Source file ssrfwd.ml
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open Pp
open Names
open Constr
open Context
open Tacmach.Old
open Ssrmatching_plugin.Ssrmatching
open Ssrprinters
open Ssrcommon
open Ssrtacticals
module RelDecl = Context.Rel.Declaration
(** 8. Forward chaining tactics (pose, set, have, suffice, wlog) *)
(** Defined identifier *)
let ssrposetac (id, (_, t)) =
let open Proofview.Notations in
Proofview.Goal.enter begin fun gl ->
let env = Proofview.Goal.env gl in
let sigma = Proofview.Goal.sigma gl in
let ist, t =
match t.Ssrast.interp_env with
| Some ist -> ist, Ssrcommon.ssrterm_of_ast_closure_term t
| None -> assert false in
let sigma, t, _ = abs_ssrterm ist env sigma t in
Proofview.Unsafe.tclEVARS sigma <*>
Tactics.pose_tac (Name id) t
end
let ssrsettac id ((_, (pat, pty)), (_, occ)) =
Proofview.V82.tactic begin fun gl ->
let pty = Option.map (fun { Ssrast.body; interp_env } ->
let ist = Option.get interp_env in
(mkRHole, Some body), ist) pty in
let pat = interp_cpattern (pf_env gl) (project gl) pat pty in
let cl, sigma, env = pf_concl gl, project gl, pf_env gl in
let (c, ucst), cl =
let cl = EConstr.Unsafe.to_constr cl in
try fill_occ_pattern ~raise_NoMatch:true env sigma cl pat occ 1
with NoMatch -> redex_of_pattern ~resolve_typeclasses:true env pat, cl in
let gl = pf_merge_uc ucst gl in
let c = EConstr.of_constr c in
let cl = EConstr.of_constr cl in
if Termops.occur_existential sigma c then errorstrm(str"The pattern"++spc()++
pr_econstr_pat env sigma c++spc()++str"did not match and has holes."++spc()++
str"Did you mean pose?") else
let c, (gl, cty) = match EConstr.kind sigma c with
| Cast(t, DEFAULTcast, ty) -> t, (gl, ty)
| _ -> c, pfe_type_of gl c in
let cl' = EConstr.mkLetIn (make_annot (Name id) Sorts.Relevant, c, cty, cl) in
Proofview.V82.of_tactic (Tacticals.tclTHEN (convert_concl ~check:true cl') (introid id)) gl
end
open Util
open Printer
open Ssrast
open Ssripats
let ssrhaveNOtcresolution = Summary.ref ~name:"SSR:havenotcresolution" false
let () =
Goptions.(declare_bool_option
{ optkey = ["SsrHave";"NoTCResolution"];
optread = (fun _ -> !ssrhaveNOtcresolution);
optdepr = false;
optwrite = (fun b -> ssrhaveNOtcresolution := b);
})
open Constrexpr
open Glob_term
let combineCG t1 t2 f g = match t1, t2 with
| (x, (t1, None)), (_, (t2, None)) -> x, (g t1 t2, None)
| (x, (_, Some t1)), (_, (_, Some t2)) -> x, (mkRHole, Some (f t1 t2))
| _, (_, (_, None)) -> anomaly "have: mixed C-G constr"
| _ -> anomaly "have: mixed G-C constr"
let basecuttac name t =
let open Proofview.Notations in
Ssrcommon.tacMK_SSR_CONST name >>= fun hd ->
let t = EConstr.mkApp (hd, [|t|]) in
Ssrcommon.tacTYPEOF t >>= fun _ty ->
Tactics.apply t
let basesufftac t =
let open Proofview.Notations in
Ssrcommon.tacMK_SSR_CONST "ssr_suff" >>= fun hd ->
let t = EConstr.mkApp (hd, [|t|]) in
Ssrcommon.tacTYPEOF t >>= fun _ty ->
Ssrcommon.applyn ~with_evars:true 3 t
let evarcuttac name cs =
let open Proofview.Notations in
Ssrcommon.tacMK_SSR_CONST name >>= fun hd ->
let t = EConstr.mkApp (hd, cs) in
Ssrcommon.tacTYPEOF t >>= fun _ty ->
applyn ~with_evars:true ~with_shelve:false (Array.length cs) t
let introstac ipats = tclIPAT ipats
let havetac ist
