src/HOL/Tools/BNF/bnf_fp_n2m.ML
author blanchet
Mon Feb 17 13:31:42 2014 +0100 (2014-02-17)
changeset 55530 3dfb724db099
parent 55478 3a6efda01da4
child 55531 601ca8efa000
permissions -rw-r--r--
renamed 'primrec_new' to 'primrec', overriding the old command (which it still uses as a fallback for old-style datatypes)
     1 (*  Title:      HOL/Tools/BNF/bnf_fp_n2m.ML
     2     Author:     Dmitriy Traytel, TU Muenchen
     3     Copyright   2013
     4 
     5 Flattening of nested to mutual (co)recursion.
     6 *)
     7 
     8 signature BNF_FP_N2M =
     9 sig
    10   val construct_mutualized_fp: BNF_FP_Util.fp_kind  -> typ list -> BNF_FP_Def_Sugar.fp_sugar list ->
    11     binding list -> (string * sort) list -> typ list * typ list list -> BNF_Def.bnf list ->
    12     local_theory -> BNF_FP_Util.fp_result * local_theory
    13 end;
    14 
    15 structure BNF_FP_N2M : BNF_FP_N2M =
    16 struct
    17 
    18 open BNF_Def
    19 open BNF_Util
    20 open BNF_FP_Util
    21 open BNF_FP_Def_Sugar
    22 open BNF_Tactics
    23 open BNF_FP_N2M_Tactics
    24 
    25 fun force_typ ctxt T =
    26   map_types Type_Infer.paramify_vars
    27   #> Type.constraint T
    28   #> Syntax.check_term ctxt
    29   #> singleton (Variable.polymorphic ctxt);
    30 
    31 fun mk_prod_map f g =
    32   let
    33     val ((fAT, fBT), fT) = `dest_funT (fastype_of f);
    34     val ((gAT, gBT), gT) = `dest_funT (fastype_of g);
    35   in
    36     Const (@{const_name map_pair},
    37       fT --> gT --> HOLogic.mk_prodT (fAT, gAT) --> HOLogic.mk_prodT (fBT, gBT)) $ f $ g
    38   end;
    39 
    40 fun mk_sum_map f g =
    41   let
    42     val ((fAT, fBT), fT) = `dest_funT (fastype_of f);
    43     val ((gAT, gBT), gT) = `dest_funT (fastype_of g);
    44   in
    45     Const (@{const_name sum_map}, fT --> gT --> mk_sumT (fAT, gAT) --> mk_sumT (fBT, gBT)) $ f $ g
    46   end;
    47 
    48 fun construct_mutualized_fp fp fpTs fp_sugars bs resBs (resDs, Dss) bnfs lthy =
    49   let
    50     fun steal get = map (of_fp_sugar (get o #fp_res)) fp_sugars;
    51 
    52     val n = length bnfs;
    53     val deads = fold (union (op =)) Dss resDs;
    54     val As = subtract (op =) deads (map TFree resBs);
    55     val names_lthy = fold Variable.declare_typ (As @ deads) lthy;
    56     val m = length As;
    57     val live = m + n;
    58     val ((Xs, Bs), names_lthy) = names_lthy
    59       |> mk_TFrees n
    60       ||>> mk_TFrees m;
    61     val allAs = As @ Xs;
    62     val phiTs = map2 mk_pred2T As Bs;
    63     val theta = As ~~ Bs;
    64     val fpTs' = map (Term.typ_subst_atomic theta) fpTs;
    65     val pre_phiTs = map2 mk_pred2T fpTs fpTs';
    66 
    67     fun mk_co_algT T U = fp_case fp (T --> U) (U --> T);
    68     fun co_swap pair = fp_case fp I swap pair;
    69     val dest_co_algT = co_swap o dest_funT;
    70     val co_alg_argT = fp_case fp range_type domain_type;
    71     val co_alg_funT = fp_case fp domain_type range_type;
    72     val mk_co_product = curry (fp_case fp mk_convol mk_case_sum);
    73     val mk_map_co_product = fp_case fp mk_prod_map mk_sum_map;
    74     val co_proj1_const = fp_case fp (fst_const o fst) (uncurry Inl_const o dest_sumT o snd);
    75     val mk_co_productT = curry (fp_case fp HOLogic.mk_prodT mk_sumT);
    76     val dest_co_productT = fp_case fp HOLogic.dest_prodT dest_sumT;
    77 
    78     val ((ctors, dtors), (xtor's, xtors)) =
    79       let
    80         val ctors = map2 (force_typ names_lthy o (fn T => dummyT --> T)) fpTs (steal #ctors);
    81         val dtors = map2 (force_typ names_lthy o (fn T => T --> dummyT)) fpTs (steal #dtors);
    82       in
    83         ((ctors, dtors), `(map (Term.subst_atomic_types theta)) (fp_case fp ctors dtors))
    84       end;
    85 
    86     val xTs = map (domain_type o fastype_of) xtors;
