diff options
Diffstat (limited to 'contrib/funind')
| -rw-r--r-- | contrib/funind/Recdef.v | 48 | ||||
| -rw-r--r-- | contrib/funind/functional_principles_proofs.ml | 1658 | ||||
| -rw-r--r-- | contrib/funind/functional_principles_proofs.mli | 19 | ||||
| -rw-r--r-- | contrib/funind/functional_principles_types.ml | 733 | ||||
| -rw-r--r-- | contrib/funind/functional_principles_types.mli | 34 | ||||
| -rw-r--r-- | contrib/funind/g_indfun.ml4 | 524 | ||||
| -rw-r--r-- | contrib/funind/indfun.ml | 752 | ||||
| -rw-r--r-- | contrib/funind/indfun_common.ml | 512 | ||||
| -rw-r--r-- | contrib/funind/indfun_common.mli | 117 | ||||
| -rw-r--r-- | contrib/funind/invfun.ml | 1022 | ||||
| -rw-r--r-- | contrib/funind/merge.ml | 1034 | ||||
| -rw-r--r-- | contrib/funind/rawterm_to_relation.ml | 1262 | ||||
| -rw-r--r-- | contrib/funind/rawterm_to_relation.mli | 16 | ||||
| -rw-r--r-- | contrib/funind/rawtermops.ml | 718 | ||||
| -rw-r--r-- | contrib/funind/rawtermops.mli | 126 | ||||
| -rw-r--r-- | contrib/funind/recdef.ml | 1436 |
16 files changed, 0 insertions, 10011 deletions
diff --git a/contrib/funind/Recdef.v b/contrib/funind/Recdef.v deleted file mode 100644 index 2d206220..00000000 --- a/contrib/funind/Recdef.v +++ /dev/null @@ -1,48 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) -Require Compare_dec. -Require Wf_nat. - -Section Iter. -Variable A : Type. - -Fixpoint iter (n : nat) : (A -> A) -> A -> A := - fun (fl : A -> A) (def : A) => - match n with - | O => def - | S m => fl (iter m fl def) - end. -End Iter. - -Theorem SSplus_lt : forall p p' : nat, p < S (S (p + p')). - intro p; intro p'; change (S p <= S (S (p + p'))); - apply le_S; apply Gt.gt_le_S; change (p < S (p + p')); - apply Lt.le_lt_n_Sm; apply Plus.le_plus_l. -Qed. - - -Theorem Splus_lt : forall p p' : nat, p' < S (p + p'). - intro p; intro p'; change (S p' <= S (p + p')); - apply Gt.gt_le_S; change (p' < S (p + p')); apply Lt.le_lt_n_Sm; - apply Plus.le_plus_r. -Qed. - -Theorem le_lt_SS : forall x y, x <= y -> x < S (S y). -intro x; intro y; intro H; change (S x <= S (S y)); - apply le_S; apply Gt.gt_le_S; change (x < S y); - apply Lt.le_lt_n_Sm; exact H. -Qed. - -Inductive max_type (m n:nat) : Set := - cmt : forall v, m <= v -> n <= v -> max_type m n. - -Definition max : forall m n:nat, max_type m n. -intros m n; case (Compare_dec.le_gt_dec m n). -intros h; exists n; [exact h | apply le_n]. -intros h; exists m; [apply le_n | apply Lt.lt_le_weak; exact h]. -Defined. diff --git a/contrib/funind/functional_principles_proofs.ml b/contrib/funind/functional_principles_proofs.ml deleted file mode 100644 index b13bea9d..00000000 --- a/contrib/funind/functional_principles_proofs.ml +++ /dev/null @@ -1,1658 +0,0 @@ -open Printer -open Util -open Term -open Termops -open Names -open Declarations -open Pp -open Entries -open Hiddentac -open Evd -open Tacmach -open Proof_type -open Tacticals -open Tactics -open Indfun_common -open Libnames - -let msgnl = Pp.msgnl - - -let observe strm = - if do_observe () - then Pp.msgnl strm - else () - -let observennl strm = - if do_observe () - then begin Pp.msg strm;Pp.pp_flush () end - else () - - - - -let do_observe_tac s tac g = - try let v = tac g in (* msgnl (goal ++ fnl () ++ (str s)++(str " ")++(str "finished")); *) v - with e -> - let goal = begin try (Printer.pr_goal (sig_it g)) with _ -> assert false end in - msgnl (str "observation "++ s++str " raised exception " ++ - Cerrors.explain_exn e ++ str " on goal " ++ goal ); - raise e;; - -let observe_tac_stream s tac g = - if do_observe () - then do_observe_tac s tac g - else tac g - -let observe_tac s tac g = observe_tac_stream (str s) tac g - -(* let tclTRYD tac = *) -(* if !Flags.debug || do_observe () *) -(* then (fun g -> try (\* do_observe_tac "" *\)tac g with _ -> tclIDTAC g) *) -(* else tac *) - - -let list_chop ?(msg="") n l = - try - list_chop n l - with Failure (msg') -> - failwith (msg ^ msg') - - -let make_refl_eq type_of_t t = - let refl_equal_term = Lazy.force refl_equal in - mkApp(refl_equal_term,[|type_of_t;t|]) - - -type pte_info = - { - proving_tac : (identifier list -> Tacmach.tactic); - is_valid : constr -> bool - } - -type ptes_info = pte_info Idmap.t - -type 'a dynamic_info = - { - nb_rec_hyps : int; - rec_hyps : identifier list ; - eq_hyps : identifier list; - info : 'a - } - -type body_info = constr dynamic_info - - -let finish_proof dynamic_infos g = - observe_tac "finish" - ( h_assumption) - g - - -let refine c = - Tacmach.refine_no_check c - -let thin l = - Tacmach.thin_no_check l - - -let cut_replacing id t tac :tactic= - tclTHENS (cut t) - [ tclTHEN (thin_no_check [id]) (introduction_no_check id); - tac - ] - -let intro_erasing id = tclTHEN (thin [id]) (introduction id) - - - -let rec_hyp_id = id_of_string "rec_hyp" - -let is_trivial_eq t = - match kind_of_term t with - | App(f,[|_;t1;t2|]) when eq_constr f (Lazy.force eq) -> - eq_constr t1 t2 - | _ -> false - - -let rec incompatible_constructor_terms t1 t2 = - let c1,arg1 = decompose_app t1 - and c2,arg2 = decompose_app t2 - in - (not (eq_constr t1 t2)) && - isConstruct c1 && isConstruct c2 && - ( - not (eq_constr c1 c2) || - List.exists2 incompatible_constructor_terms arg1 arg2 - ) - -let is_incompatible_eq t = - match kind_of_term t with - | App(f,[|_;t1;t2|]) when eq_constr f (Lazy.force eq) -> - incompatible_constructor_terms t1 t2 - | _ -> false - -let change_hyp_with_using msg hyp_id t tac : tactic = - fun g -> - let prov_id = pf_get_new_id hyp_id g in - tclTHENS - ((* observe_tac msg *) (assert_by (Name prov_id) t (tclCOMPLETE tac))) - [tclTHENLIST - [ - (* observe_tac "change_hyp_with_using thin" *) (thin [hyp_id]); - (* observe_tac "change_hyp_with_using rename " *) (h_rename [prov_id,hyp_id]) - ]] g - -exception TOREMOVE - - -let prove_trivial_eq h_id context (type_of_term,term) = - let nb_intros = List.length context in - tclTHENLIST - [ - tclDO nb_intros intro; (* introducing context *) - (fun g -> - let context_hyps = - fst (list_chop ~msg:"prove_trivial_eq : " nb_intros (pf_ids_of_hyps g)) - in - let context_hyps' = - (mkApp(Lazy.force refl_equal,[|type_of_term;term|])):: - (List.map mkVar context_hyps) - in - let to_refine = applist(mkVar h_id,List.rev context_hyps') in - refine to_refine g - ) - ] - - -let isAppConstruct t = - if isApp t - then isConstruct (fst (destApp t)) - else false - -let nf_betaiotazeta = (* Reductionops.local_strong Reductionops.whd_betaiotazeta *) - let clos_norm_flags flgs env sigma t = - Closure.norm_val (Closure.create_clos_infos flgs env) (Closure.inject (Reductionops.nf_evar sigma t)) in - clos_norm_flags Closure.betaiotazeta Environ.empty_env Evd.empty - - -let change_eq env sigma hyp_id (context:Sign.rel_context) x t end_of_type = - let nochange msg = - begin -(* observe (str ("Not treating ( "^msg^" )") ++ pr_lconstr t ); *) - failwith "NoChange"; - end - in - let eq_constr = Reductionops.is_conv env sigma in - if not (noccurn 1 end_of_type) - then nochange "dependent"; (* if end_of_type depends on this term we don't touch it *) - if not (isApp t) then nochange "not an equality"; - let f_eq,args = destApp t in - if not (eq_constr f_eq (Lazy.force eq)) then nochange "not an equality"; - let t1 = args.(1) - and t2 = args.(2) - and t1_typ = args.(0) - in - if not (closed0 t1) then nochange "not a closed lhs"; - let rec compute_substitution sub t1 t2 = -(* observe (str "compute_substitution : " ++ pr_lconstr t1 ++ str " === " ++ pr_lconstr t2); *) - if isRel t2 - then - let t2 = destRel t2 in - begin - try - let t1' = Intmap.find t2 sub in - if not (eq_constr t1 t1') then nochange "twice bound variable"; - sub - with Not_found -> - assert (closed0 t1); - Intmap.add t2 t1 sub - end - else if isAppConstruct t1 && isAppConstruct t2 - then - begin - let c1,args1 = destApp t1 - and c2,args2 = destApp t2 - in - if not (eq_constr c1 c2) then anomaly "deconstructing equation"; - array_fold_left2 compute_substitution sub args1 args2 - end - else - if (eq_constr t1 t2) then sub else nochange "cannot solve" - in - let sub = compute_substitution Intmap.empty t1 t2 in - let end_of_type_with_pop = pop end_of_type in (*the equation will be removed *) - let new_end_of_type = - (* Ugly hack to prevent Map.fold order change between ocaml-3.08.3 and ocaml-3.08.4 - Can be safely replaced by the next comment for Ocaml >= 3.08.4 - *) - let sub' = Intmap.fold (fun i t acc -> (i,t)::acc) sub [] in - let sub'' = List.sort (fun (x,_) (y,_) -> Pervasives.compare x y) sub' in - List.fold_left (fun end_of_type (i,t) -> lift 1 (substnl [t] (i-1) end_of_type)) - end_of_type_with_pop - sub'' - in - let old_context_length = List.length context + 1 in - let witness_fun = - mkLetIn(Anonymous,make_refl_eq t1_typ t1,t, - mkApp(mkVar hyp_id,Array.init old_context_length (fun i -> mkRel (old_context_length - i))) - ) - in - let new_type_of_hyp,ctxt_size,witness_fun = - list_fold_left_i - (fun i (end_of_type,ctxt_size,witness_fun) ((x',b',t') as decl) -> - try - let witness = Intmap.find i sub in - if b' <> None then anomaly "can not redefine a rel!"; - (pop end_of_type,ctxt_size,mkLetIn(x',witness,t',witness_fun)) - with Not_found -> - (mkProd_or_LetIn decl end_of_type, ctxt_size + 1, mkLambda_or_LetIn decl witness_fun) - ) - 1 - (new_end_of_type,0,witness_fun) - context - in - let new_type_of_hyp = - Reductionops.nf_betaiota Evd.empty new_type_of_hyp in - let new_ctxt,new_end_of_type = - Sign.decompose_prod_n_assum ctxt_size new_type_of_hyp - in - let prove_new_hyp : tactic = - tclTHEN - (tclDO ctxt_size intro) - (fun g -> - let all_ids = pf_ids_of_hyps g in - let new_ids,_ = list_chop ctxt_size all_ids in - let to_refine = applist(witness_fun,List.rev_map mkVar new_ids) in - refine to_refine g - ) - in - let simpl_eq_tac = - change_hyp_with_using "prove_pattern_simplification" hyp_id new_type_of_hyp prove_new_hyp - in -(* observe (str "In " ++ Ppconstr.pr_id hyp_id ++ *) -(* str "removing an equation " ++ fnl ()++ *) -(* str "old_typ_of_hyp :=" ++ *) -(* Printer.pr_lconstr_env *) -(* env *) -(* (it_mkProd_or_LetIn ~init:end_of_type ((x,None,t)::context)) *) -(* ++ fnl () ++ *) -(* str "new_typ_of_hyp := "++ *) -(* Printer.pr_lconstr_env env new_type_of_hyp ++ fnl () *) -(* ++ str "old context := " ++ pr_rel_context env context ++ fnl () *) -(* ++ str "new context := " ++ pr_rel_context env new_ctxt ++ fnl () *) -(* ++ str "old type := " ++ pr_lconstr end_of_type ++ fnl () *) -(* ++ str "new type := " ++ pr_lconstr new_end_of_type ++ fnl () *) -(* ); *) - new_ctxt,new_end_of_type,simpl_eq_tac - - -let is_property ptes_info t_x full_type_of_hyp = - if isApp t_x - then - let pte,args = destApp t_x in - if isVar pte && array_for_all closed0 args - then - try - let info = Idmap.find (destVar pte) ptes_info in - info.is_valid full_type_of_hyp - with Not_found -> false - else false - else false - -let isLetIn t = - match kind_of_term t with - | LetIn _ -> true - | _ -> false - - -let h_reduce_with_zeta = - h_reduce - (Rawterm.Cbv - {Rawterm.all_flags - with Rawterm.rDelta = false; - }) - - - -let rewrite_until_var arg_num eq_ids : tactic = - (* tests if the declares recursive argument is neither a Constructor nor - an applied Constructor since such a form for the recursive argument - will break the Guard when trying to save the Lemma. - *) - let test_var g = - let _,args = destApp (pf_concl g) in - not ((isConstruct args.(arg_num)) || isAppConstruct args.(arg_num)) - in - let rec do_rewrite eq_ids g = - if test_var g - then tclIDTAC g - else - match eq_ids with - | [] -> anomaly "Cannot find a way to prove recursive property"; - | eq_id::eq_ids -> - tclTHEN - (tclTRY (Equality.rewriteRL (mkVar eq_id))) - (do_rewrite eq_ids) - g - in - do_rewrite eq_ids - - -let rec_pte_id = id_of_string "Hrec" -let clean_hyp_with_heq ptes_infos eq_hyps hyp_id env sigma = - let coq_False = Coqlib.build_coq_False () in - let coq_True = Coqlib.build_coq_True () in - let coq_I = Coqlib.build_coq_I () in - let rec scan_type context type_of_hyp : tactic = - if isLetIn type_of_hyp then - let real_type_of_hyp = it_mkProd_or_LetIn ~init:type_of_hyp context in - let reduced_type_of_hyp = nf_betaiotazeta real_type_of_hyp in - (* length of context didn't change ? *) - let new_context,new_typ_of_hyp = - Sign.decompose_prod_n_assum (List.length context) reduced_type_of_hyp - in - tclTHENLIST - [ - h_reduce_with_zeta - (Tacticals.onHyp hyp_id) - ; - scan_type new_context new_typ_of_hyp - - ] - else if isProd type_of_hyp - then - begin - let (x,t_x,t') = destProd type_of_hyp in - let actual_real_type_of_hyp = it_mkProd_or_LetIn ~init:t' context in - if is_property ptes_infos t_x actual_real_type_of_hyp then - begin - let pte,pte_args = (destApp t_x) in - let (* fix_info *) prove_rec_hyp = (Idmap.find (destVar pte) ptes_infos).proving_tac in - let popped_t' = pop t' in - let real_type_of_hyp = it_mkProd_or_LetIn ~init:popped_t' context in - let prove_new_type_of_hyp = - let context_length = List.length context in - tclTHENLIST - [ - tclDO context_length intro; - (fun g -> - let context_hyps_ids = - fst (list_chop ~msg:"rec hyp : context_hyps" - context_length (pf_ids_of_hyps g)) - in - let rec_pte_id = pf_get_new_id rec_pte_id g in - let to_refine = - applist(mkVar hyp_id, - List.rev_map mkVar (rec_pte_id::context_hyps_ids) - ) - in -(* observe_tac "rec hyp " *) - (tclTHENS - (assert_tac (Name rec_pte_id) t_x) - [ - (* observe_tac "prove rec hyp" *) (prove_rec_hyp eq_hyps); -(* observe_tac "prove rec hyp" *) - (refine to_refine) - ]) - g - ) - ] - in - tclTHENLIST - [ -(* observe_tac "hyp rec" *) - (change_hyp_with_using "rec_hyp_tac" hyp_id real_type_of_hyp prove_new_type_of_hyp); - scan_type context popped_t' - ] - end - else if eq_constr t_x coq_False then - begin -(* observe (str "Removing : "++ Ppconstr.pr_id hyp_id++ *) -(* str " since it has False in its preconds " *) -(* ); *) - raise TOREMOVE; (* False -> .. useless *) - end - else if is_incompatible_eq t_x then raise TOREMOVE (* t_x := C1 ... = C2 ... *) - else if eq_constr t_x coq_True (* Trivial => we remove this precons *) - then -(* observe (str "In "++Ppconstr.pr_id hyp_id++ *) -(* str " removing useless precond True" *) -(* ); *) - let popped_t' = pop t' in - let real_type_of_hyp = - it_mkProd_or_LetIn ~init:popped_t' context - in - let prove_trivial = - let nb_intro = List.length context in - tclTHENLIST [ - tclDO nb_intro intro; - (fun g -> - let context_hyps = - fst (list_chop ~msg:"removing True : context_hyps "nb_intro (pf_ids_of_hyps g)) - in - let to_refine = - applist (mkVar hyp_id, - List.rev (coq_I::List.map mkVar context_hyps) - ) - in - refine to_refine g - ) - ] - in - tclTHENLIST[ - change_hyp_with_using "prove_trivial" hyp_id real_type_of_hyp - ((* observe_tac "prove_trivial" *) prove_trivial); - scan_type context popped_t' - ] - else if is_trivial_eq t_x - then (* t_x := t = t => we remove this precond *) - let popped_t' = pop t' in - let real_type_of_hyp = - it_mkProd_or_LetIn ~init:popped_t' context - in - let _,args = destApp t_x in - tclTHENLIST - [ - change_hyp_with_using - "prove_trivial_eq" - hyp_id - real_type_of_hyp - ((* observe_tac "prove_trivial_eq" *) (prove_trivial_eq hyp_id context (args.(0),args.(1)))); - scan_type context popped_t' - ] - else - begin - try - let new_context,new_t',tac = change_eq env sigma hyp_id context x t_x t' in - tclTHEN - tac - (scan_type new_context new_t') - with Failure "NoChange" -> - (* Last thing todo : push the rel in the context and continue *) - scan_type ((x,None,t_x)::context) t' - end - end - else - tclIDTAC - in - try - scan_type [] (Typing.type_of env sigma (mkVar hyp_id)), [hyp_id] - with TOREMOVE -> - thin [hyp_id],[] - - -let clean_goal_with_heq ptes_infos continue_tac dyn_infos = - fun g -> - let env = pf_env g - and sigma = project g - in - let tac,new_hyps = - List.fold_left ( - fun (hyps_tac,new_hyps) hyp_id -> - let hyp_tac,new_hyp = - clean_hyp_with_heq ptes_infos dyn_infos.eq_hyps hyp_id env sigma - in - (tclTHEN hyp_tac hyps_tac),new_hyp@new_hyps - ) - (tclIDTAC,[]) - dyn_infos.rec_hyps - in - let new_infos = - { dyn_infos with - rec_hyps = new_hyps; - nb_rec_hyps = List.length new_hyps - } - in - tclTHENLIST - [ - tac ; - (* observe_tac "clean_hyp_with_heq continue" *) (continue_tac new_infos) - ] - g - -let heq_id = id_of_string "Heq" - -let treat_new_case ptes_infos nb_prod continue_tac term dyn_infos = - fun g -> - let heq_id = pf_get_new_id heq_id g in - let nb_first_intro = nb_prod - 1 - dyn_infos.nb_rec_hyps in - tclTHENLIST - [ - (* We first introduce the variables *) - tclDO nb_first_intro (intro_avoiding dyn_infos.rec_hyps); - (* Then the equation itself *) - introduction_no_check heq_id; - (* Then the new hypothesis *) - tclMAP introduction_no_check dyn_infos.rec_hyps; - (* observe_tac "after_introduction" *)(fun g' -> - (* We get infos on the equations introduced*) - let new_term_value_eq = pf_type_of g' (mkVar heq_id) in - (* compute the new value of the body *) - let new_term_value = - match kind_of_term new_term_value_eq with - | App(f,[| _;_;args2 |]) -> args2 - | _ -> - observe (str "cannot compute new term value : " ++ pr_gls g' ++ fnl () ++ str "last hyp is" ++ - pr_lconstr_env (pf_env g') new_term_value_eq - ); - anomaly "cannot compute new term value" - in - let fun_body = - mkLambda(Anonymous, - pf_type_of g' term, - replace_term term (mkRel 1) dyn_infos.info - ) - in - let new_body = pf_nf_betaiota g' (mkApp(fun_body,[| new_term_value |])) in - let new_infos = - {dyn_infos with - info = new_body; - eq_hyps = heq_id::dyn_infos.eq_hyps - } - in - clean_goal_with_heq ptes_infos continue_tac new_infos g' - ) - ] - g - - -let my_orelse tac1 tac2 g = - try - tac1 g - with e -> -(* observe (str "using snd tac since : " ++ Cerrors.explain_exn e); *) - tac2 g - -let instanciate_hyps_with_args (do_prove:identifier list -> tactic) hyps args_id = - let args = Array.of_list (List.map mkVar args_id) in - let instanciate_one_hyp hid = - my_orelse - ( (* we instanciate the hyp if possible *) - fun g -> - let prov_hid = pf_get_new_id hid g in - tclTHENLIST[ - pose_proof (Name prov_hid) (mkApp(mkVar hid,args)); - thin [hid]; - h_rename [prov_hid,hid] - ] g - ) - ( (* - if not then we are in a mutual function block - and this hyp is a recursive hyp on an other function. - - We are not supposed to use it while proving this - principle so that we can trash it - - *) - (fun g -> -(* observe (str "Instanciation: removing hyp " ++ Ppconstr.pr_id hid); *) - thin [hid] g - ) - ) - in - if args_id = [] - then - tclTHENLIST [ - tclMAP (fun hyp_id -> h_reduce_with_zeta (Tacticals.onHyp hyp_id)) hyps; - do_prove hyps - ] - else - tclTHENLIST - [ - tclMAP (fun hyp_id -> h_reduce_with_zeta (Tacticals.onHyp hyp_id)) hyps; - tclMAP instanciate_one_hyp hyps; - (fun g -> - let all_g_hyps_id = - List.fold_right Idset.add (pf_ids_of_hyps g) Idset.empty - in - let remaining_hyps = - List.filter (fun id -> Idset.mem id all_g_hyps_id) hyps - in - do_prove remaining_hyps g - ) - ] - -let build_proof - (interactive_proof:bool) - (fnames:constant list) - ptes_infos - dyn_infos - : tactic = - let rec build_proof_aux do_finalize dyn_infos : tactic = - fun g -> -(* observe (str "proving on " ++ Printer.pr_lconstr_env (pf_env g) term);*) - match kind_of_term dyn_infos.info with - | Case(ci,ct,t,cb) -> - let do_finalize_t dyn_info' = - fun g -> - let t = dyn_info'.info in - let dyn_infos = {dyn_info' with info = - mkCase(ci,ct,t,cb)} in - let g_nb_prod = nb_prod (pf_concl g) in - let type_of_term = pf_type_of g t in - let term_eq = - make_refl_eq type_of_term t - in - tclTHENSEQ - [ - h_generalize (term_eq::(List.map mkVar dyn_infos.rec_hyps)); - thin dyn_infos.rec_hyps; - pattern_option [(false,[1]),t] None; - h_simplest_case t; - (fun g' -> - let g'_nb_prod = nb_prod (pf_concl g') in - let nb_instanciate_partial = g'_nb_prod - g_nb_prod in - observe_tac "treat_new_case" - (treat_new_case - ptes_infos - nb_instanciate_partial - (build_proof do_finalize) - t - dyn_infos) - g' - ) - - ] g - in - build_proof do_finalize_t {dyn_infos with info = t} g - | Lambda(n,t,b) -> - begin - match kind_of_term( pf_concl g) with - | Prod _ -> - tclTHEN - intro - (fun g' -> - let (id,_,_) = pf_last_hyp g' in - let new_term = - pf_nf_betaiota g' - (mkApp(dyn_infos.info,[|mkVar id|])) - in - let new_infos = {dyn_infos with info = new_term} in - let do_prove new_hyps = - build_proof do_finalize - {new_infos with - rec_hyps = new_hyps; - nb_rec_hyps = List.length new_hyps - } - in -(* observe_tac "Lambda" *) (instanciate_hyps_with_args do_prove new_infos.rec_hyps [id]) g' - (* build_proof do_finalize new_infos g' *) - ) g - | _ -> - do_finalize dyn_infos g - end - | Cast(t,_,_) -> - build_proof do_finalize {dyn_infos with info = t} g - | Const _ | Var _ | Meta _ | Evar _ | Sort _ | Construct _ | Ind _ -> - do_finalize dyn_infos g - | App(_,_) -> - let f,args = decompose_app dyn_infos.info in - begin - match kind_of_term f with - | App _ -> assert false (* we have collected all the app in decompose_app *) - | Var _ | Construct _ | Rel _ | Evar _ | Meta _ | Ind _ | Sort _ | Prod _ -> - let new_infos = - { dyn_infos with - info = (f,args) - } - in - build_proof_args do_finalize new_infos g - | Const c when not (List.mem c fnames) -> - let new_infos = - { dyn_infos with - info = (f,args) - } - in -(* Pp.msgnl (str "proving in " ++ pr_lconstr_env (pf_env g) dyn_infos.info); *) - build_proof_args do_finalize new_infos g - | Const _ -> - do_finalize dyn_infos g - | Lambda _ -> - let new_term = - Reductionops.nf_beta Evd.empty dyn_infos.info in - build_proof do_finalize {dyn_infos with info = new_term} - g - | LetIn _ -> - let new_infos = - { dyn_infos with info = nf_betaiotazeta dyn_infos.info } - in - - tclTHENLIST - [tclMAP - (fun hyp_id -> h_reduce_with_zeta (Tacticals.onHyp hyp_id)) - dyn_infos.rec_hyps; - h_reduce_with_zeta Tacticals.onConcl; - build_proof do_finalize new_infos - ] - g - | Cast(b,_,_) -> - build_proof do_finalize {dyn_infos with info = b } g - | Case _ | Fix _ | CoFix _ -> - let new_finalize dyn_infos = - let new_infos = - { dyn_infos with - info = dyn_infos.info,args - } - in - build_proof_args do_finalize new_infos - in - build_proof new_finalize {dyn_infos with info = f } g - end - | Fix _ | CoFix _ -> - error ( "Anonymous local (co)fixpoints are not handled yet") - - | Prod _ -> error "Prod" - | LetIn _ -> - let new_infos = - { dyn_infos with - info = nf_betaiotazeta dyn_infos.info - } - in - - tclTHENLIST - [tclMAP - (fun hyp_id -> h_reduce_with_zeta (Tacticals.onHyp hyp_id)) - dyn_infos.rec_hyps; - h_reduce_with_zeta Tacticals.onConcl; - build_proof do_finalize new_infos - ] g - | Rel _ -> anomaly "Free var in goal conclusion !" - and build_proof do_finalize dyn_infos g = -(* observe (str "proving with "++Printer.pr_lconstr dyn_infos.info++ str " on goal " ++ pr_gls g); *) - observe_tac "build_proof" (build_proof_aux do_finalize dyn_infos) g - and build_proof_args do_finalize dyn_infos (* f_args' args *) :tactic = - fun g -> - let (f_args',args) = dyn_infos.info in - let tac : tactic = - fun g -> - match args with - | [] -> - do_finalize {dyn_infos with info = f_args'} g - | arg::args -> -(* observe (str "build_proof_args with arg := "++ pr_lconstr_env (pf_env g) arg++ *) -(* fnl () ++ *) -(* pr_goal (Tacmach.sig_it g) *) -(* ); *) - let do_finalize dyn_infos = - let new_arg = dyn_infos.info in - (* tclTRYD *) - (build_proof_args - do_finalize - {dyn_infos with info = (mkApp(f_args',[|new_arg|])), args} - ) - in - build_proof do_finalize - {dyn_infos with info = arg } - g - in - (* observe_tac "build_proof_args" *) (tac ) g - in - let do_finish_proof dyn_infos = - (* tclTRYD *) (clean_goal_with_heq - ptes_infos - finish_proof dyn_infos) - in - (* observe_tac "build_proof" *) - (build_proof (clean_goal_with_heq ptes_infos do_finish_proof) dyn_infos) - - - - - - - - - - - - -(* Proof of principles from structural functions *) -let is_pte_type t = - isSort (snd (decompose_prod t)) - -let is_pte (_,_,t) = is_pte_type t - - - - -type static_fix_info = - { - idx : int; - name : identifier; - types : types; - offset : int; - nb_realargs : int; - body_with_param : constr; - num_in_block : int - } - - - -let prove_rec_hyp_for_struct fix_info = - (fun eq_hyps -> tclTHEN - (rewrite_until_var (fix_info.idx) eq_hyps) - (fun g -> - let _,pte_args = destApp (pf_concl g) in - let rec_hyp_proof = - mkApp(mkVar fix_info.name,array_get_start pte_args) - in - refine rec_hyp_proof g - )) - -let prove_rec_hyp fix_info = - { proving_tac = prove_rec_hyp_for_struct fix_info - ; - is_valid = fun _ -> true - } - - -exception Not_Rec - -let generalize_non_dep hyp g = -(* observe (str "rec id := " ++ Ppconstr.pr_id hyp); *) - let hyps = [hyp] in - let env = Global.env () in - let hyp_typ = pf_type_of g (mkVar hyp) in - let to_revert,_ = - Environ.fold_named_context_reverse (fun (clear,keep) (hyp,_,_ as decl) -> - if List.mem hyp hyps - or List.exists (occur_var_in_decl env hyp) keep - or occur_var env hyp hyp_typ - or Termops.is_section_variable hyp (* should be dangerous *) - then (clear,decl::keep) - else (hyp::clear,keep)) - ~init:([],[]) (pf_env g) - in -(* observe (str "to_revert := " ++ prlist_with_sep spc Ppconstr.pr_id to_revert); *) - tclTHEN - ((* observe_tac "h_generalize" *) (h_generalize (List.map mkVar to_revert) )) - ((* observe_tac "thin" *) (thin to_revert)) - g - -let id_of_decl (na,_,_) = (Nameops.out_name na) -let var_of_decl decl = mkVar (id_of_decl decl) -let revert idl = - tclTHEN - (generalize (List.map mkVar idl)) - (thin idl) - -let generate_equation_lemma fnames f fun_num nb_params nb_args rec_args_num = -(* observe (str "nb_args := " ++ str (string_of_int nb_args)); *) -(* observe (str "nb_params := " ++ str (string_of_int nb_params)); *) -(* observe (str "rec_args_num := " ++ str (string_of_int (rec_args_num + 1) )); *) - let f_def = Global.lookup_constant (destConst f) in - let eq_lhs = mkApp(f,Array.init (nb_params + nb_args) (fun i -> mkRel(nb_params + nb_args - i))) in - let f_body = - force (Option.get f_def.const_body) - in - let params,f_body_with_params = decompose_lam_n nb_params f_body in - let (_,num),(_,_,bodies) = destFix f_body_with_params in - let fnames_with_params = - let params = Array.init nb_params (fun i -> mkRel(nb_params - i)) in - let fnames = List.rev (Array.to_list (Array.map (fun f -> mkApp(f,params)) fnames)) in - fnames - in -(* observe (str "fnames_with_params " ++ prlist_with_sep fnl pr_lconstr fnames_with_params); *) -(* observe (str "body " ++ pr_lconstr bodies.(num)); *) - let f_body_with_params_and_other_fun = substl fnames_with_params bodies.(num) in -(* observe (str "f_body_with_params_and_other_fun " ++ pr_lconstr f_body_with_params_and_other_fun); *) - let eq_rhs = nf_betaiotazeta (mkApp(compose_lam params f_body_with_params_and_other_fun,Array.init (nb_params + nb_args) (fun i -> mkRel(nb_params + nb_args - i)))) in -(* observe (str "eq_rhs " ++ pr_lconstr eq_rhs); *) - let type_ctxt,type_of_f = Sign.decompose_prod_n_assum (nb_params + nb_args) - (Typeops.type_of_constant_type (Global.env()) f_def.const_type) in - let eqn = mkApp(Lazy.force eq,[|type_of_f;eq_lhs;eq_rhs|]) in - let lemma_type = it_mkProd_or_LetIn ~init:eqn type_ctxt in - let f_id = id_of_label (con_label (destConst f)) in - let prove_replacement = - tclTHENSEQ - [ - tclDO (nb_params + rec_args_num + 1) intro; - (* observe_tac "" *) (fun g -> - let rec_id = pf_nth_hyp_id g 1 in - tclTHENSEQ - [(* observe_tac "generalize_non_dep in generate_equation_lemma" *) (generalize_non_dep rec_id); - (* observe_tac "h_case" *) (h_case false (mkVar rec_id,Rawterm.NoBindings)); - intros_reflexivity] g - ) - ] - in - Command.start_proof - (*i The next call to mk_equation_id is valid since we are constructing the lemma - Ensures by: obvious - i*) - (mk_equation_id f_id) - (Decl_kinds.Global,(Decl_kinds.Proof Decl_kinds.Theorem)) - lemma_type - (fun _ _ -> ()); - Pfedit.by (prove_replacement); - Command.save_named false - - - - -let do_replace params rec_arg_num rev_args_id f fun_num all_funs g = - let equation_lemma = - try - let finfos = find_Function_infos (destConst f) in - mkConst (Option.get finfos.equation_lemma) - with (Not_found | Option.IsNone as e) -> - let f_id = id_of_label (con_label (destConst f)) in - (*i The next call to mk_equation_id is valid since we will construct the lemma - Ensures by: obvious - i*) - let equation_lemma_id = (mk_equation_id f_id) in - generate_equation_lemma all_funs f fun_num (List.length params) (List.length rev_args_id) rec_arg_num; - let _ = - match e with - | Option.IsNone -> - let finfos = find_Function_infos (destConst f) in - update_Function - {finfos with - equation_lemma = Some (match Nametab.locate (make_short_qualid equation_lemma_id) with - ConstRef c -> c - | _ -> Util.anomaly "Not a constant" - ) - } - | _ -> () - - in - Tacinterp.constr_of_id (pf_env g) equation_lemma_id - in - let nb_intro_to_do = nb_prod (pf_concl g) in - tclTHEN - (tclDO nb_intro_to_do intro) - ( - fun g' -> - let just_introduced = nLastHyps nb_intro_to_do g' in - let just_introduced_id = List.map (fun (id,_,_) -> id) just_introduced in - tclTHEN (Equality.rewriteLR equation_lemma) (revert just_introduced_id) g' - ) - g - -let prove_princ_for_struct interactive_proof fun_num fnames all_funs _nparams : tactic = - fun g -> - let princ_type = pf_concl g in - let princ_info = compute_elim_sig princ_type in - let fresh_id = - let avoid = ref (pf_ids_of_hyps g) in - (fun na -> - let new_id = - match na with - Name id -> fresh_id !avoid (string_of_id id) - | Anonymous -> fresh_id !avoid "H" - in - avoid := new_id :: !avoid; - (Name new_id) - ) - in - let fresh_decl = - (fun (na,b,t) -> - (fresh_id na,b,t) - ) - in - let princ_info : elim_scheme = - { princ_info with - params = List.map fresh_decl princ_info.params; - predicates = List.map fresh_decl princ_info.predicates; - branches = List.map fresh_decl princ_info.branches; - args = List.map fresh_decl princ_info.args - } - in - let get_body const = - match (Global.lookup_constant const ).const_body with - | Some b -> - let body = force b in - Tacred.cbv_norm_flags - (Closure.RedFlags.mkflags [Closure.RedFlags.fZETA]) - (Global.env ()) - (Evd.empty) - body - | None -> error ( "Cannot define a principle over an axiom ") - in - let fbody = get_body fnames.(fun_num) in - let f_ctxt,f_body = decompose_lam fbody in - let f_ctxt_length = List.length f_ctxt in - let diff_params = princ_info.nparams - f_ctxt_length in - let full_params,princ_params,fbody_with_full_params = - if diff_params > 0 - then - let princ_params,full_params = - list_chop diff_params princ_info.params - in - (full_params, (* real params *) - princ_params, (* the params of the principle which are not params of the function *) - substl (* function instanciated with real params *) - (List.map var_of_decl full_params) - f_body - ) - else - let f_ctxt_other,f_ctxt_params = - list_chop (- diff_params) f_ctxt in - let f_body = compose_lam f_ctxt_other f_body in - (princ_info.params, (* real params *) - [],(* all params are full params *) - substl (* function instanciated with real params *) - (List.map var_of_decl princ_info.params) - f_body - ) - in -(* observe (str "full_params := " ++ *) -(* prlist_with_sep spc (fun (na,_,_) -> Ppconstr.pr_id (Nameops.out_name na)) *) -(* full_params *) -(* ); *) -(* observe (str "princ_params := " ++ *) -(* prlist_with_sep spc (fun (na,_,_) -> Ppconstr.pr_id (Nameops.out_name na)) *) -(* princ_params *) -(* ); *) -(* observe (str "fbody_with_full_params := " ++ *) -(* pr_lconstr fbody_with_full_params *) -(* ); *) - let all_funs_with_full_params = - Array.map (fun f -> applist(f, List.rev_map var_of_decl full_params)) all_funs - in - let fix_offset = List.length princ_params in - let ptes_to_fix,infos = - match kind_of_term fbody_with_full_params with - | Fix((idxs,i),(names,typess,bodies)) -> - let bodies_with_all_params = - Array.map - (fun body -> - Reductionops.nf_betaiota Evd.empty - (applist(substl (List.rev (Array.to_list all_funs_with_full_params)) body, - List.rev_map var_of_decl princ_params)) - ) - bodies - in - let info_array = - Array.mapi - (fun i types -> - let types = prod_applist types (List.rev_map var_of_decl princ_params) in - { idx = idxs.(i) - fix_offset; - name = Nameops.out_name (fresh_id names.(i)); - types = types; - offset = fix_offset; - nb_realargs = - List.length - (fst (decompose_lam bodies.(i))) - fix_offset; - body_with_param = bodies_with_all_params.(i); - num_in_block = i - } - ) - typess - in - let pte_to_fix,rev_info = - list_fold_left_i - (fun i (acc_map,acc_info) (pte,_,_) -> - let infos = info_array.(i) in - let type_args,_ = decompose_prod infos.types in - let nargs = List.length type_args in - let f = applist(mkConst fnames.(i), List.rev_map var_of_decl princ_info.params) in - let first_args = Array.init nargs (fun i -> mkRel (nargs -i)) in - let app_f = mkApp(f,first_args) in - let pte_args = (Array.to_list first_args)@[app_f] in - let app_pte = applist(mkVar (Nameops.out_name pte),pte_args) in - let body_with_param,num = - let body = get_body fnames.(i) in - let body_with_full_params = - Reductionops.nf_betaiota Evd.empty ( - applist(body,List.rev_map var_of_decl full_params)) - in - match kind_of_term body_with_full_params with - | Fix((_,num),(_,_,bs)) -> - Reductionops.nf_betaiota Evd.empty - ( - (applist - (substl - (List.rev - (Array.to_list all_funs_with_full_params)) - bs.(num), - List.rev_map var_of_decl princ_params)) - ),num - | _ -> error "Not a mutual block" - in - let info = - {infos with - types = compose_prod type_args app_pte; - body_with_param = body_with_param; - num_in_block = num - } - in -(* observe (str "binding " ++ Ppconstr.pr_id (Nameops.out_name pte) ++ *) -(* str " to " ++ Ppconstr.pr_id info.name); *) - (Idmap.add (Nameops.out_name pte) info acc_map,info::acc_info) - ) - 0 - (Idmap.empty,[]) - (List.rev princ_info.predicates) - in - pte_to_fix,List.rev rev_info - | _ -> Idmap.empty,[] - in - let mk_fixes : tactic = - let pre_info,infos = list_chop fun_num infos in - match pre_info,infos with - | [],[] -> tclIDTAC - | _, this_fix_info::others_infos -> - let other_fix_infos = - List.map - (fun fi -> fi.name,fi.idx + 1 ,fi.types) - (pre_info@others_infos) - in - if other_fix_infos = [] - then - (* observe_tac ("h_fix") *) (h_fix (Some this_fix_info.name) (this_fix_info.idx +1)) - else - h_mutual_fix false this_fix_info.name (this_fix_info.idx + 1) - other_fix_infos - | _ -> anomaly "Not a valid information" - in - let first_tac : tactic = (* every operations until fix creations *) - tclTHENSEQ - [ (* observe_tac "introducing params" *) (intros_using (List.rev_map id_of_decl princ_info.params)); - (* observe_tac "introducing predictes" *) (intros_using (List.rev_map id_of_decl princ_info.predicates)); - (* observe_tac "introducing branches" *) (intros_using (List.rev_map id_of_decl princ_info.branches)); - (* observe_tac "building fixes" *) mk_fixes; - ] - in - let intros_after_fixes : tactic = - fun gl -> - let ctxt,pte_app = (Sign.decompose_prod_assum (pf_concl gl)) in - let pte,pte_args = (decompose_app pte_app) in - try - let pte = try destVar pte with _ -> anomaly "Property is not a variable" in - let fix_info = Idmap.find pte ptes_to_fix in - let nb_args = fix_info.nb_realargs in - tclTHENSEQ - [ - (* observe_tac ("introducing args") *) (tclDO nb_args intro); - (fun g -> (* replacement of the function by its body *) - let args = nLastHyps nb_args g in - let fix_body = fix_info.body_with_param in -(* observe (str "fix_body := "++ pr_lconstr_env (pf_env gl) fix_body); *) - let args_id = List.map (fun (id,_,_) -> id) args in - let dyn_infos = - { - nb_rec_hyps = -100; - rec_hyps = []; - info = - Reductionops.nf_betaiota Evd.empty - (applist(fix_body,List.rev_map mkVar args_id)); - eq_hyps = [] - } - in - tclTHENSEQ - [ -(* observe_tac "do_replace" *) - (do_replace - full_params - (fix_info.idx + List.length princ_params) - (args_id@(List.map (fun (id,_,_) -> Nameops.out_name id ) princ_params)) - (all_funs.