| Quellcodebibliothek Statistik Leitseite products/sources/formale Sprachen/Roqc/plugins/funind/ (Beweissystem des Inria Version 9.1.0©) Datei vom 15.8.2025 mit Größe 84 kB |
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Quelle gen_principle.ml Sprache: SML |
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(* * The Rocq Prover / The Rocq 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 Util open Names open Indfun_common module RelDecl = Context.Rel.Declaration module ERelevance = EConstr.ERelevance let observe_tac s = observe_tac ~header:(Pp.str "observation") (fun _ _ -> Pp.str s) (* Construct a fixpoint as a Glob_term and not as a constr *) let rec abstract_glob_constr c = function | [] -> c | Constrexpr.CLocalDef (x, _, b, t) :: bl -> Constrexpr_ops.mkLetInC (x, b, t, abstract_glob_constr c bl) | Constrexpr.CLocalAssum (idl, _, k, t) :: bl -> List.fold_right (fun x b -> Constrexpr_ops.mkLambdaC ([x], k, t, b)) idl (abstract_glob_constr c bl) | Constrexpr.CLocalPattern _ :: bl -> assert false let interp_casted_constr_with_implicits env sigma impls c = Constrintern.intern_gen Pretyping.WithoutTypeConstraint env sigma ~impls c let build_newrecursive lnameargsardef = let env0 = Global.env () in let sigma = Evd.from_env env0 in let rec_sign, rec_impls = List.fold_left (fun (env, impls) {Vernacexpr.fname = {CAst.v = recname}; binders; rtype} -> let arityc = Constrexpr_ops.mkCProdN binders rtype in let arity, _ctx = Constrintern.interp_type env0 sigma arityc in let evd = Evd.from_env env0 in let evd, (_, (_, impls', _locs)) = Constrintern.interp_context_evars ~program_mode:false env evd binders in let impl = Constrintern.compute_internalization_data env0 evd recname Constrintern.Recursive arity impls' in let open Context.Named.Declaration in let r = ERelevance.relevant in (* TODO relevance *) ( EConstr.push_named (LocalAssum (Context.make_annot recname r, arity)) env , Id.Map.add recname impl impls )) (env0, Constrintern.empty_internalization_env) lnameargsardef in let recdef = (* Declare local notations *) let f {Vernacexpr.binders; body_def} = match body_def with | Some body_def -> let def = abstract_glob_constr body_def binders in interp_casted_constr_with_implicits rec_sign sigma rec_impls def | None -> CErrors.user_err (Pp.str "Body of Function must be given.") in Vernacstate.System.protect (List.map f) lnameargsardef in (recdef, rec_impls) (* Checks whether or not the mutual bloc is recursive *) let is_rec names = let open Glob_term in let names = List.fold_right Id.Set.add names Id.Set.empty in let check_id id names = Id.Set.mem id names in let rec lookup names gt = match DAst.get gt with | GVar id -> check_id id names | GRef _ | GEvar _ | GPatVar _ | GSort _ | GHole _ | GGenarg _ | GInt _ | GFloat _ | GString _ -> false | GCast (b, _, _) -> lookup names b | GRec _ -> CErrors.user_err (Pp.str "GRec not handled") | GIf (b, _, lhs, rhs) -> lookup names b || lookup names lhs || lookup names rhs | GProd (na, _, _, t, b) | GLambda (na, _, _, t, b) -> lookup names t || lookup (Nameops.Name.fold_right Id.Set.remove na names) b | GLetIn (na, _, b, t, c) -> lookup names b || Option.cata (lookup names) true t || lookup (Nameops.Name.fold_right Id.Set.remove na names) c | GLetTuple (nal, _, t, b) -> lookup names t || lookup (List.fold_left (fun acc na -> Nameops.Name.fold_right Id.Set.remove na acc) names nal) b | GApp (c, args) | GProj (_, args, c) -> List.exists (lookup names) (c :: args) | GArray (_u, t, def, ty) -> Array.exists (lookup names) t || lookup names def || lookup names ty | GCases (_, _, el, brl) -> List.exists (fun (e, _) -> lookup names e) el || List.exists (lookup_br names) brl and lookup_br names {CAst.v = idl, _, rt} = let new_names = List.fold_right Id.Set.remove idl names in lookup new_names rt in lookup names let rec rebuild_bl aux bl typ = let open Constrexpr in match (bl, typ) with | [], _ -> (List.rev aux, typ) | CLocalAssum (nal, _, bk, _) :: bl', typ -> rebuild_nal aux bk bl' nal typ | CLocalDef (na, _, _, _) :: bl', {CAst.v = CLetIn (_, nat, ty, typ')} -> rebuild_bl (Constrexpr.CLocalDef (na, None, nat, ty) :: aux) bl' typ' | _ -> assert false and rebuild_nal aux bk bl' nal typ = let open Constrexpr in match (nal, typ) with | _, {CAst.v = CProdN ([], typ)} -> rebuild_nal aux bk bl' nal typ | [], _ -> rebuild_bl aux bl' typ | ( na :: nal , {CAst.v = CProdN (CLocalAssum (na' :: nal', _, bk', nal't) :: rest, typ')} ) -> if Name.equal na.CAst.v na'.CAst.v || Name.is_anonymous na'.CAst.v then let assum = CLocalAssum ([na], None, bk, nal't) in let new_rest = if nal' = [] then rest else CLocalAssum (nal', None, bk', nal't) :: rest in rebuild_nal (assum :: aux) bk bl' nal (CAst.make @@ CProdN (new_rest, typ')) else let assum = CLocalAssum ([na'], None, bk, nal't) in let new_rest = if nal' = [] then rest else CLocalAssum (nal', None, bk', nal't) :: rest in rebuild_nal (assum :: aux) bk bl' (na :: nal) (CAst.make @@ CProdN (new_rest, typ')) | _ -> assert false let rebuild_bl aux bl typ = rebuild_bl aux bl typ let recompute_binder_list (rec_order, fixpoint_exprl) = let typel, sigma = ComFixpoint.interp_fixpoint_short rec_order fixpoint_exprl in let constr_expr_typel = with_full_print (List.map (fun c -> Constrextern.extern_constr (Global.env ()) sigma (EConstr.of_constr c))) typel in let fixpoint_exprl_with_new_bl = List.map2 (fun ({Vernacexpr.binders} as fp) fix_typ -> let binders, rtype = rebuild_bl [] binders fix_typ in {fp with Vernacexpr.binders; rtype}) fixpoint_exprl constr_expr_typel in fixpoint_exprl_with_new_bl let rec local_binders_length = function (* Assume that no `{ ... } contexts occur *) | [] -> 0 | Constrexpr.CLocalDef _ :: bl -> 1 + local_binders_length bl | Constrexpr.CLocalAssum (idl, _, _, _) :: bl -> List.length idl + local_binders_length bl | Constrexpr.CLocalPattern _ :: bl -> assert false let prepare_body {Vernacexpr.binders} rt = let n = local_binders_length binders in (* Pp.msgnl (str "nb lambda to chop : " ++ str (string_of_int n) ++ fnl () ++Printer.pr_glob_con let fun_args, rt' = chop_rlambda_n n rt in (fun_args, rt') let build_functional_principle env (sigma : Evd.evar_map) old_princ_type sorts funs _i proof_tac hook = (* First we get the type of the old graph principle *) let mutr_nparams = (Induction.compute_elim_sig sigma (EConstr.of_constr old_princ_type)) .Induction.nparams in let new_principle_type = Functional_principles_types.compute_new_princ_type_from_rel (Global.env ()) (Array.map