(transp,((((clr, orig_pats), binders), simpl), (((fk, _), t), hint)))
suff namefst
=
let open Proofview.Notations in
Ssrcommon.tacMK_SSR_CONST "abstract_key" >>= fun abstract_key ->
Ssrcommon.tacMK_SSR_CONST "abstract" >>= fun abstract ->
Proofview.V82.tactic begin fun gl ->
let concl = pf_concl gl in
let pats = tclCompileIPats orig_pats in
let binders = tclCompileIPats binders in
let simpl = tclCompileIPats simpl in
let skols, pats =
List.partition (function IOpAbstractVars _ -> true | _ -> false) pats in
let itac_mkabs = introstac skols in
let itac_c, clr =
match clr with
| None -> introstac pats, []
| Some clr -> introstac (tclCompileIPats (IPatClear clr :: orig_pats)), clr in
let itac, id, clr = introstac pats, Tacticals.tclIDTAC, cleartac clr in
let binderstac n =
let rec aux = function 0 -> [] | n -> IOpInaccessible None :: aux (n-1) in
Tacticals.tclTHEN (if binders <> [] then introstac (aux n) else Tacticals.tclIDTAC)
(introstac binders) in
let simpltac = introstac simpl in
let fixtc =
not !ssrhaveNOtcresolution &&
match fk with FwdHint(_,true) -> false | _ -> true in
let hint = hinttac ist true hint in
let cuttac t = Proofview.Goal.enter begin fun gl ->
if transp then evarcuttac "ssr_have_let" [|concl;t|]
else basecuttac "ssr_have" t
end in
let unlock_abs (idty,args_id) gl =
let gl, _ = pf_e_type_of gl idty in
pf_unify_HO gl args_id.(2) abstract_key in
Tacticals.Old.tclTHENFIRST (Proofview.V82.of_tactic itac_mkabs) (fun gl ->
let mkt t = mk_term NoFlag t in
let mkl t = (NoFlag, (t, None)) in
let interp gl rtc t =
let sigma, t, n = abs_ssrterm ~resolve_typeclasses:rtc ist (pf_env gl) (project gl) t in
re_sig (sig_it gl) sigma, t, n
in
let interp_ty gl rtc t =
let a,b,_,u = pf_interp_ty ~resolve_typeclasses:rtc (pf_env gl) (project gl) ist t in a,b,u in
let open CAst in
let ct, cty, hole, loc = match Ssrcommon.ssrterm_of_ast_closure_term t with
| _, (_, Some { loc; v = CCast (ct, DEFAULTcast, cty)}) ->
mkt ct, mkt cty, mkt (mkCHole None), loc
| _, (_, Some ct) ->
mkt ct, mkt (mkCHole None), mkt (mkCHole None), None
| _, (t, None) ->
begin match DAst.get t with
| GCast (ct, DEFAULTcast, cty) ->
mkl ct, mkl cty, mkl mkRHole, t.CAst.loc
| _ -> mkl t, mkl mkRHole, mkl mkRHole, None
end
in
let gl, cut, sol, itac1, itac2 =
match fk, namefst, suff with
| FwdHave, true, true ->
errorstrm (str"Suff have does not accept a proof term")
| FwdHave, false, true ->
let cty = combineCG cty hole (mkCArrow ?loc) mkRArrow in
let gl, t, _ = interp gl false (combineCG ct cty (mkCCast ?loc) mkRCast) in
let gl, ty = pfe_type_of gl t in
let ctx, _ = EConstr.decompose_prod_n_assum (project gl) 1 ty in
let assert_is_conv gl =
try Proofview.V82.of_tactic (convert_concl ~check:true (EConstr.it_mkProd_or_LetIn concl ctx)) gl
with _ -> errorstrm (str "Given proof term is not of type " ++
pr_econstr_env (pf_env gl) (project gl) (EConstr.mkArrow (EConstr.mkVar (Id.of_string "_")) Sorts.Relevant concl)) in
gl, ty, Tacticals.tclTHEN (Proofview.V82.tactic assert_is_conv) (Tactics.apply t), id, itac_c
| FwdHave, false, false ->
let skols = List.flatten (List.map (function
| IOpAbstractVars ids -> ids
| _ -> assert false) skols) in
let skols_args =
List.map (fun id -> snd @@
Ssripats.Internal.examine_abstract (pf_env gl) (project gl) (EConstr.mkVar id)) skols in