(fix_info.num_in_block)) - fix_info.num_in_block - all_funs - ); -(* observe_tac "do_replace" *) -(* (do_replace princ_info.params fix_info.idx args_id *) -(* (List.hd (List.rev pte_args)) fix_body); *) - let do_prove = - build_proof - interactive_proof - (Array.to_list fnames) - (Idmap.map prove_rec_hyp ptes_to_fix) - in - let prove_tac branches = - let dyn_infos = - {dyn_infos with - rec_hyps = branches; - nb_rec_hyps = List.length branches - } - in - (* observe_tac "cleaning" *) (clean_goal_with_heq - (Idmap.map prove_rec_hyp ptes_to_fix) - do_prove - dyn_infos) - in -(* observe (str "branches := " ++ *) -(* prlist_with_sep spc (fun decl -> Ppconstr.pr_id (id_of_decl decl)) princ_info.branches ++ fnl () ++ *) -(* str "args := " ++ prlist_with_sep spc Ppconstr.pr_id args_id *) - -(* ); *) - (* observe_tac "instancing" *) (instanciate_hyps_with_args prove_tac - (List.rev_map id_of_decl princ_info.branches) - (List.rev args_id)) - ] - g - ); - ] gl - with Not_found -> - let nb_args = min (princ_info.nargs) (List.length ctxt) in - tclTHENSEQ - [ - tclDO nb_args intro; - (fun g -> (* replacement of the function by its body *) - let args = nLastHyps nb_args g in - let args_id = List.map (fun (id,_,_) -> id) args in - let dyn_infos = - { - nb_rec_hyps = -100; - rec_hyps = []; - info = - Reductionops.nf_betaiota Evd.empty - (applist(fbody_with_full_params, - (List.rev_map var_of_decl princ_params)@ - (List.rev_map mkVar args_id) - )); - eq_hyps = [] - } - in - let fname = destConst (fst (decompose_app (List.hd (List.rev pte_args)))) in - tclTHENSEQ - [unfold_in_concl [(all_occurrences,Names.EvalConstRef fname)]; - let do_prove = - build_proof - interactive_proof - (Array.to_list fnames) - (Idmap.map prove_rec_hyp ptes_to_fix) - in - let prove_tac branches = - let dyn_infos = - {dyn_infos with - rec_hyps = branches; - nb_rec_hyps = List.length branches - } - in - clean_goal_with_heq - (Idmap.map prove_rec_hyp ptes_to_fix) - do_prove - dyn_infos - in - instanciate_hyps_with_args prove_tac - (List.rev_map id_of_decl princ_info.branches) - (List.rev args_id) - ] - g - ) - ] - gl - in - tclTHEN - first_tac - intros_after_fixes - g - - - - - - -(* Proof of principles of general functions *) -let h_id = Recdef.h_id -and hrec_id = Recdef.hrec_id -and acc_inv_id = Recdef.acc_inv_id -and ltof_ref = Recdef.ltof_ref -and acc_rel = Recdef.acc_rel -and well_founded = Recdef.well_founded -and delayed_force = Recdef.delayed_force -and h_intros = Recdef.h_intros -and list_rewrite = Recdef.list_rewrite -and evaluable_of_global_reference = Recdef.evaluable_of_global_reference - - - - - -let prove_with_tcc tcc_lemma_constr eqs : tactic = - match !tcc_lemma_constr with - | None -> anomaly "No tcc proof !!" - | Some lemma -> - fun gls -> -(* let hid = next_global_ident_away true h_id (pf_ids_of_hyps gls) in *) -(* let ids = hid::pf_ids_of_hyps gls in *) - tclTHENSEQ - [ -(* generalize [lemma]; *) -(* h_intro hid; *) -(* Elim.h_decompose_and (mkVar hid); *) - tclTRY(list_rewrite true eqs); -(* (fun g -> *) -(* let ids' = pf_ids_of_hyps g in *) -(* let ids = List.filter (fun id -> not (List.mem id ids)) ids' in *) -(* rewrite *) -(* ) *) - Eauto.gen_eauto false (false,5) [] (Some []) - ] - gls - - -let backtrack_eqs_until_hrec hrec eqs : tactic = - fun gls -> - let eqs = List.map mkVar eqs in - let rewrite = - tclFIRST (List.map Equality.rewriteRL eqs ) - in - let _,hrec_concl = decompose_prod (pf_type_of gls (mkVar hrec)) in - let f_app = array_last (snd (destApp hrec_concl)) in - let f = (fst (destApp f_app)) in - let rec backtrack : tactic = - fun g -> - let f_app = array_last (snd (destApp (pf_concl g))) in - match kind_of_term f_app with - | App(f',_) when eq_constr f' f -> tclIDTAC g - | _ -> tclTHEN rewrite backtrack g - in - backtrack gls - - - -let build_clause eqs = - { - Tacexpr.onhyps = - Some (List.map - (fun id -> (Rawterm.all_occurrences_expr,id),InHyp) - eqs - ); - Tacexpr.concl_occs = Rawterm.no_occurrences_expr - } - -let rec rewrite_eqs_in_eqs eqs = - match eqs with - | [] -> tclIDTAC - | eq::eqs -> - - tclTHEN - (tclMAP - (fun id gl -> - observe_tac - (Format.sprintf "rewrite %s in %s " (string_of_id eq) (string_of_id id)) - (tclTRY (Equality.general_rewrite_in true all_occurrences id (mkVar eq) false)) - gl - ) - eqs - ) - (rewrite_eqs_in_eqs eqs) - -let new_prove_with_tcc is_mes acc_inv hrec tcc_hyps eqs : tactic = - fun gls -> - (tclTHENSEQ - [ - backtrack_eqs_until_hrec hrec eqs; - (* observe_tac ("new_prove_with_tcc ( applying "^(string_of_id hrec)^" )" ) *) - (tclTHENS (* We must have exactly ONE subgoal !*) - (apply (mkVar hrec)) - [ tclTHENSEQ - [ - keep (tcc_hyps@eqs); - apply (Lazy.force acc_inv); - (fun g -> - if is_mes - then - unfold_in_concl [(all_occurrences, evaluable_of_global_reference (delayed_force ltof_ref))] g - else tclIDTAC g - ); - observe_tac "rew_and_finish" - (tclTHENLIST - [tclTRY(Recdef.list_rewrite false (List.map mkVar eqs)); - observe_tac "rewrite_eqs_in_eqs" (rewrite_eqs_in_eqs eqs); - (observe_tac "finishing using" - ( - tclCOMPLETE( - Eauto.eauto_with_bases - false - (true,5) - [Lazy.force refl_equal] - [Auto.Hint_db.empty empty_transparent_state false] - ) - ) - ) - ] - ) - ] - ]) - ]) - gls - - -let is_valid_hypothesis predicates_name = - let predicates_name = List.fold_right Idset.add predicates_name Idset.empty in - let is_pte typ = - if isApp typ - then - let pte,_ = destApp typ in - if isVar pte - then Idset.mem (destVar pte) predicates_name - else false - else false - in - let rec is_valid_hypothesis typ = - is_pte typ || - match kind_of_term typ with - | Prod(_,pte,typ') -> is_pte pte && is_valid_hypothesis typ' - | _ -> false - in - is_valid_hypothesis - -let prove_principle_for_gen - (f_ref,functional_ref,eq_ref) tcc_lemma_ref is_mes - rec_arg_num rec_arg_type relation gl = - let princ_type = pf_concl gl in - let princ_info = compute_elim_sig princ_type in - let fresh_id = - let avoid = ref (pf_ids_of_hyps gl) in - fun na -> - let new_id = - match na with - | Name id -> fresh_id !avoid (string_of_id id) - | Anonymous -> fresh_id !avoid "H" - in - avoid := new_id :: !avoid; - Name new_id - in - let fresh_decl (na,b,t) = (fresh_id na,b,t) in - let princ_info : elim_scheme = - { princ_info with - params = List.map fresh_decl princ_info.params; - predicates = List.map fresh_decl princ_info.predicates; - branches = List.map fresh_decl princ_info.branches; - args = List.map fresh_decl princ_info.args - } - in - let wf_tac = - if is_mes - then - (fun b -> Recdef.tclUSER_if_not_mes tclIDTAC b None) - else fun _ -> prove_with_tcc tcc_lemma_ref [] - in - let real_rec_arg_num = rec_arg_num - princ_info.nparams in - let npost_rec_arg = princ_info.nargs - real_rec_arg_num + 1 in -(* observe ( *) -(* str "princ_type := " ++ pr_lconstr princ_type ++ fnl () ++ *) -(* str "princ_info.nparams := " ++ int princ_info.nparams ++ fnl () ++ *) - -(* str "princ_info.nargs := " ++ int princ_info.nargs ++ fnl () ++ *) -(* str "rec_arg_num := " ++ int rec_arg_num ++ fnl() ++ *) -(* str "real_rec_arg_num := " ++ int real_rec_arg_num ++ fnl () ++ *) -(* str "npost_rec_arg := " ++ int npost_rec_arg ); *) - let (post_rec_arg,pre_rec_arg) = - Util.list_chop npost_rec_arg princ_info.args - in - let rec_arg_id = - match List.rev post_rec_arg with - | (Name id,_,_)::_ -> id - | _ -> assert false - in -(* observe (str "rec_arg_id := " ++ pr_lconstr (mkVar rec_arg_id)); *) - let subst_constrs = List.map (fun (na,_,_) -> mkVar (Nameops.out_name na)) (pre_rec_arg@princ_info.params) in - let relation = substl subst_constrs relation in - let input_type = substl subst_constrs rec_arg_type in - let wf_thm_id = Nameops.out_name (fresh_id (Name (id_of_string "wf_R"))) in - let acc_rec_arg_id = - Nameops.out_name (fresh_id (Name (id_of_string ("Acc_"^(string_of_id rec_arg_id))))) - in - let revert l = - tclTHEN (h_generalize (List.map mkVar l)) (clear l) - in - let fix_id = Nameops.out_name (fresh_id (Name hrec_id)) in - let prove_rec_arg_acc g = - ((* observe_tac "prove_rec_arg_acc" *) - (tclCOMPLETE - (tclTHEN - (assert_by (Name wf_thm_id) - (mkApp (delayed_force well_founded,[|input_type;relation|])) - (fun g -> (* observe_tac "prove wf" *) (tclCOMPLETE (wf_tac is_mes)) g)) - ( - (* observe_tac *) -(* "apply wf_thm" *) - h_simplest_apply (mkApp(mkVar wf_thm_id,[|mkVar rec_arg_id|])) - ) - ) - ) - ) - g - in - let args_ids = List.map (fun (na,_,_) -> Nameops.out_name na) princ_info.args in - let lemma = - match !tcc_lemma_ref with - | None -> anomaly ( "No tcc proof !!") - | Some lemma -> lemma - in -(* let rec list_diff del_list check_list = *) -(* match del_list with *) -(* [] -> *) -(* [] *) -(* | f::r -> *) -(* if List.mem f check_list then *) -(* list_diff r check_list *) -(* else *) -(* f::(list_diff r check_list) *) -(* in *) - let tcc_list = ref [] in - let start_tac gls = - let hyps = pf_ids_of_hyps gls in - let hid = - next_global_ident_away true - (id_of_string "prov") - hyps - in - tclTHENSEQ - [ - generalize [lemma]; - h_intro hid; - Elim.h_decompose_and (mkVar hid); - (fun g -> - let new_hyps = pf_ids_of_hyps g in - tcc_list := List.rev (list_subtract new_hyps (hid::hyps)); - if !tcc_list = [] - then - begin - tcc_list := [hid]; - tclIDTAC g - end - else thin [hid] g - ) - ] - gls - in - tclTHENSEQ - [ - observe_tac "start_tac" start_tac; - h_intros - (List.rev_map (fun (na,_,_) -> Nameops.out_name na) - (princ_info.args@princ_info.branches@princ_info.predicates@princ_info.params) - ); - (* observe_tac "" *) (assert_by - (Name acc_rec_arg_id) - (mkApp (delayed_force acc_rel,[|input_type;relation;mkVar rec_arg_id|])) - (prove_rec_arg_acc) - ); -(* observe_tac "reverting" *) (revert (List.rev (acc_rec_arg_id::args_ids))); -(* (fun g -> observe (Printer.pr_goal (sig_it g) ++ fnl () ++ *) -(* str "fix arg num" ++ int (List.length args_ids + 1) ); tclIDTAC g); *) - (* observe_tac "h_fix " *) (h_fix (Some fix_id) (List.length args_ids + 1)); -(* (fun g -> observe (Printer.pr_goal (sig_it g) ++ fnl() ++ pr_lconstr_env (pf_env g ) (pf_type_of g (mkVar fix_id) )); tclIDTAC g); *) - h_intros (List.rev (acc_rec_arg_id::args_ids)); - Equality.rewriteLR (mkConst eq_ref); - (* observe_tac "finish" *) (fun gl' -> - let body = - let _,args = destApp (pf_concl gl') in - array_last args - in - let body_info rec_hyps = - { - nb_rec_hyps = List.length rec_hyps; - rec_hyps = rec_hyps; - eq_hyps = []; - info = body - } - in - let acc_inv = - lazy ( - mkApp ( - delayed_force acc_inv_id, - [|input_type;relation;mkVar rec_arg_id|] - ) - ) - in - let acc_inv = lazy (mkApp(Lazy.force acc_inv, [|mkVar acc_rec_arg_id|])) in - let predicates_names = - List.map (fun (na,_,_) -> Nameops.out_name na) princ_info.predicates - in - let pte_info = - { proving_tac = - (fun eqs -> -(* msgnl (str "tcc_list := "++ prlist_with_sep spc Ppconstr.pr_id !tcc_list); *) -(* msgnl (str "princ_info.args := "++ prlist_with_sep spc Ppconstr.pr_id (List.map (fun (na,_,_) -> (Nameops.out_name na)) princ_info.args)); *) -(* msgnl (str "princ_info.params := "++ prlist_with_sep spc Ppconstr.pr_id (List.map (fun (na,_,_) -> (Nameops.out_name na)) princ_info.params)); *) -(* msgnl (str "acc_rec_arg_id := "++ Ppconstr.pr_id acc_rec_arg_id); *) -(* msgnl (str "eqs := "++ prlist_with_sep spc Ppconstr.pr_id eqs); *) - - (* observe_tac "new_prove_with_tcc" *) - (new_prove_with_tcc - is_mes acc_inv fix_id - - (!tcc_list@(List.map - (fun (na,_,_) -> (Nameops.out_name na)) - (princ_info.args@princ_info.params) - )@ ([acc_rec_arg_id])) eqs - ) - - ); - is_valid = is_valid_hypothesis predicates_names - } - in - let ptes_info : pte_info Idmap.t = - List.fold_left - (fun map pte_id -> - Idmap.add pte_id - pte_info - map - ) - Idmap.empty - predicates_names - in - let make_proof rec_hyps = - build_proof - false - [f_ref] - ptes_info - (body_info rec_hyps) - in - (* observe_tac "instanciate_hyps_with_args" *) - (instanciate_hyps_with_args - make_proof - (List.map (fun (na,_,_) -> Nameops.out_name na) princ_info.branches) - (List.rev args_ids) - ) - gl' - ) - - ] - gl - - - - - - - - diff --git a/contrib/funind/functional_principles_proofs.mli b/contrib/funind/functional_principles_proofs.mli deleted file mode 100644 index 62eb528e..00000000 --- a/contrib/funind/functional_principles_proofs.mli +++ /dev/null @@ -1,19 +0,0 @@ -open Names -open Term - -val prove_princ_for_struct : - bool -> - int -> constant array -> constr array -> int -> Tacmach.tactic - - -val prove_principle_for_gen : - constant*constant*constant -> (* name of the function, the fonctionnal and the fixpoint equation *) - constr option ref -> (* a pointer to the obligation proofs lemma *) - bool -> (* is that function uses measure *) - int -> (* the number of recursive argument *) - types -> (* the type of the recursive argument *) - constr -> (* the wf relation used to prove the function *) - Tacmach.tactic - - -(* val is_pte : rel_declaration -> bool *) diff --git a/contrib/funind/functional_principles_types.ml b/contrib/funind/functional_principles_types.ml deleted file mode 100644 index b03bdf31..00000000 --- a/contrib/funind/functional_principles_types.ml +++ /dev/null @@ -1,733 +0,0 @@ -open Printer -open Util -open Term -open Termops -open Names -open Declarations -open Pp -open Entries -open Hiddentac -open Evd -open Tacmach -open Proof_type -open Tacticals -open Tactics -open Indfun_common -open Functional_principles_proofs - -exception Toberemoved_with_rel of int*constr -exception Toberemoved - - -let pr_elim_scheme el = - let env = Global.env () in - let msg = str "params := " ++ Printer.pr_rel_context env el.params in - let env = Environ.push_rel_context el.params env in - let msg = msg ++ fnl () ++ str "predicates := "++ Printer.pr_rel_context env el.predicates in - let env = Environ.push_rel_context el.predicates env in - let msg = msg ++ fnl () ++ str "branches := " ++ Printer.pr_rel_context env el.branches in - let env = Environ.push_rel_context el.branches env in - let msg = msg ++ fnl () ++ str "args := " ++ Printer.pr_rel_context env el.args in - let env = Environ.push_rel_context el.args env in - msg ++ fnl () ++ str "concl := " ++ pr_lconstr_env env el.concl - - -let observe s = - if do_observe () - then Pp.msgnl s - - -let pr_elim_scheme el = - let env = Global.env () in - let msg = str "params := " ++ Printer.pr_rel_context env el.params in - let env = Environ.push_rel_context el.params env in - let msg = msg ++ fnl () ++ str "predicates := "++ Printer.pr_rel_context env el.predicates in - let env = Environ.push_rel_context el.predicates env in - let msg = msg ++ fnl () ++ str "branches := " ++ Printer.pr_rel_context env el.branches in - let env = Environ.push_rel_context el.branches env in - let msg = msg ++ fnl () ++ str "args := " ++ Printer.pr_rel_context env el.args in - let env = Environ.push_rel_context el.args env in - msg ++ fnl () ++ str "concl := " ++ pr_lconstr_env env el.concl - - -let observe s = - if do_observe () - then Pp.msgnl s - -(* - Transform an inductive induction principle into - a functional one -*) -let compute_new_princ_type_from_rel rel_to_fun sorts princ_type = - let princ_type_info = compute_elim_sig princ_type in - let env = Global.env () in - let env_with_params = Environ.push_rel_context princ_type_info.params env in - let tbl = Hashtbl.create 792 in - let rec change_predicates_names (avoid:identifier list) (predicates:Sign.rel_context) : Sign.rel_context = - match predicates with - | [] -> [] - |(Name x,v,t)::predicates -> - let id = Nameops.next_ident_away x avoid in - Hashtbl.add tbl id x; - (Name id,v,t)::(change_predicates_names (id::avoid) predicates) - | (Anonymous,_,_)::_ -> anomaly "Anonymous property binder " - in - let avoid = (Termops.ids_of_context env_with_params ) in - let princ_type_info = - { princ_type_info with - predicates = change_predicates_names avoid princ_type_info.predicates - } - in -(* observe (str "starting princ_type := " ++ pr_lconstr_env env princ_type); *) -(* observe (str "princ_infos : " ++ pr_elim_scheme princ_type_info); *) - let change_predicate_sort i (x,_,t) = - let new_sort = sorts.(i) in - let args,_ = decompose_prod t in - let real_args = - if princ_type_info.indarg_in_concl - then List.tl args - else args - in - Nameops.out_name x,None,compose_prod real_args (mkSort new_sort) - in - let new_predicates = - list_map_i - change_predicate_sort - 0 - princ_type_info.predicates - in - let env_with_params_and_predicates = List.fold_right Environ.push_named new_predicates env_with_params in - let rel_as_kn = - fst (match princ_type_info.indref with - | Some (Libnames.IndRef ind) -> ind - | _ -> error "Not a valid predicate" - ) - in - let ptes_vars = List.map (fun (id,_,_) -> id) new_predicates in - let is_pte = - let set = List.fold_right Idset.add ptes_vars Idset.empty in - fun t -> - match kind_of_term t with - | Var id -> Idset.mem id set - | _ -> false - in - let pre_princ = - it_mkProd_or_LetIn - ~init: - (it_mkProd_or_LetIn - ~init:(Option.fold_right - mkProd_or_LetIn - princ_type_info.indarg - princ_type_info.concl - ) - princ_type_info.args - ) - princ_type_info.branches - in - let pre_princ = substl (List.map mkVar ptes_vars) pre_princ in - let is_dom c = - match kind_of_term c with - | Ind((u,_)) -> u = rel_as_kn - | Construct((u,_),_) -> u = rel_as_kn - | _ -> false - in - let get_fun_num c = - match kind_of_term c with - | Ind(_,num) -> num - | Construct((_,num),_) -> num - | _ -> assert false - in - let dummy_var = mkVar (id_of_string "________") in - let mk_replacement c i args = - let res = mkApp(rel_to_fun.(i),Array.map pop (array_get_start args)) in -(* observe (str "replacing " ++ pr_lconstr c ++ str " by " ++ pr_lconstr res); *) - res - in - let rec has_dummy_var t = - fold_constr - (fun b t -> b || (eq_constr t dummy_var) || (has_dummy_var t)) - false - t - in - let rec compute_new_princ_type remove env pre_princ : types*(constr list) = - let (new_princ_type,_) as res = - match kind_of_term pre_princ with - | Rel n -> - begin - try match Environ.lookup_rel n env with - | _,_,t when is_dom t -> raise Toberemoved - | _ -> pre_princ,[] with Not_found -> assert false - end - | Prod(x,t,b) -> - compute_new_princ_type_for_binder remove mkProd env x t b - | Lambda(x,t,b) -> - compute_new_princ_type_for_binder remove mkLambda env x t b - | Ind _ | Construct _ when is_dom pre_princ -> raise Toberemoved - | App(f,args) when is_dom f -> - let var_to_be_removed = destRel (array_last args) in - let num = get_fun_num f in - raise (Toberemoved_with_rel (var_to_be_removed,mk_replacement pre_princ num args)) - | App(f,args) -> - let args = - if is_pte f && remove - then array_get_start args - else args - in - let new_args,binders_to_remove = - Array.fold_right (compute_new_princ_type_with_acc remove env) - args - ([],[]) - in - let new_f,binders_to_remove_from_f = compute_new_princ_type remove env f in - applist(new_f, new_args), - list_union_eq eq_constr binders_to_remove_from_f binders_to_remove - | LetIn(x,v,t,b) -> - compute_new_princ_type_for_letin remove env x v t b - | _ -> pre_princ,[] - in -(* let _ = match kind_of_term pre_princ with *) -(* | Prod _ -> *) -(* observe(str "compute_new_princ_type for "++ *) -(* pr_lconstr_env env pre_princ ++ *) -(* str" is "++ *) -(* pr_lconstr_env env new_princ_type ++ fnl ()) *) -(* | _ -> () in *) - res - - and compute_new_princ_type_for_binder remove bind_fun env x t b = - begin - try - let new_t,binders_to_remove_from_t = compute_new_princ_type remove env t in - let new_x : name = get_name (ids_of_context env) x in - let new_env = Environ.push_rel (x,None,t) env in - let new_b,binders_to_remove_from_b = compute_new_princ_type remove new_env b in - if List.exists (eq_constr (mkRel 1)) binders_to_remove_from_b - then (pop new_b),filter_map (eq_constr (mkRel 1)) pop binders_to_remove_from_b - else - ( - bind_fun(new_x,new_t,new_b), - list_union_eq - eq_constr - binders_to_remove_from_t - (List.map pop binders_to_remove_from_b) - ) - - with - | Toberemoved -> -(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *) - let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [dummy_var] 1 b) in - new_b, List.map pop binders_to_remove_from_b - | Toberemoved_with_rel (n,c) -> -(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *) - let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [c] n b) in - new_b, list_add_set_eq eq_constr (mkRel n) (List.map pop binders_to_remove_from_b) - end - and compute_new_princ_type_for_letin remove env x v t b = - begin - try - let new_t,binders_to_remove_from_t = compute_new_princ_type remove env t in - let new_v,binders_to_remove_from_v = compute_new_princ_type remove env v in - let new_x : name = get_name (ids_of_context env) x in - let new_env = Environ.push_rel (x,Some v,t) env in - let new_b,binders_to_remove_from_b = compute_new_princ_type remove new_env b in - if List.exists (eq_constr (mkRel 1)) binders_to_remove_from_b - then (pop new_b),filter_map (eq_constr (mkRel 1)) pop binders_to_remove_from_b - else - ( - mkLetIn(new_x,new_v,new_t,new_b), - list_union_eq - eq_constr - (list_union_eq eq_constr binders_to_remove_from_t binders_to_remove_from_v) - (List.map pop binders_to_remove_from_b) - ) - - with - | Toberemoved -> -(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *) - let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [dummy_var] 1 b) in - new_b, List.map pop binders_to_remove_from_b - | Toberemoved_with_rel (n,c) -> -(* observe (str "Decl of "++Ppconstr.pr_name x ++ str " is removed "); *) - let new_b,binders_to_remove_from_b = compute_new_princ_type remove env (substnl [c] n b) in - new_b, list_add_set_eq eq_constr (mkRel n) (List.map pop binders_to_remove_from_b) - end - and compute_new_princ_type_with_acc remove env e (c_acc,to_remove_acc) = - let new_e,to_remove_from_e = compute_new_princ_type remove env e - in - new_e::c_acc,list_union_eq eq_constr to_remove_from_e to_remove_acc - in -(* observe (str "Computing new principe from " ++ pr_lconstr_env env_with_params_and_predicates pre_princ); *) - let pre_res,_ = - compute_new_princ_type princ_type_info.indarg_in_concl env_with_params_and_predicates pre_princ - in - let pre_res = - replace_vars - (list_map_i (fun i id -> (id, mkRel i)) 1 ptes_vars) - (lift (List.length ptes_vars) pre_res) - in - it_mkProd_or_LetIn - ~init:(it_mkProd_or_LetIn - ~init:pre_res (List.map (fun (id,t,b) -> Name(Hashtbl.find tbl id), t,b) - new_predicates) - ) - princ_type_info.params - - - -let change_property_sort toSort princ princName = - let princ_info = compute_elim_sig princ in - let change_sort_in_predicate (x,v,t) = - (x,None, - let args,_ = decompose_prod t in - compose_prod args (mkSort toSort) - ) - in - let princName_as_constr = Tacinterp.constr_of_id (Global.env ()) princName in - let init = - let nargs = (princ_info.nparams + (List.length princ_info.predicates)) in - mkApp(princName_as_constr, - Array.init nargs - (fun i -> mkRel (nargs - i ))) - in - it_mkLambda_or_LetIn - ~init: - (it_mkLambda_or_LetIn ~init - (List.map change_sort_in_predicate princ_info.predicates) - ) - princ_info.params - - -let pp_dur time time' = - str (string_of_float (System.time_difference time time')) - -(* let qed () = save_named true *) -let defined () = - try - Command.save_named false - with - | UserError("extract_proof",msg) -> - Util.errorlabstrm - "defined" - ((try - str "On goal : " ++ fnl () ++ pr_open_subgoals () ++ fnl () - with _ -> mt () - ) ++msg) - | e -> raise e - - - -let build_functional_principle interactive_proof old_princ_type sorts funs i proof_tac hook = - (* First we get the type of the old graph principle *) - let mutr_nparams = (compute_elim_sig old_princ_type).nparams in - (* let time1 = System.get_time () in *) - let new_principle_type = - compute_new_princ_type_from_rel - (Array.map mkConst funs) - sorts - old_princ_type - in - (* let time2 = System.get_time () in *) - (* Pp.msgnl (str "computing principle type := " ++ System.fmt_time_difference time1 time2); *) - (* observe (str "new_principle_type : " ++ pr_lconstr new_principle_type); *) - let new_princ_name = - next_global_ident_away true (id_of_string "___________princ_________") [] - in - begin - Command.start_proof - new_princ_name - (Decl_kinds.Global,(Decl_kinds.Proof Decl_kinds.Theorem)) - new_principle_type - (hook new_principle_type) - ; - (* let _tim1 = System.get_time () in *) - Pfedit.by (proof_tac (Array.map mkConst funs) mutr_nparams); - (* let _tim2 = System.get_time () in *) - (* begin *) - (* let dur1 = System.time_difference tim1 tim2 in *) - (* Pp.msgnl (str ("Time to compute proof: ") ++ str (string_of_float dur1)); *) - (* end; *) - get_proof_clean true - end - - - -let generate_functional_principle - interactive_proof - old_princ_type sorts new_princ_name funs i proof_tac - = - try - let f = funs.(i) in - let type_sort = Termops.new_sort_in_family InType in - 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 = - match new_princ_name with - | Some (id) -> id,id - | None -> - let id_of_f = id_of_label (con_label f) in - id_of_f,Indrec.make_elimination_ident id_of_f (family_of_sort type_sort) - in - let names = ref [new_princ_name] in - let hook new_principle_type _ _ = - if sorts = None - then - (* let id_of_f = id_of_label (con_label f) in *) - let register_with_sort fam_sort = - let s = Termops.new_sort_in_family fam_sort in - let name = Indrec.make_elimination_ident base_new_princ_name fam_sort in - let value = change_property_sort s new_principle_type new_princ_name in - (* Pp.msgnl (str "new principle := " ++ pr_lconstr value); *) - let ce = - { const_entry_body = value; - const_entry_type = None; - const_entry_opaque = false; - const_entry_boxed = Flags.boxed_definitions() - } - in - ignore( - Declare.declare_constant - name - (Entries.DefinitionEntry ce, - Decl_kinds.IsDefinition (Decl_kinds.Scheme) - ) - ); - Flags.if_verbose - (fun id -> Pp.msgnl (Ppconstr.pr_id id ++ str " is defined")) - name; - names := name :: !names - in - register_with_sort InProp; - register_with_sort InSet - in - let (id,(entry,g_kind,hook)) = - build_functional_principle interactive_proof old_princ_type new_sorts funs i proof_tac hook - in - (* Pr 1278 : - Don't forget to close the goal if an error is raised !!!! - *) - save false new_princ_name entry g_kind hook - with e -> - begin - begin - try - let id = Pfedit.get_current_proof_name () in - let s = string_of_id id in - let n = String.length "___________princ_________" in - if String.length s >= n - then if String.sub s 0 n = "___________princ_________" - then Pfedit.delete_current_proof () - else () - else () - with _ -> () - end; - raise (Defining_principle e) - end -(* defined () *) - - -exception Not_Rec - -let get_funs_constant mp dp = - let rec get_funs_constant const e : (Names.constant*int) array = - match kind_of_term (snd (decompose_lam e)) with - | Fix((_,(na,_,_))) -> - Array.mapi - (fun i na -> - match na with - | Name id -> - let const = make_con mp dp (label_of_id id) in - const,i - | Anonymous -> - anomaly "Anonymous fix" - ) - na - | _ -> [|const,0|] - in - function const -> - let find_constant_body const = - match (Global.lookup_constant const ).const_body with - | Some b -> - let body = force b in - let body = Tacred.cbv_norm_flags - (Closure.RedFlags.mkflags [Closure.RedFlags.fZETA]) - (Global.env ()) - (Evd.empty) - body - in - body - | None -> error ( "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 stange 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 decompose_lam l_bodies) in - (* all the paremeter must be equal*) - let _check_params = - let first_params = List.hd l_params in - List.iter - (fun params -> - if not ((=) first_params params) - then error "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 kind_of_term body with - | Fix((idxs,_),(na,ta,ca)) -> (idxs,na,ta,ca) - | _ -> - if is_first && (List.length l_bodies = 1) - then raise Not_Rec - else error "Not a mutal recursive block" - in - let first_infos = extract_info true (List.hd l_bodies) in - let check body = (* Hope this is correct *) - if not (first_infos = (extract_info false body)) - then error "Not a mutal recursive block" - in - List.iter check l_bodies - with Not_Rec -> () - in - l_const - -exception No_graph_found -exception Found_type of int - -let make_scheme (fas : (constant*Rawterm.rawsort) list) : Entries.definition_entry list = - let env = Global.env () - and sigma = Evd.empty in - let funs = List.map fst fas in - let first_fun = List.hd funs in - - - let funs_mp,funs_dp,_ = Names.repr_con first_fun in - let first_fun_kn = - try - fst (find_Function_infos first_fun).graph_ind - with Not_found -> raise No_graph_found - in - let this_block_funs_indexes = get_funs_constant funs_mp funs_dp first_fun in - let this_block_funs = Array.map fst this_block_funs_indexes in - let prop_sort = InProp in - let funs_indexes = - let this_block_funs_indexes = Array.to_list this_block_funs_indexes in - List.map - (function const -> List.assoc const this_block_funs_indexes) - funs - in - let ind_list = - List.map - (fun (idx) -> - let ind = first_fun_kn,idx in - let (mib,mip) = Global.lookup_inductive ind in - ind,mib,mip,true,prop_sort - ) - funs_indexes - in - let l_schemes = - List.map - (Typing.type_of env sigma) - (Indrec.build_mutual_indrec env sigma ind_list) - in - let i = ref (-1) in - let sorts = - List.rev_map (fun (_,x) -> - Termops.new_sort_in_family (Pretyping.interp_elimination_sort x) - ) - fas - in - (* We create the first priciple by tactic *) - let first_type,other_princ_types = - match l_schemes with - s::l_schemes -> s,l_schemes - | _ -> anomaly "" - in - let (_,(const,_,_)) = - try - build_functional_principle false - first_type - (Array.of_list sorts) - this_block_funs - 0 - (prove_princ_for_struct false 0 (Array.of_list funs)) - (fun _ _ _ -> ()) - with e -> - begin - begin - try - let id = Pfedit.get_current_proof_name () in - let s = string_of_id id in - let n = String.length "___________princ_________" in - if String.length s >= n - then if String.sub s 0 n = "___________princ_________" - then Pfedit.delete_current_proof () - else () - else () - with _ -> () - end; - raise (Defining_principle e) - end - - in - incr i; - let opacity = - let finfos = find_Function_infos this_block_funs.(0) in - try - let equation = Option.get finfos.equation_lemma in - (Global.lookup_constant equation).Declarations.const_opaque - with Option.IsNone -> (* non recursive definition *) - false - in - let const = {const with const_entry_opaque = opacity } in - (* The others are just deduced *) - if other_princ_types = [] - then - [const] - else - let other_fun_princ_types = - let funs = Array.map mkConst this_block_funs in - let sorts = Array.of_list sorts in - List.map (compute_new_princ_type_from_rel funs sorts) other_princ_types - in - let first_princ_body,first_princ_type = const.Entries.const_entry_body, const.Entries.const_entry_type in - let ctxt,fix = Sign.decompose_lam_assum first_princ_body in (* the principle has for forall ...., fix .*) - let (idxs,_),(_,ta,_ as decl) = destFix fix in - let other_result = - List.map (* we can now compute the other principles *) - (fun scheme_type -> - incr i; - observe (Printer.pr_lconstr scheme_type); - let type_concl = snd (Sign.decompose_prod_assum scheme_type) in - let applied_f = List.hd (List.rev (snd (decompose_app type_concl))) in - let f = fst (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 = snd (Sign.decompose_prod_assum t) in - let applied_g = List.hd (List.rev (snd (decompose_app t))) in - let g = fst (decompose_app applied_g) in - if eq_constr f g - then raise (Found_type j); - observe (Printer.pr_lconstr f ++ str " <> " ++ - Printer.pr_lconstr g) - - ) - ta; - (* If we reach this point, the two principle are not mutually recursive - We fall back to the previous method - *) - let (_,(const,_,_)) = - build_functional_principle - false - (List.nth other_princ_types (!i - 1)) - (Array.of_list sorts) - this_block_funs - !i - (prove_princ_for_struct false !i (Array.of_list funs)) - (fun _ _ _ -> ()) - in - const - with Found_type i -> - let princ_body = - Termops.it_mkLambda_or_LetIn ~init:(mkFix((idxs,i),decl)) ctxt - in - {const with - Entries.const_entry_body = princ_body; - Entries.const_entry_type = Some scheme_type - } - ) - other_fun_princ_types - in - const::other_result - -let build_scheme fas = - let bodies_types = - make_scheme - (List.map - (fun (_,f,sort) -> - let f_as_constant = - try - match Nametab.global f with - | Libnames.ConstRef c -> c - | _ -> Util.error "Functional Scheme can only be used with functions" - with Not_found -> - Util.error ("Cannot find "^ Libnames.string_of_reference f) - in - (f_as_constant,sort) - ) - fas - ) - in - List.iter2 - (fun (princ_id,_,_) def_entry -> - ignore - (Declare.declare_constant - princ_id - (Entries.DefinitionEntry def_entry,Decl_kinds.IsProof Decl_kinds.Theorem)); - Flags.if_verbose - (fun id -> Pp.msgnl (Ppconstr.pr_id id ++ str " is defined")) princ_id - ) - fas - bodies_types - - - -let build_case_scheme fa = - let env = Global.env () - and sigma = Evd.empty in -(* let id_to_constr id = *) -(* Tacinterp.constr_of_id env id *) -(* in *) - let funs = (fun (_,f,_) -> - try Libnames.constr_of_global (Nametab.global f) - with Not_found -> - Util.error ("Cannot find "^ Libnames.string_of_reference f)) fa in - let first_fun = destConst funs in - - let funs_mp,funs_dp,_ = Names.repr_con first_fun in - let first_fun_kn = try fst (find_Function_infos first_fun).graph_ind with Not_found -> raise No_graph_found in - - - - let this_block_funs_indexes = get_funs_constant funs_mp funs_dp first_fun in - let this_block_funs = Array.map fst this_block_funs_indexes in - let prop_sort = InProp in - let funs_indexes = - let this_block_funs_indexes = Array.to_list this_block_funs_indexes in - List.assoc (destConst funs) this_block_funs_indexes - in - let ind_fun = - let ind = first_fun_kn,funs_indexes in - ind,prop_sort - in - let scheme_type = (Typing.type_of env sigma ) ((fun (ind,sf) -> Indrec.make_case_gen env sigma ind sf) ind_fun) in - let sorts = - (fun (_,_,x) -> - Termops.new_sort_in_family (Pretyping.interp_elimination_sort x) - ) - fa - in - let princ_name = (fun (x,_,_) -> x) fa in - let _ = -(* observe (str "Generating " ++ Ppconstr.pr_id princ_name ++str " with " ++ *) -(* pr_lconstr scheme_type ++ str " and " ++ (fun a -> prlist_with_sep spc (fun c -> pr_lconstr (mkConst c)) (Array.to_list a)) this_block_funs *) -(* ); *) - generate_functional_principle - false - scheme_type - (Some ([|sorts|])) - (Some princ_name) - this_block_funs - 0 - (prove_princ_for_struct false 0 [|destConst funs|]) - in - () diff --git a/contrib/funind/functional_principles_types.mli b/contrib/funind/functional_principles_types.mli deleted file mode 100644 index cf28c6e6..00000000 --- a/contrib/funind/functional_principles_types.mli +++ /dev/null @@ -1,34 +0,0 @@ -open Names -open Term - - -val generate_functional_principle : - (* do we accept interactive proving *) - bool -> - (* induction principle on rel *) - types -> - (* *) - sorts array option -> - (* Name of the new principle *) - (identifier) option -> - (* the compute functions to use *) - constant array -> - (* We prove the nth- principle *) - int -> - (* The tactic to use to make the proof w.r - the number of params - *) - (constr array -> int -> Tacmach.tactic) -> - unit - -val compute_new_princ_type_from_rel : constr array -> sorts array -> - types -> types - - -exception No_graph_found - -val make_scheme : (constant*Rawterm.rawsort) list -> Entries.definition_entry list - -val build_scheme : (identifier*Libnames.reference*Rawterm.rawsort) list -> unit -val build_case_scheme : (identifier*Libnames.reference*Rawterm.rawsort) -> unit - diff --git a/contrib/funind/g_indfun.ml4 b/contrib/funind/g_indfun.ml4 deleted file mode 100644 index a79b46d9..00000000 --- a/contrib/funind/g_indfun.ml4 +++ /dev/null @@ -1,524 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) -(*i camlp4deps: "parsing/grammar.cma" i*) -open Util -open Term -open Names -open Pp -open Topconstr -open Indfun_common -open Indfun -open Genarg -open Pcoq -open Tacticals - -let pr_binding prc = function - | loc, Rawterm.NamedHyp id, c -> hov 1 (Ppconstr.pr_id id ++ str " := " ++ cut () ++ prc c) - | loc, Rawterm.AnonHyp n, c -> hov 1 (int n ++ str " := " ++ cut () ++ prc c) - -let pr_bindings prc prlc = function - | Rawterm.ImplicitBindings l -> - brk (1,1) ++ str "with" ++ brk (1,1) ++ - Util.prlist_with_sep spc prc l - | Rawterm.ExplicitBindings l -> - brk (1,1) ++ str "with" ++ brk (1,1) ++ - Util.prlist_with_sep spc (fun b -> str"(" ++ pr_binding prlc b ++ str")") l - | Rawterm.NoBindings -> mt () - -let pr_with_bindings prc prlc (c,bl) = - prc c ++ hv 0 (pr_bindings prc prlc bl) - -let pr_fun_ind_using prc prlc _ opt_c = - match opt_c with - | None -> mt () - | Some (p,b) -> spc () ++ hov 2 (str "using" ++ spc () ++ pr_with_bindings prc prlc (p,b)) - -(* Duplication of printing functions because "'a with_bindings" is - (internally) not uniform in 'a: indeed constr_with_bindings at the - "typed" level has type "open_constr with_bindings" instead of - "constr with_bindings"; hence, its printer cannot be polymorphic in - (prc,prlc)... *) - -let pr_with_bindings_typed prc prlc (c,bl) = - prc c ++ - hv 0 (pr_bindings (fun c -> prc (snd c)) (fun c -> prlc (snd c)) bl) - -let pr_fun_ind_using_typed prc prlc _ opt_c = - match opt_c with - | None -> mt () - | Some (p,b) -> spc () ++ hov 2 (str "using" ++ spc () ++ pr_with_bindings_typed prc prlc (p,b)) - - -ARGUMENT EXTEND fun_ind_using - TYPED AS constr_with_bindings_opt - PRINTED BY pr_fun_ind_using_typed - RAW_TYPED AS constr_with_bindings_opt - RAW_PRINTED BY pr_fun_ind_using - GLOB_TYPED AS constr_with_bindings_opt - GLOB_PRINTED BY pr_fun_ind_using -| [ "using" constr_with_bindings(c) ] -> [ Some c ] -| [ ] -> [ None ] -END - - -TACTIC EXTEND newfuninv - [ "functional" "inversion" quantified_hypothesis(hyp) reference_opt(fname) ] -> - [ - Invfun.invfun hyp fname - ] -END - - -let pr_intro_as_pat prc _ _ pat = - match pat with - | Some pat -> spc () ++ str "as" ++ spc () ++ pr_intro_pattern pat - | None -> mt () - - -ARGUMENT EXTEND with_names TYPED AS intro_pattern_opt PRINTED BY pr_intro_as_pat -| [ "as" simple_intropattern(ipat) ] -> [ Some ipat ] -| [] ->[ None ] -END - - - - -TACTIC EXTEND newfunind - ["functional" "induction" ne_constr_list(cl) fun_ind_using(princl) with_names(pat)] -> - [ - let c = match cl with - | [] -> assert false - | [c] -> c - | c::cl -> applist(c,cl) - in - functional_induction true c princl pat ] -END -(***** debug only ***) -TACTIC EXTEND snewfunind - ["soft" "functional" "induction" ne_constr_list(cl) fun_ind_using(princl) with_names(pat)] -> - [ - let c = match cl with - | [] -> assert false - | [c] -> c - | c::cl -> applist(c,cl) - in - functional_induction false c princl pat ] -END - - -let pr_constr_coma_sequence prc _ _ = Util.prlist_with_sep