Constr.mkConstU funs) (Array.map (fun s -> EConstr.ESorts.kind sigma s) sorts) old_princ_type in let sigma, _ = Typing.type_of ~refresh:true env sigma (EConstr.of_constr new_principle_type) in let map (c, u) = EConstr.mkConstU (c, EConstr.EInstance.make u) in let ftac = proof_tac (Array.map map funs) mutr_nparams in let uctx = Evd.ustate sigma in let typ = EConstr.of_constr new_principle_type in let body, typ, univs, _safe, _uctx = Declare.build_by_tactic env ~uctx ~poly:false ~typ ftac in (* uctx was ignored before *) let hook = Declare.Hook.make (hook new_principle_type) in (body, typ, univs, hook, sigma) let change_property_sort evd toSort princ princName = let open Context.Rel.Declaration in let toSort = EConstr.ESorts.kind evd toSort in let princ = EConstr.of_constr princ in let princ_info = Induction.compute_elim_sig evd princ in let change_sort_in_predicate decl = LocalAssum ( EConstr.Unsafe.to_binder_annot @@ get_annot decl , let args, ty = Term.decompose_prod (EConstr.Unsafe.to_constr (get_type decl)) in let s = Constr.destSort ty in Global.add_constraints @@ UnivSubst.enforce_leq_sort toSort s Univ.Constraints.empty; Term.compose_prod args (Constr.mkSort toSort) ) in let evd, princName_as_constr = Evd.fresh_global (Global.env ()) evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident princName))) in let init = let nargs = princ_info.Induction.nparams + List.length princ_info.Induction.predicates in Constr.mkApp ( EConstr.Unsafe.to_constr princName_as_constr , Array.init nargs (fun i -> Constr.mkRel (nargs - i)) ) in ( evd , Term.it_mkLambda_or_LetIn (Term.it_mkLambda_or_LetIn init (List.map change_sort_in_predicate princ_info.Induction.predicates)) (EConstr.Unsafe.to_rel_context princ_info.Induction.params) ) let generate_functional_principle (evd : Evd.evar_map ref) old_princ_type sorts new_princ_name funs i proof_tac = try let f = funs.(i) in let sigma, type_sort = Evd.fresh_sort_in_quality !evd UnivGen.QualityOrSet.qtype in evd := sigma; let new_sorts = match sorts with | None -> Array.make (Array.length funs) type_sort | Some a -> a in let base_new_princ_name, new_princ_name, loc = match new_princ_name with | Some {CAst.v=id; loc} -> (id, id, loc) | None -> let id_of_f = Label.to_id (Constant.label (fst f)) in (id_of_f, Indrec.make_elimination_ident id_of_f (EConstr.ESorts.quality_or_set !evd t in let names = ref [new_princ_name] in let hook new_principle_type _ = if Option.is_empty sorts then ( (* let id_of_f = Label.to_id (con_label f) in *) let register_with_sort sort = let evd' = Evd.from_env (Global.env ()) in let evd', s = Evd.fresh_sort_in_quality evd' sort in let name = Indrec.make_elimination_ident base_new_princ_name sort in let evd', value = change_property_sort evd' s new_principle_type new_princ_name in let evd' = fst (Typing.type_of ~refresh:true (Global.env ()) evd' (EConstr.of_constr value)) in (* Pp.msgnl (str "new principle := " ++ pr_lconstr value); *) let univs = Evd.univ_entry ~poly:false evd' in let ce = Declare.definition_entry ~univs value in ignore (Declare.declare_constant ?loc ~name ~kind:Decls.(IsDefinition Scheme) (Declare.DefinitionEntry ce)); Declare.definition_message name; names := name :: !names in register_with_sort UnivGen.QualityOrSet.prop; register_with_sort UnivGen.QualityOrSet.set ) in let body, types, univs, hook, sigma0 = build_functional_principle (Global.env ()) !evd old_princ_type new_sorts funs i proof_ta hook in evd := sigma0; (* Pr 1278 : Don't forget to close the goal if an error is raised !!!! *) let uctx = Evd.ustate sigma in let entry = Declare.definition_entry ~univs ?types body in let (_ : Names.GlobRef.t) = Declare.declare_entry ~name:new_princ_name ~hook ~kind:Decls.(IsProof Theorem) ~impargs:[] ~uctx entry in () with e when CErrors.noncritical e -> raise (Defining_principle e) let generate_principle (evd : Evd.evar_map ref) pconstants on_error is_general do_built fix_rec_l recdefs (continue_proof : int -> Names.Constant.t array -> EConstr.constr array -> int -> unit Proofview.tactic) : unit = let names = List.map (function {Vernacexpr.fname = {CAst.v = name}} -> name) fix_rec_l in let fun_bodies = List.map2 prepare_body fix_rec_l recdefs in let funs_args = List.map fst fun_bodies in let funs_types = List.map (function {Vernacexpr.rtype} -> rtype) fix_rec_l in try (* We then register the Inductive graphs of the functions *) Glob_term_to_relation.build_inductive !evd pconstants funs_args funs_types recdefs; if do_built then begin (*i The next call to mk_rel_id is valid since we have just construct the graph Ensures by : do_built i*) let f_R_mut = Libnames.qualid_of_ident @@ mk_rel_id (List.nth names 0) in let ind_kn = fst (locate_with_msg Pp.(Libnames.pr_qualid f_R_mut ++ str ": Not an inductive type!") locate_ind f_R_mut) in let fname_kn {Vernacexpr.fname} = let f_ref = Libnames.qualid_of_ident ?loc:fname.CAst.loc fname.CAst.v in locate_with_msg Pp.(Libnames.pr_qualid f_ref ++ str ": Not an inductive type!") locate_constant f_ref in let funs_kn = Array.of_list (List.map fname_kn fix_rec_l) in let _ = List.map_i (fun i _x -> let env = Global.env () in let princ = Indrec.lookup_eliminator env (ind_kn, i) UnivGen.QualityOrSet.prop in let evd = ref (Evd.from_env env) in let evd', uprinc = Evd.fresh_global env !evd princ in let _ = evd := evd' in let sigma, princ_type = Typing.type_of ~refresh:true env !evd uprinc in evd := sigma; let princ_type = EConstr.Unsafe.to_constr princ_type in generate_functional_principle evd princ_type None None (Array.of_list pconstants) (* funs_kn *) i (continue_proof 0 [|funs_kn.(i)|])) 0 fix_rec_l in Array.iter (add_Function is_general) funs_kn; () end with e when CErrors.noncritical e -> on_error names e let register_struct is_rec (rec_order, fixpoint_exprl) = let open EConstr in match fixpoint_exprl with | [{Vernacexpr.fname; univs; binders; rtype; body_def}] when not is_rec -> let body = match body_def with | Some body -> body | None -> CErrors.user_err Pp.