    87     val yTs = map (domain_type o fastype_of) xtor's;
    88 
    89     val (((((phis, phis'), pre_phis), xs), ys), names_lthy) = names_lthy
    90       |> mk_Frees' "R" phiTs
    91       ||>> mk_Frees "S" pre_phiTs
    92       ||>> mk_Frees "x" xTs
    93       ||>> mk_Frees "y" yTs;
    94 
    95     val fp_bnfs = steal #bnfs;
    96     val pre_bnfs = map (of_fp_sugar #pre_bnfs) fp_sugars;
    97     val pre_bnfss = map #pre_bnfs fp_sugars;
    98     val nesty_bnfss = map (fn sugar => #nested_bnfs sugar @ #nesting_bnfs sugar) fp_sugars;
    99     val fp_nesty_bnfss = fp_bnfs :: nesty_bnfss;
   100     val fp_nesty_bnfs = distinct (op = o pairself T_of_bnf) (flat fp_nesty_bnfss);
   101 
   102     val rels =
   103       let
   104         fun find_rel T As Bs = fp_nesty_bnfss
   105           |> map (filter_out (curry (op = o pairself name_of_bnf) BNF_Comp.DEADID_bnf))
   106           |> get_first (find_first (fn bnf => Type.could_unify (T_of_bnf bnf, T)))
   107           |> Option.map (fn bnf =>
   108             let val live = live_of_bnf bnf;
   109             in (mk_rel live As Bs (rel_of_bnf bnf), live) end)
   110           |> the_default (HOLogic.eq_const T, 0);
   111 
   112         fun mk_rel (T as Type (_, Ts)) (Type (_, Us)) =
   113               let
   114                 val (rel, live) = find_rel T Ts Us;
   115                 val (Ts', Us') = fastype_of rel |> strip_typeN live |> fst |> map_split dest_pred2T;
   116                 val rels = map2 mk_rel Ts' Us';
   117               in
   118                 Term.list_comb (rel, rels)
   119               end
   120           | mk_rel (T as TFree _) _ = (nth phis (find_index (curry op = T) As)
   121               handle General.Subscript => HOLogic.eq_const T)
   122           | mk_rel _ _ = raise Fail "fpTs contains schematic type variables";
   123       in
   124         map2 (fold_rev Term.absfree phis' oo mk_rel) fpTs fpTs'
   125       end;
   126 
   127     val pre_rels = map2 (fn Ds => mk_rel_of_bnf Ds (As @ fpTs) (Bs @ fpTs')) Dss bnfs;
   128 
   129     val rel_unfoldss = map (maps (fn bnf => no_refl [rel_def_of_bnf bnf])) pre_bnfss;
   130     val rel_xtor_co_inducts = steal (split_conj_thm o #rel_xtor_co_induct_thm)
   131       |> map2 (fn unfs => unfold_thms lthy (id_apply :: unfs)) rel_unfoldss;
   132 
   133     val rel_defs = map rel_def_of_bnf bnfs;
   134     val rel_monos = map rel_mono_of_bnf bnfs;
   135 
   136     val rel_xtor_co_induct_thm =
   137       mk_rel_xtor_co_induct_thm fp pre_rels pre_phis rels phis xs ys xtors xtor's
   138         (mk_rel_xtor_co_induct_tactic fp rel_xtor_co_inducts rel_defs rel_monos) lthy;
   139 
   140     val rel_eqs = no_refl (map rel_eq_of_bnf fp_nesty_bnfs);
   141     val map_id0s = no_refl (map map_id0_of_bnf bnfs);
   142 
   143     val xtor_co_induct_thm =
   144       (case fp of
   145         Least_FP =>
   146           let
   147             val (Ps, names_lthy) = names_lthy
   148               |> mk_Frees "P" (map (fn T => T --> HOLogic.boolT) fpTs);
   149             fun mk_Grp_id P =
   150               let val T = domain_type (fastype_of P);
   151               in mk_Grp (HOLogic.Collect_const T $ P) (HOLogic.id_const T) end;
   152             val cts = map (SOME o certify lthy) (map HOLogic.eq_const As @ map mk_Grp_id Ps);
   153           in
   154             cterm_instantiate_pos cts rel_xtor_co_induct_thm
   155             |> singleton (Proof_Context.export names_lthy lthy)
   156             |> unfold_thms lthy (@{thms eq_le_Grp_id_iff all_simps(1,2)[symmetric]} @ rel_eqs)
   157             |> funpow n (fn thm => thm RS spec)
   158             |> unfold_thms lthy (@{thm eq_alt} :: map rel_Grp_of_bnf bnfs @ map_id0s)
   159             |> unfold_thms lthy @{thms Grp_id_mono_subst eqTrueI[OF subset_UNIV] simp_thms(22)}
   160             |> unfold_thms lthy @{thms subset_iff mem_Collect_eq