Util.pr_coma prc - -ARGUMENT EXTEND constr_coma_sequence' - TYPED AS constr_list - PRINTED BY pr_constr_coma_sequence -| [ constr(c) "," constr_coma_sequence'(l) ] -> [ c::l ] -| [ constr(c) ] -> [ [c] ] -END - -let pr_auto_using prc _prlc _prt = Pptactic.pr_auto_using prc - -ARGUMENT EXTEND auto_using' - TYPED AS constr_list - PRINTED BY pr_auto_using -| [ "using" constr_coma_sequence'(l) ] -> [ l ] -| [ ] -> [ [] ] -END - -let pr_rec_annotation2_aux s r id l = - str ("{"^s^" ") ++ Ppconstr.pr_constr_expr r ++ - Util.pr_opt Nameops.pr_id id ++ - Pptactic.pr_auto_using Ppconstr.pr_constr_expr l ++ str "}" - -let pr_rec_annotation2 = function - | Struct id -> str "{struct" ++ Nameops.pr_id id ++ str "}" - | Wf(r,id,l) -> pr_rec_annotation2_aux "wf" r id l - | Mes(r,id,l) -> pr_rec_annotation2_aux "measure" r id l - -VERNAC ARGUMENT EXTEND rec_annotation2 -PRINTED BY pr_rec_annotation2 - [ "{" "struct" ident(id) "}"] -> [ Struct id ] -| [ "{" "wf" constr(r) ident_opt(id) auto_using'(l) "}" ] -> [ Wf(r,id,l) ] -| [ "{" "measure" constr(r) ident_opt(id) auto_using'(l) "}" ] -> [ Mes(r,id,l) ] -END - -let pr_binder2 (idl,c) = - str "(" ++ Util.prlist_with_sep spc Nameops.pr_id idl ++ spc () ++ - str ": " ++ Ppconstr.pr_lconstr_expr c ++ str ")" - -VERNAC ARGUMENT EXTEND binder2 -PRINTED BY pr_binder2 - [ "(" ne_ident_list(idl) ":" lconstr(c) ")"] -> [ (idl,c) ] -END - -let make_binder2 (idl,c) = - LocalRawAssum (List.map (fun id -> (Util.dummy_loc,Name id)) idl,Topconstr.default_binder_kind,c) - -let pr_rec_definition2 (id,bl,annot,type_,def) = - Nameops.pr_id id ++ spc () ++ Util.prlist_with_sep spc pr_binder2 bl ++ - Util.pr_opt pr_rec_annotation2 annot ++ spc () ++ str ":" ++ spc () ++ - Ppconstr.pr_lconstr_expr type_ ++ str " :=" ++ spc () ++ - Ppconstr.pr_lconstr_expr def - -VERNAC ARGUMENT EXTEND rec_definition2 -PRINTED BY pr_rec_definition2 - [ ident(id) binder2_list(bl) - rec_annotation2_opt(annot) ":" lconstr(type_) - ":=" lconstr(def)] -> - [ (id,bl,annot,type_,def) ] -END - -let make_rec_definitions2 (id,bl,annot,type_,def) = - let bl = List.map make_binder2 bl in - let names = List.map snd (Topconstr.names_of_local_assums bl) in - let check_one_name () = - if List.length names > 1 then - Util.user_err_loc - (Util.dummy_loc,"Function", - Pp.str "the recursive argument needs to be specified"); - in - let check_exists_args an = - try - let id = match an with - | Struct id -> id | Wf(_,Some id,_) -> id | Mes(_,Some id,_) -> id - | Wf(_,None,_) | Mes(_,None,_) -> failwith "check_exists_args" - in - (try ignore(Util.list_index0 (Name id) names); annot - with Not_found -> Util.user_err_loc - (Util.dummy_loc,"Function", - Pp.str "No argument named " ++ Nameops.pr_id id) - ) - with Failure "check_exists_args" -> check_one_name ();annot - in - let ni = - match annot with - | None -> - annot - | Some an -> - check_exists_args an - in - ((Util.dummy_loc,id), ni, bl, type_, def) - - -VERNAC COMMAND EXTEND Function - ["Function" ne_rec_definition2_list_sep(recsl,"with")] -> - [ - do_generate_principle false (List.map make_rec_definitions2 recsl); - - ] -END - -let pr_fun_scheme_arg (princ_name,fun_name,s) = - Nameops.pr_id princ_name ++ str " :=" ++ spc() ++ str "Induction for " ++ - Libnames.pr_reference fun_name ++ spc() ++ str "Sort " ++ - Ppconstr.pr_rawsort s - -VERNAC ARGUMENT EXTEND fun_scheme_arg -PRINTED BY pr_fun_scheme_arg -| [ ident(princ_name) ":=" "Induction" "for" reference(fun_name) "Sort" sort(s) ] -> [ (princ_name,fun_name,s) ] -END - - -let warning_error names e = - match e with - | Building_graph e -> - Pp.msg_warning - (str "Cannot define graph(s) for " ++ - h 1 (prlist_with_sep (fun _ -> str","++spc ()) Libnames.pr_reference names) ++ - if do_observe () then (spc () ++ Cerrors.explain_exn e) else mt ()) - | Defining_principle e -> - Pp.msg_warning - (str "Cannot define principle(s) for "++ - h 1 (prlist_with_sep (fun _ -> str","++spc ()) Libnames.pr_reference names) ++ - if do_observe () then Cerrors.explain_exn e else mt ()) - | _ -> anomaly "" - - -VERNAC COMMAND EXTEND NewFunctionalScheme - ["Functional" "Scheme" ne_fun_scheme_arg_list_sep(fas,"with") ] -> - [ - begin - try - Functional_principles_types.build_scheme fas - with Functional_principles_types.No_graph_found -> - begin - match fas with - | (_,fun_name,_)::_ -> - begin - begin - make_graph (Nametab.global fun_name) - end - ; - try Functional_principles_types.build_scheme fas - with Functional_principles_types.No_graph_found -> - Util.error ("Cannot generate induction principle(s)") - | e -> - let names = List.map (fun (_,na,_) -> na) fas in - warning_error names e - - end - | _ -> assert false (* we can only have non empty list *) - end - | e -> - let names = List.map (fun (_,na,_) -> na) fas in - warning_error names e - - end - ] -END -(***** debug only ***) - -VERNAC COMMAND EXTEND NewFunctionalCase - ["Functional" "Case" fun_scheme_arg(fas) ] -> - [ - Functional_principles_types.build_case_scheme fas - ] -END - -(***** debug only ***) -VERNAC COMMAND EXTEND GenerateGraph -["Generate" "graph" "for" reference(c)] -> [ make_graph (Nametab.global c) ] -END - - - - - -(* FINDUCTION *) - -(* comment this line to see debug msgs *) -let msg x = () ;; let pr_lconstr c = str "" - (* uncomment this to see debugging *) -let prconstr c = msg (str" " ++ Printer.pr_lconstr c ++ str"\n") -let prlistconstr lc = List.iter prconstr lc -let prstr s = msg(str s) -let prNamedConstr s c = - begin - msg(str ""); - msg(str(s^"==>\n ") ++ Printer.pr_lconstr c ++ str "\n<==\n"); - msg(str ""); - end - - - -(** Information about an occurrence of a function call (application) - inside a term. *) -type fapp_info = { - fname: constr; (** The function applied *) - largs: constr list; (** List of arguments *) - free: bool; (** [true] if all arguments are debruijn free *) - max_rel: int; (** max debruijn index in the funcall *) - onlyvars: bool (** [true] if all arguments are variables (and not debruijn) *) -} - - -(** [constr_head_match(a b c) a] returns true, false otherwise. *) -let constr_head_match u t= - if isApp u - then - let uhd,args= destApp u in - uhd=t - else false - -(** [hdMatchSub inu t] returns the list of occurrences of [t] in - [inu]. DeBruijn are not pushed, so some of them may be unbound in - the result. *) -let rec hdMatchSub inu (test: constr -> bool) : fapp_info list = - let subres = - match kind_of_term inu with - | Lambda (nm,tp,cstr) | Prod (nm,tp,cstr) -> - hdMatchSub tp test @ hdMatchSub (lift 1 cstr) test - | Fix (_,(lna,tl,bl)) -> (* not sure Fix is correct *) - Array.fold_left - (fun acc cstr -> acc @ hdMatchSub (lift (Array.length tl) cstr) test) - [] bl - | _ -> (* Cofix will be wrong *) - fold_constr - (fun l cstr -> - l @ hdMatchSub cstr test) [] inu in - if not (test inu) then subres - else - let f,args = decompose_app inu in - let freeset = Termops.free_rels inu in - let max_rel = try Util.Intset.max_elt freeset with Not_found -> -1 in - {fname = f; largs = args; free = Util.Intset.is_empty freeset; - max_rel = max_rel; onlyvars = List.for_all isVar args } - ::subres - -let mkEq typ c1 c2 = - mkApp (Coqlib.build_coq_eq(),[| typ; c1; c2|]) - - -let poseq_unsafe idunsafe cstr gl = - let typ = Tacmach.pf_type_of gl cstr in - tclTHEN - (Tactics.letin_tac None (Name idunsafe) cstr None allClauses) - (tclTHENFIRST - (Tactics.assert_tac Anonymous (mkEq typ (mkVar idunsafe) cstr)) - Tactics.reflexivity) - gl - - -let poseq id cstr gl = - let x = Tactics.fresh_id [] id gl in - poseq_unsafe x cstr gl - -(* dirty? *) - -let list_constr_largs = ref [] - -let rec poseq_list_ids_rec lcstr gl = - match lcstr with - | [] -> tclIDTAC gl - | c::lcstr' -> - match kind_of_term c with - | Var _ -> - (list_constr_largs:=c::!list_constr_largs ; poseq_list_ids_rec lcstr' gl) - | _ -> - let _ = prstr "c = " in - let _ = prconstr c in - let _ = prstr "\n" in - let typ = Tacmach.pf_type_of gl c in - let cname = Termops.id_of_name_using_hdchar (Global.env()) typ Anonymous in - let x = Tactics.fresh_id [] cname gl in - let _ = list_constr_largs:=mkVar x :: !list_constr_largs in - let _ = prstr " list_constr_largs = " in - let _ = prlistconstr !list_constr_largs in - let _ = prstr "\n" in - - tclTHEN - (poseq_unsafe x c) - (poseq_list_ids_rec lcstr') - gl - -let poseq_list_ids lcstr gl = - let _ = list_constr_largs := [] in - poseq_list_ids_rec lcstr gl - -(** [find_fapp test g] returns the list of [app_info] of all calls to - functions that satisfy [test] in the conclusion of goal g. Trivial - repetition (not modulo conversion) are deleted. *) -let find_fapp (test:constr -> bool) g : fapp_info list = - let pre_res = hdMatchSub (Tacmach.pf_concl g) test in - let res = - List.fold_right (fun x acc -> if List.mem x acc then acc else x::acc) pre_res [] in - (prlistconstr (List.map (fun x -> applist (x.fname,x.largs)) res); - res) - - - -(** [finduction id filter g] tries to apply functional induction on - an occurence of function [id] in the conclusion of goal [g]. If - [id]=[None] then calls to any function are selected. In any case - [heuristic] is used to select the most pertinent occurrence. *) -let finduction (oid:identifier option) (heuristic: fapp_info list -> fapp_info list) - (nexttac:Proof_type.tactic) g = - let test = match oid with - | Some id -> - let idconstr = mkConst (const_of_id id) in - (fun u -> constr_head_match u idconstr) (* select only id *) - | None -> (fun u -> isApp u) in (* select calls to any function *) - let info_list = find_fapp test g in - let ordered_info_list = heuristic info_list in - prlistconstr (List.map (fun x -> applist (x.fname,x.largs)) ordered_info_list); - if List.length ordered_info_list = 0 then Util.error "function not found in goal\n"; - let taclist: Proof_type.tactic list = - List.map - (fun info -> - (tclTHEN - (tclTHEN (poseq_list_ids info.largs) - ( - fun gl -> - (functional_induction - true (applist (info.fname, List.rev !list_constr_largs)) - None None) gl)) - nexttac)) ordered_info_list in - (* we try each (f t u v) until one does not fail *) - (* TODO: try also to mix functional schemes *) - tclFIRST taclist g - - - - -(** [chose_heuristic oi x] returns the heuristic for reordering - (and/or forgetting some elts of) a list of occurrences of - function calls infos to chose first with functional induction. *) -let chose_heuristic (oi:int option) : fapp_info list -> fapp_info list = - match oi with - | Some i -> (fun l -> [ List.nth l (i-1) ]) (* occurrence was given by the user *) - | None -> - (* Default heuristic: put first occurrences where all arguments - are *bound* (meaning already introduced) variables *) - let ordering x y = - if x.free && x.onlyvars && y.free && y.onlyvars then 0 (* both pertinent *) - else if x.free && x.onlyvars then -1 - else if y.free && y.onlyvars then 1 - else 0 (* both not pertinent *) - in - List.sort ordering - - - -TACTIC EXTEND finduction - ["finduction" ident(id) natural_opt(oi)] -> - [ - match oi with - | Some(n) when n<=0 -> Util.error "numerical argument must be > 0" - | _ -> - let heuristic = chose_heuristic oi in - finduction (Some id) heuristic tclIDTAC - ] -END - - - -TACTIC EXTEND fauto - [ "fauto" tactic(tac)] -> - [ - let heuristic = chose_heuristic None in - finduction None heuristic (snd tac) - ] - | - [ "fauto" ] -> - [ - let heuristic = chose_heuristic None in - finduction None heuristic tclIDTAC - ] - -END - - -TACTIC EXTEND poseq - [ "poseq" ident(x) constr(c) ] -> - [ poseq x c ] -END - -VERNAC COMMAND EXTEND Showindinfo - [ "showindinfo" ident(x) ] -> [ Merge.showind x ] -END - -VERNAC COMMAND EXTEND MergeFunind - [ "Mergeschemes" "(" ident(id1) ne_ident_list(cl1) ")" - "with" "(" ident(id2) ne_ident_list(cl2) ")" "using" ident(id) ] -> - [ - let f1 = Constrintern.interp_constr Evd.empty (Global.env()) - (CRef (Libnames.Ident (Util.dummy_loc,id1))) in - let f2 = Constrintern.interp_constr Evd.empty (Global.env()) - (CRef (Libnames.Ident (Util.dummy_loc,id2))) in - let f1type = Typing.type_of (Global.env()) Evd.empty f1 in - let f2type = Typing.type_of (Global.env()) Evd.empty f2 in - let ar1 = List.length (fst (decompose_prod f1type)) in - let ar2 = List.length (fst (decompose_prod f2type)) in - let _ = - if ar1 <> List.length cl1 then - Util.error ("not the right number of arguments for " ^ string_of_id id1) in - let _ = - if ar2 <> List.length cl2 then - Util.error ("not the right number of arguments for " ^ string_of_id id2) in - Merge.merge id1 id2 (Array.of_list cl1) (Array.of_list cl2) id - ] -END diff --git a/contrib/funind/indfun.ml b/contrib/funind/indfun.ml deleted file mode 100644 index b6b2cbd1..00000000 --- a/contrib/funind/indfun.ml +++ /dev/null @@ -1,752 +0,0 @@ -open Util -open Names -open Term -open Pp -open Indfun_common -open Libnames -open Rawterm -open Declarations - -let is_rec_info scheme_info = - let test_branche min acc (_,_,br) = - acc || ( - let new_branche = - Sign.it_mkProd_or_LetIn mkProp (fst (Sign.decompose_prod_assum br)) in - let free_rels_in_br = Termops.free_rels new_branche in - let max = min + scheme_info.Tactics.npredicates in - Util.Intset.exists (fun i -> i >= min && i< max) free_rels_in_br - ) - in - Util.list_fold_left_i test_branche 1 false (List.rev scheme_info.Tactics.branches) - - -let choose_dest_or_ind scheme_info = - if is_rec_info scheme_info - then Tactics.new_induct false - else Tactics.new_destruct false - - -let functional_induction with_clean c princl pat = - let f,args = decompose_app c in - fun g -> - let princ,bindings, princ_type = - match princl with - | None -> (* No principle is given let's find the good one *) - begin - match kind_of_term f with - | Const c' -> - let princ_option = - let finfo = (* we first try to find out a graph on f *) - try find_Function_infos c' - with Not_found -> - errorlabstrm "" (str "Cannot find induction information on "++ - Printer.pr_lconstr (mkConst c') ) - in - match Tacticals.elimination_sort_of_goal g with - | InProp -> finfo.prop_lemma - | InSet -> finfo.rec_lemma - | InType -> finfo.rect_lemma - in - let princ = (* then we get the principle *) - try mkConst (Option.get princ_option ) - with Option.IsNone -> - (*i If there is not default lemma defined then, - we cross our finger and try to find a lemma named f_ind - (or f_rec, f_rect) i*) - let princ_name = - Indrec.make_elimination_ident - (id_of_label (con_label c')) - (Tacticals.elimination_sort_of_goal g) - in - try - mkConst(const_of_id princ_name ) - with Not_found -> (* This one is neither defined ! *) - errorlabstrm "" (str "Cannot find induction principle for " - ++Printer.pr_lconstr (mkConst c') ) - in - (princ,Rawterm.NoBindings, Tacmach.pf_type_of g princ) - | _ -> raise (UserError("",str "functional induction must be used with a function" )) - - end - | Some ((princ,binding)) -> - princ,binding,Tacmach.pf_type_of g princ - in - let princ_infos = Tactics.compute_elim_sig princ_type in - let args_as_induction_constr = - let c_list = - if princ_infos.Tactics.farg_in_concl - then [c] else [] - in - List.map (fun c -> Tacexpr.ElimOnConstr (c,NoBindings)) (args@c_list) - in - let princ' = Some (princ,bindings) in - let princ_vars = - List.fold_right - (fun a acc -> - try Idset.add (destVar a) acc - with _ -> acc - ) - args - Idset.empty - in - let old_idl = List.fold_right Idset.add (Tacmach.pf_ids_of_hyps g) Idset.empty in - let old_idl = Idset.diff old_idl princ_vars in - let subst_and_reduce g = - if with_clean - then - let idl = - map_succeed - (fun id -> - if Idset.mem id old_idl then failwith "subst_and_reduce"; - id - ) - (Tacmach.pf_ids_of_hyps g) - in - let flag = - Rawterm.Cbv - {Rawterm.all_flags - with Rawterm.rDelta = false; - } - in - Tacticals.tclTHEN - (Tacticals.tclMAP (fun id -> Tacticals.tclTRY (Equality.subst [id])) idl ) - (Hiddentac.h_reduce flag Tacticals.allClauses) - g - else Tacticals.tclIDTAC g - - in - Tacticals.tclTHEN - (choose_dest_or_ind - princ_infos - args_as_induction_constr - princ' - (None,pat) - None) - subst_and_reduce - g - - - - -type annot = - Struct of identifier - | Wf of Topconstr.constr_expr * identifier option * Topconstr.constr_expr list - | Mes of Topconstr.constr_expr * identifier option * Topconstr.constr_expr list - - -type newfixpoint_expr = - identifier * annot * Topconstr.local_binder list * Topconstr.constr_expr * Topconstr.constr_expr - -let rec abstract_rawconstr c = function - | [] -> c - | Topconstr.LocalRawDef (x,b)::bl -> Topconstr.mkLetInC(x,b,abstract_rawconstr c bl) - | Topconstr.LocalRawAssum (idl,k,t)::bl -> - List.fold_right (fun x b -> Topconstr.mkLambdaC([x],k,t,b)) idl - (abstract_rawconstr c bl) - -let interp_casted_constr_with_implicits sigma env impls c = -(* Constrintern.interp_rawconstr_with_implicits sigma env [] impls c *) - Constrintern.intern_gen false sigma env ~impls:([],impls) - ~allow_patvar:false ~ltacvars:([],[]) c - - -(* - Construct a fixpoint as a Rawterm - and not as a constr -*) -let build_newrecursive -(lnameargsardef) = - let env0 = Global.env() - and sigma = Evd.empty - in - let (rec_sign,rec_impls) = - List.fold_left - (fun (env,impls) ((_,recname),_,bl,arityc,_) -> - let arityc = Command.generalize_constr_expr arityc bl in - let arity = Constrintern.interp_type sigma env0 arityc in - let impl = - if Impargs.is_implicit_args() - then Impargs.compute_implicits env0 arity - else [] in - let impls' =(recname,(Constrintern.Recursive,[],impl,Notation.compute_arguments_scope arity))::impls in - (Environ.push_named (recname,None,arity) env, impls')) - (env0,[]) lnameargsardef in - let recdef = - (* Declare local notations *) - let fs = States.freeze() in - let def = - try - List.map - (fun (_,_,bl,_,def) -> - let def = abstract_rawconstr def bl in - interp_casted_constr_with_implicits - sigma rec_sign rec_impls def - ) - lnameargsardef - with e -> - States.unfreeze fs; raise e in - States.unfreeze fs; def - in - recdef,rec_impls - - -let compute_annot (name,annot,args,types,body) = - let names = List.map snd (Topconstr.names_of_local_assums args) in - match annot with - | None -> - if List.length names > 1 then - user_err_loc - (dummy_loc,"Function", - Pp.str "the recursive argument needs to be specified"); - let new_annot = (id_of_name (List.hd names)) in - (name,Struct new_annot,args,types,body) - | Some r -> (name,r,args,types,body) - - -(* Checks whether or not the mutual bloc is recursive *) -let rec is_rec names = - let names = List.fold_right Idset.add names Idset.empty in - let check_id id names = Idset.mem id names in - let rec lookup names = function - | RVar(_,id) -> check_id id names - | RRef _ | REvar _ | RPatVar _ | RSort _ | RHole _ | RDynamic _ -> false - | RCast(_,b,_) -> lookup names b - | RRec _ -> error "RRec not handled" - | RIf(_,b,_,lhs,rhs) -> - (lookup names b) || (lookup names lhs) || (lookup names rhs) - | RLetIn(_,na,t,b) | RLambda(_,na,_,t,b) | RProd(_,na,_,t,b) -> - lookup names t || lookup (Nameops.name_fold Idset.remove na names) b - | RLetTuple(_,nal,_,t,b) -> lookup names t || - lookup - (List.fold_left - (fun acc na -> Nameops.name_fold Idset.remove na acc) - names - nal - ) - b - | RApp(_,f,args) -> List.exists (lookup names) (f::args) - | RCases(_,_,_,el,brl) -> - List.exists (fun (e,_) -> lookup names e) el || - List.exists (lookup_br names) brl - and lookup_br names (_,idl,_,rt) = - let new_names = List.fold_right Idset.remove idl names in - lookup new_names rt - in - lookup names - -let prepare_body (name,annot,args,types,body) rt = - let n = (Topconstr.local_binders_length args) in -(* Pp.msgnl (str "nb lambda to chop : " ++ str (string_of_int n) ++ fnl () ++Printer.pr_rawconstr rt); *) - let fun_args,rt' = chop_rlambda_n n rt in - (fun_args,rt') - - -let derive_inversion fix_names = - try - (* we first transform the fix_names identifier into their corresponding constant *) - let fix_names_as_constant = - List.map (fun id -> destConst (Tacinterp.constr_of_id (Global.env ()) id)) fix_names - 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 c)) fix_names_as_constant ; - try - Invfun.derive_correctness - Functional_principles_types.make_scheme - functional_induction - fix_names_as_constant - (*i The next call to mk_rel_id is valid since we have just construct the graph - Ensures by : register_built - i*) - (List.map - (fun id -> destInd (Tacinterp.constr_of_id (Global.env ()) (mk_rel_id id))) - fix_names - ) - with e -> - msg_warning - (str "Cannot built inversion information" ++ - if do_observe () then Cerrors.explain_exn e else mt ()) - with _ -> () - -let warning_error names e = - match e with - | Building_graph e -> - Pp.msg_warning - (str "Cannot define graph(s) for " ++ - h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++ - if do_observe () then (spc () ++ Cerrors.explain_exn e) else mt ()) - | Defining_principle e -> - Pp.msg_warning - (str "Cannot define principle(s) for "++ - h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++ - if do_observe () then Cerrors.explain_exn e else mt ()) - | _ -> anomaly "" - -let error_error names e = - match e with - | Building_graph e -> - errorlabstrm "" - (str "Cannot define graph(s) for " ++ - h 1 (prlist_with_sep (fun _ -> str","++spc ()) Ppconstr.pr_id names) ++ - if do_observe () then (spc () ++ Cerrors.explain_exn e) else mt ()) - | _ -> anomaly "" - -let generate_principle on_error - is_general do_built fix_rec_l recdefs interactive_proof - (continue_proof : int -> Names.constant array -> Term.constr array -> int -> - Tacmach.tactic) : unit = - let names = List.map (function ((_, 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 (_,_,_,types,_) -> types) fix_rec_l in - try - (* We then register the Inductive graphs of the functions *) - Rawterm_to_relation.build_inductive names 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 = Ident (dummy_loc,mk_rel_id (List.nth names 0)) in - let ind_kn = - fst (locate_with_msg - (pr_reference f_R_mut++str ": Not an inductive type!") - locate_ind - f_R_mut) - in - let fname_kn (fname,_,_,_,_) = - let f_ref = Ident fname in - locate_with_msg - (pr_reference 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 princ = destConst (Indrec.lookup_eliminator (ind_kn,i) (InProp)) in - let princ_type = Typeops.type_of_constant (Global.env()) princ - in - Functional_principles_types.generate_functional_principle - interactive_proof - princ_type - None - None - 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 -> - on_error names e - -let register_struct is_rec fixpoint_exprl = - match fixpoint_exprl with - | [((_,fname),_,bl,ret_type,body),_] when not is_rec -> - Command.declare_definition - fname - (Decl_kinds.Global,Flags.boxed_definitions (),Decl_kinds.Definition) - bl - None - body - (Some ret_type) - (fun _ _ -> ()) - | _ -> - Command.build_recursive fixpoint_exprl (Flags.boxed_definitions()) - -let generate_correction_proof_wf f_ref tcc_lemma_ref - is_mes functional_ref eq_ref rec_arg_num rec_arg_type nb_args relation - (_: int) (_:Names.constant array) (_:Term.constr array) (_:int) : Tacmach.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 - - -let register_wf ?(is_mes=false) fname rec_impls wf_rel_expr wf_arg using_lemmas args ret_type body - pre_hook - = - let type_of_f = Command.generalize_constr_expr ret_type args in - let rec_arg_num = - let names = - List.map - snd - (Topconstr.names_of_local_assums args) - in - match wf_arg with - | None -> - if List.length names = 1 then 1 - else error "Recursive argument must be specified" - | Some wf_arg -> - list_index (Name wf_arg) names - in - let unbounded_eq = - let f_app_args = - Topconstr.CAppExpl - (dummy_loc, - (None,(Ident (dummy_loc,fname))) , - (List.map - (function - | _,Anonymous -> assert false - | _,Name e -> (Topconstr.mkIdentC e) - ) - (Topconstr.names_of_local_assums args) - ) - ) - in - Topconstr.CApp (dummy_loc,(None,Topconstr.mkRefC (Qualid (dummy_loc,(qualid_of_string "Logic.eq")))), - [(f_app_args,None);(body,None)]) - in - let eq = Command.generalize_constr_expr unbounded_eq args in - let hook f_ref tcc_lemma_ref functional_ref eq_ref rec_arg_num rec_arg_type - nb_args relation = - try - pre_hook - (generate_correction_proof_wf f_ref tcc_lemma_ref is_mes - functional_ref eq_ref rec_arg_num rec_arg_type nb_args relation - ); - derive_inversion [fname] - with e -> - (* No proof done *) - () - in - Recdef.recursive_definition - is_mes fname rec_impls - type_of_f - wf_rel_expr - rec_arg_num - eq - hook - using_lemmas - - -let register_mes fname rec_impls wf_mes_expr wf_arg using_lemmas args ret_type body = - let wf_arg_type,wf_arg = - match wf_arg with - | None -> - begin - match args with - | [Topconstr.LocalRawAssum ([(_,Name x)],k,t)] -> t,x - | _ -> error "Recursive argument must be specified" - end - | Some wf_args -> - try - match - List.find - (function - | Topconstr.LocalRawAssum(l,k,t) -> - List.exists - (function (_,Name id) -> id = wf_args | _ -> false) - l - | _ -> false - ) - args - with - | Topconstr.LocalRawAssum(_,k,t) -> t,wf_args - | _ -> assert false - with Not_found -> assert false - in - let ltof = - let make_dir l = make_dirpath (List.map id_of_string (List.rev l)) in - Libnames.Qualid (dummy_loc,Libnames.qualid_of_sp - (Libnames.make_path (make_dir ["Arith";"Wf_nat"]) (id_of_string "ltof"))) - in - let fun_from_mes = - let applied_mes = - Topconstr.mkAppC(wf_mes_expr,[Topconstr.mkIdentC wf_arg]) in - Topconstr.mkLambdaC ([(dummy_loc,Name wf_arg)],Topconstr.default_binder_kind,wf_arg_type,applied_mes) - in - let wf_rel_from_mes = - Topconstr.mkAppC(Topconstr.mkRefC ltof,[wf_arg_type;fun_from_mes]) - in - register_wf ~is_mes:true fname rec_impls wf_rel_from_mes (Some wf_arg) - using_lemmas args ret_type body - - -let do_generate_principle on_error register_built interactive_proof fixpoint_exprl = - let recdefs,rec_impls = build_newrecursive fixpoint_exprl in - let _is_struct = - match fixpoint_exprl with - | [(((_,name),Some (Wf (wf_rel,wf_x,using_lemmas)),args,types,body))] -> - let pre_hook = - generate_principle - on_error - true - register_built - fixpoint_exprl - recdefs - true - in - if register_built - then register_wf name rec_impls wf_rel wf_x using_lemmas args types body pre_hook; - false - | [(((_,name),Some (Mes (wf_mes,wf_x,using_lemmas)),args,types,body))] -> - let pre_hook = - generate_principle - on_error - true - register_built - fixpoint_exprl - recdefs - true - in - if register_built - then register_mes name rec_impls wf_mes wf_x using_lemmas args types body pre_hook; - true - | _ -> - let fix_names = - List.map (function ((_,name),_,_,_,_) -> name) fixpoint_exprl - in - let is_one_rec = is_rec fix_names in - let old_fixpoint_exprl = - List.map - (function - | (name,Some (Struct id),args,types,body),_ -> - let annot = - try Some (dummy_loc, id), Topconstr.CStructRec - with Not_found -> - raise (UserError("",str "Cannot find argument " ++ - Ppconstr.pr_id id)) - in - (name,annot,args,types,body),(None:Vernacexpr.decl_notation) - | (name,None,args,types,body),recdef -> - let names = (Topconstr.names_of_local_assums args) in - if is_one_rec recdef && List.length names > 1 then - user_err_loc - (dummy_loc,"Function", - Pp.str "the recursive argument needs to be specified in Function") - else - let loc, na = List.hd names in - (name,(Some (loc, Nameops.out_name na), Topconstr.CStructRec),args,types,body), - (None:Vernacexpr.decl_notation) - | (_,Some (Wf _),_,_,_),_ | (_,Some (Mes _),_,_,_),_-> - error - ("Cannot use mutual definition with well-founded recursion or measure") - ) - (List.combine fixpoint_exprl recdefs) - in - (* ok all the expressions are structural *) - let fix_names = - List.map (function ((_,name),_,_,_,_) -> name) fixpoint_exprl - in - let is_rec = List.exists (is_rec fix_names) recdefs in - if register_built then register_struct is_rec old_fixpoint_exprl; - generate_principle - on_error - false - register_built - fixpoint_exprl - recdefs - interactive_proof - (Functional_principles_proofs.prove_princ_for_struct interactive_proof); - if register_built then derive_inversion fix_names; - true; - in - () - -open Topconstr -let rec add_args id new_args b = - match b with - | CRef r -> - begin match r with - | Libnames.Ident(loc,fname) when fname = id -> - CAppExpl(dummy_loc,(None,r),new_args) - | _ -> b - end - | CFix _ | CCoFix _ -> anomaly "add_args : todo" - | CArrow(loc,b1,b2) -> - CArrow(loc,add_args id new_args b1, add_args id new_args b2) - | CProdN(loc,nal,b1) -> - CProdN(loc, - List.map (fun (nal,k,b2) -> (nal,k,add_args id new_args b2)) nal, - add_args id new_args b1) - | CLambdaN(loc,nal,b1) -> - CLambdaN(loc, - List.map (fun (nal,k,b2) -> (nal,k,add_args id new_args b2)) nal, - add_args id new_args b1) - | CLetIn(loc,na,b1,b2) -> - CLetIn(loc,na,add_args id new_args b1,add_args id new_args b2) - | CAppExpl(loc,(pf,r),exprl) -> - begin - match r with - | Libnames.Ident(loc,fname) when fname = id -> - CAppExpl(loc,(pf,r),new_args@(List.map (add_args id new_args) exprl)) - | _ -> CAppExpl(loc,(pf,r),List.map (add_args id new_args) exprl) - end - | CApp(loc,(pf,b),bl) -> - CApp(loc,(pf,add_args id new_args b), - List.map (fun (e,o) -> add_args id new_args e,o) bl) - | CCases(loc,sty,b_option,cel,cal) -> - CCases(loc,sty,Option.map (add_args id new_args) b_option, - List.map (fun (b,(na,b_option)) -> - add_args id new_args b, - (na,Option.map (add_args id new_args) b_option)) cel, - List.map (fun (loc,cpl,e) -> (loc,cpl,add_args id new_args e)) cal - ) - | CLetTuple(loc,nal,(na,b_option),b1,b2) -> - CLetTuple(loc,nal,(na,Option.map (add_args id new_args) b_option), - add_args id new_args b1, - add_args id new_args b2 - ) - - | CIf(loc,b1,(na,b_option),b2,b3) -> - CIf(loc,add_args id new_args b1, - (na,Option.map (add_args id new_args) b_option), - add_args id new_args b2, - add_args id new_args b3 - ) - | CHole _ -> b - | CPatVar _ -> b - | CEvar _ -> b - | CSort _ -> b - | CCast(loc,b1,CastConv(ck,b2)) -> - CCast(loc,add_args id new_args b1,CastConv(ck,add_args id new_args b2)) - | CCast(loc,b1,CastCoerce) -> - CCast(loc,add_args id new_args b1,CastCoerce) - | CRecord _ -> anomaly "add_args : CRecord" - | CNotation _ -> anomaly "add_args : CNotation" - | CGeneralization _ -> anomaly "add_args : CGeneralization" - | CPrim _ -> b - | CDelimiters _ -> anomaly "add_args : CDelimiters" - | CDynamic _ -> anomaly "add_args : CDynamic" -exception Stop of Topconstr.constr_expr - - -(* [chop_n_arrow n t] chops the [n] first arrows in [t] - Acts on Topconstr.constr_expr -*) -let rec chop_n_arrow n t = - if n <= 0 - then t (* If we have already removed all the arrows then return the type *) - else (* If not we check the form of [t] *) - match t with - | Topconstr.CArrow(_,_,t) -> (* If we have an arrow, we discard it and recall [chop_n_arrow] *) - chop_n_arrow (n-1) t - | Topconstr.CProdN(_,nal_ta',t') -> (* If we have a forall, to result are possible : - either we need to discard more than the number of arrows contained - in this product declaration then we just recall [chop_n_arrow] on - the remaining number of arrow to chop and [t'] we discard it and - recall [chop_n_arrow], either this product contains more arrows - than the number we need to chop and then we return the new type - *) - begin - try - let new_n = - let rec aux (n:int) = function - [] -> n - | (nal,k,t'')::nal_ta' -> - let nal_l = List.length nal in - if n >= nal_l - then - aux (n - nal_l) nal_ta' - else - let new_t' = - Topconstr.CProdN(dummy_loc, - ((snd (list_chop n nal)),k,t'')::nal_ta',t') - in - raise (Stop new_t') - in - aux n nal_ta' - in - chop_n_arrow new_n t' - with Stop t -> t - end - | _ -> anomaly "Not enough products" - - -let rec get_args b t : Topconstr.local_binder list * - Topconstr.constr_expr * Topconstr.constr_expr = - match b with - | Topconstr.CLambdaN (loc, (nal_ta), b') -> - begin - let n = - (List.fold_left (fun n (nal,_,_) -> - n+List.length nal) 0 nal_ta ) - in - let nal_tas,b'',t'' = get_args b' (chop_n_arrow n t) in - (List.map (fun (nal,k,ta) -> - (Topconstr.LocalRawAssum (nal,k,ta))) nal_ta)@nal_tas, b'',t'' - end - | _ -> [],b,t - - -let make_graph (f_ref:global_reference) = - let c,c_body = - match f_ref with - | ConstRef c -> - begin try c,Global.lookup_constant c - with Not_found -> - raise (UserError ("",str "Cannot find " ++ Printer.pr_lconstr (mkConst c)) ) - end - | _ -> raise (UserError ("", str "Not a function reference") ) - - in - match c_body.const_body with - | None -> error "Cannot build a graph over an axiom !" - | Some b -> - let env = Global.env () in - let body = (force b) in - let extern_body,extern_type = - with_full_print - (fun () -> - (Constrextern.extern_constr false env body, - Constrextern.extern_type false env - (Typeops.type_of_constant_type env c_body.const_type) - ) - ) - () - in - let (nal_tas,b,t) = get_args extern_body extern_type in - let expr_list = - match b with - | Topconstr.CFix(loc,l_id,fixexprl) -> - let l = - List.map - (fun (id,(n,recexp),bl,t,b) -> - let loc, rec_id = Option.get n in - let new_args = - List.flatten - (List.map - (function - | Topconstr.LocalRawDef (na,_)-> [] - | Topconstr.LocalRawAssum (nal,_,_) -> - List.map - (fun (loc,n) -> - CRef(Libnames.Ident(loc, Nameops.out_name n))) - nal - ) - nal_tas - ) - in - let b' = add_args (snd id) new_args b in - (id, Some (Struct rec_id),nal_tas@bl,t,b') - ) - fixexprl - in - l - | _ -> - let id = id_of_label (con_label c) in - [((dummy_loc,id),None,nal_tas,t,b)] - in - do_generate_principle error_error false false expr_list; - (* We register the infos *) - let mp,dp,_ = repr_con c in - List.iter - (fun ((_,id),_,_,_,_) -> add_Function false (make_con mp dp (label_of_id id))) - expr_list - - -(* let make_graph _ = assert false *) - -let do_generate_principle = do_generate_principle warning_error true - - diff --git a/contrib/funind/indfun_common.ml b/contrib/funind/indfun_common.ml deleted file mode 100644 index a3c169b7..00000000 --- a/contrib/funind/indfun_common.ml +++ /dev/null @@ -1,512 +0,0 @@ -open Names -open Pp - -open Libnames - -let mk_prefix pre id = id_of_string (pre^(string_of_id id)) -let mk_rel_id = mk_prefix "R_" -let mk_correct_id id = Nameops.add_suffix (mk_rel_id id) "_correct" -let mk_complete_id id = Nameops.add_suffix (mk_rel_id id) "_complete" -let mk_equation_id id = Nameops.add_suffix id "_equation" - -let msgnl m = - () - -let invalid_argument s = raise (Invalid_argument s) - - -let fresh_id avoid s = Termops.next_global_ident_away true (id_of_string s) avoid - -let fresh_name avoid s = Name (fresh_id avoid s) - -let get_name avoid ?(default="H") = function - | Anonymous -> fresh_name avoid default - | Name n -> Name n - -let array_get_start a = - try - Array.init - (Array.length a - 1) - (fun i -> a.