(str "Body of Function must be given.") in ComDefinition.do_definition ?loc:fname.CAst.loc ~name:fname.CAst.v ~poly:false ~kind:Decls.Definition univs binders None body (Some rtype); let evd, rev_pconstants = List.fold_left (fun (evd, l) {Vernacexpr.fname} -> let evd, c = Evd.fresh_global (Global.env ()) evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident fname.CAst.v))) in let cst, u = destConst evd c in let u = EInstance.kind evd u in (evd, (cst, u) :: l)) (Evd.from_env (Global.env ()), []) fixpoint_exprl in (None, evd, List.rev rev_pconstants) | _ -> let pm, p = ComFixpoint.do_mutually_recursive ~refine:false ~program_mode:false ~poly:f assert (Option.is_empty pm && Option.is_empty p); let evd, rev_pconstants = List.fold_left (fun (evd, l) {Vernacexpr.fname} -> let evd, c = Evd.fresh_global (Global.env ()) evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident fname.CAst.v))) in let cst, u = destConst evd c in let u = EInstance.kind evd u in (evd, (cst, u) :: l)) (Evd.from_env (Global.env ()), []) fixpoint_exprl in (None, evd, List.rev rev_pconstants) let generate_correction_proof_wf f_ref tcc_lemma_ref is_mes functional_ref eq_ref rec_arg_num rec_arg_type relation (_ : int) (_ : Names.Constant.t array) (_ : EConstr.constr array) (_ : int) : unit Proofview.tactic = Functional_principles_proofs.prove_principle_for_gen (f_ref, functional_ref, eq_ref) tcc_lemma_ref is_mes rec_arg_num rec_arg_type relation (* [generate_type g_to_f f graph i] build the completeness (resp. correctness) lemma type if [ (resp. g_to_f = false) where [graph] is the graph of [f] and is the [i]th function in the block. [generate_type true f i] returns \[\forall (x_1:t_1)\ldots(x_n:t_n), let fv := f x_1\ldots x_n in, forall res, graph\ x_1\ldots x_n\ res \rightarrow res = fv \] decomposed as the context and the conclusion [generate_type false f i] returns \[\forall (x_1:t_1)\ldots(x_n:t_n), let fv := f x_1\ldots x_n in, forall res, res = fv \rightarrow graph\ x_1\ldots x_n\ res\] decomposed as the context and the conclusion *) let generate_type env evd g_to_f f graph = let open Context.Rel.Declaration in let open EConstr in let open EConstr.Vars in (*i we deduce the number of arguments of the function and its returned type from the graph i*) let evd', graph = Evd.fresh_global env !evd (GlobRef.IndRef (fst (destInd !evd graph))) in evd := evd'; let sigma, graph_arity = Typing.type_of env !evd graph in evd := sigma; let ctxt, _ = decompose_prod_decls !evd graph_arity in let fun_ctxt, res_type = match ctxt with | [] | [_] -> CErrors.anomaly (Pp.str "Not a valid context.") | decl :: fun_ctxt -> (fun_ctxt, RelDecl.get_type decl) in let rec args_from_decl i accu = function | [] -> accu | LocalDef _ :: l -> args_from_decl (succ i) accu l | _ :: l -> let t = mkRel i in args_from_decl (succ i) (t :: accu) l in (*i We need to name the vars [res] and [fv] i*) let filter decl = match RelDecl.get_name decl with Name id -> Some id | Anonymous -> None in let named_ctxt = Id.Set.of_list (List.map_filter filter fun_ctxt) in let res_id = Namegen.next_ident_away_in_goal env (Id.of_string "_res") named_ctxt in let fv_id = Namegen.next_ident_away_in_goal env (Id.of_string "fv") (Id.Set.add res_id named_ctxt) in (*i we can then type the argument to be applied to the function [f] i*) let args_as_rels = Array.of_list (args_from_decl 1 [] fun_ctxt) in (*i the hypothesis [res = fv] can then be computed We will need to lift it by one in order to use it as a conclusion i*) let make_eq = make_eq () in let res_eq_f_of_args = mkApp (make_eq, [|lift 2 res_type; mkRel 1; mkRel 2|]) in (*i The hypothesis [graph\ x_1\ldots x_n\ res] can then be computed We will need to lift it by one in order to use it as a conclusion i*) let args_and_res_as_rels = Array.of_list (args_from_decl 3 [] fun_ctxt) in let args_and_res_as_rels = Array.append args_and_res_as_rels [|mkRel 1|] in let graph_applied = mkApp (graph, args_and_res_as_rels) in (*i The [pre_context] is the defined to be the context corresponding to \[\forall (x_1:t_1)\ldots(x_n:t_n), let fv := f x_1\ldots x_n in, forall res, \] i*) let pre_ctxt = LocalAssum (Context.make_annot (Name res_id) ERelevance.relevant, lift 1 res_type) :: LocalDef ( Context.make_annot (Name fv_id) ERelevance.relevant , mkApp (f, args_as_rels) , res_type ) :: fun_ctxt in (*i and we can return the solution depending on which lemma type we are defining i*) if g_to_f then ( LocalAssum (Context.make_annot Anonymous ERelevance.relevant, graph_applied) :: pre_ctxt , lift 1 res_eq_f_of_args , graph ) else ( LocalAssum (Context.make_annot Anonymous ERelevance.relevant, res_eq_f_of_args) :: pre_ctxt , lift 1 graph_applied , graph ) (** [find_induction_principle f] searches and returns the [body] and the [type] of [f_rect] WARNING: while convertible, [type_of body] and [type] can be non equal *) let find_induction_principle env evd f = let f_as_constant, _u = match EConstr.kind !evd f with | Constr.Const c' -> c' | _ -> CErrors.user_err Pp.(str "Must be used with a function") in match find_Function_infos f_as_constant with | None -> raise Not_found | Some infos -> ( match infos.rect_lemma with | None -> raise Not_found | Some rect_lemma -> let evd', rect_lemma = Evd.fresh_global env !evd (GlobRef.ConstRef rect_lemma) in let evd', typ = Typing.type_of ~refresh:true env evd' rect_lemma in evd := evd'; (rect_lemma, typ) ) (* [prove_fun_correct funs_constr graphs_constr schemes lemmas_types_infos i ] is the tactic used to prove correctness lemma. [funs_constr], [graphs_constr] [schemes] [lemmas_types_infos] are the mutually recursiv (resp. graphs of the functions and principles and correctness lemma types) to prove correct. [i] is the indice of the function to prove correct The lemma to prove if suppose to have been generated by [generate_type] (in $\zeta$ normal form it looks like~: [\forall (x_1:t_1)\ldots(x_n:t_n), forall res, res = f x_1\ldots x_n in, \rightarrow graph\ x_1\ldots x_n\ res] The sketch of the proof is the following one~: \begin{enumerate} \item intros until $x_n$ \item $functional\ induction\ (f.(i)\ x_1\ldots x_n)$ using schemes.(i) \item for each generated branch intro [res] and [hres :res = f x_1\ldots x_n], rewrite [hres] an apply the corresponding constructor of the corresponding graph inductive. \end{enumerate} *) let rec generate_fresh_id x avoid i = if i == 0 then [] else let id = Namegen.next_ident_away_in_goal (Global.env ()) x (Id.Set.of_list avoid) in id :: generate_fresh_id x (id :: avoid) (pred i) let prove_fun_correct evd graphs_constr schemes lemmas_types_infos i : unit Proofview.tactic = let open Constr in let open EConstr in let open Context.Rel.Declaration in let open Tacmach in let open Tactics in let open Tacticals in Proofview.Goal.enter (fun g -> (* first of all we recreate the lemmas types to be used as predicates of the induction principle that is~: \[fun (x_1:t_1)\ldots(x_n:t_n)=> fun fv => fun res => res = fv \rightarrow graph\ x_1\ldots x_n\ r *) (* we the get the definition of the graphs block *) let graph_ind, u = destInd evd graphs_constr.