let gl = List.fold_right unlock_abs skols_args gl in
let gl, t, n_evars =
interp gl false (combineCG ct cty (mkCCast ?loc) mkRCast) in
if skols <> [] && n_evars <> 0 then
CErrors.user_err (Pp.strbrk @@ "Automatic generalization of unresolved implicit "^
"arguments together with abstract variables is "^
"not supported");
let gs =
List.map (fun (_,a) ->
Ssripats.Internal.find_abstract_proof (pf_env gl) (project gl) false a.(1)) skols_args in
let tacopen_skols = Proofview.V82.tactic (fun gl -> re_sig (gs @ [gl.Evd.it]) gl.Evd.sigma) in
let gl, ty = pf_e_type_of gl t in
gl, ty, Tactics.apply t, id,
Tacticals.tclTHEN (Tacticals.tclTHEN itac_c simpltac)
(Tacticals.tclTHEN tacopen_skols (Proofview.V82.tactic (fun gl ->
Proofview.V82.of_tactic (unfold [abstract; abstract_key]) gl)))
| _,true,true ->
let _, ty, uc = interp_ty gl fixtc cty in let gl = pf_merge_uc uc gl in
gl, EConstr.mkArrow ty Sorts.Relevant concl, hint, itac, clr
| _,false,true ->
let _, ty, uc = interp_ty gl fixtc cty in let gl = pf_merge_uc uc gl in
gl, EConstr.mkArrow ty Sorts.Relevant concl, hint, id, itac_c
| _, false, false ->
let n, cty, uc = interp_ty gl fixtc cty in let gl = pf_merge_uc uc gl in
gl, cty, Tacticals.tclTHEN (binderstac n) hint, id, Tacticals.tclTHEN itac_c simpltac
| _, true, false -> assert false in
Proofview.V82.of_tactic (Tacticals.tclTHENS (cuttac cut) [ Tacticals.tclTHEN sol itac1; itac2 ]) gl)
gl
end
let destProd_or_LetIn sigma c =
match EConstr.kind sigma c with
| Prod (n,ty,c) -> RelDecl.LocalAssum (n, ty), c
| LetIn (n,bo,ty,c) -> RelDecl.LocalDef (n, bo, ty), c
| _ -> raise DestKO
let wlogtac ist (((clr0, pats),_),_) (gens, ((_, ct))) hint suff ghave =
Proofview.V82.tactic begin fun gl ->
let clr0 = Option.default [] clr0 in
let pats = tclCompileIPats pats in
let mkabs gen = abs_wgen false (fun x -> x) gen in
let mkclr gen clrs = clr_of_wgen gen clrs in
let mkpats = function
| _, Some ((x, _), _) -> fun pats -> IOpId (hoi_id x) :: pats
| _ -> fun x -> x in
let ct = match Ssrcommon.ssrterm_of_ast_closure_term ct with
| (a, (b, Some ct)) ->
begin match ct.CAst.v with
| CCast (_, DEFAULTcast, cty) -> a, (b, Some cty)
| _ -> anomaly "wlog: ssr cast hole deleted by typecheck"
end
| (a, (t, None)) ->
begin match DAst.get t with
| GCast (_, DEFAULTcast, cty) -> a, (cty, None)
| _ -> anomaly "wlog: ssr cast hole deleted by typecheck"
end
in
let cut_implies_goal = not (suff || ghave <> `NoGen) in
let c, args, ct, gl =
let gens = List.filter (function _, Some _ -> true | _ -> false) gens in
let concl = pf_concl gl in
let c = EConstr.mkProp in
let c = if cut_implies_goal then EConstr.mkArrow c Sorts.Relevant concl else c in
let gl, args, c = List.fold_right mkabs gens (gl,[],c) in
let env, _ =
List.fold_left (fun (env, c) _ ->
let rd, c = destProd_or_LetIn (project gl) c in
EConstr.push_rel rd env, c) (pf_env gl, c) gens in
let sigma = project gl in
let (sigma, ev) = Evarutil.new_evar env sigma EConstr.mkProp in
let k, _ = EConstr.destEvar sigma ev in
let fake_gl = {Evd.it = k; Evd.sigma = sigma} in
let _, ct, _, uc = pf_interp_ty (pf_env fake_gl) sigma ist ct in
let rec var2rel c g s = match EConstr.kind sigma c, g with