(i)) - with Invalid_argument "index out of bounds" -> - invalid_argument "array_get_start" - -let id_of_name = function - Name id -> id - | _ -> raise Not_found - -let locate ref = - let (loc,qid) = qualid_of_reference ref in - Nametab.locate qid - -let locate_ind ref = - match locate ref with - | IndRef x -> x - | _ -> raise Not_found - -let locate_constant ref = - match locate ref with - | ConstRef x -> x - | _ -> raise Not_found - - -let locate_with_msg msg f x = - try - f x - with - | Not_found -> raise (Util.UserError("", msg)) - | e -> raise e - - -let filter_map filter f = - let rec it = function - | [] -> [] - | e::l -> - if filter e - then - (f e) :: it l - else it l - in - it - - -let chop_rlambda_n = - let rec chop_lambda_n acc n rt = - if n == 0 - then List.rev acc,rt - else - match rt with - | Rawterm.RLambda(_,name,k,t,b) -> chop_lambda_n ((name,t,false)::acc) (n-1) b - | Rawterm.RLetIn(_,name,v,b) -> chop_lambda_n ((name,v,true)::acc) (n-1) b - | _ -> - raise (Util.UserError("chop_rlambda_n", - str "chop_rlambda_n: Not enough Lambdas")) - in - chop_lambda_n [] - -let chop_rprod_n = - let rec chop_prod_n acc n rt = - if n == 0 - then List.rev acc,rt - else - match rt with - | Rawterm.RProd(_,name,k,t,b) -> chop_prod_n ((name,t)::acc) (n-1) b - | _ -> raise (Util.UserError("chop_rprod_n",str "chop_rprod_n: Not enough products")) - in - chop_prod_n [] - - - -let list_union_eq eq_fun l1 l2 = - let rec urec = function - | [] -> l2 - | a::l -> if List.exists (eq_fun a) l2 then urec l else a::urec l - in - urec l1 - -let list_add_set_eq eq_fun x l = - if List.exists (eq_fun x) l then l else x::l - - - - -let const_of_id id = - let _,princ_ref = - qualid_of_reference (Libnames.Ident (Util.dummy_loc,id)) - in - try Nametab.locate_constant princ_ref - with Not_found -> Util.error ("cannot find "^ string_of_id id) - -let def_of_const t = - match (Term.kind_of_term t) with - Term.Const sp -> - (try (match (Global.lookup_constant sp) with - {Declarations.const_body=Some c} -> Declarations.force c - |_ -> assert false) - with _ -> assert false) - |_ -> assert false - -let coq_constant s = - Coqlib.gen_constant_in_modules "RecursiveDefinition" - (Coqlib.init_modules @ Coqlib.arith_modules) s;; - -let constant sl s = - constr_of_global - (Nametab.locate (make_qualid(Names.make_dirpath - (List.map id_of_string (List.rev sl))) - (id_of_string s)));; - -let find_reference sl s = - (Nametab.locate (make_qualid(Names.make_dirpath - (List.map id_of_string (List.rev sl))) - (id_of_string s)));; - -let eq = lazy(coq_constant "eq") -let refl_equal = lazy(coq_constant "refl_equal") - -(*****************************************************************) -(* Copy of the standart save mechanism but without the much too *) -(* slow reduction function *) -(*****************************************************************) -open Declarations -open Entries -open Decl_kinds -open Declare -let definition_message id = - Flags.if_verbose message ((string_of_id id) ^ " is defined") - - -let save with_clean id const (locality,kind) hook = - let {const_entry_body = pft; - const_entry_type = tpo; - const_entry_opaque = opacity } = const in - let l,r = match locality with - | Local when Lib.sections_are_opened () -> - let k = logical_kind_of_goal_kind kind in - let c = SectionLocalDef (pft, tpo, opacity) in - let _ = declare_variable id (Lib.cwd(), c, k) in - (Local, VarRef id) - | Local -> - let k = logical_kind_of_goal_kind kind in - let kn = declare_constant id (DefinitionEntry const, k) in - (Global, ConstRef kn) - | Global -> - let k = logical_kind_of_goal_kind kind in - let kn = declare_constant id (DefinitionEntry const, k) in - (Global, ConstRef kn) in - if with_clean then Pfedit.delete_current_proof (); - hook l r; - definition_message id - - - - -let extract_pftreestate pts = - let pfterm,subgoals = Refiner.extract_open_pftreestate pts in - let tpfsigma = Refiner.evc_of_pftreestate pts in - let exl = Evarutil.non_instantiated tpfsigma in - if subgoals <> [] or exl <> [] then - Util.errorlabstrm "extract_proof" - (if subgoals <> [] then - str "Attempt to save an incomplete proof" - else - str "Attempt to save a proof with existential variables still non-instantiated"); - let env = Global.env_of_context (Refiner.proof_of_pftreestate pts).Proof_type.goal.Evd.evar_hyps in - env,tpfsigma,pfterm - - -let nf_betaiotazeta = - let clos_norm_flags flgs env sigma t = - Closure.norm_val (Closure.create_clos_infos flgs env) (Closure.inject (Reductionops.nf_evar sigma t)) in - clos_norm_flags Closure.betaiotazeta - -let nf_betaiota = - let clos_norm_flags flgs env sigma t = - Closure.norm_val (Closure.create_clos_infos flgs env) (Closure.inject (Reductionops.nf_evar sigma t)) in - clos_norm_flags Closure.betaiota - -let cook_proof do_reduce = - let pfs = Pfedit.get_pftreestate () -(* and ident = Pfedit.get_current_proof_name () *) - and (ident,strength,concl,hook) = Pfedit.current_proof_statement () in - let env,sigma,pfterm = extract_pftreestate pfs in - let pfterm = - if do_reduce - then nf_betaiota env sigma pfterm - else pfterm - in - (ident, - ({ const_entry_body = pfterm; - const_entry_type = Some concl; - const_entry_opaque = false; - const_entry_boxed = false}, - strength, hook)) - - -let new_save_named opacity = - let id,(const,persistence,hook) = cook_proof true in - let const = { const with const_entry_opaque = opacity } in - save true id const persistence hook - -let get_proof_clean do_reduce = - let result = cook_proof do_reduce in - Pfedit.delete_current_proof (); - result - -let with_full_print f a = - let old_implicit_args = Impargs.is_implicit_args () - and old_strict_implicit_args = Impargs.is_strict_implicit_args () - and old_contextual_implicit_args = Impargs.is_contextual_implicit_args () in - let old_rawprint = !Flags.raw_print in - Flags.raw_print := true; - Impargs.make_implicit_args false; - Impargs.make_strict_implicit_args false; - Impargs.make_contextual_implicit_args false; - Impargs.make_contextual_implicit_args false; - Dumpglob.pause (); - try - let res = f a in - Impargs.make_implicit_args old_implicit_args; - Impargs.make_strict_implicit_args old_strict_implicit_args; - Impargs.make_contextual_implicit_args old_contextual_implicit_args; - Flags.raw_print := old_rawprint; - Dumpglob.continue (); - res - with - | e -> - Impargs.make_implicit_args old_implicit_args; - Impargs.make_strict_implicit_args old_strict_implicit_args; - Impargs.make_contextual_implicit_args old_contextual_implicit_args; - Flags.raw_print := old_rawprint; - Dumpglob.continue (); - raise e - - - - - - -(**********************) - -type function_info = - { - function_constant : constant; - graph_ind : inductive; - equation_lemma : constant option; - correctness_lemma : constant option; - completeness_lemma : constant option; - rect_lemma : constant option; - rec_lemma : constant option; - prop_lemma : constant option; - is_general : bool; (* Has this function been defined using general recursive definition *) - } - - -(* type function_db = function_info list *) - -(* let function_table = ref ([] : function_db) *) - - -let from_function = ref Cmap.empty -let from_graph = ref Indmap.empty -(* -let rec do_cache_info finfo = function - | [] -> raise Not_found - | (finfo'::finfos as l) -> - if finfo' == finfo then l - else if finfo'.function_constant = finfo.function_constant - then finfo::finfos - else - let res = do_cache_info finfo finfos in - if res == finfos then l else finfo'::l - - -let cache_Function (_,(finfos)) = - let new_tbl = - try do_cache_info finfos !function_table - with Not_found -> finfos::!function_table - in - if new_tbl != !function_table - then function_table := new_tbl -*) - -let cache_Function (_,finfos) = - from_function := Cmap.add finfos.function_constant finfos !from_function; - from_graph := Indmap.add finfos.graph_ind finfos !from_graph - - -let load_Function _ = cache_Function -let open_Function _ = cache_Function -let subst_Function (_,subst,finfos) = - let do_subst_con c = fst (Mod_subst.subst_con subst c) - and do_subst_ind (kn,i) = (Mod_subst.subst_kn subst kn,i) - in - let function_constant' = do_subst_con finfos.function_constant in - let graph_ind' = do_subst_ind finfos.graph_ind in - let equation_lemma' = Option.smartmap do_subst_con finfos.equation_lemma in - let correctness_lemma' = Option.smartmap do_subst_con finfos.correctness_lemma in - let completeness_lemma' = Option.smartmap do_subst_con finfos.completeness_lemma in - let rect_lemma' = Option.smartmap do_subst_con finfos.rect_lemma in - let rec_lemma' = Option.smartmap do_subst_con finfos.rec_lemma in - let prop_lemma' = Option.smartmap do_subst_con finfos.prop_lemma in - if function_constant' == finfos.function_constant && - graph_ind' == finfos.graph_ind && - equation_lemma' == finfos.equation_lemma && - correctness_lemma' == finfos.correctness_lemma && - completeness_lemma' == finfos.completeness_lemma && - rect_lemma' == finfos.rect_lemma && - rec_lemma' == finfos.rec_lemma && - prop_lemma' == finfos.prop_lemma - then finfos - else - { function_constant = function_constant'; - graph_ind = graph_ind'; - equation_lemma = equation_lemma' ; - correctness_lemma = correctness_lemma' ; - completeness_lemma = completeness_lemma' ; - rect_lemma = rect_lemma' ; - rec_lemma = rec_lemma'; - prop_lemma = prop_lemma'; - is_general = finfos.is_general - } - -let classify_Function (_,infos) = Libobject.Substitute infos - -let export_Function infos = Some infos - - -let discharge_Function (_,finfos) = - let function_constant' = Lib.discharge_con finfos.function_constant - and graph_ind' = Lib.discharge_inductive finfos.graph_ind - and equation_lemma' = Option.smartmap Lib.discharge_con finfos.equation_lemma - and correctness_lemma' = Option.smartmap Lib.discharge_con finfos.correctness_lemma - and completeness_lemma' = Option.smartmap Lib.discharge_con finfos.completeness_lemma - and rect_lemma' = Option.smartmap Lib.discharge_con finfos.rect_lemma - and rec_lemma' = Option.smartmap Lib.discharge_con finfos.rec_lemma - and prop_lemma' = Option.smartmap Lib.discharge_con finfos.prop_lemma - in - if function_constant' == finfos.function_constant && - graph_ind' == finfos.graph_ind && - equation_lemma' == finfos.equation_lemma && - correctness_lemma' == finfos.correctness_lemma && - completeness_lemma' == finfos.completeness_lemma && - rect_lemma' == finfos.rect_lemma && - rec_lemma' == finfos.rec_lemma && - prop_lemma' == finfos.prop_lemma - then Some finfos - else - Some { function_constant = function_constant' ; - graph_ind = graph_ind' ; - equation_lemma = equation_lemma' ; - correctness_lemma = correctness_lemma' ; - completeness_lemma = completeness_lemma'; - rect_lemma = rect_lemma'; - rec_lemma = rec_lemma'; - prop_lemma = prop_lemma' ; - is_general = finfos.is_general - } - -open Term -let pr_info f_info = - str "function_constant := " ++ Printer.pr_lconstr (mkConst f_info.function_constant)++ fnl () ++ - str "function_constant_type := " ++ - (try Printer.pr_lconstr (Global.type_of_global (ConstRef f_info.function_constant)) with _ -> mt ()) ++ fnl () ++ - str "equation_lemma := " ++ (Option.fold_right (fun v acc -> Printer.pr_lconstr (mkConst v)) f_info.equation_lemma (mt ()) ) ++ fnl () ++ - str "completeness_lemma :=" ++ (Option.fold_right (fun v acc -> Printer.pr_lconstr (mkConst v)) f_info.completeness_lemma (mt ()) ) ++ fnl () ++ - str "correctness_lemma := " ++ (Option.fold_right (fun v acc -> Printer.pr_lconstr (mkConst v)) f_info.correctness_lemma (mt ()) ) ++ fnl () ++ - str "rect_lemma := " ++ (Option.fold_right (fun v acc -> Printer.pr_lconstr (mkConst v)) f_info.rect_lemma (mt ()) ) ++ fnl () ++ - str "rec_lemma := " ++ (Option.fold_right (fun v acc -> Printer.pr_lconstr (mkConst v)) f_info.rec_lemma (mt ()) ) ++ fnl () ++ - str "prop_lemma := " ++ (Option.fold_right (fun v acc -> Printer.pr_lconstr (mkConst v)) f_info.prop_lemma (mt ()) ) ++ fnl () ++ - str "graph_ind := " ++ Printer.pr_lconstr (mkInd f_info.graph_ind) ++ fnl () - -let pr_table tb = - let l = Cmap.fold (fun k v acc -> v::acc) tb [] in - Util.prlist_with_sep fnl pr_info l - -let in_Function,out_Function = - Libobject.declare_object - {(Libobject.default_object "FUNCTIONS_DB") with - Libobject.cache_function = cache_Function; - Libobject.load_function = load_Function; - Libobject.classify_function = classify_Function; - Libobject.subst_function = subst_Function; - Libobject.export_function = export_Function; - Libobject.discharge_function = discharge_Function -(* Libobject.open_function = open_Function; *) - } - - - -(* Synchronisation with reset *) -let freeze () = - !from_function,!from_graph -let unfreeze (functions,graphs) = -(* Pp.msgnl (str "unfreezing function_table : " ++ pr_table l); *) - from_function := functions; - from_graph := graphs - -let init () = -(* Pp.msgnl (str "reseting function_table"); *) - from_function := Cmap.empty; - from_graph := Indmap.empty - -let _ = - Summary.declare_summary "functions_db_sum" - { Summary.freeze_function = freeze; - Summary.unfreeze_function = unfreeze; - Summary.init_function = init; - Summary.survive_module = false; - Summary.survive_section = false } - -let find_or_none id = - try Some - (match Nametab.locate (make_short_qualid id) with ConstRef c -> c | _ -> Util.anomaly "Not a constant" - ) - with Not_found -> None - - - -let find_Function_infos f = - Cmap.find f !from_function - - -let find_Function_of_graph ind = - Indmap.find ind !from_graph - -let update_Function finfo = -(* Pp.msgnl (pr_info finfo); *) - Lib.add_anonymous_leaf (in_Function finfo) - - -let add_Function is_general f = - let f_id = id_of_label (con_label f) in - let equation_lemma = find_or_none (mk_equation_id f_id) - and correctness_lemma = find_or_none (mk_correct_id f_id) - and completeness_lemma = find_or_none (mk_complete_id f_id) - and rect_lemma = find_or_none (Nameops.add_suffix f_id "_rect") - and rec_lemma = find_or_none (Nameops.add_suffix f_id "_rec") - and prop_lemma = find_or_none (Nameops.add_suffix f_id "_ind") - and graph_ind = - match Nametab.locate (make_short_qualid (mk_rel_id f_id)) - with | IndRef ind -> ind | _ -> Util.anomaly "Not an inductive" - in - let finfos = - { function_constant = f; - equation_lemma = equation_lemma; - completeness_lemma = completeness_lemma; - correctness_lemma = correctness_lemma; - rect_lemma = rect_lemma; - rec_lemma = rec_lemma; - prop_lemma = prop_lemma; - graph_ind = graph_ind; - is_general = is_general - - } - in - update_Function finfos - -let pr_table () = pr_table !from_function -(*********************************) -(* Debuging *) -let function_debug = ref false -open Goptions - -let function_debug_sig = - { - optsync = false; - optname = "Function debug"; - optkey = PrimaryTable("Function_debug"); - optread = (fun () -> !function_debug); - optwrite = (fun b -> function_debug := b) - } - -let _ = declare_bool_option function_debug_sig - - -let do_observe () = - !function_debug = true - - - -exception Building_graph of exn -exception Defining_principle of exn diff --git a/contrib/funind/indfun_common.mli b/contrib/funind/indfun_common.mli deleted file mode 100644 index 7da1d6f0..00000000 --- a/contrib/funind/indfun_common.mli +++ /dev/null @@ -1,117 +0,0 @@ -open Names -open Pp - -(* - The mk_?_id function build different name w.r.t. a function - Each of their use is justified in the code -*) -val mk_rel_id : identifier -> identifier -val mk_correct_id : identifier -> identifier -val mk_complete_id : identifier -> identifier -val mk_equation_id : identifier -> identifier - - -val msgnl : std_ppcmds -> unit - -val invalid_argument : string -> 'a - -val fresh_id : identifier list -> string -> identifier -val fresh_name : identifier list -> string -> name -val get_name : identifier list -> ?default:string -> name -> name - -val array_get_start : 'a array -> 'a array - -val id_of_name : name -> identifier - -val locate_ind : Libnames.reference -> inductive -val locate_constant : Libnames.reference -> constant -val locate_with_msg : - Pp.std_ppcmds -> (Libnames.reference -> 'a) -> - Libnames.reference -> 'a - -val filter_map : ('a -> bool) -> ('a -> 'b) -> 'a list -> 'b list -val list_union_eq : - ('a -> 'a -> bool) -> 'a list -> 'a list -> 'a list -val list_add_set_eq : - ('a -> 'a -> bool) -> 'a -> 'a list -> 'a list - -val chop_rlambda_n : int -> Rawterm.rawconstr -> - (name*Rawterm.rawconstr*bool) list * Rawterm.rawconstr - -val chop_rprod_n : int -> Rawterm.rawconstr -> - (name*Rawterm.rawconstr) list * Rawterm.rawconstr - -val def_of_const : Term.constr -> Term.constr -val eq : Term.constr Lazy.t -val refl_equal : Term.constr Lazy.t -val const_of_id: identifier -> constant - - -(* [save_named] is a copy of [Command.save_named] but uses - [nf_betaiotazeta] instead of [nf_betaiotaevar_preserving_vm_cast] - - - - DON'T USE IT if you cannot ensure that there is no VMcast in the proof - -*) - -(* val nf_betaiotazeta : Reductionops.reduction_function *) - -val new_save_named : bool -> unit - -val save : bool -> identifier -> Entries.definition_entry -> Decl_kinds.goal_kind -> - Tacexpr.declaration_hook -> unit - -(* [get_proof_clean do_reduce] : returns the proof name, definition, kind and hook and - abort the proof -*) -val get_proof_clean : bool -> - Names.identifier * - (Entries.definition_entry * Decl_kinds.goal_kind * - Tacexpr.declaration_hook) - - - -(* [with_full_print f a] applies [f] to [a] in full printing environment - - This function preserves the print settings -*) -val with_full_print : ('a -> 'b) -> 'a -> 'b - - -(*****************) - -type function_info = - { - function_constant : constant; - graph_ind : inductive; - equation_lemma : constant option; - correctness_lemma : constant option; - completeness_lemma : constant option; - rect_lemma : constant option; - rec_lemma : constant option; - prop_lemma : constant option; - is_general : bool; - } - -val find_Function_infos : constant -> function_info -val find_Function_of_graph : inductive -> function_info -(* WARNING: To be used just after the graph definition !!! *) -val add_Function : bool -> constant -> unit - -val update_Function : function_info -> unit - - -(** debugging *) -val pr_info : function_info -> Pp.std_ppcmds -val pr_table : unit -> Pp.std_ppcmds - - -(* val function_debug : bool ref *) -val do_observe : unit -> bool - -(* To localize pb *) -exception Building_graph of exn -exception Defining_principle of exn - diff --git a/contrib/funind/invfun.ml b/contrib/funind/invfun.ml deleted file mode 100644 index 5c8f0871..00000000 --- a/contrib/funind/invfun.ml +++ /dev/null @@ -1,1022 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) -open Tacexpr -open Declarations -open Util -open Names -open Term -open Pp -open Libnames -open Tacticals -open Tactics -open Indfun_common -open Tacmach -open Termops -open Sign -open Hiddentac - -(* Some pretty printing function for debugging purpose *) - -let pr_binding prc = - function - | loc, Rawterm.NamedHyp id, (_,c) -> hov 1 (Ppconstr.pr_id id ++ str " := " ++ Pp.cut () ++ prc c) - | loc, Rawterm.AnonHyp n, (_,c) -> hov 1 (int n ++ str " := " ++ Pp.cut () ++ prc c) - -let pr_bindings prc prlc = function - | Rawterm.ImplicitBindings l -> - brk (1,1) ++ str "with" ++ brk (1,1) ++ - Util.prlist_with_sep spc (fun (_,c) -> prc c) l - | Rawterm.ExplicitBindings l -> - brk (1,1) ++ str "with" ++ brk (1,1) ++ - Util.prlist_with_sep spc (fun b -> str"(" ++ pr_binding prlc b ++ str")") l - | Rawterm.NoBindings -> mt () - - -let pr_with_bindings prc prlc (c,bl) = - prc c ++ hv 0 (pr_bindings prc prlc bl) - - - -let pr_constr_with_binding prc (c,bl) : Pp.std_ppcmds = - pr_with_bindings prc prc (c,bl) - -(* The local debuging mechanism *) -let msgnl = Pp.msgnl - -let observe strm = - if do_observe () - then Pp.msgnl strm - else () - -let observennl strm = - if do_observe () - then begin Pp.msg strm;Pp.pp_flush () end - else () - - -let do_observe_tac s tac g = - let goal = begin try (Printer.pr_goal (sig_it g)) with _ -> assert false end in - try - let v = tac g in msgnl (goal ++ fnl () ++ s ++(str " ")++(str "finished")); v - with e -> - msgnl (str "observation "++ s++str " raised exception " ++ - Cerrors.explain_exn e ++ str " on goal " ++ goal ); - raise e;; - - -let observe_tac s tac g = - if do_observe () - then do_observe_tac (str s) tac g - else tac g - -(* [nf_zeta] $\zeta$-normalization of a term *) -let nf_zeta = - Reductionops.clos_norm_flags (Closure.RedFlags.mkflags [Closure.RedFlags.fZETA]) - Environ.empty_env - Evd.empty - - -(* [id_to_constr id] finds the term associated to [id] in the global environment *) -let id_to_constr id = - try - Tacinterp.constr_of_id (Global.env ()) id - with Not_found -> - raise (UserError ("",str "Cannot find " ++ Ppconstr.pr_id id)) - -(* [generate_type g_to_f f graph i] build the completeness (resp. correctness) lemma type if [g_to_f = true] - (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 g_to_f f graph i = - (*i we deduce the number of arguments of the function and its returned type from the graph i*) - let graph_arity = Inductive.type_of_inductive (Global.env()) (Global.lookup_inductive (destInd graph)) in - let ctxt,_ = decompose_prod_assum graph_arity in - let fun_ctxt,res_type = - match ctxt with - | [] | [_] -> anomaly "Not a valid context" - | (_,_,res_type)::fun_ctxt -> fun_ctxt,res_type - in - let nb_args = List.length fun_ctxt in - let args_from_decl i decl = - match decl with - | (_,Some _,_) -> incr i; failwith "args_from_decl" - | _ -> let j = !i in incr i;mkRel (nb_args - j + 1) - in - (*i We need to name the vars [res] and [fv] i*) - let res_id = - Termops.next_global_ident_away - true - (id_of_string "res") - (map_succeed (function (Name id,_,_) -> id | (Anonymous,_,_) -> failwith "") fun_ctxt) - in - let fv_id = - Termops.next_global_ident_away - true - (id_of_string "fv") - (res_id::(map_succeed (function (Name id,_,_) -> id | (Anonymous,_,_) -> failwith "Anonymous!") fun_ctxt)) - in - (*i we can then type the argument to be applied to the function [f] i*) - let args_as_rels = - let i = ref 0 in - Array.of_list ((map_succeed (args_from_decl i) (List.rev fun_ctxt))) - in - let args_as_rels = Array.map Termops.pop args_as_rels 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 res_eq_f_of_args = - mkApp(Coqlib.build_coq_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 graph_applied = - let args_and_res_as_rels = - let i = ref 0 in - Array.of_list ((map_succeed (args_from_decl i) (List.rev ((Name res_id,None,res_type)::fun_ctxt))) ) - in - let args_and_res_as_rels = - Array.mapi (fun i c -> if i <> Array.length args_and_res_as_rels - 1 then lift 1 c else c) args_and_res_as_rels - in - 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 = - (Name res_id,None,lift 1 res_type)::(Name fv_id,Some (mkApp(mkConst 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 (Anonymous,None,graph_applied)::pre_ctxt,(lift 1 res_eq_f_of_args) - else (Anonymous,None,res_eq_f_of_args)::pre_ctxt,(lift 1 graph_applied) - - -(* - [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 f = - let f_as_constant = match kind_of_term f with - | Const c' -> c' - | _ -> error "Must be used with a function" - in - let infos = find_Function_infos f_as_constant in - match infos.rect_lemma with - | None -> raise Not_found - | Some rect_lemma -> - let rect_lemma = mkConst rect_lemma in - let typ = Typing.type_of (Global.env ()) Evd.empty rect_lemma in - rect_lemma,typ - - - -(* let fname = *) -(* match kind_of_term f with *) -(* | Const c' -> *) -(* id_of_label (con_label c') *) -(* | _ -> error "Must be used with a function" *) -(* in *) - -(* let princ_name = *) -(* ( *) -(* Indrec.make_elimination_ident *) -(* fname *) -(* InType *) -(* ) *) -(* in *) -(* let c = (\* mkConst(mk_from_const (destConst f) princ_name ) in *\) failwith "" in *) -(* c,Typing.type_of (Global.env ()) Evd.empty c *) - - -let rec generate_fresh_id x avoid i = - if i == 0 - then [] - else - let id = Termops.next_global_ident_away true x avoid in - id::(generate_fresh_id x (id::avoid) (pred i)) - - -(* [prove_fun_correct functional_induction funs_constr graphs_constr schemes lemmas_types_infos i ] - is the tactic used to prove correctness lemma. - - [functional_induction] is the tactic defined in [indfun] (dependency problem) - [funs_constr], [graphs_constr] [schemes] [lemmas_types_infos] are the mutually recursive functions - (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 that is - 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] and the - apply the corresponding constructor of the corresponding graph inductive. - \end{enumerate} - -*) -let prove_fun_correct functional_induction funs_constr graphs_constr schemes lemmas_types_infos i : tactic = - fun g -> - (* first of all we recreate the lemmas types to be used as predicates of the induction principle - that is~: - \[fun (x_1:t_1)\ldots(x_n:t_n)=> fun fv => fun res => res = fv \rightarrow graph\ x_1\ldots x_n\ res\] - *) - let lemmas = - Array.map - (fun (_,(ctxt,concl)) -> - match ctxt with - | [] | [_] | [_;_] -> anomaly "bad context" - | hres::res::(x,_,t)::ctxt -> - Termops.it_mkLambda_or_LetIn - ~init:(Termops.it_mkProd_or_LetIn ~init:concl [hres;res]) - ((x,None,t)::ctxt) - ) - lemmas_types_infos - in - (* we the get the definition of the graphs block *) - let graph_ind = destInd 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 = nf_zeta princ_type in - let princ_infos = Tactics.compute_elim_sig princ_type in - (* The number of args of the function is then easilly computable *) - let nb_fun_args = nb_prod (pf_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 funcitonnal principle is defined in the - environement and due to the bug #1174, we will need to pose the principle - using a name - *) - let principle_id = Termops.next_global_ident_away true (id_of_string "princ") ids in - let ids = principle_id :: ids in - (* We get the branches of the principle *) - let branches = List.rev princ_infos.branches in - (* and built the intro pattern for each of them *) - let intro_pats = - List.map - (fun (_,_,br_type) -> - List.map - (fun id -> dummy_loc, Genarg.IntroIdentifier id) - (generate_fresh_id (id_of_string "y") ids (List.length (fst (decompose_prod_assum br_type)))) - ) - branches - in - (* before building the full intro pattern for the principle *) - let pat = Some (dummy_loc,Genarg.IntroOrAndPattern intro_pats) in - let eq_ind = Coqlib.build_coq_eq () in - let eq_construct = mkConstruct((destInd 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_branche i g = - (* We get the identifiers of this branch *) - let this_branche_ids = - List.fold_right - (fun (_,pat) acc -> - match pat with - | Genarg.IntroIdentifier id -> Idset.add id acc - | _ -> anomaly "Not an identifier" - ) - (List.nth intro_pats (pred i)) - Idset.empty - in - (* and get the real args of the branch by unfolding the defined constant *) - let pre_args,pre_tac = - List.fold_right - (fun (id,b,t) (pre_args,pre_tac) -> - if Idset.mem id this_branche_ids - then - match b with - | None -> (id::pre_args,pre_tac) - | Some b -> - (pre_args, - tclTHEN (h_reduce (Rawterm.Unfold([Rawterm.all_occurrences_expr,EvalVarRef id])) allHyps) pre_tac - ) - - else (pre_args,pre_tac) - ) - (pf_hyps g) - ([],tclIDTAC) - in - (* - 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 are - [ fv (hid fv (refl_equal fv)) ]. - - If [hid] has another type the corresponding argument of the constructor is [hid] - *) - let constructor_args = - List.fold_right - (fun hid acc -> - let type_of_hid = pf_type_of g (mkVar hid) in - match kind_of_term type_of_hid with - | Prod(_,_,t') -> - begin - match kind_of_term t' with - | Prod(_,t'',t''') -> - begin - match kind_of_term t'',kind_of_term t''' with - | App(eq,args), App(graph',_) - when - (eq_constr eq eq_ind) && - array_exists (eq_constr graph') graphs_constr -> - ((mkApp(mkVar hid,[|args.(2);(mkApp(eq_construct,[|args.(0);args.(2)|]))|])) - ::args.(2)::acc) - | _ -> mkVar hid :: acc - end - | _ -> mkVar hid :: acc - end - | _ -> mkVar hid :: acc - ) pre_args [] - in - (* in fact we must also add the parameters to the constructor args *) - let constructor_args = - let params_id = fst (list_chop princ_infos.nparams args_names) in - (List.map mkVar params_id)@(List.rev constructor_args) - 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 - begin - (kn,!ind_number),constructor_num - end - 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 = applist((mkConstruct(constructor)),constructor_args) 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); - ( - tclTHENSEQ - [ - (* unfolding of all the defined variables introduced by this branch *) - observe_tac "unfolding" pre_tac; - (* $zeta$ normalizing of the conclusion *) - h_reduce - (Rawterm.Cbv - { Rawterm.all_flags with - Rawterm.rDelta = false ; - Rawterm.rConst = [] - } - ) - onConcl; - (* introducing the the result of the graph and the equality hypothesis *) - observe_tac "introducing" (tclMAP h_intro [res;hres]); - (* replacing [res] with its value *) - observe_tac "rewriting res value" (Equality.rewriteLR (mkVar hres)); - (* Conclusion *) - observe_tac "exact" (h_exact app_constructor) - ] - ) - g - in - (* end of branche proof *) - 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) (x,_,_) p -> - let id = Nameops.next_ident_away (Nameops.out_name x) avoid in - (dummy_loc,Rawterm.NamedHyp id,inj_open 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) (x,_,_) p -> - let id = Nameops.next_ident_away (Nameops.out_name x) avoid in - (dummy_loc,Rawterm.NamedHyp id,inj_open (nf_zeta p))::bindings,id::avoid) - ([],avoid) - princ_infos.predicates - (lemmas))) - in - Rawterm.ExplicitBindings (params_bindings@lemmas_bindings) - in - tclTHENSEQ - [ observe_tac "intro args_names" (tclMAP h_intro args_names); - observe_tac "principle" (assert_by - (Name principle_id) - princ_type - (h_exact f_principle)); - tclTHEN_i - (observe_tac "functional_induction" ( - fun g -> - observe - (pr_constr_with_binding (Printer.pr_lconstr_env (pf_env g)) (mkVar principle_id,bindings)); - functional_induction false (applist(funs_constr.(i),List.map mkVar args_names)) - (Some (mkVar principle_id,bindings)) - pat g - )) - (fun i g -> observe_tac ("proving branche "^string_of_int i) (prove_branche i) g ) - ] - g - -(* [generalize_dependent_of x hyp g] - generalize every hypothesis which depends of [x] but [hyp] -*) -let generalize_dependent_of x hyp g = - tclMAP - (function - | (id,None,t) when not (id = hyp) && - (Termops.occur_var (pf_env g) x t) -> tclTHEN (h_generalize [mkVar id]) (thin [id]) - | _ -> tclIDTAC - ) - (pf_hyps g) - g - - - - - - (* [intros_with_rewrite] do the intros in each branch and treat each new hypothesis - (unfolding, substituting, destructing cases \ldots) - *) -let rec intros_with_rewrite g = - observe_tac "intros_with_rewrite" intros_with_rewrite_aux g -and intros_with_rewrite_aux : tactic = - fun g -> - let eq_ind = Coqlib.build_coq_eq () in - match kind_of_term (pf_concl g) with - | Prod(_,t,t') -> - begin - match kind_of_term t with - | App(eq,args) when (eq_constr eq eq_ind) -> - if Reductionops.is_conv (pf_env g) (project g) args.(1) args.(2) - then - let id = pf_get_new_id (id_of_string "y") g in - tclTHENSEQ [ h_intro id; thin [id]; intros_with_rewrite ] g - - else if isVar args.(1) - then - let id = pf_get_new_id (id_of_string "y") g in - tclTHENSEQ [ h_intro id; - generalize_dependent_of (destVar args.(1)) id; - tclTRY (Equality.rewriteLR (mkVar id)); - intros_with_rewrite - ] - g - else - begin - let id = pf_get_new_id (id_of_string "y") g in - tclTHENSEQ[ - h_intro id; - tclTRY (Equality.rewriteLR (mkVar id)); - intros_with_rewrite - ] g - end - | Ind _ when eq_constr t (Coqlib.build_coq_False ()) -> - Tauto.tauto g - | Case(_,_,v,_) -> - tclTHENSEQ[ - h_case false (v,Rawterm.NoBindings); - intros_with_rewrite - ] g - | LetIn _ -> - tclTHENSEQ[ - h_reduce - (Rawterm.Cbv - {Rawterm.all_flags - with Rawterm.rDelta = false; - }) - onConcl - ; - intros_with_rewrite - ] g - | _ -> - let id = pf_get_new_id (id_of_string "y") g in - tclTHENSEQ [ h_intro id;intros_with_rewrite] g - end - | LetIn _ -> - tclTHENSEQ[ - h_reduce - (Rawterm.Cbv - {Rawterm.all_flags - with Rawterm.rDelta = false; - }) - onConcl - ; - intros_with_rewrite - ] g - | _ -> tclIDTAC g - -let rec reflexivity_with_destruct_cases g = - let destruct_case () = - try - match kind_of_term (snd (destApp (pf_concl g))).(2) with - | Case(_,_,v,_) -> - tclTHENSEQ[ - h_case false (v,Rawterm.NoBindings); - intros; - observe_tac "reflexivity_with_destruct_cases" reflexivity_with_destruct_cases - ] - | _ -> reflexivity - with _ -> reflexivity - in - let eq_ind = Coqlib.build_coq_eq () in - let discr_inject = - Tacticals.onAllClauses ( - fun sc g -> - match sc with - None -> tclIDTAC g - | Some ((_,id),_) -> - match kind_of_term (pf_type_of g (mkVar id)) with - | App(eq,[|_;t1;t2|]) when eq_constr eq eq_ind -> - if Equality.discriminable (pf_env g) (project g) t1 t2 - then Equality.discrHyp id g - else if Equality.injectable (pf_env g) (project g) t1 t2 - then tclTHENSEQ [Equality.injHyp id;thin [id];intros_with_rewrite] g - else tclIDTAC g - | _ -> tclIDTAC g - ) - in - (tclFIRST - [ reflexivity; - tclTHEN (tclPROGRESS discr_inject) (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 - *) - tclTHEN (tclPROGRESS discr_inject ) reflexivity_with_destruct_cases - ]) - g - - -(* [prove_fun_complete funs graphs schemes lemmas_types_infos i] - is the tactic used to prove completness 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 prove correct. - - [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 that is - 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] has - 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 prove_fun_complete funcs graphs schemes lemmas_types_infos i : tactic = - fun g -> - (* We compute the types of the different mutually recursive lemmas - in $\zeta$ normal form - *) - let lemmas = - Array.map - (fun (_,(ctxt,concl)) -> nf_zeta (Termops.it_mkLambda_or_LetIn ~init: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 = nf_zeta schemes.(i) in - let princ_type = pf_type_of g graph_principle in - let princ_infos = Tactics.compute_elim_sig 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 = nb_prod (pf_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 branche of the principle *) - let branches = List.rev princ_infos.branches in - let intro_pats = - List.map - (fun (_,_,br_type) -> - List.map - (fun id -> id) - (generate_fresh_id (id_of_string "y") ids (nb_prod br_type)) - ) - 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 : tactic = - let graph_def = graphs.(j) in - let infos = try find_Function_infos (destConst funcs.(j)) with Not_found -> error "No graph found" in - if infos.is_general || Rtree.is_infinite graph_def.mind_recargs - then - let eq_lemma = - try Option.get (infos).equation_lemma - with Option.IsNone -> anomaly "Cannot find equation lemma" - in - tclTHENSEQ[ - tclMAP h_intro ids; - Equality.rewriteLR (mkConst eq_lemma); - (* Don't forget to $\zeta$ normlize the term since the principles have been $\zeta$-normalized *) - h_reduce - (Rawterm.Cbv - {Rawterm.all_flags - with Rawterm.rDelta = false; - }) - onConcl - ; - h_generalize (List.map mkVar ids); - thin ids - ] - else unfold_in_concl [(all_occurrences,Names.EvalConstRef (destConst f))] - in - (* The proof of each branche itself *) - let ind_number = ref 0 in - let min_constr_number = ref 0 in - let prove_branche i g = - (* 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 - let this_branche_ids = List.nth intro_pats (pred i) in - tclTHENSEQ[ - (* 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" intros_with_rewrite; - (* The proof is (almost) complete *) - observe_tac "reflexivity" (reflexivity_with_destruct_cases) - ] - g - in - let params_names = fst (list_chop princ_infos.nparams args_names) in - let params = List.map mkVar params_names in - tclTHENSEQ - [ tclMAP h_intro (args_names@[res;hres]); - observe_tac "h_generalize" - (h_generalize [mkApp(applist(graph_principle,params),Array.map (fun c -> applist(c,params)) lemmas)]); - h_intro graph_principle_id; - observe_tac "" (tclTHEN_i - (observe_tac "elim" ((elim false (mkVar hres,Rawterm.NoBindings) (Some (mkVar graph_principle_id,Rawterm.NoBindings))))) - (fun i g -> observe_tac "prove_branche" (prove_branche i) g )) - ] - g - - - - -let do_save () = Command.save_named false - - -(* [derive_correctness make_scheme functional_induction funs graphs] create correctness and completeness - lemmas for each function in [funs] w.r.t. [graphs] - - [make_scheme] is Functional_principle_types.make_scheme (dependency pb) and - [functional_induction] is Indfun.functional_induction (same pb) -*) - -let derive_correctness make_scheme functional_induction (funs: constant list) (graphs:inductive list) = - let funs = Array.of_list funs and graphs = Array.of_list graphs in - let funs_constr = Array.map mkConst funs in - try - let graphs_constr = Array.map mkInd graphs in - let lemmas_types_infos = - Util.array_map2_i - (fun i f_constr graph -> - let const_of_f = destConst f_constr in - let (type_of_lemma_ctxt,type_of_lemma_concl) as type_info = - generate_type false const_of_f graph i - in - let type_of_lemma = Termops.it_mkProd_or_LetIn ~init:type_of_lemma_concl type_of_lemma_ctxt in - let type_of_lemma = nf_zeta type_of_lemma in - observe (str "type_of_lemma := " ++ Printer.pr_lconstr 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 function - if the block contains only one function we can safely reuse [f_rect] - *) - try - if Array.length funs_constr <> 1 then raise Not_found; - [| find_induction_principle funs_constr.(0) |] - with Not_found -> - Array.of_list - (List.map - (fun entry -> - (entry.Entries.const_entry_body, Option.get entry.Entries.const_entry_type ) - ) - (make_scheme (array_map_to_list (fun const -> const,Rawterm.RType None) funs)) - ) - in - let proving_tac = - prove_fun_correct functional_induction funs_constr graphs_constr schemes lemmas_types_infos - in - Array.iteri - (fun i f_as_constant -> - let f_id = id_of_label (con_label f_as_constant) in - Command.start_proof - (*i The next call to mk_correct_id is valid since we are constructing the lemma - Ensures by: obvious - i*) - (mk_correct_id f_id) - (Decl_kinds.Global,(Decl_kinds.Proof Decl_kinds.Theorem)) - (fst lemmas_types_infos.(i)) - (fun _ _ -> ()); - Pfedit.by (observe_tac ("prove correctness ("^(string_of_id f_id)^")") (proving_tac i)); - do_save (); - let finfo = find_Function_infos f_as_constant in - update_Function - {finfo with - correctness_lemma = Some (destConst (Tacinterp.constr_of_id (Global.env ())(mk_correct_id f_id))) - } - - ) - funs; - let lemmas_types_infos = - Util.array_map2_i - (fun i f_constr graph -> - let const_of_f = destConst f_constr in - let (type_of_lemma_ctxt,type_of_lemma_concl) as type_info = - generate_type true const_of_f graph i - in - let type_of_lemma = Termops.it_mkProd_or_LetIn ~init:type_of_lemma_concl type_of_lemma_ctxt in - let type_of_lemma = nf_zeta type_of_lemma in - observe (str "type_of_lemma := " ++ Printer.pr_lconstr type_of_lemma); - type_of_lemma,type_info - ) - funs_constr - graphs_constr - in - let kn,_ as graph_ind = destInd graphs_constr.(0) in - let mib,mip = Global.lookup_inductive graph_ind in - let schemes = - Array.of_list - (Indrec.build_mutual_indrec (Global.env ()) Evd.empty - (Array.to_list - (Array.mapi - (fun i mip -> (kn,i),mib,mip,true,InType) - mib.Declarations.mind_packets - ) - ) - ) - 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 = id_of_label (con_label f_as_constant) in - Command.start_proof - (*i The next call to mk_complete_id is valid since we are constructing the lemma - Ensures by: obvious - i*) - (mk_complete_id f_id) - (Decl_kinds.Global,(Decl_kinds.Proof Decl_kinds.Theorem)) - (fst lemmas_types_infos.(i)) - (fun _ _ -> ()); - Pfedit.by (observe_tac ("prove completeness ("^(string_of_id f_id)^")") (proving_tac i)); - do_save (); - let finfo = find_Function_infos f_as_constant in - update_Function - {finfo with - completeness_lemma = Some (destConst (Tacinterp.constr_of_id (Global.env ())(mk_complete_id f_id))) - } - ) - funs; - with e -> - (* In case of problem, we reset all the lemmas *) - (*i The next call to mk_correct_id is valid since we are erasing the lemmas - Ensures by: obvious - i*) - let first_lemma_id = - let f_id = id_of_label (con_label funs.