(i) in let kn = fst graph_ind in let mib, _ = Global.lookup_inductive graph_ind in (* and the principle to use in this lemma in $\zeta$ normal form *) let f_principle, princ_type = schemes.(i) in let princ_type = Reductionops.nf_zeta (Global.env ()) evd princ_type in let princ_infos = Induction.compute_elim_sig evd princ_type in (* The number of args of the function is then easily computable *) let nb_fun_args = Termops.nb_prod (Proofview.Goal.sigma g) (Proofview.Goal.concl g) - 2 in let args_names = generate_fresh_id (Id.of_string "x") [] nb_fun_args in let ids = args_names @ pf_ids_of_hyps g in (* Since we cannot ensure that the functional principle is defined in the environment and due to the bug #1174, we will need to pose the principle using a name *) let principle_id = Namegen.next_ident_away_in_goal (Global.env ()) (Id.of_string "princ") (Id.Set.of_list ids) in let ids = principle_id :: ids in (* We get the branches of the principle *) let branches = List.rev princ_infos.Induction.branches in (* and built the intro pattern for each of them *) let intro_pats = List.map (fun decl -> List.map (fun id -> CAst.make @@ Tactypes.IntroNaming (Namegen.IntroIdentifier id)) (generate_fresh_id (Id.of_string "y") ids (List.length (fst (decompose_prod_decls evd (RelDecl.get_type decl)))))) branches in (* before building the full intro pattern for the principle *) let eq_ind = make_eq () in let eq_construct = mkConstructUi (destInd evd eq_ind, 1) in (* The next to referencies will be used to find out which constructor to apply in each branch *) let ind_number = ref 0 and min_constr_number = ref 0 in (* The tactic to prove the ith branch of the principle *) let prove_branch i pat = (* We get the identifiers of this branch *) let pre_args = List.fold_right (fun {CAst.v = pat} acc -> match pat with | Tactypes.IntroNaming (Namegen.IntroIdentifier id) -> id :: acc | _ -> CErrors.anomaly (Pp.str "Not an identifier.")) pat [] in (* and get the real args of the branch by unfolding the defined constant *) (* We can then recompute the arguments of the constructor. For each [hid] introduced by this branch, if [hid] has type $forall res, res=fv -> graph.(j)\ x_1\ x_n res$ the corresponding arguments of the constructor [ fv (hid fv (refl_equal fv)) ]. If [hid] has another type the corresponding argument of the constructor is [hid] *) let constructor_args g = List.fold_right (fun hid acc -> let type_of_hid = pf_get_hyp_typ hid g in let sigma = Proofview.Goal.sigma g in match EConstr.kind sigma type_of_hid with | Prod (_, _, t') -> ( match EConstr.kind sigma t' with | Prod (_, t'', t''') -> ( match (EConstr.kind sigma t'', EConstr.kind sigma t''') with | App (eq, args), App (graph', _) when EConstr.eq_constr sigma eq eq_ind && Array.exists (EConstr.eq_constr_nounivs sigma graph') graphs_constr -> args.(2) :: mkApp ( mkVar hid , [| args.(2) ; mkApp (eq_construct, [|args.(0); args.(2)|]) |] ) :: acc | _ -> mkVar hid :: acc ) | _ -> mkVar hid :: acc ) | _ -> mkVar hid :: acc) pre_args [] in (* in fact we must also add the parameters to the constructor args *) let constructor_args g = let params_id = fst (List.chop princ_infos.Induction.nparams args_names) in List.map mkVar params_id @ constructor_args g in (* We then get the constructor corresponding to this branch and modifies the references has needed i.e. if the constructor is the last one of the current inductive then add one the number of the inductive to take and add the number of constructor of the previous graph to the minimal constructor number *) let constructor = let constructor_num = i - !min_constr_number in let length = Array.length mib.Declarations.mind_packets.(!ind_number) .Declarations.mind_consnames in if constructor_num <= length then ((kn, !ind_number), constructor_num) else begin incr ind_number; min_constr_number := !min_constr_number + length; ((kn, !ind_number), 1) end in (* we can then build the final proof term *) let app_constructor g = applist (mkConstructU (constructor, u), constructor_args g) in (* an apply the tactic *) let res, hres = match generate_fresh_id (Id.of_string "z") ids (* @this_branche_ids *) 2 with | [res; hres] -> (res, hres) | _ -> assert false in (* observe (str "constructor := " ++ Printer.pr_lconstr_env (pf_env g) app_constructor); *) tclTHENLIST [ observe_tac "h_intro_patterns " (match pat with [] -> tclIDTAC | _ -> intro_patterns false pat) ; (* unfolding of all the defined variables introduced by this branch *) (* observe_tac "unfolding" pre_tac; *) (* $zeta$ normalizing of the conclusion *) reduce (Genredexpr.Cbv { Redops.all_flags with Genredexpr.rDelta = false ; Genredexpr.rConst = [] }) Locusops.onConcl ; observe_tac "toto " (Proofview.tclUNIT ()) ; (* introducing the result of the graph and the equality hypothesis *) observe_tac "introducing" (tclMAP Simple.intro [res; hres]) ; (* replacing [res] with its value *) observe_tac "rewriting res value" (Equality.rewriteLR (mkVar hres)) ; (* Conclusion *) observe_tac "exact" (Proofview.Goal.enter (fun g -> exact_check (app_constructor g))) ] in (* end of branche proof *) let lemmas = Array.map (fun (_, (ctxt, concl)) -> match ctxt with | [] | [_] | [_; _] -> CErrors.anomaly (Pp.str "bad context.") | hres :: res :: decl :: ctxt -> let res = EConstr.it_mkLambda_or_LetIn (EConstr.it_mkProd_or_LetIn concl [hres; res]) ( LocalAssum (RelDecl.get_annot decl, RelDecl.get_type decl) :: ctxt ) in res) lemmas_types_infos in let param_names = fst (List.chop princ_infos.nparams args_names) in let params = List.map mkVar param_names in let lemmas = Array.to_list (Array.map (fun c -> applist (c, params)) lemmas) in (* The bindings of the principle that is the params of the principle and the different lemma types *) let bindings = let params_bindings, avoid = List.fold_left2 (fun (bindings, avoid) decl p -> let id = Namegen.next_ident_away (Nameops.Name.get_id (RelDecl.get_name decl)) (Id.Set.of_list avoid) in (p :: bindings, id :: avoid)) ([], pf_ids_of_hyps g) princ_infos.params (List.rev params) in let lemmas_bindings = List.rev (fst (List.fold_left2 (fun (bindings, avoid) decl p -> let id = Namegen.next_ident_away (Nameops.Name.get_id (RelDecl.get_name decl)) (Id.Set.of_list avoid) in ( Reductionops.nf_zeta (Proofview.Goal.env g) (Proofview.Goal.sigma g) p :: bindings , id :: avoid )) ([], avoid) princ_infos.predicates