   161                atomize_conjL[symmetric] atomize_all[symmetric] atomize_imp[symmetric]}
   162             |> unfold_thms lthy (maps set_defs_of_bnf bnfs)
   163           end
   164       | Greatest_FP =>
   165           let
   166             val cts = NONE :: map (SOME o certify lthy) (map HOLogic.eq_const As);
   167           in
   168             cterm_instantiate_pos cts rel_xtor_co_induct_thm
   169             |> unfold_thms lthy (@{thms le_fun_def le_bool_def all_simps(1,2)[symmetric]} @ rel_eqs)
   170             |> funpow (2 * n) (fn thm => thm RS spec)
   171             |> Conv.fconv_rule (Object_Logic.atomize lthy)
   172             |> funpow n (fn thm => thm RS mp)
   173           end);
   174 
   175     val fold_preTs = map2 (fn Ds => mk_T_of_bnf Ds allAs) Dss bnfs;
   176     val fold_pre_deads_only_Ts = map2 (fn Ds => mk_T_of_bnf Ds (replicate live dummyT)) Dss bnfs;
   177     val rec_theta = Xs ~~ map2 mk_co_productT fpTs Xs;
   178     val rec_preTs = map (Term.typ_subst_atomic rec_theta) fold_preTs;
   179 
   180     val fold_strTs = map2 mk_co_algT fold_preTs Xs;
   181     val rec_strTs = map2 mk_co_algT rec_preTs Xs;
   182     val resTs = map2 mk_co_algT fpTs Xs;
   183 
   184     val (((fold_strs, fold_strs'), (rec_strs, rec_strs')), names_lthy) = names_lthy
   185       |> mk_Frees' "s" fold_strTs
   186       ||>> mk_Frees' "s" rec_strTs;
   187 
   188     val co_iters = steal #xtor_co_iterss;
   189     val ns = map (length o #pre_bnfs) fp_sugars;
   190     fun substT rho (Type (@{type_name "fun"}, [T, U])) = substT rho T --> substT rho U
   191       | substT rho (Type (s, Ts)) = Type (s, map (typ_subst_nonatomic rho) Ts)
   192       | substT _ T = T;
   193     fun force_iter is_rec i TU TU_rec raw_iters =
   194       let
   195         val approx_fold = un_fold_of raw_iters
   196           |> force_typ names_lthy
   197             (replicate (nth ns i) dummyT ---> (if is_rec then TU_rec else TU));
   198         val subst = Term.typ_subst_atomic (Xs ~~ fpTs);
   199         val TUs = map_split dest_co_algT (binder_fun_types (fastype_of approx_fold))
   200           |>> map subst
   201           |> uncurry (map2 mk_co_algT);
   202         val js = find_indices Type.could_unify TUs
   203           (map2 (fn T => fn U => mk_co_algT (subst T) U) fold_preTs Xs);
   204         val Tpats = map (fn j => mk_co_algT (nth fold_pre_deads_only_Ts j) (nth Xs j)) js;
   205         val iter = raw_iters |> (if is_rec then co_rec_of else un_fold_of);
   206       in
   207         force_typ names_lthy (Tpats ---> TU) iter
   208       end;
   209 
   210     fun mk_iter b_opt is_rec iters lthy TU =
   211       let
   212         val x = co_alg_argT TU;
   213         val i = find_index (fn T => x = T) Xs;
   214         val TUiter =
   215           (case find_first (fn f => body_fun_type (fastype_of f) = TU) iters of
   216             NONE => nth co_iters i
   217               |> force_iter is_rec i
   218                 (TU |> (is_none b_opt andalso not is_rec) ? substT (fpTs ~~ Xs))
   219                 (TU |> (is_none b_opt) ? substT (map2 mk_co_productT fpTs Xs ~~ Xs))
   220           | SOME f => f);
   221         val TUs = binder_fun_types (fastype_of TUiter);
   222         val iter_preTs = if is_rec then rec_preTs else fold_preTs;
   223         val iter_strs = if is_rec then rec_strs else fold_strs;
   224         fun mk_s TU' =
   225           let
   226             val i = find_index (fn T => co_alg_argT TU' = T) Xs;
   227             val sF = co_alg_funT TU';
   228             val F = nth iter_preTs i;
   229             val s = nth iter_strs i;
   230           in
   231             (if sF = F then s
   232             else
   233               let
   234                 val smapT = replicate live dummyT ---> mk_co_algT sF F;