| Prod({binder_name=Anonymous} as x,_,c), [] -> EConstr.mkProd(x, EConstr.Vars.subst_vars s ct, c)
| Sort _, [] -> EConstr.Vars.subst_vars s ct
| LetIn({binder_name=Name id} as n,b,ty,c), _::g -> EConstr.mkLetIn (n,b,ty,var2rel c g (id::s))
| Prod({binder_name=Name id} as n,ty,c), _::g -> EConstr.mkProd (n,ty,var2rel c g (id::s))
| _ -> CErrors.anomaly(str"SSR: wlog: var2rel: " ++ pr_econstr_env env sigma c) in
let c = var2rel c gens [] in
let rec pired c = function
| [] -> c
| t::ts as args -> match EConstr.kind sigma c with
| Prod(_,_,c) -> pired (EConstr.Vars.subst1 t c) ts
| LetIn(id,b,ty,c) -> EConstr.mkLetIn (id,b,ty,pired c args)
| _ -> CErrors.anomaly(str"SSR: wlog: pired: " ++ pr_econstr_env env sigma c) in
c, args, pired c args, pf_merge_uc uc gl in
let tacipat pats = introstac pats in
let tacigens =
Tacticals.tclTHEN
(Tacticals.tclTHENLIST(List.rev(List.fold_right mkclr gens [cleartac clr0])))
(introstac (List.fold_right mkpats gens [])) in
let hinttac = hinttac ist true hint in
let cut_kind, fst_goal_tac, snd_goal_tac =
match suff, ghave with
| true, `NoGen -> "ssr_wlog", Tacticals.tclTHEN hinttac (tacipat pats), tacigens
| false, `NoGen -> "ssr_wlog", hinttac, Tacticals.tclTHEN tacigens (tacipat pats)
| true, `Gen _ -> assert false
| false, `Gen id ->
if gens = [] then errorstrm(str"gen have requires some generalizations");
let clear0 = cleartac clr0 in
let id, name_general_hyp, cleanup, pats = match id, pats with
| None, (IOpId id as ip)::pats -> Some id, tacipat [ip], clear0, pats
| None, _ -> None, Tacticals.tclIDTAC, clear0, pats
| Some (Some id),_ -> Some id, introid id, clear0, pats
| Some _,_ ->
let id = mk_anon_id "tmp" (Tacmach.Old.pf_ids_of_hyps gl) in
Some id, introid id, Tacticals.tclTHEN clear0 (Tactics.clear [id]), pats in
let tac_specialize = match id with
| None -> Tacticals.tclIDTAC
| Some id ->
if pats = [] then Tacticals.tclIDTAC else
let args = Array.of_list args in
debug_ssr (fun () -> str"specialized="++ pr_econstr_env (pf_env gl) (project gl) EConstr.(mkApp (mkVar id,args)));
debug_ssr (fun () -> str"specialized_ty="++ pr_econstr_env (pf_env gl) (project gl) ct);
Tacticals.tclTHENS (basecuttac "ssr_have" ct)
[Tactics.apply EConstr.(mkApp (mkVar id,args)); Tacticals.tclIDTAC] in
"ssr_have",
(if hint = nohint then tacigens else hinttac),
Tacticals.tclTHENLIST [name_general_hyp; tac_specialize; tacipat pats; cleanup]
in
Proofview.V82.of_tactic (Tacticals.tclTHENS (basecuttac cut_kind c) [fst_goal_tac; snd_goal_tac]) gl
end
(** The "suffice" tactic *)
open Proofview.Notations
let sufftac ist ((((clr, pats),binders),simpl), ((_, c), hint)) =
let clr = Option.default [] clr in
let pats = tclCompileIPats pats in
let binders = tclCompileIPats binders in
let simpl = tclCompileIPats simpl in
let htac = Tacticals.tclTHEN (introstac pats) (hinttac ist true hint) in
let c = match Ssrcommon.ssrterm_of_ast_closure_term c with
| (a, (b, Some ct)) ->
begin match ct.CAst.v with
| CCast (_, DEFAULTcast, cty) -> a, (b, Some cty)
| _ -> anomaly "suff: ssr cast hole deleted by typecheck"
end
| (a, (t, None)) ->
begin match DAst.get t with
| GCast (_, DEFAULTcast, cty) -> a, (cty, None)
| _ -> anomaly "suff: ssr cast hole deleted by typecheck"
end
in
let ctac =
let open Tacmach in
Proofview.Goal.enter begin fun gl ->