lemmas)) in params_bindings @ lemmas_bindings in tclTHENLIST [ observe_tac "principle" (assert_by (Name principle_id) princ_type (exact_check f_principle)) ; observe_tac "intro args_names" (tclMAP Simple.intro args_names) ; (* observe_tac "titi" (pose_proof (Name (Id.of_string "__")) (Reductionops.nf_beta Evd. observe_tac "idtac" tclIDTAC ; tclTHENS (observe_tac "functional_induction" (Proofview.Goal.enter (fun gl -> let term = mkApp (mkVar principle_id, Array.of_list bindings) in tclTYPEOFTHEN ~refresh:true term (fun _ _ -> apply term)))) (List.map_i (fun i pat -> observe_tac ("proving branch " ^ string_of_int i) (prove_branch i pat)) 1 intro_pats) ]) (* [prove_fun_complete funs graphs schemes lemmas_types_infos i] is the tactic used to prove completeness lemma. [funcs], [graphs] [schemes] [lemmas_types_infos] are the mutually recursive functions (resp. definitions of the graphs of the functions, principles and correctness lemma types) to [i] is the indice of the function to prove complete The lemma to prove if suppose to have been generated by [generate_type] (in $\zeta$ normal form it looks like~: [\forall (x_1:t_1)\ldots(x_n:t_n), forall res, graph\ x_1\ldots x_n\ res, \rightarrow res = f x_1\ldots x_n in] The sketch of the proof is the following one~: \begin{enumerate} \item intros until $H:graph\ x_1\ldots x_n\ res$ \item $elim\ H$ using schemes.(i) \item for each generated branch, intro the news hyptohesis, for each such hyptohesis [h], if [h type [x=?] with [x] a variable, then subst [x], if [h] has type [t=?] with [t] not a variable then rewrite [t] in the subterms, else if [h] is a match then destruct it, else do just introduce it, after all intros, the conclusion should be a reflexive equality. \end{enumerate} *) let thin = Tactics.clear (* [intros_with_rewrite] do the intros in each branch and treat each new hypothesis (unfolding, substituting, destructing cases \ldots) *) let tauto = let open Ltac_plugin in let dp = List.map Id.of_string ["Tauto"; "Init"; "Corelib"] in let mp = ModPath.MPfile (DirPath.make dp) in let kn = KerName.make mp (Label.make "tauto") in Proofview.tclBIND (Proofview.tclUNIT ()) (fun () -> let body = Tacenv.interp_ltac kn in Tacinterp.eval_tactic body) (* [generalize_dependent_of x hyp g] generalize every hypothesis which depends of [x] but [hyp] *) let generalize_dependent_of x hyp = let open Context.Named.Declaration in let open Tacticals in Proofview.Goal.enter (fun g -> tclMAP (function | LocalAssum ({Context.binder_name = id}, t) when (not (Id.equal id hyp)) && Termops.occur_var (Proofview.Goal.env g) (Proofview.Goal.sigma g) x t -> tclTHEN (Generalize.generalize [EConstr.mkVar id]) (thin [id]) | _ -> Proofview.tclUNIT ()) (Proofview.Goal.hyps g)) let rec intros_with_rewrite () = observe_tac "intros_with_rewrite" (intros_with_rewrite_aux ()) and intros_with_rewrite_aux () : unit Proofview.tactic = let open Constr in let open EConstr in let open Tacmach in let open Tactics in let open Tacticals in Proofview.Goal.enter (fun g -> let eq_ind = make_eq () in let sigma = Proofview.Goal.sigma g in match EConstr.kind sigma (Proofview.Goal.concl g) with | Prod (_, t, t') -> ( match EConstr.kind sigma t with | App (eq, args) when EConstr.eq_constr sigma eq eq_ind -> if Reductionops.is_conv (Proofview.Goal.env g) (Proofview.Goal.sigma g) args.(1) args.(2) then let id = pf_get_new_id (Id.of_string "y") g in tclTHENLIST [Simple.intro id; thin [id]; intros_with_rewrite ()] else if isVar sigma args.(1) && Environ.evaluable_named (destVar sigma args.(1)) (Proofview.Goal.env g) then tclTHENLIST [ unfold_in_concl [ ( Locus.AllOccurrences , Evaluable.EvalVarRef (destVar sigma args.(1)) ) ] ; tclMAP (fun id -> tclTRY (unfold_in_hyp [ ( Locus.AllOccurrences , Evaluable.EvalVarRef (destVar sigma args.(1)) ) ] (destVar sigma args.(1), Locus.InHyp))) (pf_ids_of_hyps g) ; intros_with_rewrite () ] else if isVar sigma args.(2) && Environ.evaluable_named (destVar sigma args.(2)) (Proofview.Goal.env g) then tclTHENLIST [ unfold_in_concl [ ( Locus.AllOccurrences , Evaluable.EvalVarRef (destVar sigma args.(2)) ) ] ; tclMAP (fun id -> tclTRY (unfold_in_hyp [ ( Locus.AllOccurrences , Evaluable.EvalVarRef (destVar sigma args.(2)) ) ] (destVar sigma args.(2), Locus.InHyp))) (pf_ids_of_hyps g) ; intros_with_rewrite () ] else if isVar sigma args.(1) then let id = pf_get_new_id (Id.of_string "y") g in tclTHENLIST [ Simple.intro id ; generalize_dependent_of (destVar sigma args.(1)) id ; tclTRY (Equality.rewriteLR (mkVar id)) ; intros_with_rewrite () ] else if isVar sigma args.(2) then let id = pf_get_new_id (Id.of_string "y") g in tclTHENLIST [ Simple.intro id ; generalize_dependent_of (destVar sigma args.(2)) id ; tclTRY (Equality.rewriteRL (mkVar id)) ; intros_with_rewrite () ] else let id = pf_get_new_id (Id.of_string "y") g in tclTHENLIST [ Simple.intro id ; tclTRY (Equality.rewriteLR (mkVar id)) ; intros_with_rewrite () ] | Ind _ when EConstr.eq_constr sigma t (EConstr.of_constr ( UnivGen.constr_of_monomorphic_global (Global.env ()) @@ Rocqlib.lib_ref "core.False.type" )) -> tauto | Case (_, _, _, _, _, v, _) -> tclTHENLIST [simplest_case v; intros_with_rewrite ()] | LetIn _ -> tclTHENLIST [ reduce (Genredexpr.Cbv {Redops.all_flags with Genredexpr.rDelta = false}) Locusops.onConcl ; intros_with_rewrite () ] | _ -> let id = pf_get_new_id (Id.of_string "y") g in tclTHENLIST [Simple.intro id; intros_with_rewrite ()] ) | LetIn _ -> tclTHENLIST [ reduce (Genredexpr.Cbv {Redops.all_flags with Genredexpr.rDelta = false}) Locusops.onConcl ; intros_with_rewrite () ] | _ -> Proofview.tclUNIT ()) let rec reflexivity_with_destruct_cases () = let open Constr in let open EConstr in let open Tacmach in let open Tactics in let open Tacticals in Proofview.Goal.enter (fun g -> let destruct_case () = try match EConstr.kind (Proofview.Goal.sigma g) (snd (destApp (Proofview.Goal.sigma g) (Proofview.Goal.concl g))).