(0)) in - - mk_correct_id f_id - in - ignore(try Vernacentries.vernac_reset_name (Util.dummy_loc,first_lemma_id) with _ -> ()); - raise e - - - - - -(***********************************************) - -(* [revert_graph kn post_tac hid] transforme an hypothesis [hid] having type Ind(kn,num) t1 ... tn res - when [kn] denotes a graph block into - f_num t1... tn = res (by applying [f_complete] to the first type) before apply post_tac on the result - - if the type of hypothesis has not this form or if we cannot find the completeness lemma then we do nothing -*) -let revert_graph kn post_tac hid g = - let typ = pf_type_of g (mkVar hid) in - match kind_of_term typ with - | App(i,args) when isInd i -> - let ((kn',num) as ind') = destInd i in - if kn = kn' - then (* We have generated a graph hypothesis so that we must change it if we can *) - let info = - try find_Function_of_graph ind' - with Not_found -> (* The graphs are mutually recursive but we cannot find one of them !*) - anomaly "Cannot retrieve infos about a mutual block" - in - (* if we can find a completeness lemma for this function - then we can come back to the functional form. If not, we do nothing - *) - match info.completeness_lemma with - | None -> tclIDTAC g - | Some f_complete -> - let f_args,res = array_chop (Array.length args - 1) args in - tclTHENSEQ - [ - h_generalize [applist(mkConst f_complete,(Array.to_list f_args)@[res.(0);mkVar hid])]; - thin [hid]; - h_intro hid; - post_tac hid - ] - g - - else tclIDTAC g - | _ -> tclIDTAC g - - -(* - [functional_inversion hid fconst f_correct ] is the functional version of [inversion] - - [hid] is the hypothesis to invert, [fconst] is the function to invert and [f_correct] - is the correctness lemma for [fconst]. - - The sketch is the follwing~: - \begin{enumerate} - \item Transforms the hypothesis [hid] such that its type is now $res\ =\ f\ t_1 \ldots t_n$ - (fails if it is not possible) - \item replace [hid] with $R\_f t_1 \ldots t_n res$ using [f_correct] - \item apply [inversion] on [hid] - \item finally in each branch, replace each hypothesis [R\_f ..] by [f ...] using [f_complete] (whenever - such a lemma exists) - \end{enumerate} -*) - -let functional_inversion kn hid fconst f_correct : tactic = - fun g -> - let old_ids = List.fold_right Idset.add (pf_ids_of_hyps g) Idset.empty in - let type_of_h = pf_type_of g (mkVar hid) in - match kind_of_term type_of_h with - | App(eq,args) when eq_constr eq (Coqlib.build_coq_eq ()) -> - let pre_tac,f_args,res = - match kind_of_term args.(1),kind_of_term args.(2) with - | App(f,f_args),_ when eq_constr f fconst -> - ((fun hid -> h_symmetry (onHyp hid)),f_args,args.(2)) - |_,App(f,f_args) when eq_constr f fconst -> - ((fun hid -> tclIDTAC),f_args,args.(1)) - | _ -> (fun hid -> tclFAIL 1 (mt ())),[||],args.(2) - in - tclTHENSEQ[ - pre_tac hid; - h_generalize [applist(f_correct,(Array.to_list f_args)@[res;mkVar hid])]; - thin [hid]; - h_intro hid; - Inv.inv FullInversion None (Rawterm.NamedHyp hid); - (fun g -> - let new_ids = List.filter (fun id -> not (Idset.mem id old_ids)) (pf_ids_of_hyps g) in - tclMAP (revert_graph kn pre_tac) (hid::new_ids) g - ); - ] g - | _ -> tclFAIL 1 (mt ()) g - - - -let invfun qhyp f = - let f = - match f with - | ConstRef f -> f - | _ -> raise (Util.UserError("",str "Not a function")) - in - try - let finfos = find_Function_infos f in - let f_correct = mkConst(Option.get finfos.correctness_lemma) - and kn = fst finfos.graph_ind - in - Tactics.try_intros_until (fun hid -> functional_inversion kn hid (mkConst f) f_correct) qhyp - with - | Not_found -> error "No graph found" - | Option.IsNone -> error "Cannot use equivalence with graph!" - - -let invfun qhyp f g = - match f with - | Some f -> invfun qhyp f g - | None -> - Tactics.try_intros_until - (fun hid g -> - let hyp_typ = pf_type_of g (mkVar hid) in - match kind_of_term hyp_typ with - | App(eq,args) when eq_constr eq (Coqlib.build_coq_eq ()) -> - begin - let f1,_ = decompose_app args.(1) in - try - if not (isConst f1) then failwith ""; - let finfos = find_Function_infos (destConst f1) in - let f_correct = mkConst(Option.get finfos.correctness_lemma) - and kn = fst finfos.graph_ind - in - functional_inversion kn hid f1 f_correct g - with | Failure "" | Option.IsNone | Not_found -> - try - let f2,_ = decompose_app args.(2) in - if not (isConst f2) then failwith ""; - let finfos = find_Function_infos (destConst f2) in - let f_correct = mkConst(Option.get finfos.correctness_lemma) - and kn = fst finfos.graph_ind - in - functional_inversion kn hid f2 f_correct g - with - | Failure "" -> - errorlabstrm "" (str "Hypothesis" ++ Ppconstr.pr_id hid ++ str " must contain at leat one Function") - | Option.IsNone -> - if do_observe () - then - error "Cannot use equivalence with graph for any side of the equality" - else errorlabstrm "" (str "Cannot find inversion information for hypothesis " ++ Ppconstr.pr_id hid) - | Not_found -> - if do_observe () - then - error "No graph found for any side of equality" - else errorlabstrm "" (str "Cannot find inversion information for hypothesis " ++ Ppconstr.pr_id hid) - end - | _ -> errorlabstrm "" (Ppconstr.pr_id hid ++ str " must be an equality ") - ) - qhyp - g diff --git a/contrib/funind/merge.ml b/contrib/funind/merge.ml deleted file mode 100644 index 9bbd165d..00000000 --- a/contrib/funind/merge.ml +++ /dev/null @@ -1,1034 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -(* Merging of induction principles. *) - -(*i $Id: i*) -open Libnames -open Tactics -open Indfun_common -open Util -open Topconstr -open Vernacexpr -open Pp -open Names -open Term -open Termops -open Declarations -open Environ -open Rawterm -open Rawtermops - -(** {1 Utilities} *) - -(** {2 Useful operations on constr and rawconstr} *) - -let rec popn i c = if i<=0 then c else pop (popn (i-1) c) - -(** Substitutions in constr *) -let compare_constr_nosub t1 t2 = - if compare_constr (fun _ _ -> false) t1 t2 - then true - else false - -let rec compare_constr' t1 t2 = - if compare_constr_nosub t1 t2 - then true - else (compare_constr (compare_constr') t1 t2) - -let rec substitterm prof t by_t in_u = - if (compare_constr' (lift prof t) in_u) - then (lift prof by_t) - else map_constr_with_binders succ - (fun i -> substitterm i t by_t) prof in_u - -let lift_ldecl n ldecl = List.map (fun (x,y) -> x,lift n y) ldecl - -let understand = Pretyping.Default.understand Evd.empty (Global.env()) - -(** Operations on names and identifiers *) -let id_of_name = function - Anonymous -> id_of_string "H" - | Name id -> id;; -let name_of_string str = Name (id_of_string str) -let string_of_name nme = string_of_id (id_of_name nme) - -(** [isVarf f x] returns [true] if term [x] is of the form [(Var f)]. *) -let isVarf f x = - match x with - | RVar (_,x) -> Pervasives.compare x f = 0 - | _ -> false - -(** [ident_global_exist id] returns true if identifier [id] is linked - in global environment. *) -let ident_global_exist id = - try - let ans = CRef (Libnames.Ident (dummy_loc,id)) in - let _ = ignore (Constrintern.intern_constr Evd.empty (Global.env()) ans) in - true - with _ -> false - -(** [next_ident_fresh id] returns a fresh identifier (ie not linked in - global env) with base [id]. *) -let next_ident_fresh (id:identifier) = - let res = ref id in - while ident_global_exist !res do res := Nameops.lift_ident !res done; - !res - - -(** {2 Debugging} *) -(* comment this line to see debug msgs *) -let msg x = () ;; let pr_lconstr c = str "" -(* uncomment this to see debugging *) -let prconstr c = msg (str" " ++ Printer.pr_lconstr c) -let prconstrnl c = msg (str" " ++ Printer.pr_lconstr c ++ str"\n") -let prlistconstr lc = List.iter prconstr lc -let prstr s = msg(str s) -let prNamedConstr s c = - begin - msg(str ""); - msg(str(s^" {§ ") ++ Printer.pr_lconstr c ++ str " §} "); - msg(str ""); - end -let prNamedRConstr s c = - begin - msg(str ""); - msg(str(s^" {§ ") ++ Printer.pr_rawconstr c ++ str " §} "); - msg(str ""); - end -let prNamedLConstr_aux lc = List.iter (prNamedConstr "\n") lc -let prNamedLConstr s lc = - begin - prstr "[§§§ "; - prstr s; - prNamedLConstr_aux lc; - prstr " §§§]\n"; - end -let prNamedLDecl s lc = - begin - prstr s; prstr "\n"; - List.iter (fun (nm,_,tp) -> prNamedConstr (string_of_name nm) tp) lc; - prstr "\n"; - end -let prNamedRLDecl s lc = - begin - prstr s; prstr "\n"; prstr "{§§ "; - List.iter - (fun x -> - match x with - | (nm,None,Some tp) -> prNamedRConstr (string_of_name nm) tp - | (nm,Some bdy,None) -> prNamedRConstr ("(letin) "^string_of_name nm) bdy - | _ -> assert false - ) lc; - prstr " §§}\n"; - prstr "\n"; - end - -let showind (id:identifier) = - let cstrid = Tacinterp.constr_of_id (Global.env()) id in - let ind1,cstrlist = Inductiveops.find_inductive (Global.env()) Evd.empty cstrid in - let mib1,ib1 = Inductive.lookup_mind_specif (Global.env()) ind1 in - List.iter (fun (nm, optcstr, tp) -> - print_string (string_of_name nm^":"); - prconstr tp; print_string "\n") - ib1.mind_arity_ctxt; - (match ib1.mind_arity with - | Monomorphic x -> - Printf.printf "arity :"; prconstr x.mind_user_arity - | Polymorphic x -> - Printf.printf "arity : universe?"); - Array.iteri - (fun i x -> Printf.printf"type constr %d :" i ; prconstr x) - ib1.mind_user_lc - -(** {2 Misc} *) - -exception Found of int - -(* Array scanning *) -let array_find (arr: 'a array) (pred: int -> 'a -> bool): int option = - try - for i=0 to Array.length arr - 1 do if pred i (arr.(i)) then raise (Found i) done; - None - with Found i -> Some i - -let array_prfx (arr: 'a array) (pred: int -> 'a -> bool): int = - try - for i=0 to Array.length arr - 1 do if pred i (arr.(i)) then raise (Found i) done; - Array.length arr (* all elt are positive *) - with Found i -> i - -let array_fold_lefti (f: int -> 'a -> 'b -> 'a) (acc:'a) (arr:'b array): 'a = - let i = ref 0 in - Array.fold_left - (fun acc x -> - let res = f !i acc x in i := !i + 1; res) - acc arr - -(* Like list_chop but except that [i] is the size of the suffix of [l]. *) -let list_chop_end i l = - let size_prefix = List.length l -i in - if size_prefix < 0 then failwith "list_chop_end" - else list_chop size_prefix l - -let list_fold_lefti (f: int -> 'a -> 'b -> 'a) (acc:'a) (arr:'b list): 'a = - let i = ref 0 in - List.fold_left - (fun acc x -> - let res = f !i acc x in i := !i + 1; res) - acc arr - -let list_filteri (f: int -> 'a -> bool) (l:'a list):'a list = - let i = ref 0 in - List.filter (fun x -> let res = f !i x in i := !i + 1; res) l - - -(** Iteration module *) -module For = -struct - let rec map i j (f: int -> 'a) = if i>j then [] else f i :: (map (i+1) j f) - let rec foldup i j (f: 'a -> int -> 'a) acc = - if i>j then acc else let newacc = f acc i in foldup (i+1) j f newacc - let rec folddown i j (f: 'a -> int -> 'a) acc = - if i>j then acc else let newacc = f acc j in folddown i (j-1) f newacc - let fold i j = if i<j then foldup i j else folddown i j -end - - -(** {1 Parameters shifting and linking information} *) - -(** This type is used to deal with debruijn linked indices. When a - variable is linked to a previous one, we will ignore it and refer - to previous one. *) -type linked_var = - | Linked of int - | Unlinked - | Funres - -(** When merging two graphs, parameters may become regular arguments, - and thus be shifted. This type describes the result of computing - the changes. *) -type 'a shifted_params = - { - nprm1:'a; - nprm2:'a; - prm2_unlinked:'a list; (* ranks of unlinked params in nprms2 *) - nuprm1:'a; - nuprm2:'a; - nargs1:'a; - nargs2:'a; - } - - -let prlinked x = - match x with - | Linked i -> Printf.sprintf "Linked %d" i - | Unlinked -> Printf.sprintf "Unlinked" - | Funres -> Printf.sprintf "Funres" - -let linkmonad f lnkvar = - match lnkvar with - | Linked i -> Linked (f i) - | Unlinked -> Unlinked - | Funres -> Funres - -let linklift lnkvar i = linkmonad (fun x -> x+i) lnkvar - -(* This map is used to deal with debruijn linked indices. *) -module Link = Map.Make (struct type t = int let compare = Pervasives.compare end) - -let pr_links l = - Printf.printf "links:\n"; - Link.iter (fun k e -> Printf.printf "%d : %s\n" k (prlinked e)) l; - Printf.printf "_____________\n" - -type 'a merged_arg = - | Prm_stable of 'a - | Prm_linked of 'a - | Prm_arg of 'a - | Arg_stable of 'a - | Arg_linked of 'a - | Arg_funres - -(** Information about graph merging of two inductives. - All rel_decl list are IN REVERSE ORDER (ie well suited for compose) *) - -type merge_infos = - { - ident:identifier; (** new inductive name *) - mib1: mutual_inductive_body; - oib1: one_inductive_body; - mib2: mutual_inductive_body; - oib2: one_inductive_body; - - (** Array of links of the first inductive (should be all stable) *) - lnk1: int merged_arg array; - - (** Array of links of the second inductive (point to the first ind param/args) *) - lnk2: int merged_arg array; - - (** rec params which remain rec param (ie not linked) *) - recprms1: rel_declaration list; - recprms2: rel_declaration list; - nrecprms1: int; - nrecprms2: int; - - (** rec parms which became non parm (either linked to something - or because after a rec parm that became non parm) *) - otherprms1: rel_declaration list; - otherprms2: rel_declaration list; - notherprms1:int; - notherprms2:int; - - (** args which remain args in merge *) - args1:rel_declaration list; - args2:rel_declaration list; - nargs1:int; - nargs2:int; - - (** functional result args *) - funresprms1: rel_declaration list; - funresprms2: rel_declaration list; - nfunresprms1:int; - nfunresprms2:int; - } - - -let pr_merginfo x = - let i,s= - match x with - | Prm_linked i -> Some i,"Prm_linked" - | Arg_linked i -> Some i,"Arg_linked" - | Prm_stable i -> Some i,"Prm_stable" - | Prm_arg i -> Some i,"Prm_arg" - | Arg_stable i -> Some i,"Arg_stable" - | Arg_funres -> None , "Arg_funres" in - match i with - | Some i -> Printf.sprintf "%s(%d)" s i - | None -> Printf.sprintf "%s" s - -let isPrm_stable x = match x with Prm_stable _ -> true | _ -> false - -(* ?? prm_linked?? *) -let isArg_stable x = match x with Arg_stable _ | Prm_arg _ -> true | _ -> false - -let is_stable x = - match x with Arg_stable _ | Prm_stable _ | Prm_arg _ -> true | _ -> false - -let isArg_funres x = match x with Arg_funres -> true | _ -> false - -let filter_shift_stable (lnk:int merged_arg array) (l:'a list): 'a list = - let prms = list_filteri (fun i _ -> isPrm_stable lnk.(i)) l in - let args = list_filteri (fun i _ -> isArg_stable lnk.(i)) l in - let fres = list_filteri (fun i _ -> isArg_funres lnk.(i)) l in - prms@args@fres - -(** Reverse the link map, keeping only linked vars, elements are list - of int as several vars may be linked to the same var. *) -let revlinked lnk = - For.fold 0 (Array.length lnk - 1) - (fun acc k -> - match lnk.(k) with - | Unlinked | Funres -> acc - | Linked i -> - let old = try Link.find i acc with Not_found -> [] in - Link.add i (k::old) acc) - Link.empty - -let array_switch arr i j = - let aux = arr.(j) in arr.(j) <- arr.(i); arr.(i) <- aux - -let filter_shift_stable_right (lnk:int merged_arg array) (l:'a list): 'a list = - let larr = Array.of_list l in - let _ = - Array.iteri - (fun j x -> - match x with - | Prm_linked i -> array_switch larr i j - | Arg_linked i -> array_switch larr i j - | Prm_stable i -> () - | Prm_arg i -> () - | Arg_stable i -> () - | Arg_funres -> () - ) lnk in - filter_shift_stable lnk (Array.to_list larr) - - - - -(** {1 Utilities for merging} *) - -let ind1name = id_of_string "__ind1" -let ind2name = id_of_string "__ind2" - -(** Performs verifications on two graphs before merging: they must not - be co-inductive, and for the moment they must not be mutual - either. *) -let verify_inds mib1 mib2 = - if not mib1.mind_finite then error "First argument is coinductive"; - if not mib2.mind_finite then error "Second argument is coinductive"; - if mib1.mind_ntypes <> 1 then error "First argument is mutual"; - if mib2.mind_ntypes <> 1 then error "Second argument is mutual"; - () - -(* -(** [build_raw_params prms_decl avoid] returns a list of variables - attributed to the list of decl [prms_decl], avoiding names in - [avoid]. *) -let build_raw_params prms_decl avoid = - let dummy_constr = compose_prod (List.map (fun (x,_,z) -> x,z) prms_decl) (mkRel 1) in - let _ = prNamedConstr "DUMMY" dummy_constr in - let dummy_rawconstr = Detyping.detype false avoid [] dummy_constr in - let _ = prNamedRConstr "RAWDUMMY" dummy_rawconstr in - let res,_ = raw_decompose_prod dummy_rawconstr in - let comblist = List.combine prms_decl res in - comblist, res , (avoid @ (Idset.elements (ids_of_rawterm dummy_rawconstr))) -*) - -let ids_of_rawlist avoid rawl = - List.fold_left Idset.union avoid (List.map ids_of_rawterm rawl) - - - -(** {1 Merging function graphs} *) - -(** [shift_linked_params mib1 mib2 lnk] Computes which parameters (rec - uniform and ordinary ones) of mutual inductives [mib1] and [mib2] - remain uniform when linked by [lnk]. All parameters are - considered, ie we take parameters of the first inductive body of - [mib1] and [mib2]. - - Explanation: The two inductives have parameters, some of the first - are recursively uniform, some of the last are functional result of - the functional graph. - - (I x1 x2 ... xk ... xk' ... xn) - (J y1 y2 ... xl ... yl' ... ym) - - Problem is, if some rec unif params are linked to non rec unif - ones, they become non rec (and the following too). And functinal - argument have to be shifted at the end *) -let shift_linked_params mib1 mib2 (lnk1:linked_var array) (lnk2:linked_var array) id = - let _ = prstr "\nYOUHOU shift\n" in - let linked_targets = revlinked lnk2 in - let is_param_of_mib1 x = x < mib1.mind_nparams_rec in - let is_param_of_mib2 x = x < mib2.mind_nparams_rec in - let is_targetted_by_non_recparam_lnk1 i = - try - let targets = Link.find i linked_targets in - List.exists (fun x -> not (is_param_of_mib2 x)) targets - with Not_found -> false in - let mlnk1 = - Array.mapi - (fun i lkv -> - let isprm = is_param_of_mib1 i in - let prmlost = is_targetted_by_non_recparam_lnk1 i in - match isprm , prmlost, lnk1.(i) with - | true , true , _ -> Prm_arg i (* recparam becoming ordinary *) - | true , false , _-> Prm_stable i (* recparam remains recparam*) - | false , false , Funres -> Arg_funres - | _ , _ , Funres -> assert false (* fun res cannot be a rec param or lost *) - | false , _ , _ -> Arg_stable i) (* Args of lnk1 are not linked *) - lnk1 in - let mlnk2 = - Array.mapi - (fun i lkv -> - (* Is this correct if some param of ind2 is lost? *) - let isprm = is_param_of_mib2 i in - match isprm , lnk2.(i) with - | true , Linked j when not (is_param_of_mib1 j) -> - Prm_arg j (* recparam becoming ordinary *) - | true , Linked j -> Prm_linked j (*recparam linked to recparam*) - | true , Unlinked -> Prm_stable i (* recparam remains recparam*) - | false , Linked j -> Arg_linked j (* Args of lnk2 lost *) - | false , Unlinked -> Arg_stable i (* Args of lnk2 remains *) - | false , Funres -> Arg_funres - | true , Funres -> assert false (* fun res cannot be a rec param *) - ) - lnk2 in - let oib1 = mib1.mind_packets.(0) in - let oib2 = mib2.mind_packets.(0) in - (* count params remaining params *) - let n_params1 = array_prfx mlnk1 (fun i x -> not (isPrm_stable x)) in - let n_params2 = array_prfx mlnk2 (fun i x -> not (isPrm_stable x)) in - let bldprms arity_ctxt mlnk = - list_fold_lefti - (fun i (acc1,acc2,acc3,acc4) x -> - prstr (pr_merginfo mlnk.(i));prstr "\n"; - match mlnk.(i) with - | Prm_stable _ -> x::acc1 , acc2 , acc3, acc4 - | Prm_arg _ -> acc1 , x::acc2 , acc3, acc4 - | Arg_stable _ -> acc1 , acc2 , x::acc3, acc4 - | Arg_funres -> acc1 , acc2 , acc3, x::acc4 - | _ -> acc1 , acc2 , acc3, acc4) - ([],[],[],[]) arity_ctxt in -(* let arity_ctxt2 = - build_raw_params oib2.mind_arity_ctxt - (Idset.elements (ids_of_rawterm oib1.mind_arity_ctxt)) in*) - let recprms1,otherprms1,args1,funresprms1 = bldprms (List.rev oib1.mind_arity_ctxt) mlnk1 in - let _ = prstr "\n\n\n" in - let recprms2,otherprms2,args2,funresprms2 = bldprms (List.rev oib2.mind_arity_ctxt) mlnk2 in - let _ = prstr "\notherprms1:\n" in - let _ = - List.iter (fun (x,_,y) -> prstr (string_of_name x^" : ");prconstr y;prstr "\n") - otherprms1 in - let _ = prstr "\notherprms2:\n" in - let _ = - List.iter (fun (x,_,y) -> prstr (string_of_name x^" : ");prconstr y;prstr "\n") - otherprms2 in - { - ident=id; - mib1=mib1; - oib1 = oib1; - mib2=mib2; - oib2 = oib2; - lnk1 = mlnk1; - lnk2 = mlnk2; - nrecprms1 = n_params1; - recprms1 = recprms1; - otherprms1 = otherprms1; - args1 = args1; - funresprms1 = funresprms1; - notherprms1 = Array.length mlnk1 - n_params1; - nfunresprms1 = List.length funresprms1; - nargs1 = List.length args1; - nrecprms2 = n_params2; - recprms2 = recprms2; - otherprms2 = otherprms2; - args2 = args2; - funresprms2 = funresprms2; - notherprms2 = Array.length mlnk2 - n_params2; - nargs2 = List.length args2; - nfunresprms2 = List.length funresprms2; - } - - - - -(** {1 Merging functions} *) - -exception NoMerge - -let rec merge_app c1 c2 id1 id2 shift filter_shift_stable = - let lnk = Array.append shift.lnk1 shift.lnk2 in - match c1 , c2 with - | RApp(_,f1, arr1), RApp(_,f2,arr2) when isVarf id1 f1 && isVarf id2 f2 -> - let _ = prstr "\nICI1!\n";Pp.flush_all() in - let args = filter_shift_stable lnk (arr1 @ arr2) in - RApp (dummy_loc,RVar (dummy_loc,shift.ident) , args) - | RApp(_,f1, arr1), RApp(_,f2,arr2) -> raise NoMerge - | RLetIn(_,nme,bdy,trm) , _ -> - let _ = prstr "\nICI2!\n";Pp.flush_all() in - let newtrm = merge_app trm c2 id1 id2 shift filter_shift_stable in - RLetIn(dummy_loc,nme,bdy,newtrm) - | _, RLetIn(_,nme,bdy,trm) -> - let _ = prstr "\nICI3!\n";Pp.flush_all() in - let newtrm = merge_app c1 trm id1 id2 shift filter_shift_stable in - RLetIn(dummy_loc,nme,bdy,newtrm) - | _ -> let _ = prstr "\nICI4!\n";Pp.flush_all() in - raise NoMerge - -let rec merge_app_unsafe c1 c2 shift filter_shift_stable = - let lnk = Array.append shift.lnk1 shift.lnk2 in - match c1 , c2 with - | RApp(_,f1, arr1), RApp(_,f2,arr2) -> - let args = filter_shift_stable lnk (arr1 @ arr2) in - RApp (dummy_loc,RVar(dummy_loc,shift.ident) , args) - (* FIXME: what if the function appears in the body of the let? *) - | RLetIn(_,nme,bdy,trm) , _ -> - let _ = prstr "\nICI2 '!\n";Pp.flush_all() in - let newtrm = merge_app_unsafe trm c2 shift filter_shift_stable in - RLetIn(dummy_loc,nme,bdy,newtrm) - | _, RLetIn(_,nme,bdy,trm) -> - let _ = prstr "\nICI3 '!\n";Pp.flush_all() in - let newtrm = merge_app_unsafe c1 trm shift filter_shift_stable in - RLetIn(dummy_loc,nme,bdy,newtrm) - | _ -> let _ = prstr "\nICI4 '!\n";Pp.flush_all() in raise NoMerge - - - -(* Heuristic when merging two lists of hypothesis: merge every rec - calls of branch 1 with all rec calls of branch 2. *) -(* TODO: reecrire cette heuristique (jusqu'a merge_types) *) -let rec merge_rec_hyps shift accrec - (ltyp:(Names.name * rawconstr option * rawconstr option) list) - filter_shift_stable : (Names.name * rawconstr option * rawconstr option) list = - let mergeonehyp t reldecl = - match reldecl with - | (nme,x,Some (RApp(_,i,args) as ind)) - -> nme,x, Some (merge_app_unsafe ind t shift filter_shift_stable) - | (nme,Some _,None) -> error "letins with recursive calls not treated yet" - | (nme,None,Some _) -> assert false - | (nme,None,None) | (nme,Some _,Some _) -> assert false in - match ltyp with - | [] -> [] - | (nme,None,Some (RApp(_,f, largs) as t)) :: lt when isVarf ind2name f -> - let rechyps = List.map (mergeonehyp t) accrec in - rechyps @ merge_rec_hyps shift accrec lt filter_shift_stable - | e::lt -> e :: merge_rec_hyps shift accrec lt filter_shift_stable - - -let rec build_suppl_reccall (accrec:(name * rawconstr) list) concl2 shift = - List.map (fun (nm,tp) -> (nm,merge_app_unsafe tp concl2 shift)) accrec - - -let find_app (nme:identifier) ltyp = - try - ignore - (List.map - (fun x -> - match x with - | _,None,Some (RApp(_,f,_)) when isVarf nme f -> raise (Found 0) - | _ -> ()) - ltyp); - false - with Found _ -> true - -let prnt_prod_or_letin nm letbdy typ = - match letbdy , typ with - | Some lbdy , None -> prNamedRConstr ("(letin) " ^ string_of_name nm) lbdy - | None , Some tp -> prNamedRConstr (string_of_name nm) tp - | _ , _ -> assert false - - -let rec merge_types shift accrec1 - (ltyp1:(name * rawconstr option * rawconstr option) list) - (concl1:rawconstr) (ltyp2:(name * rawconstr option * rawconstr option) list) concl2 - : (name * rawconstr option * rawconstr option) list * rawconstr = - let _ = prstr "MERGE_TYPES\n" in - let _ = prstr "ltyp 1 : " in - let _ = List.iter (fun (nm,lbdy,tp) -> prnt_prod_or_letin nm lbdy tp) ltyp1 in - let _ = prstr "\nltyp 2 : " in - let _ = List.iter (fun (nm,lbdy,tp) -> prnt_prod_or_letin nm lbdy tp) ltyp2 in - let _ = prstr "\n" in - let res = - match ltyp1 with - | [] -> - let isrec1 = (accrec1<>[]) in - let isrec2 = find_app ind2name ltyp2 in - let rechyps = - if isrec1 && isrec2 - then (* merge_rec_hyps shift accrec1 ltyp2 filter_shift_stable *) - merge_rec_hyps shift [name_of_string "concl1",None,Some concl1] ltyp2 - filter_shift_stable_right - @ merge_rec_hyps shift accrec1 [name_of_string "concl2",None, Some concl2] - filter_shift_stable - else if isrec1 - (* if rec calls in accrec1 and not in ltyp2, add one to ltyp2 *) - then - merge_rec_hyps shift accrec1 - (ltyp2@[name_of_string "concl2",None,Some concl2]) filter_shift_stable - else if isrec2 - then merge_rec_hyps shift [name_of_string "concl1",None,Some concl1] ltyp2 - filter_shift_stable_right - else ltyp2 in - let _ = prstr"\nrechyps : " in - let _ = List.iter(fun (nm,lbdy,tp)-> prnt_prod_or_letin nm lbdy tp) rechyps in - let _ = prstr "MERGE CONCL : " in - let _ = prNamedRConstr "concl1" concl1 in - let _ = prstr " with " in - let _ = prNamedRConstr "concl2" concl2 in - let _ = prstr "\n" in - let concl = - merge_app concl1 concl2 ind1name ind2name shift filter_shift_stable in - let _ = prstr "FIN " in - let _ = prNamedRConstr "concl" concl in - let _ = prstr "\n" in - - rechyps , concl - | (nme,None, Some t1)as e ::lt1 -> - (match t1 with - | RApp(_,f,carr) when isVarf ind1name f -> - merge_types shift (e::accrec1) lt1 concl1 ltyp2 concl2 - | _ -> - let recres, recconcl2 = - merge_types shift accrec1 lt1 concl1 ltyp2 concl2 in - ((nme,None,Some t1) :: recres) , recconcl2) - | (nme,Some bd, None) ::lt1 -> - (* FIXME: what if ind1name appears in bd? *) - let recres, recconcl2 = - merge_types shift accrec1 lt1 concl1 ltyp2 concl2 in - ((nme,Some bd,None) :: recres) , recconcl2 - | (_,None,None)::_ | (_,Some _,Some _)::_ -> assert false - in - res - - -(** [build_link_map_aux allargs1 allargs2 shift] returns the mapping of - linked args [allargs2] to target args of [allargs1] as specified - in [shift]. [allargs1] and [allargs2] are in reverse order. Also - returns the list of unlinked vars of [allargs2]. *) -let build_link_map_aux (allargs1:identifier array) (allargs2:identifier array) - (lnk:int merged_arg array) = - array_fold_lefti - (fun i acc e -> - if i = Array.length lnk - 1 then acc (* functional arg, not in allargs *) - else - match e with - | Prm_linked j | Arg_linked j -> Idmap.add allargs2.(i) allargs1.(j) acc - | _ -> acc) - Idmap.empty lnk - -let build_link_map allargs1 allargs2 lnk = - let allargs1 = - Array.of_list (List.rev (List.map (fun (x,_,_) -> id_of_name x) allargs1)) in - let allargs2 = - Array.of_list (List.rev (List.map (fun (x,_,_) -> id_of_name x) allargs2)) in - build_link_map_aux allargs1 allargs2 lnk - - -(** [merge_one_constructor lnk shift typcstr1 typcstr2] merges the two - constructor rawtypes [typcstr1] and [typcstr2]. [typcstr1] and - [typcstr2] contain all parameters (including rec. unif. ones) of - their inductive. - - if [typcstr1] and [typcstr2] are of the form: - - forall recparams1, forall ordparams1, H1a -> H2a... (I1 x1 y1 ... z1) - forall recparams2, forall ordparams2, H2b -> H2b... (I2 x2 y2 ... z2) - - we build: - - forall recparams1 (recparams2 without linked params), - forall ordparams1 (ordparams2 without linked params), - H1a' -> H2a' -> ... -> H2a' -> H2b'(shifted) -> ... - -> (newI x1 ... z1 x2 y2 ...z2 without linked params) - - where Hix' have been adapted, ie: - - linked vars have been changed, - - rec calls to I1 and I2 have been replaced by rec calls to - newI. More precisely calls to I1 and I2 have been merge by an - experimental heuristic (in particular if n o rec calls for I1 - or I2 is found, we use the conclusion as a rec call). See - [merge_types] above. - - Precond: vars sets of [typcstr1] and [typcstr2] must be disjoint. - - TODO: return nothing if equalities (after linking) are contradictory. *) -let merge_one_constructor (shift:merge_infos) (typcstr1:rawconstr) - (typcstr2:rawconstr) : rawconstr = - (* FIXME: les noms des parametres corerspondent en principe au - parametres du niveau mib, mais il faudrait s'en assurer *) - (* shift.nfunresprmsx last args are functional result *) - let nargs1 = - shift.mib1.mind_nparams + shift.oib1.mind_nrealargs - shift.nfunresprms1 in - let nargs2 = - shift.mib2.mind_nparams + shift.oib2.mind_nrealargs - shift.nfunresprms2 in - let allargs1,rest1 = raw_decompose_prod_or_letin_n nargs1 typcstr1 in - let allargs2,rest2 = raw_decompose_prod_or_letin_n nargs2 typcstr2 in - (* Build map of linked args of [typcstr2], and apply it to [typcstr2]. *) - let linked_map = build_link_map allargs1 allargs2 shift.lnk2 in - let rest2 = change_vars linked_map rest2 in - let hyps1,concl1 = raw_decompose_prod_or_letin rest1 in - let hyps2,concl2' = raw_decompose_prod_or_letin rest2 in - let ltyp,concl2 = - merge_types shift [] (List.rev hyps1) concl1 (List.rev hyps2) concl2' in - let _ = prNamedRLDecl "ltyp result:" ltyp in - let typ = raw_compose_prod_or_letin concl2 (List.rev ltyp) in - let revargs1 = - list_filteri (fun i _ -> isArg_stable shift.lnk1.(i)) (List.rev allargs1) in - let _ = prNamedRLDecl "ltyp allargs1" allargs1 in - let _ = prNamedRLDecl "ltyp revargs1" revargs1 in - let revargs2 = - list_filteri (fun i _ -> isArg_stable shift.lnk2.(i)) (List.rev allargs2) in - let _ = prNamedRLDecl "ltyp allargs2" allargs2 in - let _ = prNamedRLDecl "ltyp revargs2" revargs2 in - let typwithprms = - raw_compose_prod_or_letin typ (List.rev revargs2 @ List.rev revargs1) in - typwithprms - - -(** constructor numbering *) -let fresh_cstror_suffix , cstror_suffix_init = - let cstror_num = ref 0 in - (fun () -> - let res = string_of_int !cstror_num in - cstror_num := !cstror_num + 1; - res) , - (fun () -> cstror_num := 0) - -(** [merge_constructor_id id1 id2 shift] returns the identifier of the - new constructor from the id of the two merged constructor and - the merging info. *) -let merge_constructor_id id1 id2 shift:identifier = - let id = string_of_id shift.ident ^ "_" ^ fresh_cstror_suffix () in - next_ident_fresh (id_of_string id) - - - -(** [merge_constructors lnk shift avoid] merges the two list of - constructor [(name*type)]. These are translated to rawterms - first, each of them having distinct var names. *) -let rec merge_constructors (shift:merge_infos) (avoid:Idset.t) - (typcstr1:(identifier * rawconstr) list) - (typcstr2:(identifier * rawconstr) list) : (identifier * rawconstr) list = - List.flatten - (List.map - (fun (id1,rawtyp1) -> - List.map - (fun (id2,rawtyp2) -> - let typ = merge_one_constructor shift rawtyp1 rawtyp2 in - let newcstror_id = merge_constructor_id id1 id2 shift in - let _ = prstr "\n**************\n" in - newcstror_id , typ) - typcstr2) - typcstr1) - -(** [merge_inductive_body lnk shift avoid oib1 oib2] merges two - inductive bodies [oib1] and [oib2], linking with [lnk], params - info in [shift], avoiding identifiers in [avoid]. *) -let rec merge_inductive_body (shift:merge_infos) avoid (oib1:one_inductive_body) - (oib2:one_inductive_body) = - (* building rawconstr type of constructors *) - let mkrawcor nme avoid typ = - (* first replace rel 1 by a varname *) - let substindtyp = substitterm 0 (mkRel 1) (mkVar nme) typ in - Detyping.detype false (Idset.elements avoid) [] substindtyp in - let lcstr1: rawconstr list = - Array.to_list (Array.map (mkrawcor ind1name avoid) oib1.mind_user_lc) in - (* add to avoid all indentifiers of lcstr1 *) - let avoid2 = Idset.union avoid (ids_of_rawlist avoid lcstr1) in - let lcstr2 = - Array.to_list (Array.map (mkrawcor ind2name avoid2) oib2.mind_user_lc) in - let avoid3 = Idset.union avoid (ids_of_rawlist avoid lcstr2) in - - let params1 = - try fst (raw_decompose_prod_n shift.nrecprms1 (List.hd lcstr1)) - with _ -> [] in - let params2 = - try fst (raw_decompose_prod_n shift.nrecprms2 (List.hd lcstr2)) - with _ -> [] in - - let lcstr1 = List.combine (Array.to_list oib1.mind_consnames) lcstr1 in - let lcstr2 = List.combine (Array.to_list oib2.mind_consnames) lcstr2 in - - cstror_suffix_init(); - params1,params2,merge_constructors shift avoid3 lcstr1 lcstr2 - - -(** [merge_mutual_inductive_body lnk mib1 mib2 shift] merge mutual - inductive bodies [mib1] and [mib2] linking vars with - [lnk]. [shift] information on parameters of the new inductive. - For the moment, inductives are supposed to be non mutual. -*) -let rec merge_mutual_inductive_body - (mib1:mutual_inductive_body) (mib2:mutual_inductive_body) (shift:merge_infos) = - (* Mutual not treated, we take first ind body of each. *) - merge_inductive_body shift Idset.empty mib1.mind_packets.(0) mib2.mind_packets.(0) - - -let rawterm_to_constr_expr x = (* build a constr_expr from a rawconstr *) - Flags.with_option Flags.raw_print (Constrextern.extern_rawtype Idset.empty) x - -let merge_rec_params_and_arity prms1 prms2 shift (concl:constr) = - let params = prms2 @ prms1 in - let resparams = - List.fold_left - (fun acc (nme,tp) -> - let _ = prstr "param :" in - let _ = prNamedRConstr (string_of_name nme) tp in - let _ = prstr " ; " in - let typ = rawterm_to_constr_expr tp in - LocalRawAssum ([(dummy_loc,nme)], Topconstr.default_binder_kind, typ) :: acc) - [] params in - let concl = Constrextern.extern_constr false (Global.env()) concl in - let arity,_ = - List.fold_left - (fun (acc,env) (nm,_,c) -> - let typ = Constrextern.extern_constr false env c in - let newenv = Environ.push_rel (nm,None,c) env in - CProdN (dummy_loc, [[(dummy_loc,nm)],Topconstr.default_binder_kind,typ] , acc) , newenv) - (concl,Global.env()) - (shift.funresprms2 @ shift.funresprms1 - @ shift.args2 @ shift.args1 @ shift.otherprms2 @ shift.otherprms1) in - resparams,arity - - - -(** [rawterm_list_to_inductive_expr ident rawlist] returns the - induct_expr corresponding to the the list of constructor types - [rawlist], named ident. - FIXME: params et cstr_expr (arity) *) -let rawterm_list_to_inductive_expr prms1 prms2 mib1 mib2 shift - (rawlist:(identifier * rawconstr) list) = - let lident = dummy_loc, shift.ident in - let bindlist , cstr_expr = (* params , arities *) - merge_rec_params_and_arity prms1 prms2 shift mkSet in - let lcstor_expr : (bool * (lident * constr_expr)) list = - List.map (* zeta_normalize t ? *) - (fun (id,t) -> false, ((dummy_loc,id),rawterm_to_constr_expr t)) - rawlist in - lident , bindlist , Some cstr_expr , lcstor_expr - - - -let mkProd_reldecl (rdecl:rel_declaration) (t2:rawconstr) = - match rdecl with - | (nme,None,t) -> - let traw = Detyping.detype false [] [] t in - RProd (dummy_loc,nme,Explicit,traw,t2) - | (_,Some _,_) -> assert false - - - - -let mkProd_reldecl (rdecl:rel_declaration) (t2:rawconstr) = - match rdecl with - | (nme,None,t) -> - let traw = Detyping.detype false [] [] t in - RProd (dummy_loc,nme,Explicit,traw,t2) - | (_,Some _,_) -> assert false - - -(** [merge_inductive ind1 ind2 lnk] merges two graphs, linking - variables specified in [lnk]. Graphs are not supposed to be mutual - inductives for the moment. *) -let merge_inductive (ind1: inductive) (ind2: inductive) - (lnk1: linked_var array) (lnk2: linked_var array) id = - let env = Global.env() in - let mib1,_ = Inductive.lookup_mind_specif env ind1 in - let mib2,_ = Inductive.lookup_mind_specif env ind2 in - let _ = verify_inds mib1 mib2 in (* raises an exception if something wrong *) - (* compute params that become ordinary args (because linked to ord. args) *) - let shift_prm = shift_linked_params mib1 mib2 lnk1 lnk2 id in - let prms1,prms2, rawlist = merge_mutual_inductive_body mib1 mib2 shift_prm in - let _ = prstr "\nrawlist : " in - let _ = - List.iter (fun (nm,tp) -> prNamedRConstr (string_of_id nm) tp;prstr "\n") rawlist in - let _ = prstr "\nend rawlist\n" in -(* FIX: retransformer en constr ici - let shift_prm = - { shift_prm with - recprms1=prms1; - recprms1=prms1; - } in *) - let indexpr = rawterm_list_to_inductive_expr prms1 prms2 mib1 mib2 shift_prm rawlist in - (* Declare inductive *) - Command.build_mutual [(indexpr,None)] true (* means: not coinductive *) - - -(* Find infos on identifier id. *) -let find_Function_infos_safe (id:identifier): Indfun_common.function_info = - let kn_of_id x = - let f_ref = Libnames.Ident (dummy_loc,x) in - locate_with_msg (str "Don't know what to do with " ++ Libnames.pr_reference f_ref) - locate_constant f_ref in - try find_Function_infos (kn_of_id id) - with Not_found -> - errorlabstrm "indfun" (Nameops.pr_id id ++ str " has no functional scheme") - -(** [merge id1 id2 args1 args2 id] builds and declares a new inductive - type called [id], representing the merged graphs of both graphs - [ind1] and [ind2]. identifiers occuring in both arrays [args1] and - [args2] are considered linked (i.e. are the same variable) in the - new graph. - - Warning: For the moment, repetitions of an id in [args1] or - [args2] are not supported. *) -let merge (id1:identifier) (id2:identifier) (args1:identifier array) - (args2:identifier array) id : unit = - let finfo1 = find_Function_infos_safe id1 in - let finfo2 = find_Function_infos_safe id2 in - (* FIXME? args1 are supposed unlinked. mergescheme (G x x) ?? *) - (* We add one arg (functional arg of the graph) *) - let lnk1 = Array.make (Array.length args1 + 1) Unlinked in - let lnk2' = (* args2 may be linked to args1 members. FIXME: same - as above: vars may be linked inside args2?? *) - Array.mapi - (fun i c -> - match array_find args1 (fun i x -> x=c) with - | Some j -> Linked j - | None -> Unlinked) - args2 in - (* We add one arg (functional arg of the graph) *) - let lnk2 = Array.append lnk2' (Array.make 1 Unlinked) in - (* setting functional results *) - let _ = lnk1.