let _,ty,_,uc = pf_interp_ty (pf_env gl) (project gl) ist c in
merge_uc uc <*> basesufftac ty
end in
Tacticals.tclTHENS ctac [htac; Tacticals.tclTHEN (cleartac clr) (introstac (binders@simpl))]
let is_app_evar sigma t =
match EConstr.kind sigma t with
| Constr.Evar _ -> true
| Constr.App(t,_) ->
begin match EConstr.kind sigma t with
| Constr.Evar _ -> true
| _ -> false end
| _ -> false
let rec ncons n e = match n with
| 0 -> []
| n when n > 0 -> e :: ncons (n - 1) e
| _ -> failwith "ncons"
let intro_lock ipats =
let hnf' = Proofview.numgoals >>= fun ng ->
Proofview.tclDISPATCH
(ncons (ng - 1) ssrsmovetac @ [Proofview.tclUNIT ()]) in
let protect_subgoal env sigma hd args =
Ssrcommon.tacMK_SSR_CONST "Under_rel" >>= fun under_rel ->
Ssrcommon.tacMK_SSR_CONST "Under_rel_from_rel" >>= fun under_from_rel ->
Tactics.New.refine ~typecheck:true (fun sigma ->
let lm2 = Array.length args - 2 in
let sigma, carrier =
Typing.type_of env sigma args.(lm2) in
let rel = EConstr.mkApp (hd, Array.sub args 0 lm2) in
let rel_args = Array.sub args lm2 2 in
let under_rel_args = Array.append [|carrier; rel|] rel_args in
let ty = EConstr.mkApp (under_rel, under_rel_args) in
let sigma, t = Evarutil.new_evar env sigma ty in
sigma, EConstr.mkApp(under_from_rel,Array.append under_rel_args [|t|])) in
let rec lock_eq () : unit Proofview.tactic = Proofview.Goal.enter begin fun _ ->
Proofview.tclORELSE
(Ssripats.tclIPAT [Ssripats.IOpTemporay; Ssripats.IOpEqGen (lock_eq ())])
(fun _exn -> Proofview.Goal.enter begin fun gl ->
let c = Proofview.Goal.concl gl in
let sigma = Proofview.Goal.sigma gl in
let env = Proofview.Goal.env gl in
let open EConstr in
match kind_of_type sigma c with
| AtomicType(hd, args) when
Array.length args >= 2 && is_app_evar sigma (Array.last args) &&
Ssrequality.ssr_is_setoid env sigma hd args
||
Ssrcommon.is_const_ref sigma hd (Coqlib.lib_ref "core.iff.type") &&
Array.length args = 2 && is_app_evar sigma args.(1) ->
protect_subgoal env sigma hd args
| _ ->
let t = Reductionops.whd_all env sigma c in
match kind_of_type sigma t with
| AtomicType(hd, args) when
Ssrcommon.is_ind_ref sigma hd (Coqlib.lib_ref "core.eq.type") &&
Array.length args = 3 && is_app_evar sigma args.(2) ->
protect_subgoal env sigma hd args
| _ ->
debug_ssr (fun () -> Pp.(str"under: stop:" ++ pr_econstr_env env sigma t));
Proofview.tclUNIT ()
end)
end
in
hnf' <*> Ssripats.tclIPATssr ipats <*> lock_eq ()
let pretty_rename evar_map term varnames =
let rec aux term vars =
try
match vars with
| [] -> term
| Names.Name.Anonymous :: varnames ->
let name, types, body = EConstr.destLambda evar_map term in
let res = aux body varnames in
EConstr.mkLambda (name, types, res)
| Names.Name.Name _ as name :: varnames ->
let { Context.binder_relevance = r }, types, body =
EConstr.destLambda evar_map term in
let res = aux body varnames in
EConstr.mkLambda (Context.make_annot name r, types, res)
with DestKO -> term
in
aux term varnames
let overtac = ssr_n_tac "over" ~-1
let check_numgoals ?(minus = 0) nh =
Proofview.numgoals >>= fun ng ->
if nh <> ng then
let errmsg =
str"Incorrect number of tactics" ++ spc() ++
str"(expected "++int (ng - minus)++str(String.plural ng " tactic") ++
str", was given "++ int (nh - minus)++str")."
