************************************************************************)
+(*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
+(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
+(*   \VV/  **************************************************************)
+(*    //   *      This file is distributed under the terms of the       *)
+(*         *       GNU Lesser General Public License Version 2.1        *)
+(************************************************************************)
+
+(*i $Id: implicit_quantifiers.ml 10922 2008-05-12 12:47:17Z msozeau $ i*)
+
+(*i*)
+open Names
+open Decl_kinds
+open Term
+open Sign
+open Evd
+open Environ
+open Nametab
+open Mod_subst
+open Util
+open Rawterm
+open Topconstr
+open Libnames
+open Typeclasses
+open Typeclasses_errors
+open Pp
+(*i*)
+
+let ids_of_list l = 
+  List.fold_right Idset.add l Idset.empty
+
+
+let locate_reference qid =
+  match Nametab.extended_locate qid with
+    | TrueGlobal ref -> true
+    | SyntacticDef kn -> true
+
+let is_global id =
+  try 
+    locate_reference (make_short_qualid id)
+  with Not_found -> 
+    false
+
+let is_freevar ids env x =
+  try
+    if Idset.mem x ids then false
+    else
+      try ignore(Environ.lookup_named x env) ; false
+      with _ -> not (is_global x)
+  with _ -> true
+
+(* Auxilliary functions for the inference of implicitly quantified variables. *)    
+
+let free_vars_of_constr_expr c ?(bound=Idset.empty) l = 
+  let found id bdvars l = 
+    if List.mem id l then l 
+    else if not (is_freevar bdvars (Global.env ()) id)
+    then l else id :: l 
+  in
+  let rec aux bdvars l c = match c with
+    | CRef (Ident (_,id)) -> found id bdvars l
+    | CNotation (_, "{ _ : _ | _ }", (CRef (Ident (_, id))) :: _) when not (Idset.mem id bdvars) ->
+	fold_constr_expr_with_binders (fun a l -> Idset.add a l) aux (Idset.add id bdvars) l c
+    | c -> fold_constr_expr_with_binders (fun a l -> Idset.add a l) aux bdvars l c
+  in aux bound l c
+
+let ids_of_names l = 
+  List.fold_left (fun acc x -> match snd x with Name na -> na :: acc | Anonymous -> acc) [] l
+
+let free_vars_of_binders ?(bound=Idset.empty) l (binders : local_binder list) = 
+  let rec aux bdvars l c = match c with
+      ((LocalRawAssum (n, _, c)) :: tl) ->
+	let bound = ids_of_names n in
+	let l' = free_vars_of_constr_expr c ~bound:bdvars l in
+	  aux (Idset.union (ids_of_list bound) bdvars) l' tl
+
+    | ((LocalRawDef (n, c)) :: tl) -> 
+	let bound = match snd n with Anonymous -> [] | Name n -> [n] in
+	let l' = free_vars_of_constr_expr c ~bound:bdvars l in
+	  aux (Idset.union (ids_of_list bound) bdvars) l' tl
+	
+    | [] -> bdvars, l
+  in aux bound l binders
+
+let rec make_fresh ids env x =
+  if is_freevar ids env x then x else make_fresh ids env (Nameops.lift_ident x)
+
+let freevars_of_ids env ids = 
+  List.filter (is_freevar env (Global.env())) ids
+
+let compute_constrs_freevars env constrs =
+  let ids = 
+    List.rev (List.fold_left 
+		 (fun acc x -> free_vars_of_constr_expr x acc) 
+		 [] constrs)
+  in freevars_of_ids env ids
+
+(* let compute_context_freevars env ctx = *)
+(*   let ids = *)
+(*     List.rev *)
+(*       (List.fold_left *)
