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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 Pp
open Util
open CErrors
open Names
open Sorts
open Constr
open EConstr
open Tacmach.New
open Tacticals.New
open Tactics
open Indfun_common
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 open Proofview.Notations in
Proofview.Goal.enter_one (fun gl ->
let sigma = project gl in
let f,args = decompose_app sigma c in
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 *)
match find_Function_infos c' with
| Some finfo -> finfo
| None ->
user_err (str "Cannot find induction information on "++
Printer.pr_leconstr_env (pf_env gl) sigma (mkConst c') )
in
match elimination_sort_of_goal gl with
| InSProp -> finfo.sprop_lemma
| InProp -> finfo.prop_lemma
| InSet -> finfo.rec_lemma
| InType -> finfo.rect_lemma
in
let princ = (* then we get the principle *)
match princ_option with
| Some princ ->
let sigma, princ = Evd.fresh_global (pf_env gl) (project gl) (GlobRef.ConstRef princ) in
Proofview.Unsafe.tclEVARS sigma >>= fun () ->
Proofview.tclUNIT princ
| None ->
(*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'))
(elimination_sort_of_goal gl)
in
let princ_ref =
try
Constrintern.locate_reference (Libnames.qualid_of_ident princ_name)
with
| Not_found ->
user_err (str "Cannot find induction principle for "
++ Printer.pr_leconstr_env (pf_env gl) sigma (mkConst c') )
in
let sigma, princ = Evd.fresh_global (pf_env gl) (project gl) princ_ref in
Proofview.Unsafe.tclEVARS sigma >>= fun () ->
Proofview.tclUNIT princ
in
princ >>= fun princ ->
(* We need to refresh gl due to the updated evar_map in princ *)
Proofview.Goal.enter_one (fun gl ->
Proofview.tclUNIT (princ, Tactypes.NoBindings, pf_unsafe_type_of gl princ, args))
| _ ->
CErrors.user_err (str "functional induction must be used with a function" )
end
| Some ((princ,binding)) ->
Proofview.tclUNIT (princ, binding, pf_unsafe_type_of gl princ, args)
) >>= fun (princ, bindings, princ_type, args) ->
Proofview.Goal.enter (fun gl ->
let sigma = project gl in
let princ_infos = compute_elim_sig (project gl) 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, ElimOnConstr (fun env sigma -> (sigma,(c,Tactypes.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 (pf_ids_of_hyps gl) Id.Set.empty in
let old_idl = Id.Set.diff old_idl princ_vars in
let subst_and_reduce gl =
if with_clean
then
let idl = List.filter (fun id -> not (Id.Set.mem id old_idl))(pf_ids_of_hyps gl) in
let flag = Genredexpr.Cbv { Redops.all_flags with Genredexpr.rDelta = false } in
tclTHEN
(tclMAP (fun id -> tclTRY (Equality.subst_gen (do_rewrite_dependent ()) [id])) idl)
(reduce flag Locusops.allHypsAndConcl)
else tclIDTAC
in
tclTHEN
(choose_dest_or_ind
princ_infos
(args_as_induction_constr,princ'))
(Proofview.Goal.enter subst_and_reduce))
|