( 2) with | Case (_, _, _, _, _, v, _) -> tclTHENLIST [ simplest_case v ; intros ; observe_tac "reflexivity_with_destruct_cases" (reflexivity_with_destruct_cases ()) ] | _ -> reflexivity with e when CErrors.noncritical e -> reflexivity in let eq_ind = make_eq () in let my_inj_flags = Some { Equality.keep_proof_equalities = false ; injection_pattern_l2r_order = false (* probably does not matter; except maybe with dependent hyps *) } in let discr_inject = onAllHypsAndConcl (fun sc -> match sc with | None -> Proofview.tclUNIT () | Some id -> Proofview.Goal.enter (fun g -> match EConstr.kind (Proofview.Goal.sigma g) (pf_get_hyp_typ id g) with | App (eq, [|_; t1; t2|]) when EConstr.eq_constr (Proofview.Goal.sigma g) eq eq_ind -> tclFIRST [ Equality.discrHyp id; tclTHENLIST [ Equality.injHyp my_inj_flags ~injection_in_context:false None id ; thin [id] ; intros_with_rewrite () ]; Proofview.tclUNIT () ] | _ -> Proofview.tclUNIT ())) in tclFIRST [ observe_tac "reflexivity_with_destruct_cases : reflexivity" reflexivity ; observe_tac "reflexivity_with_destruct_cases : destruct_case" (destruct_case ()) ; (* We reach this point ONLY if the same value is matched (at least) two times along binding path. In this case, either we have a discriminable hypothesis and we are done, either at least an injectable one and we do the injection before continuing *) observe_tac "reflexivity_with_destruct_cases : others" (tclTHEN (tclPROGRESS discr_inject) (reflexivity_with_destruct_cases ())) ]) let prove_fun_complete funcs graphs schemes lemmas_types_infos i : unit Proofview.tactic = let open EConstr in let open Tacmach in let open Tactics in let open Tacticals in Proofview.Goal.enter (fun g -> (* We compute the types of the different mutually recursive lemmas in $\zeta$ normal form *) let lemmas = Array.map (fun (_, (ctxt, concl)) -> Reductionops.nf_zeta (Proofview.Goal.env g) (Proofview.Goal.sigma g) (EConstr.it_mkLambda_or_LetIn concl ctxt)) lemmas_types_infos in (* We get the constant and the principle corresponding to this lemma *) let f = funcs.(i) in let graph_principle = Reductionops.nf_zeta (Proofview.Goal.env g) (Proofview.Goal.sigma g) (EConstr.of_constr schemes.(i)) in tclTYPEOFTHEN graph_principle (fun sigma princ_type -> let princ_infos = Induction.compute_elim_sig sigma princ_type in (* Then we get the number of argument of the function and compute a fresh name for each of them *) let nb_fun_args = Termops.nb_prod sigma (Proofview.Goal.concl g) - 2 in let args_names = generate_fresh_id (Id.of_string "x") [] nb_fun_args in let ids = args_names @ pf_ids_of_hyps g in (* and fresh names for res H and the principle (cf bug bug #1174) *) let res, hres, graph_principle_id = match generate_fresh_id (Id.of_string "z") ids 3 with | [res; hres; graph_principle_id] -> (res, hres, graph_principle_id) | _ -> assert false in let ids = res :: hres :: graph_principle_id :: ids in (* we also compute fresh names for each hyptohesis of each branch of the principle *) let branches = List.rev princ_infos.branches in let intro_pats = List.map (fun decl -> List.map (fun id -> id) (generate_fresh_id (Id.of_string "y") ids (Termops.nb_prod (Proofview.Goal.sigma g) (RelDecl.get_type decl)))) branches in (* We will need to change the function by its body using [f_equation] if it is recursive (that is the graph is infinite or unfold if the graph is finite *) let rewrite_tac j ids : unit Proofview.tactic = let graph_def = graphs.(j) in let infos = match find_Function_infos (fst (destConst (Proofview.Goal.sigma g) funcs.(j))) with | None -> CErrors.user_err Pp.(str "No graph found") | Some infos -> infos in if infos.is_general || Rtree.is_infinite Declareops.eq_recarg graph_def.Declarations.mind_recargs then let eq_lemma = try Option.get infos.equation_lemma with Option.IsNone -> CErrors.anomaly (Pp.str "Cannot find equation lemma.") in tclTHENLIST [ tclMAP Simple.intro ids ; Equality.rewriteLR (UnsafeMonomorphic.mkConst eq_lemma) ; (* Don't forget to $\zeta$ normlize the term since the principles have been $\zeta$-normalized *) reduce (Genredexpr.Cbv {Redops.all_flags with Genredexpr.rDelta = false}) Locusops.onConcl ; Generalize.generalize (List.map mkVar ids) ; thin ids ] else unfold_in_concl [ ( Locus.AllOccurrences , Evaluable.EvalConstRef (fst (destConst (Proofview.Goal.sigma g) f)) ) ] in (* The proof of each branche itself *) let ind_number = ref 0 in let min_constr_number = ref 0 in let prove_branch i this_branche_ids = (* we fist compute the inductive corresponding to the branch *) let this_ind_number = let constructor_num = i - !min_constr_number in let length = Array.length graphs.(!ind_number).Declarations.mind_consnames in if constructor_num <= length then !ind_number else begin incr ind_number; min_constr_number := !min_constr_number + length; !ind_number end in tclTHENLIST [ (* we expand the definition of the function *) observe_tac "rewrite_tac" (rewrite_tac this_ind_number this_branche_ids) ; (* introduce hypothesis with some rewrite *) observe_tac "intros_with_rewrite (all)" (intros_with_rewrite ()) ; (* The proof is (almost) complete *) observe_tac "reflexivity" (reflexivity_with_destruct_cases ()) ] in let params_names = fst (List.chop princ_infos.nparams args_names) in let open EConstr in let params = List.map mkVar params_names in tclTHENLIST [ tclMAP Simple.intro (args_names @ [res; hres]) ; observe_tac "h_generalize" (Generalize.generalize [ mkApp ( applist (graph_principle, params) , Array.map (fun c -> applist (c, params)) lemmas ) ]) ; Simple.intro graph_principle_id ; observe_tac "" (tclTHENS (observe_tac "elim" (elim false None (mkVar hres, Tactypes.NoBindings) (Some (mkVar graph_principle_id, Tactypes.NoBindings)))) (List.map_i (fun i pat -> observe_tac "prove_branch" (prove_branch i pat)) 1 intro_pats)) ])) exception No_graph_found let get_funs_constant mp = let open Constr in let exception Not_Rec in let get_funs_constant const e : (Names.Constant.t * int) array = match Constr.kind (Term.strip_lam e) with | Fix (_, (na, _, _)) -> Array.mapi (fun i na -> match na.Context.binder_name with | Name id -> let const = Constant.make2 mp (Label.of_id id) in (const, i) | Anonymous -> CErrors.anomaly (Pp.str "Anonymous fix.")) na | _ -> [|(const, 0)|] in function | const -> let find_constant_body const = let env = Global.env () in let body = Environ.lookup_constant const env in match body.Declarations.const_body with | Def body -> let body = Tacred.cbv_norm_flags ~strong:true (RedFlags.mkflags [RedFlags.fZETA]) env (Evd.from_env env) (EConstr.of_constr body) in let body = EConstr.Unsafe.to_constr body in body | Undef _ | OpaqueDef _ | Primitive _ | Symbol _ -> CErrors.user_err Pp.(str "Cannot define a principle over an axiom ") in let f = find_constant_body const in let l_const = get_funs_constant const f in (* We need to check that all the functions found are in the same block to prevent Reset strange thing *) let l_bodies = List.map find_constant_body (Array.to_list (Array.map fst l_const)) in let l_params, _l_fixes = List.split (List.map Term.decompose_lambda l_bodies) in (* all the parameters must be equal*) let _check_params = let first_params = List.hd l_params in List.iter (fun params -> if not (List.equal (fun (n1, c1) (n2, c2) -> Context.eq_annot Name.equal Sorts.relevance_equal n1 n2 && Constr.equal c1 c2) first_params params) then CErrors.user_err Pp.