(Array.length lnk1 - 1) <- Funres in - let _ = lnk2.(Array.length lnk2 - 1) <- Funres in - merge_inductive finfo1.graph_ind finfo2.graph_ind lnk1 lnk2 id - - -let remove_last_arg c = - let (x,y) = decompose_prod c in - let xnolast = List.rev (List.tl (List.rev x)) in - compose_prod xnolast y - -let rec remove_n_fst_list n l = if n=0 then l else remove_n_fst_list (n-1) (List.tl l) -let remove_n_last_list n l = List.rev (remove_n_fst_list n (List.rev l)) - -let remove_last_n_arg n c = - let (x,y) = decompose_prod c in - let xnolast = remove_n_last_list n x in - compose_prod xnolast y - -(* [funify_branches relinfo nfuns branch] returns the branch [branch] - of the relinfo [relinfo] modified to fit in a functional principle. - Things to do: - - remove indargs from rel applications - - replace *variables only* corresponding to function (recursive) - results by the actual function application. *) -let funify_branches relinfo nfuns branch = - let mut_induct, induct = - match relinfo.indref with - | None -> assert false - | Some (IndRef ((mutual_ind,i) as ind)) -> mutual_ind,ind - | _ -> assert false in - let is_dom c = - match kind_of_term c with - | Ind((u,_)) | Construct((u,_),_) -> u = mut_induct - | _ -> false in - let _dom_i c = - assert (is_dom c); - match kind_of_term c with - | Ind((u,i)) | Construct((u,_),i) -> i - | _ -> assert false in - let _is_pred c shift = - match kind_of_term c with - | Rel i -> let reali = i-shift in (reali>=0 && reali<relinfo.nbranches) - | _ -> false in - (* FIXME: *) - (Anonymous,Some mkProp,mkProp) - - -let relprinctype_to_funprinctype relprinctype nfuns = - let relinfo = compute_elim_sig relprinctype in - assert (not relinfo.farg_in_concl); - assert (relinfo.indarg_in_concl); - (* first remove indarg and indarg_in_concl *) - let relinfo_noindarg = { relinfo with - indarg_in_concl = false; indarg = None; - concl = remove_last_arg (pop relinfo.concl); } in - (* the nfuns last induction arguments are functional ones: remove them *) - let relinfo_argsok = { relinfo_noindarg with - nargs = relinfo_noindarg.nargs - nfuns; - (* args is in reverse order, so remove fst *) - args = remove_n_fst_list nfuns relinfo_noindarg.args; - concl = popn nfuns relinfo_noindarg.concl - } in - let new_branches = - List.map (funify_branches relinfo_argsok nfuns) relinfo_argsok.branches in - let relinfo_branches = { relinfo_argsok with branches = new_branches } in - relinfo_branches - -(* @article{ bundy93rippling, - author = "Alan Bundy and Andrew Stevens and Frank van Harmelen and Andrew Ireland and Alan Smaill", - title = "Rippling: A Heuristic for Guiding Inductive Proofs", - journal = "Artificial Intelligence", - volume = "62", - number = "2", - pages = "185-253", - year = "1993", - url = "citeseer.ist.psu.edu/bundy93rippling.html" } - - *) -(* -*** Local Variables: *** -*** compile-command: "make -C ../.. contrib/funind/merge.cmo" *** -*** indent-tabs-mode: nil *** -*** End: *** -*) diff --git a/contrib/funind/rawterm_to_relation.ml b/contrib/funind/rawterm_to_relation.ml deleted file mode 100644 index 09b7fbdf..00000000 --- a/contrib/funind/rawterm_to_relation.ml +++ /dev/null @@ -1,1262 +0,0 @@ -open Printer -open Pp -open Names -open Term -open Rawterm -open Libnames -open Indfun_common -open Util -open Rawtermops - -let observe strm = - if do_observe () - then Pp.msgnl strm - else () -let observennl strm = - if do_observe () - then Pp.msg strm - else () - - -type binder_type = - | Lambda of name - | Prod of name - | LetIn of name - -type raw_context = (binder_type*rawconstr) list - - -(* - compose_raw_context [(bt_1,n_1,t_1);......] rt returns - b_1(n_1,t_1,.....,bn(n_k,t_k,rt)) where the b_i's are the - binders corresponding to the bt_i's -*) -let compose_raw_context = - let compose_binder (bt,t) acc = - match bt with - | Lambda n -> mkRLambda(n,t,acc) - | Prod n -> mkRProd(n,t,acc) - | LetIn n -> mkRLetIn(n,t,acc) - in - List.fold_right compose_binder - - -(* - The main part deals with building a list of raw constructor expressions - from the rhs of a fixpoint equation. -*) - -type 'a build_entry_pre_return = - { - context : raw_context; (* the binding context of the result *) - value : 'a; (* The value *) - } - -type 'a build_entry_return = - { - result : 'a build_entry_pre_return list; - to_avoid : identifier list - } - -(* - [combine_results combine_fun res1 res2] combine two results [res1] and [res2] - w.r.t. [combine_fun]. - - Informally, both [res1] and [res2] are lists of "constructors" [res1_1;...] - and [res2_1,....] and we need to produce - [combine_fun res1_1 res2_1;combine_fun res1_1 res2_2;........] -*) - -let combine_results - (combine_fun : 'a build_entry_pre_return -> 'b build_entry_pre_return -> - 'c build_entry_pre_return - ) - (res1: 'a build_entry_return) - (res2 : 'b build_entry_return) - : 'c build_entry_return - = - let pre_result = List.map - ( fun res1 -> (* for each result in arg_res *) - List.map (* we add it in each args_res *) - (fun res2 -> - combine_fun res1 res2 - ) - res2.result - ) - res1.result - in (* and then we flatten the map *) - { - result = List.concat pre_result; - to_avoid = list_union res1.to_avoid res2.to_avoid - } - - -(* - The combination function for an argument with a list of argument -*) - -let combine_args arg args = - { - context = arg.context@args.context; - (* Note that the binding context of [arg] MUST be placed before the one of - [args] in order to preserve possible type dependencies - *) - value = arg.value::args.value; - } - - -let ids_of_binder = function - | LetIn Anonymous | Prod Anonymous | Lambda Anonymous -> [] - | LetIn (Name id) | Prod (Name id) | Lambda (Name id) -> [id] - -let rec change_vars_in_binder mapping = function - [] -> [] - | (bt,t)::l -> - let new_mapping = List.fold_right Idmap.remove (ids_of_binder bt) mapping in - (bt,change_vars mapping t):: - (if idmap_is_empty new_mapping - then l - else change_vars_in_binder new_mapping l - ) - -let rec replace_var_by_term_in_binder x_id term = function - | [] -> [] - | (bt,t)::l -> - (bt,replace_var_by_term x_id term t):: - if List.mem x_id (ids_of_binder bt) - then l - else replace_var_by_term_in_binder x_id term l - -let add_bt_names bt = List.append (ids_of_binder bt) - -let apply_args ctxt body args = - let need_convert_id avoid id = - List.exists (is_free_in id) args || List.mem id avoid - in - let need_convert avoid bt = - List.exists (need_convert_id avoid) (ids_of_binder bt) - in - let next_name_away (na:name) (mapping: identifier Idmap.t) (avoid: identifier list) = - match na with - | Name id when List.mem id avoid -> - let new_id = Nameops.next_ident_away id avoid in - Name new_id,Idmap.add id new_id mapping,new_id::avoid - | _ -> na,mapping,avoid - in - let next_bt_away bt (avoid:identifier list) = - match bt with - | LetIn na -> - let new_na,mapping,new_avoid = next_name_away na Idmap.empty avoid in - LetIn new_na,mapping,new_avoid - | Prod na -> - let new_na,mapping,new_avoid = next_name_away na Idmap.empty avoid in - Prod new_na,mapping,new_avoid - | Lambda na -> - let new_na,mapping,new_avoid = next_name_away na Idmap.empty avoid in - Lambda new_na,mapping,new_avoid - in - let rec do_apply avoid ctxt body args = - match ctxt,args with - | _,[] -> (* No more args *) - (ctxt,body) - | [],_ -> (* no more fun *) - let f,args' = raw_decompose_app body in - (ctxt,mkRApp(f,args'@args)) - | (Lambda Anonymous,t)::ctxt',arg::args' -> - do_apply avoid ctxt' body args' - | (Lambda (Name id),t)::ctxt',arg::args' -> - let new_avoid,new_ctxt',new_body,new_id = - if need_convert_id avoid id - then - let new_avoid = id::avoid in - let new_id = Nameops.next_ident_away id new_avoid in - let new_avoid' = new_id :: new_avoid in - let mapping = Idmap.add id new_id Idmap.empty in - let new_ctxt' = change_vars_in_binder mapping ctxt' in - let new_body = change_vars mapping body in - new_avoid',new_ctxt',new_body,new_id - else - id::avoid,ctxt',body,id - in - let new_body = replace_var_by_term new_id arg new_body in - let new_ctxt' = replace_var_by_term_in_binder new_id arg new_ctxt' in - do_apply avoid new_ctxt' new_body args' - | (bt,t)::ctxt',_ -> - let new_avoid,new_ctxt',new_body,new_bt = - let new_avoid = add_bt_names bt avoid in - if need_convert avoid bt - then - let new_bt,mapping,new_avoid = next_bt_away bt new_avoid in - ( - new_avoid, - change_vars_in_binder mapping ctxt', - change_vars mapping body, - new_bt - ) - else new_avoid,ctxt',body,bt - in - let new_ctxt',new_body = - do_apply new_avoid new_ctxt' new_body args - in - (new_bt,t)::new_ctxt',new_body - in - do_apply [] ctxt body args - - -let combine_app f args = - let new_ctxt,new_value = apply_args f.context f.value args.value in - { - (* Note that the binding context of [args] MUST be placed before the one of - the applied value in order to preserve possible type dependencies - *) - context = args.context@new_ctxt; - value = new_value; - } - -let combine_lam n t b = - { - context = []; - value = mkRLambda(n, compose_raw_context t.context t.value, - compose_raw_context b.context b.value ) - } - - - -let combine_prod n t b = - { context = t.context@((Prod n,t.value)::b.context); value = b.value} - -let combine_letin n t b = - { context = t.context@((LetIn n,t.value)::b.context); value = b.value} - - -let mk_result ctxt value avoid = - { - result = - [{context = ctxt; - value = value}] - ; - to_avoid = avoid - } -(************************************************* - Some functions to deal with overlapping patterns -**************************************************) - -let coq_True_ref = - lazy (Coqlib.gen_reference "" ["Init";"Logic"] "True") - -let coq_False_ref = - lazy (Coqlib.gen_reference "" ["Init";"Logic"] "False") - -(* - [make_discr_match_el \[e1,...en\]] builds match e1,...,en with - (the list of expresions on which we will do the matching) - *) -let make_discr_match_el = - List.map (fun e -> (e,(Anonymous,None))) - -(* - [make_discr_match_brl i \[pat_1,...,pat_n\]] constructs a discrimination pattern matching on the ith expression. - that is. - match ?????? with \\ - | pat_1 => False \\ - | pat_{i-1} => False \\ - | pat_i => True \\ - | pat_{i+1} => False \\ - \vdots - | pat_n => False - end -*) -let make_discr_match_brl i = - list_map_i - (fun j (_,idl,patl,_) -> - if j=i - then (dummy_loc,idl,patl, mkRRef (Lazy.force coq_True_ref)) - else (dummy_loc,idl,patl, mkRRef (Lazy.force coq_False_ref)) - ) - 0 -(* - [make_discr_match brl el i] generates an hypothesis such that it reduce to true iff - brl_{i} is the first branch matched by [el] - - Used when we want to simulate the coq pattern matching algorithm -*) -let make_discr_match brl = - fun el i -> - mkRCases(None, - make_discr_match_el el, - make_discr_match_brl i brl) - -let pr_name = function - | Name id -> Ppconstr.pr_id id - | Anonymous -> str "_" - -(**********************************************************************) -(* functions used to build case expression from lettuple and if ones *) -(**********************************************************************) - -(* [build_constructors_of_type] construct the array of pattern of its inductive argument*) -let build_constructors_of_type ind' argl = - let (mib,ind) = Inductive.lookup_mind_specif (Global.env()) ind' in - let npar = mib.Declarations.mind_nparams in - Array.mapi (fun i _ -> - let construct = ind',i+1 in - let constructref = ConstructRef(construct) in - let _implicit_positions_of_cst = - Impargs.implicits_of_global constructref - in - let cst_narg = - Inductiveops.mis_constructor_nargs_env - (Global.env ()) - construct - in - let argl = - if argl = [] - then - Array.to_list - (Array.init (cst_narg - npar) (fun _ -> mkRHole ()) - ) - else argl - in - let pat_as_term = - mkRApp(mkRRef (ConstructRef(ind',i+1)),argl) - in - cases_pattern_of_rawconstr Anonymous pat_as_term - ) - ind.Declarations.mind_consnames - -(* [find_type_of] very naive attempts to discover the type of an if or a letin *) -let rec find_type_of nb b = - let f,_ = raw_decompose_app b in - match f with - | RRef(_,ref) -> - begin - let ind_type = - match ref with - | VarRef _ | ConstRef _ -> - let constr_of_ref = constr_of_global ref in - let type_of_ref = Typing.type_of (Global.env ()) Evd.empty constr_of_ref in - let (_,ret_type) = Reduction.dest_prod (Global.env ()) type_of_ref in - let ret_type,_ = decompose_app ret_type in - if not (isInd ret_type) then - begin -(* Pp.msgnl (str "not an inductive" ++ pr_lconstr ret_type); *) - raise (Invalid_argument "not an inductive") - end; - destInd ret_type - | IndRef ind -> ind - | ConstructRef c -> fst c - in - let _,ind_type_info = Inductive.lookup_mind_specif (Global.env()) ind_type in - if not (Array.length ind_type_info.Declarations.mind_consnames = nb ) - then raise (Invalid_argument "find_type_of : not a valid inductive"); - ind_type - end - | RCast(_,b,_) -> find_type_of nb b - | RApp _ -> assert false (* we have decomposed any application via raw_decompose_app *) - | _ -> raise (Invalid_argument "not a ref") - - - - -(******************) -(* Main functions *) -(******************) - - - -let raw_push_named (na,raw_value,raw_typ) env = - match na with - | Anonymous -> env - | Name id -> - let value = Option.map (Pretyping.Default.understand Evd.empty env) raw_value in - let typ = Pretyping.Default.understand_type Evd.empty env raw_typ in - Environ.push_named (id,value,typ) env - - -let add_pat_variables pat typ env : Environ.env = - let rec add_pat_variables env pat typ : Environ.env = - observe (str "new rel env := " ++ Printer.pr_rel_context_of env); - - match pat with - | PatVar(_,na) -> Environ.push_rel (na,None,typ) env - | PatCstr(_,c,patl,na) -> - let Inductiveops.IndType(indf,indargs) = - try Inductiveops.find_rectype env Evd.empty typ - with Not_found -> assert false - in - let constructors = Inductiveops.get_constructors env indf in - let constructor : Inductiveops.constructor_summary = List.find (fun cs -> cs.Inductiveops.cs_cstr = c) (Array.to_list constructors) in - let cs_args_types :types list = List.map (fun (_,_,t) -> t) constructor.Inductiveops.cs_args in - List.fold_left2 add_pat_variables env patl (List.rev cs_args_types) - in - let new_env = add_pat_variables env pat typ in - let res = - fst ( - Sign.fold_rel_context - (fun (na,v,t) (env,ctxt) -> - match na with - | Anonymous -> assert false - | Name id -> - let new_t = substl ctxt t in - let new_v = Option.map (substl ctxt) v in - observe (str "for variable " ++ Ppconstr.pr_id id ++ fnl () ++ - str "old type := " ++ Printer.pr_lconstr t ++ fnl () ++ - str "new type := " ++ Printer.pr_lconstr new_t ++ fnl () ++ - Option.fold_right (fun v _ -> str "old value := " ++ Printer.pr_lconstr v ++ fnl ()) v (mt ()) ++ - Option.fold_right (fun v _ -> str "new value := " ++ Printer.pr_lconstr v ++ fnl ()) new_v (mt ()) - ); - (Environ.push_named (id,new_v,new_t) env,mkVar id::ctxt) - ) - (Environ.rel_context new_env) - ~init:(env,[]) - ) - in - observe (str "new var env := " ++ Printer.pr_named_context_of res); - res - - - - -let rec pattern_to_term_and_type env typ = function - | PatVar(loc,Anonymous) -> assert false - | PatVar(loc,Name id) -> - mkRVar id - | PatCstr(loc,constr,patternl,_) -> - let cst_narg = - Inductiveops.mis_constructor_nargs_env - (Global.env ()) - constr - in - let Inductiveops.IndType(indf,indargs) = - try Inductiveops.find_rectype env Evd.empty typ - with Not_found -> assert false - in - let constructors = Inductiveops.get_constructors env indf in - let constructor = List.find (fun cs -> cs.Inductiveops.cs_cstr = constr) (Array.to_list constructors) in - let cs_args_types :types list = List.map (fun (_,_,t) -> t) constructor.Inductiveops.cs_args in - let _,cstl = Inductiveops.dest_ind_family indf in - let csta = Array.of_list cstl in - let implicit_args = - Array.to_list - (Array.init - (cst_narg - List.length patternl) - (fun i -> Detyping.detype false [] (Termops.names_of_rel_context env) csta.(i)) - ) - in - let patl_as_term = - List.map2 (pattern_to_term_and_type env) (List.rev cs_args_types) patternl - in - mkRApp(mkRRef(ConstructRef constr), - implicit_args@patl_as_term - ) - -(* [build_entry_lc funnames avoid rt] construct the list (in fact a build_entry_return) - of constructors corresponding to [rt] when replacing calls to [funnames] by calls to the - corresponding graphs. - - - The idea to transform a term [t] into a list of constructors [lc] is the following: - \begin{itemize} - \item if the term is a binder (bind x, body) then first compute [lc'] the list corresponding - to [body] and add (bind x. _) to each elements of [lc] - \item if the term has the form (g t1 ... ... tn) where g does not appears in (fnames) - then compute [lc1] ... [lcn] the lists of constructors corresponding to [t1] ... [tn], - then combine those lists and [g] as follows~: for each element [c1,...,cn] of [lc1\times...\times lcn], - [g c1 ... cn] is an element of [lc] - \item if the term has the form (f t1 .... tn) where [f] appears in [fnames] then - compute [lc1] ... [lcn] the lists of constructors corresponding to [t1] ... [tn], - then compute those lists and [f] as follows~: for each element [c1,...,cn] of [lc1\times...\times lcn] - create a new variable [res] and [forall res, R_f c1 ... cn res] is in [lc] - \item if the term is a cast just treat its body part - \item - if the term is a match, an if or a lettuple then compute the lists corresponding to each branch of the case - and concatenate them (informally, each branch of a match produces a new constructor) - \end{itemize} - - WARNING: The terms constructed here are only USING the rawconstr syntax but are highly bad formed. - We must wait to have complete all the current calculi to set the recursive calls. - At this point, each term [f t1 ... tn] (where f appears in [funnames]) is replaced by - a pseudo term [forall res, res t1 ... tn, res]. A reconstruction phase is done later. - We in fact not create a constructor list since then end of each constructor has not the expected form - but only the value of the function -*) - - -let rec build_entry_lc env funnames avoid rt : rawconstr build_entry_return = - observe (str " Entering : " ++ Printer.pr_rawconstr rt); - match rt with - | RRef _ | RVar _ | REvar _ | RPatVar _ | RSort _ | RHole _ -> - (* do nothing (except changing type of course) *) - mk_result [] rt avoid - | RApp(_,_,_) -> - let f,args = raw_decompose_app rt in - let args_res : (rawconstr list) build_entry_return = - List.fold_right (* create the arguments lists of constructors and combine them *) - (fun arg ctxt_argsl -> - let arg_res = build_entry_lc env funnames ctxt_argsl.to_avoid arg in - combine_results combine_args arg_res ctxt_argsl - ) - args - (mk_result [] [] avoid) - in - begin - match f with - | RVar(_,id) when Idset.mem id funnames -> - (* if we have [f t1 ... tn] with [f]$\in$[fnames] - then we create a fresh variable [res], - add [res] and its "value" (i.e. [res v1 ... vn]) to each - pseudo constructor build for the arguments (i.e. a pseudo context [ctxt] and - a pseudo value "v1 ... vn". - The "value" of this branch is then simply [res] - *) - let rt_as_constr = Pretyping.Default.understand Evd.empty env rt in - let rt_typ = Typing.type_of env Evd.empty rt_as_constr in - let res_raw_type = Detyping.detype false [] (Termops.names_of_rel_context env) rt_typ in - let res = fresh_id args_res.to_avoid "res" in - let new_avoid = res::args_res.to_avoid in - let res_rt = mkRVar res in - let new_result = - List.map - (fun arg_res -> - let new_hyps = - [Prod (Name res),res_raw_type; - Prod Anonymous,mkRApp(res_rt,(mkRVar id)::arg_res.value)] - in - {context = arg_res.context@new_hyps; value = res_rt } - ) - args_res.result - in - { result = new_result; to_avoid = new_avoid } - | RVar _ | REvar _ | RPatVar _ | RHole _ | RSort _ | RRef _ -> - (* if have [g t1 ... tn] with [g] not appearing in [funnames] - then - foreach [ctxt,v1 ... vn] in [args_res] we return - [ctxt, g v1 .... vn] - *) - { - args_res with - result = - List.map - (fun args_res -> - {args_res with value = mkRApp(f,args_res.value)}) - args_res.result - } - | RApp _ -> assert false (* we have collected all the app in [raw_decompose_app] *) - | RLetIn(_,n,t,b) -> - (* if we have [(let x := v in b) t1 ... tn] , - we discard our work and compute the list of constructor for - [let x = v in (b t1 ... tn)] up to alpha conversion - *) - let new_n,new_b,new_avoid = - match n with - | Name id when List.exists (is_free_in id) args -> - (* need to alpha-convert the name *) - let new_id = Nameops.next_ident_away id avoid in - let new_avoid = id:: avoid in - let new_b = - replace_var_by_term - id - (RVar(dummy_loc,id)) - b - in - (Name new_id,new_b,new_avoid) - | _ -> n,b,avoid - in - build_entry_lc - env - funnames - avoid - (mkRLetIn(new_n,t,mkRApp(new_b,args))) - | RCases _ | RLambda _ | RIf _ | RLetTuple _ -> - (* we have [(match e1, ...., en with ..... end) t1 tn] - we first compute the result from the case and - then combine each of them with each of args one - *) - let f_res = build_entry_lc env funnames args_res.to_avoid f in - combine_results combine_app f_res args_res - | RDynamic _ ->error "Not handled RDynamic" - | RCast(_,b,_) -> - (* for an applied cast we just trash the cast part - and restart the work. - - WARNING: We need to restart since [b] itself should be an application term - *) - build_entry_lc env funnames avoid (mkRApp(b,args)) - | RRec _ -> error "Not handled RRec" - | RProd _ -> error "Cannot apply a type" - end (* end of the application treatement *) - - | RLambda(_,n,_,t,b) -> - (* we first compute the list of constructor - corresponding to the body of the function, - then the one corresponding to the type - and combine the two result - *) - let t_res = build_entry_lc env funnames avoid t in - let new_n = - match n with - | Name _ -> n - | Anonymous -> Name (Indfun_common.fresh_id [] "_x") - in - let new_env = raw_push_named (new_n,None,t) env in - let b_res = build_entry_lc new_env funnames avoid b in - combine_results (combine_lam new_n) t_res b_res - | RProd(_,n,_,t,b) -> - (* we first compute the list of constructor - corresponding to the body of the function, - then the one corresponding to the type - and combine the two result - *) - let t_res = build_entry_lc env funnames avoid t in - let new_env = raw_push_named (n,None,t) env in - let b_res = build_entry_lc new_env funnames avoid b in - combine_results (combine_prod n) t_res b_res - | RLetIn(_,n,v,b) -> - (* we first compute the list of constructor - corresponding to the body of the function, - then the one corresponding to the value [t] - and combine the two result - *) - let v_res = build_entry_lc env funnames avoid v in - let v_as_constr = Pretyping.Default.understand Evd.empty env v in - let v_type = Typing.type_of env Evd.empty v_as_constr in - let new_env = - match n with - Anonymous -> env - | Name id -> Environ.push_named (id,Some v_as_constr,v_type) env - in - let b_res = build_entry_lc new_env funnames avoid b in - combine_results (combine_letin n) v_res b_res - | RCases(_,_,_,el,brl) -> - (* we create the discrimination function - and treat the case itself - *) - let make_discr = make_discr_match brl in - build_entry_lc_from_case env funnames make_discr el brl avoid - | RIf(_,b,(na,e_option),lhs,rhs) -> - let b_as_constr = Pretyping.Default.understand Evd.empty env b in - let b_typ = Typing.type_of env Evd.empty b_as_constr in - let (ind,_) = - try Inductiveops.find_inductive env Evd.empty b_typ - with Not_found -> - errorlabstrm "" (str "Cannot find the inductive associated to " ++ - Printer.pr_rawconstr b ++ str " in " ++ - Printer.pr_rawconstr rt ++ str ". try again with a cast") - in - let case_pats = build_constructors_of_type ind [] in - assert (Array.length case_pats = 2); - let brl = - list_map_i - (fun i x -> (dummy_loc,[],[case_pats.(i)],x)) - 0 - [lhs;rhs] - in - let match_expr = - mkRCases(None,[(b,(Anonymous,None))],brl) - in - (* Pp.msgnl (str "new case := " ++ Printer.pr_rawconstr match_expr); *) - build_entry_lc env funnames avoid match_expr - | RLetTuple(_,nal,_,b,e) -> - begin - let nal_as_rawconstr = - List.map - (function - Name id -> mkRVar id - | Anonymous -> mkRHole () - ) - nal - in - let b_as_constr = Pretyping.Default.understand Evd.empty env b in - let b_typ = Typing.type_of env Evd.empty b_as_constr in - let (ind,_) = - try Inductiveops.find_inductive env Evd.empty b_typ - with Not_found -> - errorlabstrm "" (str "Cannot find the inductive associated to " ++ - Printer.pr_rawconstr b ++ str " in " ++ - Printer.pr_rawconstr rt ++ str ". try again with a cast") - in - let case_pats = build_constructors_of_type ind nal_as_rawconstr in - assert (Array.length case_pats = 1); - let br = - (dummy_loc,[],[case_pats.(0)],e) - in - let match_expr = mkRCases(None,[b,(Anonymous,None)],[br]) in - build_entry_lc env funnames avoid match_expr - - end - | RRec _ -> error "Not handled RRec" - | RCast(_,b,_) -> - build_entry_lc env funnames avoid b - | RDynamic _ -> error "Not handled RDynamic" -and build_entry_lc_from_case env funname make_discr - (el:tomatch_tuples) - (brl:Rawterm.cases_clauses) avoid : - rawconstr build_entry_return = - match el with - | [] -> assert false (* this case correspond to match <nothing> with .... !*) - | el -> - (* this case correspond to - match el with brl end - we first compute the list of lists corresponding to [el] and - combine them . - Then for each elemeent of the combinations, - we compute the result we compute one list per branch in [brl] and - finally we just concatenate those list - *) - let case_resl = - List.fold_right - (fun (case_arg,_) ctxt_argsl -> - let arg_res = build_entry_lc env funname avoid case_arg in - combine_results combine_args arg_res ctxt_argsl - ) - el - (mk_result [] [] avoid) - in - (****** The next works only if the match is not dependent ****) - let types = - List.map (fun (case_arg,_) -> - let case_arg_as_constr = Pretyping.Default.understand Evd.empty env case_arg in - Typing.type_of env Evd.empty case_arg_as_constr - ) el - in - let results = - List.map - (build_entry_lc_from_case_term - env types - funname (make_discr (* (List.map fst el) *)) - [] brl - case_resl.to_avoid) - case_resl.result - in - { - result = List.concat (List.map (fun r -> r.result) results); - to_avoid = - List.fold_left (fun acc r -> list_union acc r.to_avoid) [] results - } - -and build_entry_lc_from_case_term env types funname make_discr patterns_to_prevent brl avoid - matched_expr = - match brl with - | [] -> (* computed_branches *) {result = [];to_avoid = avoid} - | br::brl' -> - (* alpha convertion to prevent name clashes *) - let _,idl,patl,return = alpha_br avoid br in - let new_avoid = idl@avoid in (* for now we can no more use idl as an indentifier *) - (* building a list of precondition stating that we are not in this branch - (will be used in the following recursive calls) - *) - let new_env = List.fold_right2 add_pat_variables patl types env in - let not_those_patterns : (identifier list -> rawconstr -> rawconstr) list = - List.map2 - (fun pat typ -> - fun avoid pat'_as_term -> - let renamed_pat,_,_ = alpha_pat avoid pat in - let pat_ids = get_pattern_id renamed_pat in - let env_with_pat_ids = add_pat_variables pat typ new_env in - List.fold_right - (fun id acc -> - let typ_of_id = Typing.type_of env_with_pat_ids Evd.empty (mkVar id) in - let raw_typ_of_id = - Detyping.detype false [] (Termops.names_of_rel_context env_with_pat_ids) typ_of_id - in - mkRProd (Name id,raw_typ_of_id,acc)) - pat_ids - (raw_make_neq pat'_as_term (pattern_to_term renamed_pat)) - ) - patl - types - in - (* Checking if we can be in this branch - (will be used in the following recursive calls) - *) - let unify_with_those_patterns : (cases_pattern -> bool*bool) list = - List.map - (fun pat pat' -> are_unifiable pat pat',eq_cases_pattern pat pat') - patl - in - (* - we first compute the other branch result (in ordrer to keep the order of the matching - as much as possible) - *) - let brl'_res = - build_entry_lc_from_case_term - env - types - funname - make_discr - ((unify_with_those_patterns,not_those_patterns)::patterns_to_prevent) - brl' - avoid - matched_expr - in - (* We now create the precondition of this branch i.e. - - 1- the list of variable appearing in the different patterns of this branch and - the list of equation stating than el = patl (List.flatten ...) - 2- If there exists a previous branch which pattern unify with the one of this branch - then a discrimination precond stating that we are not in a previous branch (if List.exists ...) - *) - let those_pattern_preconds = - (List.flatten - ( - list_map3 - (fun pat e typ_as_constr -> - let this_pat_ids = ids_of_pat pat in - let typ = Detyping.detype false [] (Termops.names_of_rel_context new_env) typ_as_constr in - let pat_as_term = pattern_to_term pat in - List.fold_right - (fun id acc -> - if Idset.mem id this_pat_ids - then (Prod (Name id), - let typ_of_id = Typing.type_of new_env Evd.empty (mkVar id) in - let raw_typ_of_id = - Detyping.detype false [] (Termops.names_of_rel_context new_env) typ_of_id - in - raw_typ_of_id - )::acc - else acc - - ) - idl - [(Prod Anonymous,raw_make_eq ~typ pat_as_term e)] - ) - patl - matched_expr.value - types - ) - ) - @ - (if List.exists (function (unifl,_) -> - let (unif,_) = - List.split (List.map2 (fun x y -> x y) unifl patl) - in - List.for_all (fun x -> x) unif) patterns_to_prevent - then - let i = List.length patterns_to_prevent in - let pats_as_constr = List.map2 (pattern_to_term_and_type new_env) types patl in - [(Prod Anonymous,make_discr pats_as_constr i )] - else - [] - ) - in - (* We compute the result of the value returned by the branch*) - let return_res = build_entry_lc new_env funname new_avoid return in - (* and combine it with the preconds computed for this branch *) - let this_branch_res = - List.map - (fun res -> - { context = matched_expr.context@those_pattern_preconds@res.context ; - value = res.value} - ) - return_res.result - in - { brl'_res with result = this_branch_res@brl'_res.result } - - -let is_res id = - try - String.sub (string_of_id id) 0 3 = "res" - with Invalid_argument _ -> false - -(* - The second phase which reconstruct the real type of the constructor. - rebuild the raw constructors expression. - eliminates some meaningless equalities, applies some rewrites...... -*) -let rec rebuild_cons nb_args relname args crossed_types depth rt = - match rt with - | RProd(_,n,k,t,b) -> - let not_free_in_t id = not (is_free_in id t) in - let new_crossed_types = t::crossed_types in - begin - match t with - | RApp(_,(RVar(_,res_id) as res_rt),args') when is_res res_id -> - begin - match args' with - | (RVar(_,this_relname))::args' -> - let new_b,id_to_exclude = - rebuild_cons - nb_args relname - args new_crossed_types - (depth + 1) b - in - (*i The next call to mk_rel_id is valid since we are constructing the graph - Ensures by: obvious - i*) - - let new_t = - mkRApp(mkRVar(mk_rel_id this_relname),args'@[res_rt]) - in mkRProd(n,new_t,new_b), - Idset.filter not_free_in_t id_to_exclude - | _ -> (* the first args is the name of the function! *) - assert false - end - | RApp(_,RRef(_,eq_as_ref),[_;RVar(_,id);rt]) - when eq_as_ref = Lazy.force Coqlib.coq_eq_ref && n = Anonymous - -> - let is_in_b = is_free_in id b in - let _keep_eq = - not (List.exists (is_free_in id) args) || is_in_b || - List.exists (is_free_in id) crossed_types - in - let new_args = List.map (replace_var_by_term id rt) args in - let subst_b = - if is_in_b then b else replace_var_by_term id rt b - in - let new_b,id_to_exclude = - rebuild_cons - nb_args relname - new_args new_crossed_types - (depth + 1) subst_b - in - mkRProd(n,t,new_b),id_to_exclude - (* J.F:. keep this comment it explain how to remove some meaningless equalities - if keep_eq then - mkRProd(n,t,new_b),id_to_exclude - else new_b, Idset.add id id_to_exclude - *) - | _ -> - let new_b,id_to_exclude = - rebuild_cons - nb_args relname - args new_crossed_types - (depth + 1) b - in - match n with - | Name id when Idset.mem id id_to_exclude && depth >= nb_args -> - new_b,Idset.remove id - (Idset.filter not_free_in_t id_to_exclude) - | _ -> mkRProd(n,t,new_b),Idset.filter not_free_in_t id_to_exclude - end - | RLambda(_,n,k,t,b) -> - begin - let not_free_in_t id = not (is_free_in id t) in - let new_crossed_types = t :: crossed_types in - match n with - | Name id -> - let new_b,id_to_exclude = - rebuild_cons - nb_args relname - (args@[mkRVar id])new_crossed_types - (depth + 1 ) b - in - if Idset.mem id id_to_exclude && depth >= nb_args - then - new_b, Idset.remove id (Idset.filter not_free_in_t id_to_exclude) - else - RProd(dummy_loc,n,k,t,new_b),Idset.filter not_free_in_t id_to_exclude - | _ -> anomaly "Should not have an anonymous function here" - (* We have renamed all the anonymous functions during alpha_renaming phase *) - - end - | RLetIn(_,n,t,b) -> - begin - let not_free_in_t id = not (is_free_in id t) in - let new_b,id_to_exclude = - rebuild_cons - nb_args relname - args (t::crossed_types) - (depth + 1 ) b in - match n with - | Name id when Idset.mem id id_to_exclude && depth >= nb_args -> - new_b,Idset.remove id (Idset.filter not_free_in_t id_to_exclude) - | _ -> RLetIn(dummy_loc,n,t,new_b), - Idset.filter not_free_in_t id_to_exclude - end - | RLetTuple(_,nal,(na,rto),t,b) -> - assert (rto=None); - begin - let not_free_in_t id = not (is_free_in id t) in - let new_t,id_to_exclude' = - rebuild_cons - nb_args - relname - args (crossed_types) - depth t - in - let new_b,id_to_exclude = - rebuild_cons - nb_args relname - args (t::crossed_types) - (depth + 1) b - in -(* match n with *) -(* | Name id when Idset.mem id id_to_exclude -> *) -(* new_b,Idset.remove id (Idset.filter not_free_in_t id_to_exclude) *) -(* | _ -> *) - RLetTuple(dummy_loc,nal,(na,None),t,new_b), - Idset.filter not_free_in_t (Idset.union id_to_exclude id_to_exclude') - - end - - | _ -> mkRApp(mkRVar relname,args@[rt]),Idset.empty - - -(* debuging wrapper *) -let rebuild_cons nb_args relname args crossed_types rt = -(* observennl (str "rebuild_cons : rt := "++ pr_rawconstr rt ++ *) -(* str "nb_args := " ++ str (string_of_int nb_args)); *) - let res = - rebuild_cons nb_args relname args crossed_types 0 rt - in -(* observe (str " leads to "++ pr_rawconstr (fst res)); *) - res - - -(* naive implementation of parameter detection. - - A parameter is an argument which is only preceded by parameters and whose - calls are all syntaxically equal. - - TODO: Find a valid way to deal with implicit arguments here! -*) -let rec compute_cst_params relnames params = function - | RRef _ | RVar _ | REvar _ | RPatVar _ -> params - | RApp(_,RVar(_,relname'),rtl) when Idset.mem relname' relnames -> - compute_cst_params_from_app [] (params,rtl) - | RApp(_,f,args) -> - List.fold_left (compute_cst_params relnames) params (f::args) - | RLambda(_,_,_,t,b) | RProd(_,_,_,t,b) | RLetIn(_,_,t,b) | RLetTuple(_,_,_,t,b) -> - let t_params = compute_cst_params relnames params t in - compute_cst_params relnames t_params b - | RCases _ -> - params (* If there is still cases at this point they can only be - discriminitation ones *) - | RSort _ -> params - | RHole _ -> params - | RIf _ | RRec _ | RCast _ | RDynamic _ -> - raise (UserError("compute_cst_params", str "Not handled case")) -and compute_cst_params_from_app acc (params,rtl) = - match params,rtl with - | _::_,[] -> assert false (* the rel has at least nargs + 1 arguments ! *) - | ((Name id,_,is_defined) as param)::params',(RVar(_,id'))::rtl' - when id_ord id id' == 0 && not is_defined -> - compute_cst_params_from_app (param::acc) (params',rtl') - | _ -> List.rev acc - -let compute_params_name relnames (args : (Names.name * Rawterm.rawconstr * bool) list array) csts = - let rels_params = - Array.mapi - (fun i args -> - List.fold_left - (fun params (_,cst) -> compute_cst_params relnames params cst) - args - csts.(i) - ) - args - in - let l = ref [] in - let _ = - try - list_iter_i - (fun i ((n,nt,is_defined) as param) -> - if array_for_all - (fun l -> - let (n',nt',is_defined') = List.nth l i in - n = n' && Topconstr.eq_rawconstr nt nt' && is_defined = is_defined') - rels_params - then - l := param::!l - ) - rels_params.