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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) *) (************************************************************************) (* This file is (C) Copyright 2006-2015 Microsoft Corporation and Inria. *) open Pp open Names open Constr open Context open Tacmach 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 posetac id cl = Proofview.V82.of_tactic (Tactics.pose_tac (Name id) cl) let ssrposetac (id, (_, t)) gl = 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, ucst, _ = pf_abs_ssrterm ist gl t in posetac id t (pf_merge_uc ucst gl) let ssrsettac id ((_, (pat, pty)), (_, occ)) 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 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 Tacticals.tclTHEN (Proofview.V82.of_tactic (convert_concl ~check:true cl')) (introid id) gl open Util open Printer open Ssrast open Ssripats let ssrhaveNOtcresolution = Summary.ref ~name:"SSR:havenotcresolution" false let () = Goptions.(declare_bool_option { optname = "have type classes"; 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 c gl = let hd, gl = pf_mkSsrConst name gl in let t = EConstr.mkApp (hd, [|c|]) in let gl, _ = pf_e_type_of gl t in Proofview.V82.of_tactic (Tactics.apply t) gl let introstac ipats = Proofview.V82.of_tactic (tclIPAT ipats) let havetac ist (transp,((((clr, orig_pats), binders), simpl), (((fk, _), t), hint))) suff namefst 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, old_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 gl = if transp then let have_let, gl = pf_mkSsrConst "ssr_have_let" gl in let step = EConstr.mkApp (have_let, [|concl;t|]) in let gl, _ = pf_e_type_of gl step in applyn ~with_evars:true ~with_shelve:false 2 step gl else basecuttac "ssr_have" t gl in (* Introduce now abstract constants, so that everything sees them *) let abstract_key, gl = pf_mkSsrConst "abstract_key" gl 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.tclTHENFIRST itac_mkabs (fun gl -> let mkt t = mk_term xNoFlag t in let mkl t = (xNoFlag, (t, None)) in let interp gl rtc t = pf_abs_ssrterm ~resolve_typeclasses:rtc ist gl t in let interp_ty gl rtc t = let a,b,_,u = pf_interp_ty ~resolve_typeclasses:rtc ist gl 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, CastConv 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, CastConv 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 _,t,uc,_ = interp gl false (combineCG ct cty (mkCCast ?loc) mkRCast) in let gl = pf_merge_uc uc gl 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 assert_is_conv (Proofview.V82.of_tactic (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 -> Ssripats.Internal.examine_abstract (EConstr.mkVar id) gl) skols in let gl = List.fold_right unlock_abs skols_args gl in let sigma, t, uc, 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 gl = re_sig (sig_it gl) (Evd.merge_universe_context sigma uc) in let gs = List.map (fun (_,a) -> Ssripats.Internal.pf_find_abstract_proof false gl (EConstr.Unsafe.to_constr a.(1))) skols_args in let tacopen_skols gl = re_sig (gs @ [gl.Evd.it]) gl.Evd.sigma in let gl, ty = pf_e_type_of gl t in gl, ty, Proofview.V82.of_tactic (Tactics.apply t), id, Tacticals.tclTHEN (Tacticals.tclTHEN itac_c simpltac) (Tacticals.tclTHEN tacopen_skols (fun gl -> let abstract, gl = pf_mkSsrConst "abstract" gl in 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 Tacticals.tclTHENS (cuttac cut) [ Tacticals.tclTHEN sol itac1; itac2 ] gl) gl ;; 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 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 (_, CastConv cty) -> a, (b, Some cty) | _ -> anomaly "wlog: ssr cast hole deleted by typecheck" end | (a, (t, None)) -> begin match DAst.get t with | GCast (_, CastConv 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 ist fake_gl 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 [old_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 = old_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.pf_ids_of_hyps gl) in Some id, introid id, Tacticals.tclTHEN clear0 (Proofview.V82.of_tactic (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 ppdebug(lazy(str"specialized="++ pr_econstr_env (pf_env gl) (project gl) EConstr.