(str "Not a mutal recursive block")) l_params in (* The bodies has to be very similar *) let _check_bodies = try let extract_info is_first body = match Constr.kind body with | Fix ((idxs, _), (na, ta, ca)) -> (idxs, na, ta, ca) | _ -> if is_first && Int.equal (List.length l_bodies) 1 then raise Not_Rec else CErrors.user_err Pp.(str "Not a mutal recursive block") in let first_infos = extract_info true (List.hd l_bodies) in let check body = (* Hope this is correct *) let eq_infos (ia1, na1, ta1, ca1) (ia2, na2, ta2, ca2) = Array.equal Int.equal ia1 ia2 && Array.equal (Context.eq_annot Name.equal Sorts.relevance_equal) na1 na2 && Array.equal Constr.equal ta1 ta2 && Array.equal Constr.equal ca1 ca2 in if not (eq_infos first_infos (extract_info false body)) then CErrors.user_err Pp.(str "Not a mutal recursive block") in List.iter check l_bodies with Not_Rec -> () in l_const let make_scheme evd (fas : (Constr.pconstant * UnivGen.QualityOrSet.t) list) : _ list = let exception Found_type of int in let env = Global.env () in let funs = List.map fst fas in let first_fun = List.hd funs in let funs_mp = KerName.modpath (Constant.canonical (fst first_fun)) in let first_fun_kn = match find_Function_infos (fst first_fun) with | None -> raise No_graph_found | Some finfos -> fst finfos.graph_ind in let this_block_funs_indexes = get_funs_constant funs_mp (fst first_fun) in let this_block_funs = Array.map (fun (c, _) -> (c, snd first_fun)) this_block_funs_indexes in let funs_indexes = let this_block_funs_indexes = Array.to_list this_block_funs_indexes in let eq c1 c2 = Environ.QConstant.equal env c1 c2 in List.map (function cst -> List.assoc_f eq (fst cst) this_block_funs_indexes) funs in let ind_list = List.map (fun idx -> let ind = (first_fun_kn, idx) in ((ind, EConstr.EInstance.make @@ snd first_fun), true, EConstr.ESorts.prop)) funs_indexes in let sigma, schemes = Indrec.build_mutual_induction_scheme env !evd ind_list in let _ = evd := sigma in let l_schemes = List.map (Retyping.get_type_of env sigma %> EConstr.Unsafe.to_constr ) schemes in let i = ref (-1) in let sorts = List.rev_map (fun (_, x) -> let sigma, fs = Evd.fresh_sort_in_quality !evd x in evd := sigma; fs) fas in (* We create the first principle by tactic *) let first_type, other_princ_types = match l_schemes with | s :: l_schemes -> (s, l_schemes) | _ -> CErrors.anomaly (Pp.str "") in let opaque = let finfos = match find_Function_infos (fst first_fun) with | None -> raise Not_found | Some finfos -> finfos in match finfos.equation_lemma with | None -> Vernacexpr.Transparent (* non recursive definition *) | Some equation -> if Declareops.is_opaque (Global.lookup_constant equation) then Vernacexpr.Opaque else Vernacexpr.Transparent in let body, typ, univs, _hook, sigma0 = try build_functional_principle (Global.env ()) !evd first_type (Array.of_list sorts) this_block_funs 0 (Functional_principles_proofs.prove_princ_for_struct evd false 0 (Array.of_list (List.map fst funs))) (fun _ _ -> ()) with e when CErrors.noncritical e -> raise (Defining_principle e) in evd := sigma0; incr i; (* The others are just deduced *) if List.is_empty other_princ_types then [(body, typ, univs, opaque)] else let other_fun_princ_types = let funs = Array.map Constr.mkConstU this_block_funs in let sorts = Array.of_list sorts in let sorts = Array.map (fun s -> EConstr.ESorts.kind sigma s) sorts in List.map (Functional_principles_types.compute_new_princ_type_from_rel (Global.env ()) funs so other_princ_types in let first_princ_body = body in let ctxt, fix = Term.decompose_lambda_decls first_princ_body in (* the principle has for forall ...., fix .*) let (idxs, _), ((_, ta, _) as decl) = Constr.destFix fix in let other_result = List.map (* we can now compute the other principles *) (fun scheme_type -> incr i; observe (fun () -> Printer.pr_lconstr_env env sigma scheme_type); let type_concl = Term.strip_prod_decls scheme_type in let applied_f = List.hd (List.rev (snd (Constr.decompose_app_list type_concl))) in let f = fst (Constr.decompose_app applied_f) in try (* we search the number of the function in the fix block (name of the function) *) Array.iteri (fun j t -> let t = Term.strip_prod_decls t in let applied_g = List.hd (List.rev (snd (Constr.decompose_app_list t))) in let g = fst (Constr.decompose_app applied_g) in if Constr.equal f g then raise (Found_type j); observe Pp.(fun () -> Printer.pr_lconstr_env env sigma f ++ str " <> " ++ Printer.pr_lconstr_env env sigma g)) ta; (* If we reach this point, the two principle are not mutually recursive We fall back to the previous method *) let body, typ, univs, _hook, sigma0 = build_functional_principle (Global.env ()) !evd (List.nth other_princ_types (!i - 1)) (Array.of_list sorts) this_block_funs !i (Functional_principles_proofs.prove_princ_for_struct evd false !i (Array.of_list (List.map fst funs))) (fun _ _ -> ()) in evd := sigma0; (body, typ, univs, opaque) with Found_type i -> let princ_body = Term.it_mkLambda_or_LetIn (Constr.mkFix ((idxs, i), decl)) ctxt in (princ_body, Some scheme_type, univs, opaque)) other_fun_princ_types in (body, typ, univs, opaque) :: other_result (* [derive_correctness funs graphs] create correctness and completeness lemmas for each function in [funs] w.r.t. [graphs] *) let derive_correctness (funs : Constr.pconstant list) (graphs : inductive list) = let open EConstr in assert (funs <> []); assert (graphs <> []); let funs = Array.of_list funs and graphs = Array.of_list graphs in let map (c, u) = mkConstU (c, EInstance.make u) in let funs_constr = Array.map map funs in (* XXX STATE Why do we need this... why is the toplevel protection not enough *) funind_purify (fun () -> let env = Global.env () in let evd = ref (Evd.from_env env) in let graphs_constr = Array.map UnsafeMonomorphic.mkInd graphs in let lemmas_types_infos = Util.Array.map2_i (fun i f_constr graph -> let type_of_lemma_ctxt, type_of_lemma_concl, graph = generate_type env evd false f_constr graph in let type_info = (type_of_lemma_ctxt, type_of_lemma_concl) in graphs_constr.