+(* 	  (fun acc (_,i,x) -> free_vars_of_constr_expr x acc) *)
+(* 	  [] constrs) *)
+(*   in freevars_of_ids ids *)
+
+let compute_constrs_freevars_binders env constrs =
+  let elts = compute_constrs_freevars env constrs in
+    List.map (fun id -> (dummy_loc, id), CHole (dummy_loc, None)) elts
+
+let binder_list_of_ids ids =
+  List.map (fun id -> LocalRawAssum ([dummy_loc, Name id], Default Implicit, CHole (dummy_loc, None))) ids
+      
+let next_ident_away_from id avoid = make_fresh avoid (Global.env ()) id
+(*   let rec name_rec id = *)
+(*     if Idset.mem id avoid then name_rec (Nameops.lift_ident id) else id in  *)
+(*   name_rec id  *)
+
+let ids_of_named_context_avoiding avoid l =
+  List.fold_left (fun (ids, avoid) id -> 
+    let id' = next_ident_away_from id avoid in id' :: ids, Idset.add id' avoid) 
+    ([], avoid) (Termops.ids_of_named_context l)
+    
+let combine_params avoid fn applied needed =
+  let named, applied = 
+    List.partition 
+      (function
+	  (t, Some (loc, ExplByName id)) -> 
+	    if not (List.exists (fun (_, (id', _, _)) -> id = id') needed) then
+	      user_err_loc (loc,"",str "Wrong argument name: " ++ Nameops.pr_id id);
+	    true
+	| _ -> false) applied
+  in
+  let named = List.map
+    (fun x -> match x with (t, Some (loc, ExplByName id)) -> id, t | _ -> assert false)
+    named
+  in
+  let rec aux ids avoid app need =
+    match app, need with
+	[], [] -> List.rev ids, avoid
+
+      | app, (_, (id, _, _)) :: need when List.mem_assoc id named ->
+	  aux (List.assoc id named :: ids) avoid app need
+	    
+      | (x, None) :: app, (None, (id, _, _)) :: need ->
+	  aux (x :: ids) avoid app need
+	    
+      | _, (Some cl, (id, _, _) as d) :: need -> 
+	  let t', avoid' = fn avoid d in
+	    aux (t' :: ids) avoid' app need
+
+      | x :: app, (None, _) :: need -> aux (fst x :: ids) avoid app need
+
+      | [], (None, _ as decl) :: need -> 
+	  let t', avoid' = fn avoid decl in
+	    aux (t' :: ids) avoid' app need
+
+      | _ :: _, [] -> failwith "combine_params: overly applied typeclass"
+  in aux [] avoid applied needed
+
+let combine_params_freevar avoid applied needed =
+  combine_params avoid
+    (fun avoid (_, (id, _, _)) -> 
+      let id' = next_ident_away_from id avoid in
+	(CRef (Ident (dummy_loc, id')), Idset.add id' avoid))
+    applied needed
+
+let compute_context_vars env l =
+  List.fold_left (fun avoid (iid, _, c) -> 
+    (match snd iid with Name i -> [i] | Anonymous -> []) @ (free_vars_of_constr_expr c ~bound:env avoid))
+    [] l
+
+let destClassApp cl =
+  match cl with
+    | CApp (loc, (None,CRef ref), l) -> loc, ref, List.map fst l
+    | CRef ref -> loc_of_reference ref, ref, []
+    | _ -> raise Not_found
+      
+let destClassAppExpl cl =
+  match cl with
+    | CApp (loc, (None,CRef ref), l) -> loc, ref, l
+    | CRef ref -> loc_of_reference ref, ref, []
+    | _ -> raise Not_found
+
+let full_class_binders env l = 
+  let avoid = Idset.union env (ids_of_list (compute_context_vars env l)) in
+  let l', avoid =
+    List.fold_left (fun (l', avoid) (iid, bk, cl as x) -> 
+      match bk with
+	  Implicit -> 
+	    let (loc, id, l) = 
