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|
(************************************************************************)
(* * The Coq Proof Assistant / The Coq Development Team *)
(* v * Copyright INRIA, CNRS and contributors *)
(* <O___,, * (see version control and CREDITS file for authors & dates) *)
(* \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 Constr
open EConstr
open Hipattern
open Tactics
open Reductionops
open Proofview.Notations
module NamedDecl = Context.Named.Declaration
(* Absurd *)
let mk_absurd_proof env r t =
Tacticals.pf_constr_of_global (Coqlib.(lib_ref "core.not.type")) >>= fun coq_not ->
Refine.refine ~typecheck:true begin fun sigma ->
let sigma, negev = Evarutil.new_evar env sigma (mkApp (coq_not, [|t|])) in
let sigma, ev = Evarutil.new_evar ~relevance:r env sigma t in
sigma, mkApp (negev, [|ev|])
end
let absurd c =
Proofview.Goal.enter begin fun gl ->
let sigma = Proofview.Goal.sigma gl in
let env = Proofview.Goal.env gl in
let j = Retyping.get_judgment_of env sigma c in
let sigma, j = Coercion.inh_coerce_to_sort env sigma j in
let t = nf_betaiota env sigma j.Environ.utj_val in
let r = ESorts.relevance_of_sort j.Environ.utj_type in
Proofview.Unsafe.tclEVARS sigma <*>
Tactics.exfalso <*> mk_absurd_proof env r t
end
let absurd c = absurd c
(* Contradiction *)
(** [f] does not assume its argument to be [nf_evar]-ed. *)
let filter_hyp f tac =
let rec seek = function
| [] ->
let info = Exninfo.reify () in
Proofview.tclZERO ~info Not_found
| d::rest when f (NamedDecl.get_type d) -> tac (NamedDecl.get_id d)
| _::rest -> seek rest in
Proofview.Goal.enter begin fun gl ->
let hyps = Proofview.Goal.hyps gl in
seek hyps
end
let contradiction_context =
Proofview.Goal.enter begin fun gl ->
let sigma = Tacmach.project gl in
let env = Proofview.Goal.env gl in
let rec seek_neg l = match l with
| [] ->
let info = Exninfo.reify () in
Tacticals.tclZEROMSG ~info (Pp.str"No such contradiction")
| d :: rest ->
let id = NamedDecl.get_id d in
let typ = nf_evar sigma (NamedDecl.get_type d) in
let typ = whd_all env sigma typ in
if is_empty_type env sigma typ then
simplest_elim (mkVar id)
else match EConstr.kind sigma typ with
| Prod (na,t,u) when is_empty_type env sigma u ->
let is_unit_or_eq = match_with_unit_or_eq_type env sigma t in
Tacticals.tclORELSE
(match is_unit_or_eq with
| Some _ ->
let hd,args = decompose_app_list sigma t in
let (ind,_ as indu) = destInd sigma hd in
let nparams = Inductiveops.inductive_nparams env ind in
let params = Util.List.firstn nparams args in
let p = applist ((mkConstructUi (indu,1)), params) in
(* Checking on the fly that it type-checks *)
simplest_elim (mkApp (mkVar id,[|p|]))
| None ->
let info = Exninfo.reify () in
Tacticals.tclZEROMSG ~info (Pp.str"Not a negated unit type."))
(Proofview.tclORELSE
(Proofview.Goal.enter begin fun gl ->
let is_conv_leq = Tacmach.pf_apply is_conv_leq gl in
filter_hyp (fun typ -> is_conv_leq typ t)
(fun id' -> simplest_elim (mkApp (mkVar id,[|mkVar id'|])))
end)
begin function (e, info) -> match e with
| Not_found -> seek_neg rest
| e -> Proofview.tclZERO ~info e
end)
| _ -> seek_neg rest
in
let hyps = Proofview.Goal.hyps gl in
seek_neg hyps
end
let is_negation_of env sigma typ t =
match EConstr.kind sigma (whd_all env sigma t) with
| Prod (na,t,u) ->
is_empty_type env sigma u && is_conv_leq env sigma typ t
| _ -> false
let contradiction_term (c,lbind as cl) =
Proofview.Goal.enter begin fun gl ->
let sigma = Tacmach.project gl in
let env = Proofview.Goal.env gl in
let typ = Tacmach.pf_get_type_of gl c in
let _, ccl = whd_decompose_prod env sigma typ in
if is_empty_type env sigma ccl then
Tacticals.tclTHEN
(elim false None cl None)
(Tacticals.tclTRY assumption)
else
Proofview.tclORELSE
begin
if lbind = Tactypes.NoBindings then
filter_hyp (fun c -> is_negation_of env sigma typ c)
(fun id -> simplest_elim (mkApp (mkVar id,[|c|])))
else
let info = Exninfo.reify () in
Proofview.tclZERO ~info Not_found
end
begin function (e, info) -> match e with
| Not_found ->
Tacticals.tclZEROMSG ~info (Pp.str"Not a contradiction.")
| e -> Proofview.tclZERO ~info e
end
end
let contradiction = function
| None -> Tacticals.tclTHEN intros contradiction_context
| Some c -> contradiction_term c
|