(0) - with _ -> - () - in - List.rev !l - -let rec rebuild_return_type rt = - match rt with - | Topconstr.CProdN(loc,n,t') -> - Topconstr.CProdN(loc,n,rebuild_return_type t') - | Topconstr.CArrow(loc,t,t') -> - Topconstr.CArrow(loc,t,rebuild_return_type t') - | Topconstr.CLetIn(loc,na,t,t') -> - Topconstr.CLetIn(loc,na,t,rebuild_return_type t') - | _ -> Topconstr.CArrow(dummy_loc,rt,Topconstr.CSort(dummy_loc,RType None)) - - -let do_build_inductive - funnames (funsargs: (Names.name * rawconstr * bool) list list) - returned_types - (rtl:rawconstr list) = - let _time1 = System.get_time () in -(* Pp.msgnl (prlist_with_sep fnl Printer.pr_rawconstr rtl); *) - let funnames_as_set = List.fold_right Idset.add funnames Idset.empty in - let funnames = Array.of_list funnames in - let funsargs = Array.of_list funsargs in - let returned_types = Array.of_list returned_types in - (* alpha_renaming of the body to prevent variable capture during manipulation *) - let rtl_alpha = List.map (function rt -> expand_as (alpha_rt [] rt)) rtl in - let rta = Array.of_list rtl_alpha in - (*i The next call to mk_rel_id is valid since we are constructing the graph - Ensures by: obvious - i*) - let relnames = Array.map mk_rel_id funnames in - let relnames_as_set = Array.fold_right Idset.add relnames Idset.empty in - (* Construction of the pseudo constructors *) - let env = - Array.fold_right - (fun id env -> - Environ.push_named (id,None,Typing.type_of env Evd.empty (Tacinterp.constr_of_id env id)) env - ) - funnames - (Global.env ()) - in - let resa = Array.map (build_entry_lc env funnames_as_set []) rta in - (* and of the real constructors*) - let constr i res = - List.map - (function result (* (args',concl') *) -> - let rt = compose_raw_context result.context result.value in - let nb_args = List.length funsargs.(i) in - (* with_full_print (fun rt -> Pp.msgnl (str "raw constr " ++ pr_rawconstr rt)) rt; *) - fst ( - rebuild_cons nb_args relnames.(i) - [] - [] - rt - ) - ) - res.result - in - (* adding names to constructors *) - let next_constructor_id = ref (-1) in - let mk_constructor_id i = - incr next_constructor_id; - (*i The next call to mk_rel_id is valid since we are constructing the graph - Ensures by: obvious - i*) - id_of_string ((string_of_id (mk_rel_id funnames.(i)))^"_"^(string_of_int !next_constructor_id)) - in - let rel_constructors i rt : (identifier*rawconstr) list = - next_constructor_id := (-1); - List.map (fun constr -> (mk_constructor_id i),constr) (constr i rt) - in - let rel_constructors = Array.mapi rel_constructors resa in - (* Computing the set of parameters if asked *) - let rels_params = compute_params_name relnames_as_set funsargs rel_constructors in - let nrel_params = List.length rels_params in - let rel_constructors = (* Taking into account the parameters in constructors *) - Array.map (List.map - (fun (id,rt) -> (id,snd (chop_rprod_n nrel_params rt)))) - rel_constructors - in - let rel_arity i funargs = (* Reduilding arities (with parameters) *) - let rel_first_args :(Names.name * Rawterm.rawconstr * bool ) list = - (snd (list_chop nrel_params funargs)) - in - List.fold_right - (fun (n,t,is_defined) acc -> - if is_defined - then - Topconstr.CLetIn(dummy_loc,(dummy_loc, n),Constrextern.extern_rawconstr Idset.empty t, - acc) - else - Topconstr.CProdN - (dummy_loc, - [[(dummy_loc,n)],Topconstr.default_binder_kind,Constrextern.extern_rawconstr Idset.empty t], - acc - ) - ) - rel_first_args - (rebuild_return_type returned_types.(i)) - in - (* We need to lift back our work topconstr but only with all information - We mimick a Set Printing All. - Then save the graphs and reset Printing options to their primitive values - *) - let rel_arities = Array.mapi rel_arity funsargs in - let rel_params = - List.map - (fun (n,t,is_defined) -> - if is_defined - then - Topconstr.LocalRawDef((dummy_loc,n), Constrextern.extern_rawconstr Idset.empty t) - else - Topconstr.LocalRawAssum - ([(dummy_loc,n)], Topconstr.default_binder_kind, Constrextern.extern_rawconstr Idset.empty t) - ) - rels_params - in - let ext_rels_constructors = - Array.map (List.map - (fun (id,t) -> - false,((dummy_loc,id), - Flags.with_option - Flags.raw_print - (Constrextern.extern_rawtype Idset.empty) ((* zeta_normalize *) t) - ) - )) - (rel_constructors) - in - let rel_ind i ext_rel_constructors = - ((dummy_loc,relnames.(i)), - rel_params, - Some rel_arities.(i), - ext_rel_constructors),None - in - let ext_rel_constructors = (Array.mapi rel_ind ext_rels_constructors) in - let rel_inds = Array.to_list ext_rel_constructors in -(* let _ = *) -(* Pp.msgnl (\* observe *\) ( *) -(* str "Inductive" ++ spc () ++ *) -(* prlist_with_sep *) -(* (fun () -> fnl ()++spc () ++ str "with" ++ spc ()) *) -(* (function ((_,id),_,params,ar,constr) -> *) -(* Ppconstr.pr_id id ++ spc () ++ *) -(* Ppconstr.pr_binders params ++ spc () ++ *) -(* str ":" ++ spc () ++ *) -(* Ppconstr.pr_lconstr_expr ar ++ spc () ++ str ":=" ++ *) -(* prlist_with_sep *) -(* (fun _ -> fnl () ++ spc () ++ str "|" ++ spc ()) *) -(* (function (_,((_,id),t)) -> *) -(* Ppconstr.pr_id id ++ spc () ++ str ":" ++ spc () ++ *) -(* Ppconstr.pr_lconstr_expr t) *) -(* constr *) -(* ) *) -(* rel_inds *) -(* ) *) -(* in *) - let _time2 = System.get_time () in - try - with_full_print (Flags.silently (Command.build_mutual rel_inds)) true - with - | UserError(s,msg) as e -> - let _time3 = System.get_time () in -(* Pp.msgnl (str "error : "++ str (string_of_float (System.time_difference time2 time3))); *) - let repacked_rel_inds = - List.map (fun ((a , b , c , l),ntn) -> ((false,a) , b, c , Vernacexpr.Inductive_kw, Vernacexpr.Constructors l),ntn ) - rel_inds - in - let msg = - str "while trying to define"++ spc () ++ - Ppvernac.pr_vernac (Vernacexpr.VernacInductive(Decl_kinds.Finite,repacked_rel_inds)) - ++ fnl () ++ - msg - in - observe (msg); - raise e - | e -> - let _time3 = System.get_time () in -(* Pp.msgnl (str "error : "++ str (string_of_float (System.time_difference time2 time3))); *) - let repacked_rel_inds = - List.map (fun ((a , b , c , l),ntn) -> ((false,a) , b, c , Vernacexpr.Inductive_kw, Vernacexpr.Constructors l),ntn ) - rel_inds - in - let msg = - str "while trying to define"++ spc () ++ - Ppvernac.pr_vernac (Vernacexpr.VernacInductive(Decl_kinds.Finite,repacked_rel_inds)) - ++ fnl () ++ - Cerrors.explain_exn e - in - observe msg; - raise e - - - -let build_inductive funnames funsargs returned_types rtl = - try - do_build_inductive funnames funsargs returned_types rtl - with e -> raise (Building_graph e) - - diff --git a/contrib/funind/rawterm_to_relation.mli b/contrib/funind/rawterm_to_relation.mli deleted file mode 100644 index 0075fb0a..00000000 --- a/contrib/funind/rawterm_to_relation.mli +++ /dev/null @@ -1,16 +0,0 @@ - - - -(* - [build_inductive parametrize funnames funargs returned_types bodies] - constructs and saves the graphs of the functions [funnames] taking [funargs] as arguments - and returning [returned_types] using bodies [bodies] -*) - -val build_inductive : - Names.identifier list -> (* The list of function name *) - (Names.name*Rawterm.rawconstr*bool) list list -> (* The list of function args *) - Topconstr.constr_expr list -> (* The list of function returned type *) - Rawterm.rawconstr list -> (* the list of body *) - unit - diff --git a/contrib/funind/rawtermops.ml b/contrib/funind/rawtermops.ml deleted file mode 100644 index 92396af5..00000000 --- a/contrib/funind/rawtermops.ml +++ /dev/null @@ -1,718 +0,0 @@ -open Pp -open Rawterm -open Util -open Names -(* Ocaml 3.06 Map.S does not handle is_empty *) -let idmap_is_empty m = m = Idmap.empty - -(* - Some basic functions to rebuild rawconstr - In each of them the location is Util.dummy_loc -*) -let mkRRef ref = RRef(dummy_loc,ref) -let mkRVar id = RVar(dummy_loc,id) -let mkRApp(rt,rtl) = RApp(dummy_loc,rt,rtl) -let mkRLambda(n,t,b) = RLambda(dummy_loc,n,Explicit,t,b) -let mkRProd(n,t,b) = RProd(dummy_loc,n,Explicit,t,b) -let mkRLetIn(n,t,b) = RLetIn(dummy_loc,n,t,b) -let mkRCases(rto,l,brl) = RCases(dummy_loc,Term.RegularStyle,rto,l,brl) -let mkRSort s = RSort(dummy_loc,s) -let mkRHole () = RHole(dummy_loc,Evd.BinderType Anonymous) -let mkRCast(b,t) = RCast(dummy_loc,b,CastConv (Term.DEFAULTcast,t)) - -(* - Some basic functions to decompose rawconstrs - These are analogous to the ones constrs -*) -let raw_decompose_prod = - let rec raw_decompose_prod args = function - | RProd(_,n,k,t,b) -> - raw_decompose_prod ((n,t)::args) b - | rt -> args,rt - in - raw_decompose_prod [] - -let raw_decompose_prod_or_letin = - let rec raw_decompose_prod args = function - | RProd(_,n,k,t,b) -> - raw_decompose_prod ((n,None,Some t)::args) b - | RLetIn(_,n,t,b) -> - raw_decompose_prod ((n,Some t,None)::args) b - | rt -> args,rt - in - raw_decompose_prod [] - -let raw_compose_prod = - List.fold_left (fun b (n,t) -> mkRProd(n,t,b)) - -let raw_compose_prod_or_letin = - List.fold_left ( - fun concl decl -> - match decl with - | (n,None,Some t) -> mkRProd(n,t,concl) - | (n,Some bdy,None) -> mkRLetIn(n,bdy,concl) - | _ -> assert false) - -let raw_decompose_prod_n n = - let rec raw_decompose_prod i args c = - if i<=0 then args,c - else - match c with - | RProd(_,n,_,t,b) -> - raw_decompose_prod (i-1) ((n,t)::args) b - | rt -> args,rt - in - raw_decompose_prod n [] - - -let raw_decompose_prod_or_letin_n n = - let rec raw_decompose_prod i args c = - if i<=0 then args,c - else - match c with - | RProd(_,n,_,t,b) -> - raw_decompose_prod (i-1) ((n,None,Some t)::args) b - | RLetIn(_,n,t,b) -> - raw_decompose_prod (i-1) ((n,Some t,None)::args) b - | rt -> args,rt - in - raw_decompose_prod n [] - - -let raw_decompose_app = - let rec decompose_rapp acc rt = -(* msgnl (str "raw_decompose_app on : "++ Printer.pr_rawconstr rt); *) - match rt with - | RApp(_,rt,rtl) -> - decompose_rapp (List.fold_left (fun y x -> x::y) acc rtl) rt - | rt -> rt,List.rev acc - in - decompose_rapp [] - - - - -(* [raw_make_eq t1 t2] build the rawconstr corresponding to [t2 = t1] *) -let raw_make_eq ?(typ= mkRHole ()) t1 t2 = - mkRApp(mkRRef (Lazy.force Coqlib.coq_eq_ref),[typ;t2;t1]) - -(* [raw_make_neq t1 t2] build the rawconstr corresponding to [t1 <> t2] *) -let raw_make_neq t1 t2 = - mkRApp(mkRRef (Lazy.force Coqlib.coq_not_ref),[raw_make_eq t1 t2]) - -(* [raw_make_or P1 P2] build the rawconstr corresponding to [P1 \/ P2] *) -let raw_make_or t1 t2 = mkRApp (mkRRef(Lazy.force Coqlib.coq_or_ref),[t1;t2]) - -(* [raw_make_or_list [P1;...;Pn]] build the rawconstr corresponding - to [P1 \/ ( .... \/ Pn)] -*) -let rec raw_make_or_list = function - | [] -> raise (Invalid_argument "mk_or") - | [e] -> e - | e::l -> raw_make_or e (raw_make_or_list l) - - -let remove_name_from_mapping mapping na = - match na with - | Anonymous -> mapping - | Name id -> Idmap.remove id mapping - -let change_vars = - let rec change_vars mapping rt = - match rt with - | RRef _ -> rt - | RVar(loc,id) -> - let new_id = - try - Idmap.find id mapping - with Not_found -> id - in - RVar(loc,new_id) - | REvar _ -> rt - | RPatVar _ -> rt - | RApp(loc,rt',rtl) -> - RApp(loc, - change_vars mapping rt', - List.map (change_vars mapping) rtl - ) - | RLambda(loc,name,k,t,b) -> - RLambda(loc, - name, - k, - change_vars mapping t, - change_vars (remove_name_from_mapping mapping name) b - ) - | RProd(loc,name,k,t,b) -> - RProd(loc, - name, - k, - change_vars mapping t, - change_vars (remove_name_from_mapping mapping name) b - ) - | RLetIn(loc,name,def,b) -> - RLetIn(loc, - name, - change_vars mapping def, - change_vars (remove_name_from_mapping mapping name) b - ) - | RLetTuple(loc,nal,(na,rto),b,e) -> - let new_mapping = List.fold_left remove_name_from_mapping mapping nal in - RLetTuple(loc, - nal, - (na, Option.map (change_vars mapping) rto), - change_vars mapping b, - change_vars new_mapping e - ) - | RCases(loc,sty,infos,el,brl) -> - RCases(loc,sty, - infos, - List.map (fun (e,x) -> (change_vars mapping e,x)) el, - List.map (change_vars_br mapping) brl - ) - | RIf(loc,b,(na,e_option),lhs,rhs) -> - RIf(loc, - change_vars mapping b, - (na,Option.map (change_vars mapping) e_option), - change_vars mapping lhs, - change_vars mapping rhs - ) - | RRec _ -> error "Local (co)fixes are not supported" - | RSort _ -> rt - | RHole _ -> rt - | RCast(loc,b,CastConv (k,t)) -> - RCast(loc,change_vars mapping b, CastConv (k,change_vars mapping t)) - | RCast(loc,b,CastCoerce) -> - RCast(loc,change_vars mapping b,CastCoerce) - | RDynamic _ -> error "Not handled RDynamic" - and change_vars_br mapping ((loc,idl,patl,res) as br) = - let new_mapping = List.fold_right Idmap.remove idl mapping in - if idmap_is_empty new_mapping - then br - else (loc,idl,patl,change_vars new_mapping res) - in - change_vars - - - -let rec alpha_pat excluded pat = - match pat with - | PatVar(loc,Anonymous) -> - let new_id = Indfun_common.fresh_id excluded "_x" in - PatVar(loc,Name new_id),(new_id::excluded),Idmap.empty - | PatVar(loc,Name id) -> - if List.mem id excluded - then - let new_id = Nameops.next_ident_away id excluded in - PatVar(loc,Name new_id),(new_id::excluded), - (Idmap.add id new_id Idmap.empty) - else pat,excluded,Idmap.empty - | PatCstr(loc,constr,patl,na) -> - let new_na,new_excluded,map = - match na with - | Name id when List.mem id excluded -> - let new_id = Nameops.next_ident_away id excluded in - Name new_id,new_id::excluded, Idmap.add id new_id Idmap.empty - | _ -> na,excluded,Idmap.empty - in - let new_patl,new_excluded,new_map = - List.fold_left - (fun (patl,excluded,map) pat -> - let new_pat,new_excluded,new_map = alpha_pat excluded pat in - (new_pat::patl,new_excluded,Idmap.fold Idmap.add new_map map) - ) - ([],new_excluded,map) - patl - in - PatCstr(loc,constr,List.rev new_patl,new_na),new_excluded,new_map - -let alpha_patl excluded patl = - let patl,new_excluded,map = - List.fold_left - (fun (patl,excluded,map) pat -> - let new_pat,new_excluded,new_map = alpha_pat excluded pat in - new_pat::patl,new_excluded,(Idmap.fold Idmap.add new_map map) - ) - ([],excluded,Idmap.empty) - patl - in - (List.rev patl,new_excluded,map) - - - - -let raw_get_pattern_id pat acc = - let rec get_pattern_id pat = - match pat with - | PatVar(loc,Anonymous) -> assert false - | PatVar(loc,Name id) -> - [id] - | PatCstr(loc,constr,patternl,_) -> - List.fold_right - (fun pat idl -> - let idl' = get_pattern_id pat in - idl'@idl - ) - patternl - [] - in - (get_pattern_id pat)@acc - -let get_pattern_id pat = raw_get_pattern_id pat [] - -let rec alpha_rt excluded rt = - let new_rt = - match rt with - | RRef _ | RVar _ | REvar _ | RPatVar _ -> rt - | RLambda(loc,Anonymous,k,t,b) -> - let new_id = Nameops.next_ident_away (id_of_string "_x") excluded in - let new_excluded = new_id :: excluded in - let new_t = alpha_rt new_excluded t in - let new_b = alpha_rt new_excluded b in - RLambda(loc,Name new_id,k,new_t,new_b) - | RProd(loc,Anonymous,k,t,b) -> - let new_t = alpha_rt excluded t in - let new_b = alpha_rt excluded b in - RProd(loc,Anonymous,k,new_t,new_b) - | RLetIn(loc,Anonymous,t,b) -> - let new_t = alpha_rt excluded t in - let new_b = alpha_rt excluded b in - RLetIn(loc,Anonymous,new_t,new_b) - | RLambda(loc,Name id,k,t,b) -> - let new_id = Nameops.next_ident_away id excluded in - let t,b = - if new_id = id - then t,b - else - let replace = change_vars (Idmap.add id new_id Idmap.empty) in - (t,replace b) - in - let new_excluded = new_id::excluded in - let new_t = alpha_rt new_excluded t in - let new_b = alpha_rt new_excluded b in - RLambda(loc,Name new_id,k,new_t,new_b) - | RProd(loc,Name id,k,t,b) -> - let new_id = Nameops.next_ident_away id excluded in - let new_excluded = new_id::excluded in - let t,b = - if new_id = id - then t,b - else - let replace = change_vars (Idmap.add id new_id Idmap.empty) in - (t,replace b) - in - let new_t = alpha_rt new_excluded t in - let new_b = alpha_rt new_excluded b in - RProd(loc,Name new_id,k,new_t,new_b) - | RLetIn(loc,Name id,t,b) -> - let new_id = Nameops.next_ident_away id excluded in - let t,b = - if new_id = id - then t,b - else - let replace = change_vars (Idmap.add id new_id Idmap.empty) in - (t,replace b) - in - let new_excluded = new_id::excluded in - let new_t = alpha_rt new_excluded t in - let new_b = alpha_rt new_excluded b in - RLetIn(loc,Name new_id,new_t,new_b) - - - | RLetTuple(loc,nal,(na,rto),t,b) -> - let rev_new_nal,new_excluded,mapping = - List.fold_left - (fun (nal,excluded,mapping) na -> - match na with - | Anonymous -> (na::nal,excluded,mapping) - | Name id -> - let new_id = Nameops.next_ident_away id excluded in - if new_id = id - then - na::nal,id::excluded,mapping - else - (Name new_id)::nal,id::excluded,(Idmap.add id new_id mapping) - ) - ([],excluded,Idmap.empty) - nal - in - let new_nal = List.rev rev_new_nal in - let new_rto,new_t,new_b = - if idmap_is_empty mapping - then rto,t,b - else let replace = change_vars mapping in - (Option.map replace rto, t,replace b) - in - let new_t = alpha_rt new_excluded new_t in - let new_b = alpha_rt new_excluded new_b in - let new_rto = Option.map (alpha_rt new_excluded) new_rto in - RLetTuple(loc,new_nal,(na,new_rto),new_t,new_b) - | RCases(loc,sty,infos,el,brl) -> - let new_el = - List.map (function (rt,i) -> alpha_rt excluded rt, i) el - in - RCases(loc,sty,infos,new_el,List.map (alpha_br excluded) brl) - | RIf(loc,b,(na,e_o),lhs,rhs) -> - RIf(loc,alpha_rt excluded b, - (na,Option.map (alpha_rt excluded) e_o), - alpha_rt excluded lhs, - alpha_rt excluded rhs - ) - | RRec _ -> error "Not handled RRec" - | RSort _ -> rt - | RHole _ -> rt - | RCast (loc,b,CastConv (k,t)) -> - RCast(loc,alpha_rt excluded b,CastConv(k,alpha_rt excluded t)) - | RCast (loc,b,CastCoerce) -> - RCast(loc,alpha_rt excluded b,CastCoerce) - | RDynamic _ -> error "Not handled RDynamic" - | RApp(loc,f,args) -> - RApp(loc, - alpha_rt excluded f, - List.map (alpha_rt excluded) args - ) - in - new_rt - -and alpha_br excluded (loc,ids,patl,res) = - let new_patl,new_excluded,mapping = alpha_patl excluded patl in - let new_ids = List.fold_right raw_get_pattern_id new_patl [] in - let new_excluded = new_ids@excluded in - let renamed_res = change_vars mapping res in - let new_res = alpha_rt new_excluded renamed_res in - (loc,new_ids,new_patl,new_res) - -(* - [is_free_in id rt] checks if [id] is a free variable in [rt] -*) -let is_free_in id = - let rec is_free_in = function - | RRef _ -> false - | RVar(_,id') -> id_ord id' id == 0 - | REvar _ -> false - | RPatVar _ -> false - | RApp(_,rt,rtl) -> List.exists is_free_in (rt::rtl) - | RLambda(_,n,_,t,b) | RProd(_,n,_,t,b) | RLetIn(_,n,t,b) -> - let check_in_b = - match n with - | Name id' -> id_ord id' id <> 0 - | _ -> true - in - is_free_in t || (check_in_b && is_free_in b) - | RCases(_,_,_,el,brl) -> - (List.exists (fun (e,_) -> is_free_in e) el) || - List.exists is_free_in_br brl - | RLetTuple(_,nal,_,b,t) -> - let check_in_nal = - not (List.exists (function Name id' -> id'= id | _ -> false) nal) - in - is_free_in t || (check_in_nal && is_free_in b) - - | RIf(_,cond,_,br1,br2) -> - is_free_in cond || is_free_in br1 || is_free_in br2 - | RRec _ -> raise (UserError("",str "Not handled RRec")) - | RSort _ -> false - | RHole _ -> false - | RCast (_,b,CastConv (_,t)) -> is_free_in b || is_free_in t - | RCast (_,b,CastCoerce) -> is_free_in b - | RDynamic _ -> raise (UserError("",str "Not handled RDynamic")) - and is_free_in_br (_,ids,_,rt) = - (not (List.mem id ids)) && is_free_in rt - in - is_free_in - - - -let rec pattern_to_term = function - | PatVar(loc,Anonymous) -> assert false - | PatVar(loc,Name id) -> - mkRVar id - | PatCstr(loc,constr,patternl,_) -> - let cst_narg = - Inductiveops.mis_constructor_nargs_env - (Global.env ()) - constr - in - let implicit_args = - Array.to_list - (Array.init - (cst_narg - List.length patternl) - (fun _ -> mkRHole ()) - ) - in - let patl_as_term = - List.map pattern_to_term patternl - in - mkRApp(mkRRef(Libnames.ConstructRef constr), - implicit_args@patl_as_term - ) - - - -let replace_var_by_term x_id term = - let rec replace_var_by_pattern rt = - match rt with - | RRef _ -> rt - | RVar(_,id) when id_ord id x_id == 0 -> term - | RVar _ -> rt - | REvar _ -> rt - | RPatVar _ -> rt - | RApp(loc,rt',rtl) -> - RApp(loc, - replace_var_by_pattern rt', - List.map replace_var_by_pattern rtl - ) - | RLambda(_,Name id,_,_,_) when id_ord id x_id == 0 -> rt - | RLambda(loc,name,k,t,b) -> - RLambda(loc, - name, - k, - replace_var_by_pattern t, - replace_var_by_pattern b - ) - | RProd(_,Name id,_,_,_) when id_ord id x_id == 0 -> rt - | RProd(loc,name,k,t,b) -> - RProd(loc, - name, - k, - replace_var_by_pattern t, - replace_var_by_pattern b - ) - | RLetIn(_,Name id,_,_) when id_ord id x_id == 0 -> rt - | RLetIn(loc,name,def,b) -> - RLetIn(loc, - name, - replace_var_by_pattern def, - replace_var_by_pattern b - ) - | RLetTuple(_,nal,_,_,_) - when List.exists (function Name id -> id = x_id | _ -> false) nal -> - rt - | RLetTuple(loc,nal,(na,rto),def,b) -> - RLetTuple(loc, - nal, - (na,Option.map replace_var_by_pattern rto), - replace_var_by_pattern def, - replace_var_by_pattern b - ) - | RCases(loc,sty,infos,el,brl) -> - RCases(loc,sty, - infos, - List.map (fun (e,x) -> (replace_var_by_pattern e,x)) el, - List.map replace_var_by_pattern_br brl - ) - | RIf(loc,b,(na,e_option),lhs,rhs) -> - RIf(loc, replace_var_by_pattern b, - (na,Option.map replace_var_by_pattern e_option), - replace_var_by_pattern lhs, - replace_var_by_pattern rhs - ) - | RRec _ -> raise (UserError("",str "Not handled RRec")) - | RSort _ -> rt - | RHole _ -> rt - | RCast(loc,b,CastConv(k,t)) -> - RCast(loc,replace_var_by_pattern b,CastConv(k,replace_var_by_pattern t)) - | RCast(loc,b,CastCoerce) -> - RCast(loc,replace_var_by_pattern b,CastCoerce) - | RDynamic _ -> raise (UserError("",str "Not handled RDynamic")) - and replace_var_by_pattern_br ((loc,idl,patl,res) as br) = - if List.exists (fun id -> id_ord id x_id == 0) idl - then br - else (loc,idl,patl,replace_var_by_pattern res) - in - replace_var_by_pattern - - - - -(* checking unifiability of patterns *) -exception NotUnifiable - -let rec are_unifiable_aux = function - | [] -> () - | eq::eqs -> - match eq with - | PatVar _,_ | _,PatVar _ -> are_unifiable_aux eqs - | PatCstr(_,constructor1,cpl1,_),PatCstr(_,constructor2,cpl2,_) -> - if constructor2 <> constructor1 - then raise NotUnifiable - else - let eqs' = - try ((List.combine cpl1 cpl2)@eqs) - with _ -> anomaly "are_unifiable_aux" - in - are_unifiable_aux eqs' - -let are_unifiable pat1 pat2 = - try - are_unifiable_aux [pat1,pat2]; - true - with NotUnifiable -> false - - -let rec eq_cases_pattern_aux = function - | [] -> () - | eq::eqs -> - match eq with - | PatVar _,PatVar _ -> eq_cases_pattern_aux eqs - | PatCstr(_,constructor1,cpl1,_),PatCstr(_,constructor2,cpl2,_) -> - if constructor2 <> constructor1 - then raise NotUnifiable - else - let eqs' = - try ((List.combine cpl1 cpl2)@eqs) - with _ -> anomaly "eq_cases_pattern_aux" - in - eq_cases_pattern_aux eqs' - | _ -> raise NotUnifiable - -let eq_cases_pattern pat1 pat2 = - try - eq_cases_pattern_aux [pat1,pat2]; - true - with NotUnifiable -> false - - - -let ids_of_pat = - let rec ids_of_pat ids = function - | PatVar(_,Anonymous) -> ids - | PatVar(_,Name id) -> Idset.add id ids - | PatCstr(_,_,patl,_) -> List.fold_left ids_of_pat ids patl - in - ids_of_pat Idset.empty - -let id_of_name = function - | Names.Anonymous -> id_of_string "x" - | Names.Name x -> x - -(* TODO: finish Rec caes *) -let ids_of_rawterm c = - let rec ids_of_rawterm acc c = - let idof = id_of_name in - match c with - | RVar (_,id) -> id::acc - | RApp (loc,g,args) -> - ids_of_rawterm [] g @ List.flatten (List.map (ids_of_rawterm []) args) @ acc - | RLambda (loc,na,k,ty,c) -> idof na :: ids_of_rawterm [] ty @ ids_of_rawterm [] c @ acc - | RProd (loc,na,k,ty,c) -> idof na :: ids_of_rawterm [] ty @ ids_of_rawterm [] c @ acc - | RLetIn (loc,na,b,c) -> idof na :: ids_of_rawterm [] b @ ids_of_rawterm [] c @ acc - | RCast (loc,c,CastConv(k,t)) -> ids_of_rawterm [] c @ ids_of_rawterm [] t @ acc - | RCast (loc,c,CastCoerce) -> ids_of_rawterm [] c @ acc - | RIf (loc,c,(na,po),b1,b2) -> ids_of_rawterm [] c @ ids_of_rawterm [] b1 @ ids_of_rawterm [] b2 @ acc - | RLetTuple (_,nal,(na,po),b,c) -> - List.map idof nal @ ids_of_rawterm [] b @ ids_of_rawterm [] c @ acc - | RCases (loc,sty,rtntypopt,tml,brchl) -> - List.flatten (List.map (fun (_,idl,patl,c) -> idl @ ids_of_rawterm [] c) brchl) - | RRec _ -> failwith "Fix inside a constructor branch" - | (RSort _ | RHole _ | RRef _ | REvar _ | RPatVar _ | RDynamic _) -> [] - in - (* build the set *) - List.fold_left (fun acc x -> Idset.add x acc) Idset.empty (ids_of_rawterm [] c) - - - - - -let zeta_normalize = - let rec zeta_normalize_term rt = - match rt with - | RRef _ -> rt - | RVar _ -> rt - | REvar _ -> rt - | RPatVar _ -> rt - | RApp(loc,rt',rtl) -> - RApp(loc, - zeta_normalize_term rt', - List.map zeta_normalize_term rtl - ) - | RLambda(loc,name,k,t,b) -> - RLambda(loc, - name, - k, - zeta_normalize_term t, - zeta_normalize_term b - ) - | RProd(loc,name,k,t,b) -> - RProd(loc, - name, - k, - zeta_normalize_term t, - zeta_normalize_term b - ) - | RLetIn(_,Name id,def,b) -> - zeta_normalize_term (replace_var_by_term id def b) - | RLetIn(loc,Anonymous,def,b) -> zeta_normalize_term b - | RLetTuple(loc,nal,(na,rto),def,b) -> - RLetTuple(loc, - nal, - (na,Option.map zeta_normalize_term rto), - zeta_normalize_term def, - zeta_normalize_term b - ) - | RCases(loc,sty,infos,el,brl) -> - RCases(loc,sty, - infos, - List.map (fun (e,x) -> (zeta_normalize_term e,x)) el, - List.map zeta_normalize_br brl - ) - | RIf(loc,b,(na,e_option),lhs,rhs) -> - RIf(loc, zeta_normalize_term b, - (na,Option.map zeta_normalize_term e_option), - zeta_normalize_term lhs, - zeta_normalize_term rhs - ) - | RRec _ -> raise (UserError("",str "Not handled RRec")) - | RSort _ -> rt - | RHole _ -> rt - | RCast(loc,b,CastConv(k,t)) -> - RCast(loc,zeta_normalize_term b,CastConv(k,zeta_normalize_term t)) - | RCast(loc,b,CastCoerce) -> - RCast(loc,zeta_normalize_term b,CastCoerce) - | RDynamic _ -> raise (UserError("",str "Not handled RDynamic")) - and zeta_normalize_br (loc,idl,patl,res) = - (loc,idl,patl,zeta_normalize_term res) - in - zeta_normalize_term - - - - -let expand_as = - - let rec add_as map pat = - match pat with - | PatVar _ -> map - | PatCstr(_,_,patl,Name id) -> - Idmap.add id (pattern_to_term pat) (List.fold_left add_as map patl) - | PatCstr(_,_,patl,_) -> List.fold_left add_as map patl - in - let rec expand_as map rt = - match rt with - | RRef _ | REvar _ | RPatVar _ | RSort _ | RHole _ -> rt - | RVar(_,id) -> - begin - try - Idmap.find id map - with Not_found -> rt - end - | RApp(loc,f,args) -> RApp(loc,expand_as map f,List.map (expand_as map) args) - | RLambda(loc,na,k,t,b) -> RLambda(loc,na,k,expand_as map t, expand_as map b) - | RProd(loc,na,k,t,b) -> RProd(loc,na,k,expand_as map t, expand_as map b) - | RLetIn(loc,na,v,b) -> RLetIn(loc,na, expand_as map v,expand_as map b) - | RLetTuple(loc,nal,(na,po),v,b) -> - RLetTuple(loc,nal,(na,Option.map (expand_as map) po), - expand_as map v, expand_as map b) - | RIf(loc,e,(na,po),br1,br2) -> - RIf(loc,expand_as map e,(na,Option.map (expand_as map) po), - expand_as map br1, expand_as map br2) - | RRec _ -> error "Not handled RRec" - | RDynamic _ -> error "Not handled RDynamic" - | RCast(loc,b,CastConv(kind,t)) -> RCast(loc,expand_as map b,CastConv(kind,expand_as map t)) - | RCast(loc,b,CastCoerce) -> RCast(loc,expand_as map b,CastCoerce) - | RCases(loc,sty,po,el,brl) -> - RCases(loc, sty, Option.map (expand_as map) po, List.map (fun (rt,t) -> expand_as map rt,t) el, - List.map (expand_as_br map) brl) - and expand_as_br map (loc,idl,cpl,rt) = - (loc,idl,cpl, expand_as (List.fold_left add_as map cpl) rt) - in - expand_as Idmap.empty diff --git a/contrib/funind/rawtermops.mli b/contrib/funind/rawtermops.mli deleted file mode 100644 index 358c6ba6..00000000 --- a/contrib/funind/rawtermops.mli +++ /dev/null @@ -1,126 +0,0 @@ -open Rawterm - -(* Ocaml 3.06 Map.S does not handle is_empty *) -val idmap_is_empty : 'a Names.Idmap.t -> bool - - -(* [get_pattern_id pat] returns a list of all the variable appearing in [pat] *) -val get_pattern_id : cases_pattern -> Names.identifier list - -(* [pattern_to_term pat] returns a rawconstr corresponding to [pat]. - [pat] must not contain occurences of anonymous pattern -*) -val pattern_to_term : cases_pattern -> rawconstr - -(* - Some basic functions to rebuild rawconstr - In each of them the location is Util.dummy_loc -*) -val mkRRef : Libnames.global_reference -> rawconstr -val mkRVar : Names.identifier -> rawconstr -val mkRApp : rawconstr*(rawconstr list) -> rawconstr -val mkRLambda : Names.name*rawconstr*rawconstr -> rawconstr -val mkRProd : Names.name*rawconstr*rawconstr -> rawconstr -val mkRLetIn : Names.name*rawconstr*rawconstr -> rawconstr -val mkRCases : rawconstr option * tomatch_tuples * cases_clauses -> rawconstr -val mkRSort : rawsort -> rawconstr -val mkRHole : unit -> rawconstr (* we only build Evd.BinderType Anonymous holes *) -val mkRCast : rawconstr* rawconstr -> rawconstr -(* - Some basic functions to decompose rawconstrs - These are analogous to the ones constrs -*) -val raw_decompose_prod : rawconstr -> (Names.name*rawconstr) list * rawconstr -val raw_decompose_prod_or_letin : - rawconstr -> (Names.name*rawconstr option*rawconstr option) list * rawconstr -val raw_decompose_prod_n : int -> rawconstr -> (Names.name*rawconstr) list * rawconstr -val raw_decompose_prod_or_letin_n : int -> rawconstr -> - (Names.name*rawconstr option*rawconstr option) list * rawconstr -val raw_compose_prod : rawconstr -> (Names.name*rawconstr) list -> rawconstr -val raw_compose_prod_or_letin: rawconstr -> - (Names.name*rawconstr option*rawconstr option) list -> rawconstr -val raw_decompose_app : rawconstr -> rawconstr*(rawconstr list) - - -(* [raw_make_eq t1 t2] build the rawconstr corresponding to [t2 = t1] *) -val raw_make_eq : ?typ:rawconstr -> rawconstr -> rawconstr -> rawconstr -(* [raw_make_neq t1 t2] build the rawconstr corresponding to [t1 <> t2] *) -val raw_make_neq : rawconstr -> rawconstr -> rawconstr -(* [raw_make_or P1 P2] build the rawconstr corresponding to [P1 \/ P2] *) -val raw_make_or : rawconstr -> rawconstr -> rawconstr - -(* [raw_make_or_list [P1;...;Pn]] build the rawconstr corresponding - to [P1 \/ ( .... \/ Pn)] -*) -val raw_make_or_list : rawconstr list -> rawconstr - - -(* alpha_conversion functions *) - - - -(* Replace the var mapped in the rawconstr/context *) -val change_vars : Names.identifier Names.Idmap.t -> rawconstr -> rawconstr - - - -(* [alpha_pat avoid pat] rename all the variables present in [pat] s.t. - the result does not share variables with [avoid]. This function create - a fresh variable for each occurence of the anonymous pattern. - - Also returns a mapping from old variables to new ones and the concatenation of - [avoid] with the variables appearing in the result. -*) - val alpha_pat : - Names.Idmap.key list -> - Rawterm.cases_pattern -> - Rawterm.cases_pattern * Names.Idmap.key list * - Names.identifier Names.Idmap.t - -(* [alpha_rt avoid rt] alpha convert [rt] s.t. the result repects barendregt - conventions and does not share bound variables with avoid -*) -val alpha_rt : Names.identifier list -> rawconstr -> rawconstr - -(* same as alpha_rt but for case branches *) -val alpha_br : Names.identifier list -> - Util.loc * Names.identifier list * Rawterm.cases_pattern list * - Rawterm.rawconstr -> - Util.loc * Names.identifier list * Rawterm.cases_pattern list * - Rawterm.rawconstr - - -(* Reduction function *) -val replace_var_by_term : - Names.identifier -> - Rawterm.rawconstr -> Rawterm.rawconstr -> Rawterm.rawconstr - - - -(* - [is_free_in id rt] checks if [id] is a free variable in [rt] -*) -val is_free_in : Names.identifier -> rawconstr -> bool - - -val are_unifiable : cases_pattern -> cases_pattern -> bool -val eq_cases_pattern : cases_pattern -> cases_pattern -> bool - - - -(* - ids_of_pat : cases_pattern -> Idset.t - returns the set of variables appearing in a pattern -*) -val ids_of_pat : cases_pattern -> Names.Idset.t - -(* TODO: finish this function (Fix not treated) *) -val ids_of_rawterm: rawconstr -> Names.Idset.t - -(* - removing let_in construction in a rawterm -*) -val zeta_normalize : Rawterm.rawconstr -> Rawterm.rawconstr - - -val expand_as : rawconstr -> rawconstr diff --git a/contrib/funind/recdef.ml b/contrib/funind/recdef.ml deleted file mode 100644 index 14bf7cf8..00000000 --- a/contrib/funind/recdef.ml +++ /dev/null @@ -1,1436 +0,0 @@ -(************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *) -(* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) -(************************************************************************) - -(*i camlp4deps: "parsing/grammar.cma" i*) - -(* $Id: recdef.ml 12221 2009-07-04 21:53:12Z jforest $ *) - -open Term -open Termops -open Environ -open Declarations -open Entries -open Pp -open Names -open Libnames -open Nameops -open Util -open Closure -open RedFlags -open Tacticals -open Typing -open Tacmach -open Tactics -open Nametab -open Decls -open Declare -open Decl_kinds -open Tacred -open Proof_type -open Vernacinterp -open Pfedit -open Topconstr -open Rawterm -open Pretyping -open Pretyping.Default -open Safe_typing -open Constrintern -open Hiddentac - -open Equality -open Auto -open Eauto - -open Genarg - - -let compute_renamed_type gls c = - rename_bound_var (pf_env gls) [] (pf_type_of gls c) - -let qed () = Command.save_named true -let defined () = Command.save_named false - -let pf_get_new_ids idl g = - let ids = pf_ids_of_hyps g in - List.fold_right - (fun id acc -> next_global_ident_away false id (acc@ids)::acc) - idl - [] - -let pf_get_new_id id g = - List.hd (pf_get_new_ids [id] g) - -let h_intros l = - tclMAP h_intro l - -let do_observe_tac s tac g = - let goal = begin (Printer.pr_goal (sig_it g)) end in - try let v = tac g in msgnl (goal ++ fnl () ++ (str "recdef ") ++ - (str s)++(str " ")++(str "finished")); v - with e -> - msgnl (str "observation "++str s++str " raised exception " ++ - Cerrors.explain_exn e ++ str " on goal " ++ goal ); - raise e;; - - -let observe_tac s tac g = - if Tacinterp.get_debug () <> Tactic_debug.DebugOff - then do_observe_tac s tac g - else tac g - -let hyp_ids = List.map id_of_string - ["x";"v";"k";"def";"p";"h";"n";"h'"; "anonymous"; "teq"; "rec_res"; - "hspec";"heq"; "hrec"; "hex"; "teq"; "pmax";"hle"];; - -let rec nthtl = function - l, 0 -> l | _::tl, n -> nthtl (tl, n-1) | [], _ -> [];; - -let hyp_id n l = List.nth l n;; - -let (x_id:identifier) = hyp_id 0 hyp_ids;; -let (v_id:identifier) = hyp_id 1 hyp_ids;; -let (k_id:identifier) = hyp_id 2 hyp_ids;; -let (def_id:identifier) = hyp_id 3 hyp_ids;; -let (p_id:identifier) = hyp_id 4 hyp_ids;; -let (h_id:identifier) = hyp_id 5 hyp_ids;; -let (n_id:identifier) = hyp_id 6 hyp_ids;; -let (h'_id:identifier) = hyp_id 7 hyp_ids;; -let (ano_id:identifier) = hyp_id 8 hyp_ids;; -let (rec_res_id:identifier) = hyp_id 10 hyp_ids;; -let (hspec_id:identifier) = hyp_id 11 hyp_ids;; -let (heq_id:identifier) = hyp_id 12 hyp_ids;; -let (hrec_id:identifier) = hyp_id 13 hyp_ids;; -let (hex_id:identifier) = hyp_id 14 hyp_ids;; -let (teq_id:identifier) = hyp_id 15 hyp_ids;; -let (pmax_id:identifier) = hyp_id 16 hyp_ids;; -let (hle_id:identifier) = hyp_id 17 hyp_ids;; - -let message s = if Flags.is_verbose () then msgnl(str s);; - -let def_of_const t = - match (kind_of_term t) with - Const sp -> - (try (match (Global.lookup_constant sp) with - {const_body=Some c} -> Declarations.force c - |_ -> assert false) - with _ -> - anomaly ("Cannot find definition of constant "^ - (string_of_id (id_of_label (con_label sp)))) - ) - |_ -> assert false - -let type_of_const t = - match (kind_of_term t) with - Const sp -> Typeops.type_of_constant (Global.env()) sp - |_ -> assert false - -let arg_type t = - match kind_of_term (def_of_const t) with - Lambda(a,b,c) -> b - | _ -> assert false;; - -let evaluable_of_global_reference r = - match r with - ConstRef sp -> EvalConstRef sp - | VarRef id -> EvalVarRef id - | _ -> assert false;; - - -let rank_for_arg_list h = - let predicate a b = - try List.for_all2 eq_constr a b with - Invalid_argument _ -> false in - let rec rank_aux i = function - | [] -> None - | x::tl -> if predicate h x then Some i else rank_aux (i+1) tl in - rank_aux 0;; - -let rec (find_call_occs : int -> constr -> constr -> - (constr list -> constr) * constr list list) = - fun nb_lam f expr -> - match (kind_of_term expr) with - App (g, args) when g = f -> - (fun l -> List.hd l), [Array.to_list args] - | App (g, args) -> - let (largs: constr list) = Array.to_list args in - let rec find_aux = function - [] -> (fun x -> []), [] - | a::upper_tl -> - (match find_aux upper_tl with - (cf, ((arg1::args) as args_for_upper_tl)) -> - (match find_call_occs nb_lam f a with - cf2, (_ :: _ as other_args) -> - let rec avoid_duplicates args = - match args with - | [] -> (fun _ -> []), [] - | h::tl -> - let recomb_tl, args_for_tl = - avoid_duplicates tl in - match rank_for_arg_list h args_for_upper_tl with - | None -> - (fun l -> List.hd l::recomb_tl(List.tl l)), - h::args_for_tl - | Some i -> - (fun l -> List.nth l (i+List.length args_for_tl):: - recomb_tl l), - args_for_tl - in - let recombine, other_args' = - avoid_duplicates other_args in - let len1 = List.length other_args' in - (fun l -> cf2 (recombine l)::cf(nthtl(l,len1))), - other_args'@args_for_upper_tl - | _, [] -> (fun x -> a::cf x), args_for_upper_tl) - | _, [] -> - (match find_call_occs nb_lam f a with - cf, (arg1::args) -> (fun l -> cf l::upper_tl), (arg1::args) - | _, [] -> (fun x -> a::upper_tl), [])) in - begin - match (find_aux largs) with - cf, [] -> (fun l -> mkApp(g, args)), [] - | cf, args -> - (fun l -> mkApp (g, Array.of_list (cf l))), args - end - | Rel(v) -> if v > nb_lam then error "find_call_occs : Rel" else ((fun l -> expr),[]) - | Var(id) -> (fun l -> expr), [] - | Meta(_) -> error "find_call_occs : Meta" - | Evar(_) -> error "find_call_occs : Evar" - | Sort(_) -> (fun l -> expr), [] - | Cast(b,_,_) -> find_call_occs nb_lam f b - | Prod(_,_,_) -> error "find_call_occs : Prod" - | Lambda(na,t,b) -> - begin - match find_call_occs (succ nb_lam) f b with - | _, [] -> (* Lambda are authorized as long as they do not contain - recursives calls *) - (fun l -> expr),[] - | _ -> error "find_call_occs : Lambda" - end - | LetIn(na,v,t,b) -> - begin - match find_call_occs nb_lam f v, find_call_occs (succ nb_lam) f b with - | (_,[]),(_,[]) -> - ((fun l -> expr), []) - | (_,[]),(cf,(_::_ as l)) -> - ((fun l -> mkLetIn(na,v,t,cf l)),l) - | (cf,(_::_ as l)),(_,[]) -> - ((fun l -> mkLetIn(na,cf l,t,b)), l) - | _ -> error "find_call_occs : LetIn" - end - | Const(_) -> (fun l -> expr), [] - | Ind(_) -> (fun l -> expr), [] - | Construct (_, _) -> (fun l -> expr), [] - | Case(i,t,a,r) -> - (match find_call_occs nb_lam f a with - cf, (arg1::args) -> (fun l -> mkCase(i, t, (cf l), r)),(arg1::args) - | _ -> (fun l -> expr),[]) - | Fix(_) -> error "find_call_occs : Fix" - | CoFix(_) -> error "find_call_occs : CoFix";; - -let coq_constant s = - Coqlib.gen_constant_in_modules "RecursiveDefinition" - (Coqlib.init_modules @ Coqlib.arith_modules) s;; - -let constant sl s = - constr_of_global - (locate (make_qualid(Names.make_dirpath - (List.map id_of_string (List.rev sl))) - (id_of_string s)));; - -let find_reference sl s = - (locate (make_qualid(Names.make_dirpath - (List.map id_of_string (List.rev sl))) - (id_of_string s)));; - -let delayed_force f = f () - -let le_lt_SS = function () -> (constant ["Recdef"] "le_lt_SS") -let le_lt_n_Sm = function () -> (coq_constant "le_lt_n_Sm") - -let le_trans = function () -> (coq_constant "le_trans") -let le_lt_trans = function () -> (coq_constant "le_lt_trans") -let lt_S_n = function () -> (coq_constant "lt_S_n") -let le_n = function () -> (coq_constant "le_n") -let refl_equal = function () -> (coq_constant "refl_equal") -let eq = function () -> (coq_constant "eq") -let ex = function () -> (coq_constant "ex") -let coq_sig_ref = function () -> (find_reference ["Coq";"Init";"Specif"] "sig") -let coq_sig = function () -> (coq_constant "sig") -let coq_O = function () -> (coq_constant "O") -let coq_S = function () -> (coq_constant "S") - -let gt_antirefl = function () -> (coq_constant "gt_irrefl") -let lt_n_O = function () -> (coq_constant "lt_n_O") -let lt_n_Sn = function () -> (coq_constant "lt_n_Sn") - -let f_equal = function () -> (coq_constant "f_equal") -let well_founded_induction = function () -> (coq_constant "well_founded_induction") -let well_founded = function () -> (coq_constant "well_founded") -let acc_rel = function () -> (coq_constant "Acc") -let acc_inv_id = function () -> (coq_constant "Acc_inv") -let well_founded_ltof = function () -> (Coqlib.coq_constant "" ["Arith";"Wf_nat"] "well_founded_ltof") -let iter_ref = function () -> (try find_reference ["Recdef"] "iter" with Not_found -> error "module Recdef not loaded") -let max_ref = function () -> (find_reference ["Recdef"] "max") -let iter = function () -> (constr_of_global (delayed_force iter_ref)) -let max_constr = function () -> (constr_of_global (delayed_force max_ref)) - -let ltof_ref = function () -> (find_reference ["Coq";"Arith";"Wf_nat"] "ltof") -let coq_conj = function () -> find_reference ["Coq";"Init";"Logic"] "conj" - -(* These are specific to experiments in nat with lt as well_founded_relation, *) -(* but this should be made more general. *) -let nat = function () -> (coq_constant "nat") -let lt = function () -> (coq_constant "lt") - -(* This is simply an implementation of the case_eq tactic. this code - should be replaced with the tactic defined in Ltac in Init/Tactics.v *) -let mkCaseEq a : tactic = - (fun g -> - let type_of_a = pf_type_of g a in - tclTHENLIST - [h_generalize [mkApp(delayed_force refl_equal, [| type_of_a; a|])]; - (fun g2 -> - change_in_concl None - (pattern_occs [((false,[1]), a)] (pf_env g2) Evd.empty (pf_concl g2)) - g2); - simplest_case a] g);; - -(* This is like the previous one except that it also rewrite on all - hypotheses except the ones given in the first argument. All the - modified hypotheses are generalized in the process and should be - introduced back later; the result is the pair of the tactic and the - list of hypotheses that have been generalized and cleared. *) -let mkDestructEq : - identifier list -> constr -> goal sigma -> tactic * identifier list = - fun not_on_hyp expr g -> - let hyps = pf_hyps g in - let to_revert = - Util.map_succeed - (fun (id,_,t) -> - if List.mem id not_on_hyp || not (Termops.occur_term expr t) - then failwith "is_expr_context"; - id) hyps in - let to_revert_constr = List.rev_map mkVar to_revert in - let type_of_expr = pf_type_of g expr in - let new_hyps = mkApp(delayed_force refl_equal, [|type_of_expr; expr|]):: - to_revert_constr in - tclTHENLIST - [h_generalize new_hyps; - (fun g2 -> - change_in_concl None - (pattern_occs [((false,[1]), expr)] (pf_env g2) Evd.empty (pf_concl g2)) g2); - simplest_case expr], to_revert - -let rec mk_intros_and_continue thin_intros (extra_eqn:bool) - cont_function (eqs:constr list) nb_lam (expr:constr) g = - let finalize () = if extra_eqn then - let teq = pf_get_new_id teq_id g in - tclTHENLIST - [ h_intro teq; - thin thin_intros; - h_intros thin_intros; - - tclMAP - (fun eq -> tclTRY (Equality.general_rewrite_in true all_occurrences teq eq false)) - (List.rev eqs); - (fun g1 -> - let ty_teq = pf_type_of g1 (mkVar teq) in - let teq_lhs,teq_rhs = - let _,args = try destApp ty_teq with _ -> Pp.msgnl (Printer.pr_goal (sig_it g1) ++ fnl () ++ pr_id teq ++ str ":" ++ Printer.pr_lconstr ty_teq); assert false in - args.(1),args.(2) - in - cont_function (mkVar teq::eqs) (replace_term teq_lhs teq_rhs expr) g1 - ) - ] - g - else - tclTHENSEQ[ - thin thin_intros; - h_intros thin_intros; - cont_function eqs expr - ] g - in - if nb_lam = 0 - then finalize () - else - match kind_of_term expr with - | Lambda (n, _, b) -> - let n1 = - match n with - Name x -> x - | Anonymous -> ano_id - in - let new_n = pf_get_new_id n1 g in - tclTHEN (h_intro new_n) - (mk_intros_and_continue thin_intros extra_eqn cont_function eqs - (pred nb_lam) (subst1 (mkVar new_n) b)) g - | _ -> - assert false -(* finalize () *) -let const_of_ref = function - ConstRef kn -> kn - | _ -> anomaly "ConstRef expected" - -let simpl_iter clause = - reduce - (Lazy - {rBeta=true;rIota=true;rZeta= true; rDelta=false; - rConst = [ EvalConstRef (const_of_ref (delayed_force iter_ref))]}) -(* (Simpl (Some ([],mkConst (const_of_ref (delayed_force iter_ref))))) *) - clause - -(* The boolean value is_mes expresses that the termination is expressed - using a measure function instead of a well-founded relation. *) -let tclUSER tac is_mes l g = - let clear_tac = - match l with - | None -> h_clear true [] - | Some l -> tclMAP (fun id -> tclTRY (h_clear false [id])) (List.rev l) - in - tclTHENSEQ - [ - clear_tac; - if is_mes - then tclTHEN - (unfold_in_concl [(all_occurrences, evaluable_of_global_reference - (delayed_force ltof_ref))]) - tac - else tac - ] - g - - -let list_rewrite (rev:bool) (eqs: constr list) = - tclREPEAT - (List.fold_right - (fun eq i -> tclORELSE (rewriteLR eq) i) - (if rev then (List.rev eqs) else eqs) (tclFAIL 0 (mt())));; - -let base_leaf_terminate (func:global_reference) eqs expr = -(* let _ = msgnl (str "entering base_leaf") in *) - (fun g -> - let k',h = - match pf_get_new_ids [k_id;h_id] g with - [k';h] -> k',h - | _ -> assert false - in - tclTHENLIST - [observe_tac "first split" (split (ImplicitBindings [expr])); - observe_tac "second split" - (split (ImplicitBindings [delayed_force coq_O])); - observe_tac "intro k" (h_intro k'); - observe_tac "case on k" - (tclTHENS (simplest_case (mkVar k')) - [(tclTHEN (h_intro h) - (tclTHEN (simplest_elim (mkApp (delayed_force gt_antirefl, - [| delayed_force coq_O |]))) - default_auto)); tclIDTAC ]); - intros; - simpl_iter onConcl; - unfold_constr func; - list_rewrite true eqs; - default_auto] g);; - -(* La fonction est donnee en premier argument a la - fonctionnelle suivie d'autres Lambdas et de Case ... - Pour recuperer la fonction f a partir de la - fonctionnelle *) - -let get_f foncl = - match (kind_of_term (def_of_const foncl)) with - Lambda (Name f, _, _) -> f - |_ -> error "la fonctionnelle est mal definie";; - - -let rec compute_le_proofs = function - [] -> assumption - | a::tl -> - tclORELSE assumption - (tclTHENS - (fun g -> - let le_trans = delayed_force le_trans in - let t_le_trans = compute_renamed_type g le_trans in - let m_id = - let _,_,t = destProd t_le_trans in - let na,_,_ = destProd t in - Nameops.out_name na - in - apply_with_bindings - (le_trans, - ExplicitBindings[dummy_loc,NamedHyp m_id,a]) - g) - [compute_le_proofs tl; - tclORELSE (apply (delayed_force le_n)) assumption]) - -let make_lt_proof pmax le_proof = - tclTHENS - (fun g -> - let le_lt_trans = delayed_force le_lt_trans in - let t_le_lt_trans = compute_renamed_type g le_lt_trans in - let m_id = - let _,_,t = destProd t_le_lt_trans in - let na,_,_ = destProd t in - Nameops.out_name na - in - apply_with_bindings - (le_lt_trans, - ExplicitBindings[dummy_loc,NamedHyp m_id, pmax]) g) - [observe_tac "compute_le_proofs" (compute_le_proofs le_proof); - tclTHENLIST[observe_tac "lt_S_n" (apply (delayed_force lt_S_n)); default_full_auto]];; - -let rec list_cond_rewrite k def pmax cond_eqs le_proofs = - match cond_eqs with - [] -> tclIDTAC - | eq::eqs -> - (fun g -> - let t_eq = compute_renamed_type g (mkVar eq) in - let k_id,def_id = - let k_na,_,t = destProd t_eq in - let _,_,t = destProd t in - let def_na,_,_ = destProd t in - Nameops.out_name k_na,Nameops.out_name def_na - in - tclTHENS - (general_rewrite_bindings false all_occurrences - (mkVar eq, - ExplicitBindings[dummy_loc, NamedHyp k_id, mkVar k; - dummy_loc, NamedHyp def_id, mkVar def]) false) - [list_cond_rewrite k def pmax eqs le_proofs; - observe_tac "make_lt_proof" (make_lt_proof pmax le_proofs)] g - ) - -let rec introduce_all_equalities func eqs values specs bound le_proofs - cond_eqs = - match specs with - [] -> - fun g -> - let ids = pf_ids_of_hyps g in - let s_max = mkApp(delayed_force coq_S, [|bound|]) in - let k = next_global_ident_away true k_id ids in - let ids = k::ids in - let h' = next_global_ident_away true (h'_id) ids in - let ids = h'::ids in - let def = next_global_ident_away true def_id ids in - tclTHENLIST - [observe_tac "introduce_all_equalities_final split" (split (ImplicitBindings [s_max])); - observe_tac "introduce_all_equalities_final intro k" (h_intro k); - tclTHENS - (observe_tac "introduce_all_equalities_final case k" (simplest_case (mkVar k))) - [ - tclTHENLIST[h_intro h'; - simplest_elim(mkApp(delayed_force lt_n_O,[|s_max|])); - default_full_auto]; - tclIDTAC - ]; - observe_tac "clearing k " (clear [k]); - observe_tac "intros k h' def" (h_intros [k;h';def]); - observe_tac "simple_iter" (simpl_iter onConcl); - observe_tac "unfold functional" - (unfold_in_concl[((true,[1]),evaluable_of_global_reference func)]); - observe_tac "rewriting equations" - (list_rewrite true eqs); - observe_tac ("cond rewrite "^(string_of_id k)) (list_cond_rewrite k def bound cond_eqs le_proofs); - observe_tac "refl equal" (apply (delayed_force refl_equal))] g - | spec1::specs -> - fun g -> - let ids = ids_of_named_context (pf_hyps g) in - let p = next_global_ident_away true p_id ids in - let ids = p::ids in - let pmax = next_global_ident_away true pmax_id ids in - let ids = pmax::ids in - let hle1 = next_global_ident_away true hle_id ids in - let ids = hle1::ids in - let hle2 = next_global_ident_away true hle_id ids in - let ids = hle2::ids in - let heq = next_global_ident_away true heq_id ids in - tclTHENLIST - [simplest_elim (mkVar spec1); - list_rewrite true eqs; - h_intros [p; heq]; - simplest_elim (mkApp(delayed_force max_constr, [| bound; mkVar p|])); - h_intros [pmax; hle1; hle2]; - introduce_all_equalities func eqs values specs - (mkVar pmax) ((mkVar pmax)::le_proofs) - (heq::cond_eqs)] g;; - -let string_match s = - if String.length s < 3 then failwith "string_match"; - try - for i = 0 to 3 do - if String.get s i <> String.get "Acc_" i then failwith "string_match" - done; - with Invalid_argument _ -> failwith "string_match" - -let retrieve_acc_var g = - (* Julien: I don't like this version .... *) - let hyps = pf_ids_of_hyps g in - map_succeed - (fun id -> string_match (string_of_id id);id) - hyps - -let rec introduce_all_values concl_tac is_mes acc_inv func context_fn - eqs hrec args values specs = - (match args with - [] -> - tclTHENLIST - [observe_tac "split" (split(ImplicitBindings - [context_fn (List.map mkVar (List.rev values))])); - observe_tac "introduce_all_equalities" (introduce_all_equalities func eqs - (List.rev values) (List.rev specs) (delayed_force coq_O) [] [])] - | arg::args -> - (fun g -> - let ids = ids_of_named_context (pf_hyps g) in - let rec_res = next_global_ident_away true rec_res_id ids in - let ids = rec_res::ids in - let hspec = next_global_ident_away true hspec_id ids in - let tac = - observe_tac "introduce_all_values" ( - introduce_all_values concl_tac is_mes acc_inv func context_fn eqs - hrec args - (rec_res::values)(hspec::specs)) in - (tclTHENS - (observe_tac "elim h_rec" - (simplest_elim (mkApp(mkVar hrec, Array.of_list arg))) - ) - [tclTHENLIST [h_intros [rec_res; hspec]; - tac]; - (tclTHENS - (observe_tac "acc_inv" (apply (Lazy.force acc_inv))) - [(* tclTHEN (tclTRY(list_rewrite true eqs)) *) - (observe_tac "h_assumption" h_assumption) - ; - tclTHENLIST - [ - tclTRY(list_rewrite true eqs); - observe_tac "user proof" - (fun g -> - tclUSER - concl_tac - is_mes - (Some (hrec::hspec::(retrieve_acc_var g)@specs)) - g - ) - ] - ] - ) - ]) g) - - ) - - -let rec_leaf_terminate f_constr concl_tac is_mes acc_inv hrec (func:global_reference) eqs expr = - match find_call_occs 0 f_constr expr with - | context_fn, args -> - observe_tac "introduce_all_values" - (introduce_all_values concl_tac is_mes acc_inv func context_fn eqs hrec args [] []) - -let proveterminate rec_arg_id is_mes acc_inv (hrec:identifier) - (f_constr:constr) (func:global_reference) base_leaf rec_leaf = - let rec proveterminate (eqs:constr list) (expr:constr) = - try - (* let _ = msgnl (str "entering proveterminate") in *) - let v = - match (kind_of_term expr) with - Case (ci, t, a, l) -> - (match find_call_occs 0 f_constr a with - _,[] -> - (fun g -> - let destruct_tac, rev_to_thin_intro = - mkDestructEq rec_arg_id a g in - tclTHENS destruct_tac - (list_map_i - (fun i -> mk_intros_and_continue - (List.rev rev_to_thin_intro) - true - proveterminate - eqs - ci.ci_cstr_nargs.(i)) - 0 (Array.to_list l)) g) - | _, _::_ -> - (match find_call_occs 0 f_constr expr with - _,[] -> observe_tac "base_leaf" (base_leaf func eqs expr) - | _, _:: _ -> - observe_tac "rec_leaf" - (rec_leaf is_mes acc_inv hrec func eqs expr))) - | _ -> - (match find_call_occs 0 f_constr expr with - _,[] -> - (try observe_tac "base_leaf" (base_leaf func eqs expr) - with e -> (msgerrnl (str "failure in base case");raise e )) - | _, _::_ -> - observe_tac "rec_leaf" - (rec_leaf is_mes acc_inv hrec func eqs expr)) in - v - with e -> begin msgerrnl(str "failure in proveterminate"); raise e end - in - proveterminate - -let hyp_terminates nb_args func = - let a_arrow_b = arg_type (constr_of_global func) in - let rev_args,b = decompose_prod_n nb_args a_arrow_b in - let left = - mkApp(delayed_force iter, - Array.of_list - (lift 5 a_arrow_b:: mkRel 3:: - constr_of_global func::mkRel 1:: - List.rev (list_map_i (fun i _ -> mkRel (6+i)) 0 rev_args) - ) - ) - in - let right = mkRel 5 in - let equality = mkApp(delayed_force eq, [|lift 5 b; left; right|]) in - let result = (mkProd ((Name def_id) , lift 4 a_arrow_b, equality)) in - let cond = mkApp(delayed_force lt, [|(mkRel 2); (mkRel 1)|]) in - let nb_iter = - mkApp(delayed_force ex, - [|delayed_force nat; - (mkLambda - (Name - p_id, - delayed_force nat, - (mkProd (Name k_id, delayed_force nat, - mkArrow cond result))))|])in - let value = mkApp(delayed_force coq_sig, - [|b; - (mkLambda (Name v_id, b, nb_iter))|]) in - compose_prod rev_args value - - - -let tclUSER_if_not_mes concl_tac is_mes names_to_suppress = - if is_mes - then tclCOMPLETE (h_simplest_apply (delayed_force well_founded_ltof)) - else tclUSER concl_tac is_mes names_to_suppress - -let termination_proof_header is_mes input_type ids args_id relation - rec_arg_num rec_arg_id tac wf_tac : tactic = - begin - fun g -> - let nargs = List.length args_id in - let pre_rec_args = - List.rev_map - mkVar (fst (list_chop (rec_arg_num - 1) args_id)) - in - let relation = substl pre_rec_args relation in - let input_type = substl pre_rec_args input_type in - let wf_thm = next_global_ident_away true (id_of_string ("wf_R")) ids in - let wf_rec_arg = - next_global_ident_away true - (id_of_string ("Acc_"^(string_of_id rec_arg_id))) - (wf_thm::ids) - in - let hrec = next_global_ident_away true hrec_id - (wf_rec_arg::wf_thm::ids) in - let acc_inv = - lazy ( - mkApp ( - delayed_force acc_inv_id, - [|input_type;relation;mkVar rec_arg_id|] - ) - ) - in - tclTHEN - (h_intros args_id) - (tclTHENS - (observe_tac - "first assert" - (assert_tac - (Name wf_rec_arg) - (mkApp (delayed_force acc_rel, - [|input_type;relation;mkVar rec_arg_id|]) - ) - ) - ) - [ - (* accesibility proof *) - tclTHENS - (observe_tac - "second assert" - (assert_tac - (Name wf_thm) - (mkApp (delayed_force well_founded,[|input_type;relation|])) - ) - ) - [ - (* interactive proof that the relation is well_founded *) - observe_tac "wf_tac" (wf_tac is_mes (Some args_id)); - (* this gives the accessibility argument *) - observe_tac - "apply wf_thm" - (h_simplest_apply (mkApp(mkVar wf_thm,[|mkVar rec_arg_id|])) - ) - ] - ; - (* rest of the proof *) - tclTHENSEQ - [observe_tac "generalize" - (onNLastHyps (nargs+1) - (fun (id,_,_) -> - tclTHEN (h_generalize [mkVar id]) (h_clear false [id]) - )) - ; - observe_tac "h_fix" (h_fix (Some hrec) (nargs+1)); - h_intros args_id; - h_intro wf_rec_arg; - observe_tac "tac" (tac wf_rec_arg hrec acc_inv) - ] - ] - ) g - end - - - -let rec instantiate_lambda t l = - match l with - | [] -> t - | a::l -> - let (bound_name, _, body) = destLambda t in - instantiate_lambda (subst1 a body) l -;; - - -let whole_start (concl_tac:tactic) nb_args is_mes func input_type relation rec_arg_num : tactic = - begin - fun g -> - let ids = ids_of_named_context (pf_hyps g) in - let func_body = (def_of_const (constr_of_global func)) in - let (f_name, _, body1) = destLambda func_body in - let f_id = - match f_name with - | Name f_id -> next_global_ident_away true f_id ids - | Anonymous -> anomaly "Anonymous function" - in - let n_names_types,_ = decompose_lam_n nb_args body1 in - let n_ids,ids = - List.fold_left - (fun (n_ids,ids) (n_name,_) -> - match n_name with - | Name id -> - let n_id = next_global_ident_away true id ids in - n_id::n_ids,n_id::ids - | _ -> anomaly "anonymous argument" - ) - ([],(f_id::ids)) - n_names_types - in - let rec_arg_id = List.nth n_ids (rec_arg_num - 1) in - let expr = instantiate_lambda func_body (mkVar f_id::(List.map mkVar n_ids)) in - termination_proof_header - is_mes - input_type - ids - n_ids - relation - rec_arg_num - rec_arg_id - (fun rec_arg_id hrec acc_inv g -> - (proveterminate - [rec_arg_id] - is_mes - acc_inv - hrec - (mkVar f_id) - func - base_leaf_terminate - (rec_leaf_terminate (mkVar f_id) concl_tac) - [] - expr - ) - g - ) - (tclUSER_if_not_mes concl_tac) - g - end - -let get_current_subgoals_types () = - let pts = get_pftreestate () in - let _,subs = extract_open_pftreestate pts in - List.map snd ((* List.sort (fun (x,_) (y,_) -> x -y ) *)subs ) - -let build_and_l l = - let and_constr = Coqlib.build_coq_and () in - let conj_constr = coq_conj () in - let mk_and p1 p2 = - Term.mkApp(and_constr,[|p1;p2|]) in - let rec f = function - | [] -> failwith "empty list of subgoals!" - | [p] -> p,tclIDTAC,1 - | p1::pl -> - let c,tac,nb = f pl in - mk_and p1 c, - tclTHENS - (apply (constr_of_global conj_constr)) - [tclIDTAC; - tac - ],nb+1 - in f l - - -let is_rec_res id = - let rec_res_name = string_of_id rec_res_id in - let id_name = string_of_id id in - try - String.sub id_name 0 (String.length rec_res_name) = rec_res_name - with _ -> false - -let clear_goals = - let rec clear_goal t = - match kind_of_term t with - | Prod(Name id as na,t,b) -> - let b' = clear_goal b in - if noccurn 1 b' && (is_rec_res id) - then pop b' - else if b' == b then t - else mkProd(na,t,b') - | _ -> map_constr clear_goal t - in - List.map clear_goal - - -let build_new_goal_type () = - let sub_gls_types = get_current_subgoals_types () in - let sub_gls_types = clear_goals sub_gls_types in - let res = build_and_l sub_gls_types in - res - - - (* -let prove_with_tcc lemma _ : tactic = - fun gls -> - let hid = next_global_ident_away true h_id (pf_ids_of_hyps gls) in - tclTHENSEQ - [ - h_generalize [lemma]; - h_intro hid; - Elim.h_decompose_and (mkVar hid); - gen_eauto(* default_eauto *) false (false,5) [] (Some []) - (* default_auto *) - ] - gls - *) - - - -let open_new_goal (build_proof:tactic -> tactic -> unit) using_lemmas ref_ goal_name (gls_type,decompose_and_tac,nb_goal) = - let current_proof_name = get_current_proof_name () in - let name = match goal_name with - | Some s -> s - | None -> - try (add_suffix current_proof_name "_subproof") - with _ -> anomaly "open_new_goal with an unamed theorem" - in - let sign = Global.named_context () in - let sign = clear_proofs sign in - let na = next_global_ident_away false name [] in - if occur_existential gls_type then - Util.error "\"abstract\" cannot handle existentials"; - let hook _ _ = - let opacity = - let na_ref = Libnames.Ident (dummy_loc,na) in - let na_global = Nametab.global na_ref in - match na_global with - ConstRef c -> - let cb = Global.lookup_constant c in - if cb.Declarations.const_opaque then true - else begin match cb.const_body with None -> true | _ -> false end - | _ -> anomaly "equation_lemma: not a constant" - in - let lemma = mkConst (Lib.make_con na) in - ref_ := Some lemma ; - let lid = ref [] in - let h_num = ref (-1) in - Flags.silently Vernacentries.interp (Vernacexpr.VernacAbort None); - build_proof - ( fun gls -> - let hid = next_global_ident_away true h_id (pf_ids_of_hyps gls) in - tclTHENSEQ - [ - h_generalize [lemma]; - h_intro hid; - (fun g -> - let ids = pf_ids_of_hyps g in - tclTHEN - (Elim.h_decompose_and (mkVar hid)) - (fun g -> - let ids' = pf_ids_of_hyps g in - lid := List.rev (list_subtract ids' ids); - if !lid = [] then lid := [hid]; - tclIDTAC g - ) - g - ); - ] gls) - (fun g -> - match kind_of_term (pf_concl g) with - | App(f,_) when eq_constr f (well_founded ()) -> - Auto.h_auto None [] (Some []) g - | _ -> - incr h_num; - (observe_tac "finishing using" - ( - tclCOMPLETE( - tclFIRST[ - tclTHEN - (eapply_with_bindings (mkVar (List.nth !lid !h_num), NoBindings)) - e_assumption; - Eauto.eauto_with_bases - false - (true,5) - [delayed_force refl_equal] - [Auto.Hint_db.empty empty_transparent_state false] - ] - ) - ) - ) - g) -; - Command.save_named opacity; - in - start_proof - na - (Decl_kinds.Global, Decl_kinds.Proof Decl_kinds.Lemma) - sign - gls_type - hook ; - by ( - fun g -> - tclTHEN - (decompose_and_tac) - (tclORELSE - (tclFIRST - (List.map - (fun c -> - tclTHENSEQ - [intros; - h_simplest_apply (interp_constr Evd.empty (Global.env()) c); - tclCOMPLETE Auto.default_auto - ] - ) - using_lemmas) - ) tclIDTAC) - g); - try - by tclIDTAC; (* raises UserError _ if the proof is complete *) - if Flags.is_verbose () then (pp (Printer.pr_open_subgoals())) - with UserError _ -> - defined () - -;; - - -let com_terminate - tcc_lemma_name - tcc_lemma_ref - is_mes - fonctional_ref - input_type - relation - rec_arg_num - thm_name using_lemmas - nb_args - hook = - let start_proof (tac_start:tactic) (tac_end:tactic) = - let (evmap, env) = Command.get_current_context() in - start_proof thm_name - (Global, Proof Lemma) (Environ.named_context_val env) - (hyp_terminates nb_args fonctional_ref) hook; - by (observe_tac "starting_tac" tac_start); - by (observe_tac "whole_start" (whole_start tac_end nb_args is_mes fonctional_ref - input_type relation rec_arg_num )) - - in - start_proof tclIDTAC tclIDTAC; - try - let new_goal_type = build_new_goal_type () in - open_new_goal start_proof using_lemmas tcc_lemma_ref - (Some tcc_lemma_name) - (new_goal_type) - with Failure "empty list of subgoals!" -> - (* a non recursive function declared with measure ! *) - defined () - - - - -let ind_of_ref = function - | IndRef (ind,i) -> (ind,i) - | _ -> anomaly "IndRef expected" - -let (value_f:constr list -> global_reference -> constr) = - fun al fterm -> - let d0 = dummy_loc in - let rev_x_id_l = - ( - List.fold_left - (fun x_id_l _ -> - let x_id = next_global_ident_away true x_id x_id_l in - x_id::x_id_l - ) - [] - al - ) - in - let fun_body = - RCases - (d0,RegularStyle,None, - [RApp(d0, RRef(d0,fterm), List.rev_map (fun x_id -> RVar(d0, x_id)) rev_x_id_l), - (Anonymous,None)], - [d0, [v_id], [PatCstr(d0,(ind_of_ref - (delayed_force coq_sig_ref),1), - [PatVar(d0, Name v_id); - PatVar(d0, Anonymous)], - Anonymous)], - RVar(d0,v_id)]) - in - let value = - List.fold_left2 - (fun acc x_id a -> - RLambda - (d0, Name x_id, Explicit, RDynamic(d0, constr_in a), - acc - ) - ) - fun_body - rev_x_id_l - (List.rev al) - in - understand Evd.empty (Global.env()) value;; - -let (declare_fun : identifier -> logical_kind -> constr -> global_reference) = - fun f_id kind value -> - let ce = {const_entry_body = value; - const_entry_type = None; - const_entry_opaque = false; - const_entry_boxed = true} in - ConstRef(declare_constant f_id (DefinitionEntry ce, kind));; - -let (declare_f : identifier -> logical_kind -> constr list -> global_reference -> global_reference) = - fun f_id kind input_type fterm_ref -> - declare_fun f_id kind (value_f input_type fterm_ref);; - -let rec n_x_id ids n = - if n = 0 then [] - else let x = next_global_ident_away true x_id ids in - x::n_x_id (x::ids) (n-1);; - -let start_equation (f:global_reference) (term_f:global_reference) - (cont_tactic:identifier list -> tactic) g = - let ids = pf_ids_of_hyps g in - let terminate_constr = constr_of_global term_f in - let nargs = nb_prod (type_of_const terminate_constr) in - let x = n_x_id ids nargs in - tclTHENLIST [ - h_intros x; - unfold_in_concl [(all_occurrences, evaluable_of_global_reference f)]; - observe_tac "simplest_case" - (simplest_case (mkApp (terminate_constr, - Array.of_list (List.map mkVar x)))); - observe_tac "prove_eq" (cont_tactic x)] g;; - -let base_leaf_eq func eqs f_id g = - let ids = pf_ids_of_hyps g in - let k = next_global_ident_away true k_id ids in - let p = next_global_ident_away true p_id (k::ids) in - let v = next_global_ident_away true v_id (p::k::ids) in - let heq = next_global_ident_away true heq_id (v::p::k::ids) in - let heq1 = next_global_ident_away true heq_id (heq::v::p::k::ids) in - let hex = next_global_ident_away true hex_id (heq1::heq::v::p::k::ids) in - tclTHENLIST [ - h_intros [v; hex]; - simplest_elim (mkVar hex); - h_intros [p;heq1]; - tclTRY - (rewriteRL - (mkApp(mkVar heq1, - [|mkApp (delayed_force coq_S, [|mkVar p|]); - mkApp(delayed_force lt_n_Sn, [|mkVar p|]); f_id|]))); - simpl_iter onConcl; - tclTRY (unfold_in_concl [((true,[1]), evaluable_of_global_reference func)]); - list_rewrite true eqs; - apply (delayed_force refl_equal)] g;; - -let f_S t = mkApp(delayed_force coq_S, [|t|]);; - - -let rec introduce_all_values_eq cont_tac functional termine - f p heq1 pmax bounds le_proofs eqs ids = - function - [] -> - let heq2 = next_global_ident_away true heq_id ids in - tclTHENLIST - [pose_proof (Name heq2) - (mkApp(mkVar heq1, [|f_S(f_S(mkVar pmax))|])); - simpl_iter (onHyp heq2); - unfold_in_hyp [((true,[1]), evaluable_of_global_reference - (global_of_constr functional))] - ((all_occurrences_expr, heq2), InHyp); - tclTHENS - (fun gls -> - let t_eq = compute_renamed_type gls (mkVar heq2) in - let def_id = - let _,_,t = destProd t_eq in let def_na,_,_ = destProd t in - Nameops.out_name def_na - in - observe_tac "rewrite heq" (general_rewrite_bindings false all_occurrences - (mkVar heq2, - ExplicitBindings[dummy_loc,NamedHyp def_id, - f]) false) gls) - [tclTHENLIST - [observe_tac "list_rewrite" (list_rewrite true eqs); - cont_tac pmax le_proofs]; - tclTHENLIST[apply (delayed_force le_lt_SS); - compute_le_proofs le_proofs]]] - | arg::args -> - let v' = next_global_ident_away true v_id ids in - let ids = v'::ids in - let hex' = next_global_ident_away true hex_id ids in - let ids = hex'::ids in - let p' = next_global_ident_away true p_id ids in - let ids = p'::ids in - let new_pmax = next_global_ident_away true pmax_id ids in - let ids = pmax::ids in - let hle1 = next_global_ident_away true hle_id ids in - let ids = hle1::ids in - let hle2 = next_global_ident_away true hle_id ids in - let ids = hle2::ids in - let heq = next_global_ident_away true heq_id ids in - let ids = heq::ids in - let heq2 = next_global_ident_away true heq_id ids in - let ids = heq2::ids in - tclTHENLIST - [mkCaseEq(mkApp(termine, Array.of_list arg)); - h_intros [v'; hex']; - simplest_elim(mkVar hex'); - h_intros [p']; - simplest_elim(mkApp(delayed_force max_constr, [|mkVar pmax; - mkVar p'|])); - h_intros [new_pmax;hle1;hle2]; - introduce_all_values_eq - (fun pmax' le_proofs'-> - tclTHENLIST - [cont_tac pmax' le_proofs'; - h_intros [heq;heq2]; - observe_tac ("rewriteRL " ^ (string_of_id heq2)) - (tclTRY (rewriteLR (mkVar heq2))); - tclTRY (tclTHENS - ( fun g -> - let t_eq = compute_renamed_type g (mkVar heq) in - let k_id,def_id = - let k_na,_,t = destProd t_eq in - let _,_,t = destProd t in - let def_na,_,_ = destProd t in - Nameops.out_name k_na,Nameops.out_name def_na - in - let c_b = (mkVar heq, - ExplicitBindings - [dummy_loc, NamedHyp k_id, - f_S(mkVar pmax'); - dummy_loc, NamedHyp def_id, f]) - in - observe_tac "general_rewrite_bindings" ( (general_rewrite_bindings false all_occurrences - c_b false)) - g - ) - [tclIDTAC; - tclTHENLIST - [apply (delayed_force le_lt_n_Sm); - compute_le_proofs le_proofs']])]) - functional termine f p heq1 new_pmax - (p'::bounds)((mkVar pmax)::le_proofs) eqs - (heq2::heq::hle2::hle1::new_pmax::p'::hex'::v'::ids) args] - - -let rec_leaf_eq termine f ids functional eqs expr fn args = - let p = next_global_ident_away true p_id ids in - let ids = p::ids in - let v = next_global_ident_away true v_id ids in - let ids = v::ids in - let hex = next_global_ident_away true hex_id ids in - let ids = hex::ids in - let heq1 = next_global_ident_away true heq_id ids in - let ids = heq1::ids in - let hle1 = next_global_ident_away true hle_id ids in - let ids = hle1::ids in - tclTHENLIST - [observe_tac "intros v hex" (h_intros [v;hex]); - simplest_elim (mkVar hex); - h_intros [p;heq1]; - h_generalize [mkApp(delayed_force le_n,[|mkVar p|])]; - h_intros [hle1]; - observe_tac "introduce_all_values_eq" (introduce_all_values_eq - (fun _ _ -> tclIDTAC) - functional termine f p heq1 p [] [] eqs ids args); - observe_tac "failing here" (apply (delayed_force refl_equal))] - -let rec prove_eq (termine:constr) (f:constr)(functional:global_reference) - (eqs:constr list) (expr:constr) = -(* tclTRY *) - (match kind_of_term expr with - Case(ci,t,a,l) -> - (match find_call_occs 0 f a with - _,[] -> - (fun g -> - let destruct_tac,rev_to_thin_intro = mkDestructEq [] a g in - tclTHENS - destruct_tac - (list_map_i - (fun i -> mk_intros_and_continue - (List.rev rev_to_thin_intro) true - (prove_eq termine f functional) - eqs ci.ci_cstr_nargs.(i)) - 0 (Array.to_list l)) g) - | _,_::_ -> - (match find_call_occs 0 f expr with - _,[] -> base_leaf_eq functional eqs f - | fn,args -> - fun g -> - let ids = ids_of_named_context (pf_hyps g) in - rec_leaf_eq termine f ids - (constr_of_global functional) - eqs expr fn args g)) - | _ -> - (match find_call_occs 0 f expr with - _,[] -> base_leaf_eq functional eqs f - | fn,args -> - fun g -> - let ids = ids_of_named_context (pf_hyps g) in - observe_tac "rec_leaf_eq" (rec_leaf_eq - termine f ids (constr_of_global functional) - eqs expr fn args) g));; - -let (com_eqn : identifier -> - global_reference -> global_reference -> global_reference - -> constr -> unit) = - fun eq_name functional_ref f_ref terminate_ref equation_lemma_type -> - let opacity = - match terminate_ref with - | ConstRef c -> - let cb = Global.lookup_constant c in - if cb.Declarations.const_opaque then true - else begin match cb.const_body with None -> true | _ -> false end - | _ -> anomaly "terminate_lemma: not a constant" - in - let (evmap, env) = Command.get_current_context() in - let f_constr = (constr_of_global f_ref) in - let equation_lemma_type = subst1 f_constr equation_lemma_type in - (start_proof eq_name (Global, Proof Lemma) - (Environ.named_context_val env) equation_lemma_type (fun _ _ -> ()); - by - (start_equation f_ref terminate_ref - (fun x -> - prove_eq - (constr_of_global terminate_ref) - f_constr - functional_ref - [] - (instantiate_lambda - (def_of_const (constr_of_global functional_ref)) - (f_constr::List.map mkVar x) - ) - ) - ); -(* (try Vernacentries.interp (Vernacexpr.VernacShow Vernacexpr.ShowProof) with _ -> ()); *) -(* Vernacentries.interp (Vernacexpr.VernacShow Vernacexpr.ShowScript); *) - Flags.silently (fun () ->Command.save_named opacity) () ; -(* Pp.msgnl (str "eqn finished"); *) - - );; - -let nf_zeta env = - Reductionops.clos_norm_flags (Closure.RedFlags.mkflags [Closure.RedFlags.fZETA]) - env - Evd.empty - -let recursive_definition is_mes function_name rec_impls type_of_f r rec_arg_num eq - generate_induction_principle using_lemmas : unit = - let function_type = interp_constr Evd.empty (Global.env()) type_of_f in - let env = push_named (function_name,None,function_type) (Global.env()) in -(* Pp.msgnl (str "function type := " ++ Printer.pr_lconstr function_type); *) - let equation_lemma_type = interp_gen (OfType None) Evd.empty env ~impls:([],rec_impls) eq in -(* Pp.msgnl (Printer.pr_lconstr equation_lemma_type); *) - let res_vars,eq' = decompose_prod equation_lemma_type in - let env_eq' = Environ.push_rel_context (List.map (fun (x,y) -> (x,None,y)) res_vars) env in - let eq' = nf_zeta env_eq' eq' in - let res = -(* Pp.msgnl (str "res_var :=" ++ Printer.pr_lconstr_env (push_rel_context (List.map (function (x,t) -> (x,None,t)) res_vars) env) eq'); *) -(* Pp.msgnl (str "rec_arg_num := " ++ str (string_of_int rec_arg_num)); *) -(* Pp.msgnl (str "eq' := " ++ str (string_of_int rec_arg_num)); *) - match kind_of_term eq' with - | App(e,[|_;_;eq_fix|]) -> - mkLambda (Name function_name,function_type,subst_var function_name (compose_lam res_vars eq_fix)) - | _ -> failwith "Recursive Definition (res not eq)" - in - let pre_rec_args,function_type_before_rec_arg = decompose_prod_n (rec_arg_num - 1) function_type in - let (_, rec_arg_type, _) = destProd function_type_before_rec_arg in - let arg_types = List.rev_map snd (fst (decompose_prod_n (List.length res_vars) function_type)) in - let equation_id = add_suffix function_name "_equation" in - let functional_id = add_suffix function_name "_F" in - let term_id = add_suffix function_name "_terminate" in - let functional_ref = declare_fun functional_id (IsDefinition Definition) res in - let env_with_pre_rec_args = push_rel_context(List.map (function (x,t) -> (x,None,t)) pre_rec_args) env in - let relation = - interp_constr - Evd.empty - env_with_pre_rec_args - r - in - let tcc_lemma_name = add_suffix function_name "_tcc" in - let tcc_lemma_constr = ref None in -(* let _ = Pp.msgnl (str "relation := " ++ Printer.pr_lconstr_env env_with_pre_rec_args relation) in *) - let hook _ _ = - let term_ref = Nametab.locate (make_short_qualid term_id) in - let f_ref = declare_f function_name (IsProof Lemma) arg_types term_ref in -(* message "start second proof"; *) - let stop = ref false in - begin - try com_eqn equation_id functional_ref f_ref term_ref (subst_var function_name equation_lemma_type) - with e -> - begin - if Tacinterp.get_debug () <> Tactic_debug.DebugOff - then pperrnl (str "Cannot create equation Lemma " ++ Cerrors.explain_exn e) - else anomaly "Cannot create equation Lemma" - ; -(* ignore(try Vernacentries.vernac_reset_name (Util.dummy_loc,functional_id) with _ -> ()); *) - stop := true; - end - end; - if not !stop - then - let eq_ref = Nametab.locate (make_short_qualid equation_id ) in - let f_ref = destConst (constr_of_global f_ref) - and functional_ref = destConst (constr_of_global functional_ref) - and eq_ref = destConst (constr_of_global eq_ref) in - generate_induction_principle f_ref tcc_lemma_constr - functional_ref eq_ref rec_arg_num rec_arg_type (nb_prod res) relation; - if Flags.is_verbose () - then msgnl (h 1 (Ppconstr.pr_id function_name ++ - spc () ++ str"is defined" )++ fnl () ++ - h 1 (Ppconstr.pr_id equation_id ++ - spc () ++ str"is defined" ) - ) - in - try - com_terminate - tcc_lemma_name - tcc_lemma_constr - is_mes functional_ref - rec_arg_type - relation rec_arg_num - term_id - using_lemmas - (List.length res_vars) - hook - with e -> - begin - ignore(try Vernacentries.vernac_reset_name (Util.dummy_loc,functional_id) with _ -> ()); -(* anomaly "Cannot create termination Lemma" *) - raise e - end - - - |