+	      try destClassAppExpl cl 
+	      with Not_found -> 
+		user_err_loc (constr_loc cl, "class_binders", str"Not an applied type class")
+	    in
+	    let gr = Nametab.global id in
+	      (try
+		  let c = class_info gr in
+		  let args, avoid = combine_params_freevar avoid l (List.rev c.cl_context) in
+		    (iid, bk, CAppExpl (loc, (None, id), args)) :: l', avoid
+		with Not_found -> not_a_class (Global.env ()) (constr_of_global gr))
+	| Explicit -> (x :: l', avoid))
+      ([], avoid) l
+  in List.rev l'
+      
+let constr_expr_of_constraint (kind, id) l =
+  match kind with
+    | Implicit -> CAppExpl (fst id, (None, Ident id), l)
+    | Explicit -> CApp (fst id, (None, CRef (Ident id)),
+		       List.map (fun x -> x, None) l)
+
+(*    | CApp of loc * (proj_flag * constr_expr) *  *)
+(*         (constr_expr * explicitation located option) list *)
+
+
+let constrs_of_context l =
+  List.map (fun (_, id, l) -> constr_expr_of_constraint id l) l
+
+let compute_context_freevars env ctx =
+  let bound, ids = 
+    List.fold_left 
+      (fun (bound, acc) (oid, id, x) -> 
+	let bound = match snd oid with Name n -> Idset.add n bound | Anonymous -> bound in
+	  bound, free_vars_of_constr_expr x ~bound acc)
+      (env,[]) ctx
+  in freevars_of_ids env (List.rev ids)
+
+let resolve_class_binders env l = 
+  let ctx = full_class_binders env l in
+  let fv_ctx = 
+    let elts = compute_context_freevars env ctx in
+      List.map (fun id -> (dummy_loc, id), CHole (dummy_loc, None)) elts
+  in
+    fv_ctx, ctx
+
+let generalize_class_binders env l = 
+  let fv_ctx, cstrs = resolve_class_binders env l in
+    List.map (fun ((loc, id), t) -> LocalRawAssum ([loc, Name id], Default Implicit, t)) fv_ctx,
+  List.map (fun (iid, bk, c) -> LocalRawAssum ([iid], Default Implicit, c)) 
+    cstrs
+
+let generalize_class_binders_raw env l = 
+  let env = Idset.union env (Termops.vars_of_env (Global.env())) in
+  let fv_ctx, cstrs = resolve_class_binders env l in
+    List.map (fun ((loc, id), t) -> ((loc, Name id), Implicit, t)) fv_ctx,
+  List.map (fun (iid, bk, c) -> (iid, Implicit, c)) cstrs
+
+let ctx_of_class_binders env l = 
+  let (x, y) = generalize_class_binders env l in x @ y
+	
+let implicits_of_binders l = 
+  let rec aux i l = 
+    match l with 
+	[] -> []
+      | hd :: tl -> 
+	  let res, reslen = 
+	    match hd with
+		LocalRawAssum (nal, Default Implicit, t) -> 
+		  list_map_i (fun i (_,id) ->
+		    let name =
+		      match id with
+			  Name id -> Some id
+			| Anonymous -> None
+		    in ExplByPos (i, name), (true, true))
+		    i nal, List.length nal
+	      | LocalRawAssum (nal, _, _) -> [], List.length nal
+	      | LocalRawDef _ -> [], 1
+	  in res @ (aux (i + reslen) tl)
+  in aux 1 l
+  
+let implicits_of_rawterm l = 
+  let rec aux i c = 
+    match c with
+	RProd (loc, na, bk, t, b) | RLambda (loc, na, bk, t, b) -> 
+	  let rest = aux (succ i) b in
+	    if bk = Implicit then
+	      let name =
+		match na with
+		    Name id -> Some id
+		  | Anonymous -> None
+	      in
+		(ExplByPos (i, name), (true, true)) :: rest
+	    else rest
+      | RLetIn (loc, na, t, b) -> aux i b
+      | _ -> []
+  in aux 1 l