(mkApp (mkVar id,args)))); ppdebug(lazy(str"specialized_ty="++ pr_econstr_env (pf_env gl) (project gl) ct)); Tacticals.tclTHENS (basecuttac "ssr_have" ct) [Proofview.V82.of_tactic (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 Tacticals.tclTHENS (basecuttac cut_kind c) [fst_goal_tac; snd_goal_tac] gl (** The "suffice" tactic *) 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 (_, CastConv cty) -> a, (b, Some cty) | _ -> anomaly "suff: ssr cast hole deleted by typecheck" end | (a, (t, None)) -> begin match DAst.get t with | GCast (_, CastConv cty) -> a, (cty, None) | _ -> anomaly "suff: ssr cast hole deleted by typecheck" end in let ctac gl = let _,ty,_,uc = pf_interp_ty ist gl c in let gl = pf_merge_uc uc gl in basecuttac "ssr_suff" ty gl in Tacticals.tclTHENS ctac [htac; Tacticals.tclTHEN (old_cleartac clr) (introstac (binders@simpl))] open Proofview.Notations 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 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 match EConstr.kind_of_type sigma c with | Term.AtomicType(hd, args) when Ssrcommon.is_const_ref sigma hd (Coqlib.lib_ref "core.iff.type") && Array.length args = 2 && is_app_evar sigma args.(1) -> Tactics.New.refine ~typecheck:true (fun sigma -> let sigma, under_iff = Ssrcommon.mkSsrConst "Under_iff" env sigma in let sigma, under_from_iff = Ssrcommon.mkSsrConst "Under_iff_from_iff" env sigma in let ty = EConstr.mkApp (under_iff,args) in let sigma, t = Evarutil.new_evar env sigma ty in sigma, EConstr.mkApp(under_from_iff,Array.append args [|t|])) | _ -> let t = Reductionops.whd_all env sigma c in match EConstr.kind_of_type sigma t with | Term.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) -> Tactics.New.refine ~typecheck:true (fun sigma -> let sigma, under = Ssrcommon.mkSsrConst "Under_eq" env sigma in let sigma, under_from_eq = Ssrcommon.mkSsrConst "Under_eq_from_eq" env sigma in let ty = EConstr.mkApp (under,args) in let sigma, t = Evarutil.new_evar env sigma ty in sigma, EConstr.mkApp(under_from_eq,Array.append args [|t|])) | _ -> ppdebug(lazy 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 = Proofview.V82.tactic (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 = (* total number of implied hints *) 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 (* If we find a "=> [|]" we add 1 | to get "=> [||]" for the extra * goal (the one that is left once we run over) *) let ipats = match ipats with | None -> [IPatNoop] | Some l when pad_intro -> (* typically, ipats = Some [IPatAnon All] *) let new_l = ncons (nh - 1) l in [IPatCase(Regular (new_l @ [[]]))] | Some (IPatCase(Regular []) :: _ as ipats) -> ipats (* Erik: is the previous line correct/useful? *) | 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 = ppdebug(lazy Pp.(str"under vars: " ++ prlist Names.Name.print varnames)); let evar_map, ty = Typing.type_of env evar_map t in let new_t = (* pretty-rename the bound variables *) try begin match EConstr.destApp evar_map t with (f, ar) -> let lam = Array.last ar in ppdebug(lazy 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 -> ppdebug(lazy Pp.(str"under: cannot pretty-rename bound variables with destApp")); t in ppdebug(lazy 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 ~check:false (Reductionops.nf_betaiota, DEFAULTcast) in (* Usefulness of check_numgoals: tclDISPATCH would be enough, except for the error message w.r.t. the number of provided/expected tactics, as the last one is implied *) 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 = Proofview.V82.tactic (Ssrequality.ssrrewritetac ~under:true ~map_redex ist [rule]) in rew <*> intro_lock ipats <*> undertacs