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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Util
open Names
open Term
open Termops
open Inductiveops
open Hipattern
open Tacmach.New
open Tacticals.New
open Tactics
open Proofview.Notations
module NamedDecl = Context.Named.Declaration
(* Supposed to be called without as clause *)
let introElimAssumsThen tac ba =
assert (ba.Tacticals.branchnames == []);
let introElimAssums = tclDO ba.Tacticals.nassums intro in
(tclTHEN introElimAssums (elim_on_ba tac ba))
(* Supposed to be called with a non-recursive scheme *)
let introCaseAssumsThen with_evars tac ba =
let n1 = List.length ba.Tacticals.branchsign in
let n2 = List.length ba.Tacticals.branchnames in
let (l1,l2),l3 =
if n1 < n2 then List.chop n1 ba.Tacticals.branchnames, []
else (ba.Tacticals.branchnames, []), List.make (n1-n2) false in
let introCaseAssums =
tclTHEN (intro_patterns with_evars l1) (intros_clearing l3) in
(tclTHEN introCaseAssums (case_on_ba (tac l2) ba))
(* The following tactic Decompose repeatedly applies the
elimination(s) rule(s) of the types satisfying the predicate
``recognizer'' onto a certain hypothesis. For example :
Require Elim.
Require Le.
Goal (y:nat){x:nat | (le O x)/\(le x y)}->{x:nat | (le O x)}.
Intros y H.
Decompose [sig and] H;EAuto.
Qed.
Another example :
Goal (A,B,C:Prop)(A/\B/\C \/ B/\C \/ C/\A) -> C.
Intros A B C H; Decompose [and or] H; Assumption.
Qed.
*)
let elimHypThen tac id =
elimination_then tac (mkVar id)
let rec general_decompose_on_hyp recognizer =
ifOnHyp recognizer (general_decompose_aux recognizer) (fun _ -> Proofview.tclUNIT())
and general_decompose_aux recognizer id =
elimHypThen
(introElimAssumsThen
(fun bas ->
tclTHEN (clear [id])
(tclMAP (general_decompose_on_hyp recognizer)
(ids_of_named_context bas.Tacticals.assums))))
id
(* We should add a COMPLETE to be sure that the created hypothesis
doesn't stay if no elimination is possible *)
(* Best strategies but loss of compatibility *)
let tmphyp_name = Id.of_string "_TmpHyp"
let up_to_delta = ref false (* true *)
let general_decompose recognizer c =
Proofview.Goal.enter { enter = begin fun gl ->
let type_of = pf_unsafe_type_of gl in
let typc = type_of c in
tclTHENS (cut typc)
[ tclTHEN (intro_using tmphyp_name)
(onLastHypId
(ifOnHyp recognizer (general_decompose_aux recognizer)
(fun id -> clear [id])));
exact_no_check c ]
end }
let head_in indl t gl =
let env = Proofview.Goal.env gl in
let sigma = Tacmach.New.project gl in
try
let ity,_ =
if !up_to_delta
then find_mrectype env sigma t
else extract_mrectype t
in List.exists (fun i -> eq_ind (fst i) (fst ity)) indl
with Not_found -> false
let decompose_these c l =
Proofview.Goal.enter { enter = begin fun gl ->
let indl = List.map (fun x -> x, Univ.Instance.empty) l in
general_decompose (fun (_,t) -> head_in indl t gl) c
end }
let decompose_and c =
general_decompose
(fun (_,t) -> is_record t)
c
let decompose_or c =
general_decompose
(fun (_,t) -> is_disjunction t)
c
let h_decompose l c = decompose_these c l
let h_decompose_or = decompose_or
let h_decompose_and = decompose_and
(* The tactic Double performs a double induction *)
let simple_elimination c =
elimination_then (fun _ -> tclIDTAC) c
let induction_trailer abs_i abs_j bargs =
tclTHEN
(tclDO (abs_j - abs_i) intro)
(onLastHypId
(fun id ->
Proofview.Goal.nf_enter { enter = begin fun gl ->
let idty = pf_unsafe_type_of gl (mkVar id) in
let fvty = global_vars (pf_env gl) idty in
let possible_bring_hyps =
(List.tl (nLastDecls gl (abs_j - abs_i))) @ bargs.Tacticals.assums
in
let (hyps,_) =
List.fold_left
(fun (bring_ids,leave_ids) d ->
let cid = NamedDecl.get_id d in
if not (List.mem cid leave_ids)
then (d::bring_ids,leave_ids)
else (bring_ids,cid::leave_ids))
([],fvty) possible_bring_hyps
in
let ids = List.rev (ids_of_named_context hyps) in
(tclTHENLIST
[revert ids; simple_elimination (mkVar id)])
end }
))
let double_ind h1 h2 =
Proofview.Goal.nf_enter { enter = begin fun gl ->
let abs_i = depth_of_quantified_hypothesis true h1 gl in
let abs_j = depth_of_quantified_hypothesis true h2 gl in
let abs =
if abs_i < abs_j then Proofview.tclUNIT (abs_i,abs_j) else
if abs_i > abs_j then Proofview.tclUNIT (abs_j,abs_i) else
tclZEROMSG (Pp.str "Both hypotheses are the same.") in
abs >>= fun (abs_i,abs_j) ->
(tclTHEN (tclDO abs_i intro)
(onLastHypId
(fun id ->
elimination_then
(introElimAssumsThen (induction_trailer abs_i abs_j)) (mkVar id))))
end }
let h_double_induction = double_ind
|
