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|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * INRIA, CNRS and contributors - Copyright 1999-2019 *)
(* <O___,, * (see CREDITS file for the list of authors) *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(* * (see LICENSE file for the text of the license) *)
(************************************************************************)
open CErrors
open Sorts
open Util
open Names
open Constr
open EConstr
open Pp
open Indfun_common
open Tactypes
module RelDecl = Context.Rel.Declaration
let is_rec_info sigma scheme_info =
let test_branche min acc decl =
acc || (
let new_branche =
it_mkProd_or_LetIn mkProp (fst (decompose_prod_assum sigma (RelDecl.get_type decl))) in
let free_rels_in_br = Termops.free_rels sigma new_branche in
let max = min + scheme_info.Tactics.npredicates in
Int.Set.exists (fun i -> i >= min && i< max) free_rels_in_br
)
in
List.fold_left_i test_branche 1 false (List.rev scheme_info.Tactics.branches)
let choose_dest_or_ind scheme_info args =
Proofview.tclBIND Proofview.tclEVARMAP (fun sigma ->
Tactics.induction_destruct (is_rec_info sigma scheme_info) false args)
let functional_induction with_clean c princl pat =
let res =
fun g ->
let sigma = Tacmach.project g in
let f,args = decompose_app sigma c in
let princ,bindings, princ_type,g' =
match princl with
| None -> (* No principle is given let's find the good one *)
begin
match EConstr.kind sigma f with
| Const (c',u) ->
let princ_option =
let finfo = (* we first try to find out a graph on f *)
try find_Function_infos c'
with Not_found ->
user_err (str "Cannot find induction information on "++
Printer.pr_leconstr_env (Tacmach.pf_env g) sigma (mkConst c') )
in
match Tacticals.elimination_sort_of_goal g with
| InSProp -> finfo.sprop_lemma
| InProp -> finfo.prop_lemma
| InSet -> finfo.rec_lemma
| InType -> finfo.rect_lemma
in
let princ,g' = (* then we get the principle *)
try
let g',princ =
Tacmach.pf_eapply (Evd.fresh_global) g (GlobRef.ConstRef (Option.get princ_option )) in
princ,g'
with Option.IsNone ->
(*i If there is not default lemma defined then,
we cross our finger and try to find a lemma named f_ind
(or f_rec, f_rect) i*)
let princ_name =
Indrec.make_elimination_ident
(Label.to_id (Constant.label c'))
(Tacticals.elimination_sort_of_goal g)
in
try
let princ_ref = const_of_id princ_name in
let (a,b) = Tacmach.pf_eapply (Evd.fresh_global) g princ_ref in
(b,a)
(* mkConst(const_of_id princ_name ),g (\* FIXME *\) *)
with Not_found -> (* This one is neither defined ! *)
user_err (str "Cannot find induction principle for "
++ Printer.pr_leconstr_env (Tacmach.pf_env g) sigma (mkConst c') )
in
(princ,NoBindings,Tacmach.pf_unsafe_type_of g' princ,g')
| _ -> raise (UserError(None,str "functional induction must be used with a function" ))
end
| Some ((princ,binding)) ->
princ,binding,Tacmach.pf_unsafe_type_of g princ,g
in
let sigma = Tacmach.project g' in
let princ_infos = Tactics.compute_elim_sig (Tacmach.project g') princ_type in
let args_as_induction_constr =
let c_list =
if princ_infos.Tactics.farg_in_concl
then [c] else []
in
if List.length args + List.length c_list = 0
then user_err Pp.(str "Cannot recognize a valid functional scheme" );
let encoded_pat_as_patlist =
List.make (List.length args + List.length c_list - 1) None @ [pat]
in
List.map2
(fun c pat ->
((None,
Tactics.ElimOnConstr (fun env sigma -> (sigma,(c,NoBindings)))),
(None,pat),
None))
(args@c_list)
encoded_pat_as_patlist
in
let princ' = Some (princ,bindings) in
let princ_vars =
List.fold_right
(fun a acc -> try Id.Set.add (destVar sigma a) acc with DestKO -> acc)
args
Id.Set.empty
in
let old_idl = List.fold_right Id.Set.add (Tacmach.pf_ids_of_hyps g) Id.Set.empty in
let old_idl = Id.Set.diff old_idl princ_vars in
let subst_and_reduce g =
if with_clean
then
let idl =
List.filter (fun id -> not (Id.Set.mem id old_idl))
(Tacmach.pf_ids_of_hyps g)
in
let flag =
Genredexpr.Cbv
{Redops.all_flags
with Genredexpr.rDelta = false;
}
in
Tacticals.tclTHEN
(Tacticals.tclMAP (fun id -> Tacticals.tclTRY (Proofview.V82.of_tactic (Equality.subst_gen (do_rewrite_dependent ()) [id]))) idl )
(Proofview.V82.of_tactic (Tactics.reduce flag Locusops.allHypsAndConcl))
g
else Tacticals.tclIDTAC g
in
Tacticals.tclTHEN
(Proofview.V82.of_tactic (choose_dest_or_ind
princ_infos
(args_as_induction_constr,princ')))
subst_and_reduce
g'
in res
|