(i) <- graph; let type_of_lemma = EConstr.it_mkProd_or_LetIn type_of_lemma_concl type_of_lemma_ctxt in let sigma, _ = Typing.type_of env !evd type_of_lemma in evd := sigma; let type_of_lemma = Reductionops.nf_zeta env !evd type_of_lemma in observe Pp.(fun () -> str "type_of_lemma := " ++ Printer.pr_leconstr_env env !evd type_of_lemma); (type_of_lemma, type_info)) funs_constr graphs_constr in let schemes = (* The functional induction schemes are computed and not saved if there is more that one functio if the block contains only one function we can safely reuse [f_rect] *) try if not (Int.equal (Array.length funs_constr) 1) then raise Not_found; [|find_induction_principle env evd funs_constr.(0)|] with Not_found -> Array.of_list (List.map (fun (body, typ, _opaque, _univs) -> (EConstr.of_constr body, EConstr.of_constr (Option.get typ))) (make_scheme evd (Array.map_to_list (fun const -> (const, UnivGen.QualityOrSet.qtype)) funs))) in let proving_tac = prove_fun_correct !evd graphs_constr schemes lemmas_types_infos in Array.iteri (fun i f_as_constant -> let f_id = Label.to_id (Constant.label (fst f_as_constant)) in (*i The next call to mk_correct_id is valid since we are constructing the lemma Ensures by: obvious i*) let lem_id = mk_correct_id f_id in let typ, _ = lemmas_types_infos.(i) in let info = Declare.Info.make () in let cinfo = Declare.CInfo.make ~name:lem_id ~typ () in let lemma = Declare.Proof.start ~cinfo ~info !evd in let lemma = fst @@ Declare.Proof.by (proving_tac i) lemma in let (_ : _ list) = Declare.Proof.save_regular ~proof:lemma ~opaque:Vernacexpr.Transparent ~idopt:None in let finfo = match find_Function_infos (fst f_as_constant) with | None -> raise Not_found | Some finfo -> finfo in (* let lem_cst = fst (destConst (Constrintern.global_reference lem_id)) in *) let _, lem_cst_constr = Evd.fresh_global (Global.env ()) !evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident lem_id))) in let lem_cst, _ = EConstr.destConst !evd lem_cst_constr in update_Function {finfo with correctness_lemma = Some lem_cst}) funs; let env = Global.env () in let lemmas_types_infos = Util.Array.map2_i (fun i f_constr graph -> let type_of_lemma_ctxt, type_of_lemma_concl, graph = generate_type env evd true f_constr graph in let type_info = (type_of_lemma_ctxt, type_of_lemma_concl) in graphs_constr.(i) <- graph; let type_of_lemma = EConstr.it_mkProd_or_LetIn type_of_lemma_concl type_of_lemma_ctxt in let type_of_lemma = Reductionops.nf_zeta env !evd type_of_lemma in observe Pp.(fun () -> str "type_of_lemma := " ++ Printer.pr_leconstr_env env !evd type_of_lemma); (type_of_lemma, type_info)) funs_constr graphs_constr in let ((kn, _) as graph_ind), u = destInd !evd graphs_constr.(0) in let mib, _mip = Inductive.lookup_mind_specif env graph_ind in let sigma, scheme = let sigma, inds = CArray.fold_left_map_i (fun i sigma _ -> let sigma, s = Evd.fresh_sort_in_quality ~rigid:UnivRigid sigma UnivGen.QualityOrSet.qt sigma, (((kn, i), u), true, s)) !evd mib.mind_packets in Indrec.build_mutual_induction_scheme env sigma (Array.to_list inds) in let schemes = Array.map_of_list EConstr.Unsafe.to_constr scheme in let proving_tac = prove_fun_complete funs_constr mib.Declarations.mind_packets schemes lemmas_types_infos in Array.iteri (fun i f_as_constant -> let f_id = Label.to_id (Constant.label (fst f_as_constant)) in (*i The next call to mk_complete_id is valid since we are constructing the lemma Ensures by: obvious i*) let lem_id = mk_complete_id f_id in let info = Declare.Info.make () in let cinfo = Declare.CInfo.make ~name:lem_id ~typ:(fst lemmas_types_infos.(i)) () in let lemma = Declare.Proof.start ~cinfo sigma ~info in let lemma = fst (Declare.Proof.by (observe_tac ("prove completeness (" ^ Id.to_string f_id ^ ")") (proving_tac i)) lemma) in let (_ : _ list) = Declare.Proof.save_regular ~proof:lemma ~opaque:Vernacexpr.Transparent ~idopt:None in let finfo = match find_Function_infos (fst f_as_constant) with | None -> raise Not_found | Some finfo -> finfo in let _, lem_cst_constr = Evd.fresh_global (Global.env ()) !evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident lem_id))) in let lem_cst, _ = destConst !evd lem_cst_constr in update_Function {finfo with completeness_lemma = Some lem_cst}) funs) () let warn_funind_cannot_build_inversion = CWarnings.create ~name:"funind-cannot-build-inversion" ~category:CWarnings.CoreCat Pp.( fun e' -> strbrk "Cannot build inversion information" ++ if do_observe () then fnl () ++ CErrors.print e' else mt ()) let derive_inversion env fix_names = try let evd' = Evd.from_env env in (* we first transform the fix_names identifier into their corresponding constant *) let evd', fix_names_as_constant = List.fold_right (fun id (evd, l) -> let evd, c = Evd.fresh_global env evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident id))) in let cst, u = EConstr.destConst evd c in (evd, (cst, EConstr.EInstance.kind evd u) :: l)) fix_names (evd', []) in (* Then we check that the graphs have been defined If one of the graphs haven't been defined we do nothing *) List.iter (fun c -> ignore (find_Function_infos (fst c))) fix_names_as_constant; try let _evd', lind = List.fold_right (fun id (evd, l) -> let evd, id = Evd.fresh_global env evd (Option.get (Constrintern.locate_reference (Libnames.qualid_of_ident (mk_rel_id id)))) in (evd, fst (EConstr.destInd evd id) :: l)) fix_names (evd', []) in derive_correctness fix_names_as_constant lind with e when CErrors.noncritical e -> warn_funind_cannot_build_inversion e with e when CErrors.noncritical e -> warn_funind_cannot_build_inversion e let register_wf interactive_proof ?(is_mes = false) fname rec_impls wf_rel_expr wf_arg using_lemmas args ret_type body pre_hook = let type_of_f = Constrexpr_ops.mkCProdN args ret_type in let rec_arg_num = let names = List.map CAst.(with_val (fun x -> x)) (Constrexpr_ops.names_of_local_assums args) in List.index Name.equal (Name wf_arg) names in let unbounded_eq = let f_app_args = CAst.make @@ Constrexpr.CAppExpl ( (Libnames.qualid_of_ident fname, None) , List.map (function | {CAst.v = Anonymous} -> assert false | {CAst.v = Name e} -> Constrexpr_ops.mkIdentC e) (Constrexpr_ops.names_of_local_assums args) ) in CAst.make @@ Constrexpr.CApp ( Constrexpr_ops.mkRefC (Libnames.qualid_of_string "Logic.eq") , [(f_app_args, None); (body, None)] ) in --> -------------------- --> maximum size reached --> -------------------- ¤ Dauer der Verarbeitung: 0.36 Sekunden ¤*© Formatika GbR, Deutschland |
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2026-03-28