in
CErrors.user_err errmsg
else
Proofview.tclUNIT ()
let undertac ?(pad_intro = false) ist ipats ((dir,_),_ as rule) hint =
let nh = List.length (snd hint) + (if hint = nullhint then 2 else 1) in
let varnames =
let rec aux acc = function
| IPatId id :: rest -> aux (Names.Name.Name id :: acc) rest
| IPatClear _ :: rest -> aux acc rest
| IPatSimpl _ :: rest -> aux acc rest
| IPatAnon (One _ | Drop) :: rest ->
aux (Names.Name.Anonymous :: acc) rest
| _ -> List.rev acc in
aux [] @@ match ipats with
| None -> []
| Some (IPatCase(Regular (l :: _)) :: _) -> l
| Some l -> l in
let ipats =
match ipats with
| None -> [IPatNoop]
| Some l when pad_intro ->
let new_l = ncons (nh - 1) l in
[IPatCase(Regular (new_l @ [[]]))]
| Some (IPatCase(Regular []) :: _ as ipats) -> ipats
| Some (IPatCase(Regular l) :: rest) -> IPatCase(Regular(l @ [[]])) :: rest
| Some (IPatCase(Block _) :: _ as l) -> l
| Some l -> [IPatCase(Regular [l;[]])] in
let map_redex env evar_map ~before:_ ~after:t =
debug_ssr (fun () -> Pp.(str"under vars: " ++ prlist Names.Name.print varnames));
let evar_map, ty = Typing.type_of env evar_map t in
let new_t =
try begin match EConstr.destApp evar_map t with (f, ar) ->
let lam = Array.last ar in
debug_ssr(fun () -> Pp.(str"under: mapping:" ++
pr_econstr_env env evar_map lam));
let new_lam = pretty_rename evar_map lam varnames in
let new_ar, len1 = Array.copy ar, pred (Array.length ar) in
new_ar.(len1) <- new_lam;
EConstr.mkApp (f, new_ar)
end with
| DestKO ->
debug_ssr (fun () -> Pp.(str"under: cannot pretty-rename bound variables with destApp"));
t
in
debug_ssr (fun () -> Pp.(str"under: to:" ++ pr_econstr_env env evar_map new_t));
evar_map, new_t
in
let undertacs =
if hint = nohint then
Proofview.tclUNIT ()
else
let betaiota = Tactics.reduct_in_concl ~cast:false ~check:false
(Reductionops.nf_betaiota, DEFAULTcast)
in
check_numgoals ~minus:1 nh <*>
Proofview.tclDISPATCH
((List.map (function None -> overtac
| Some e -> ssrevaltac ist e <*>
overtac)
(if hint = nullhint then [None] else snd hint))
@ [betaiota])
in
let rew =
Ssrequality.ssrrewritetac ~under:true ~map_redex ist [rule]
in
rew <*> intro_lock ipats <*> undertacs