   235                 fun hidden_to_unit t =
   236                   Term.subst_TVars (map (rpair HOLogic.unitT) (Term.add_tvar_names t [])) t;
   237                 val smap = map_of_bnf (nth bnfs i)
   238                   |> force_typ names_lthy smapT
   239                   |> hidden_to_unit;
   240                 val smap_argTs = strip_typeN live (fastype_of smap) |> fst;
   241                 fun mk_smap_arg TU =
   242                   (if domain_type TU = range_type TU then
   243                     HOLogic.id_const (domain_type TU)
   244                   else if is_rec then
   245                     let
   246                       val (TY, (U, X)) = TU |> dest_co_algT ||> dest_co_productT;
   247                       val T = mk_co_algT TY U;
   248                     in
   249                       (case try (force_typ lthy T o build_map lthy co_proj1_const o dest_funT) T of
   250                         SOME f => mk_co_product f
   251                           (fst (fst (mk_iter NONE is_rec iters lthy (mk_co_algT TY X))))
   252                       | NONE => mk_map_co_product
   253                           (build_map lthy co_proj1_const
   254                             (dest_funT (mk_co_algT (dest_co_productT TY |> fst) U)))
   255                           (HOLogic.id_const X))
   256                     end
   257                   else
   258                     fst (fst (mk_iter NONE is_rec iters lthy TU)))
   259                 val smap_args = map mk_smap_arg smap_argTs;
   260               in
   261                 HOLogic.mk_comp (co_swap (s, Term.list_comb (smap, smap_args)))
   262               end)
   263           end;
   264         val t = Term.list_comb (TUiter, map mk_s TUs);
   265       in
   266         (case b_opt of
   267           NONE => ((t, Drule.dummy_thm), lthy)
   268         | SOME b => Local_Theory.define ((b, NoSyn), ((Binding.conceal (Thm.def_binding b), []),
   269             fold_rev Term.absfree (if is_rec then rec_strs' else fold_strs') t)) lthy |>> apsnd snd)
   270       end;
   271 
   272     fun mk_iters is_rec name lthy =
   273       fold2 (fn TU => fn b => fn ((iters, defs), lthy) =>
   274         mk_iter (SOME b) is_rec iters lthy TU |>> (fn (f, d) => (f :: iters, d :: defs)))
   275       resTs (map (Binding.suffix_name ("_" ^ name)) bs) (([], []), lthy)
   276       |>> apfst rev o apsnd rev;
   277     val foldN = fp_case fp ctor_foldN dtor_unfoldN;
   278     val recN = fp_case fp ctor_recN dtor_corecN;
   279     val (((raw_un_folds, raw_un_fold_defs), (raw_co_recs, raw_co_rec_defs)), (lthy, raw_lthy)) =
   280       lthy
   281       |> mk_iters false foldN
   282       ||>> mk_iters true recN
   283       ||> `Local_Theory.restore;
   284 
   285     val phi = Proof_Context.export_morphism raw_lthy lthy;
   286 
   287     val un_folds = map (Morphism.term phi) raw_un_folds;
   288     val co_recs = map (Morphism.term phi) raw_co_recs;
   289 
   290     val (xtor_un_fold_thms, xtor_co_rec_thms) =
   291       let
   292         val folds = map (fn f => Term.list_comb (f, fold_strs)) raw_un_folds;
   293         val recs = map (fn r => Term.list_comb (r, rec_strs)) raw_co_recs;
   294         val fold_mapTs = co_swap (As @ fpTs, As @ Xs);
   295         val rec_mapTs = co_swap (As @ fpTs, As @ map2 mk_co_productT fpTs Xs);
   296         val pre_fold_maps =
   297           map2 (fn Ds => fn bnf =>
   298             Term.list_comb (uncurry (mk_map_of_bnf Ds) fold_mapTs bnf,
   299               map HOLogic.id_const As @ folds))
   300           Dss bnfs;
   301         val pre_rec_maps =
   302           map2 (fn Ds => fn bnf =>
   303             Term.list_comb (uncurry (mk_map_of_bnf Ds) rec_mapTs bnf,
   304               map HOLogic.id_const As @ map2 (mk_co_product o HOLogic.id_const) fpTs recs))
   305           Dss bnfs;
   306 
   307         fun mk_goals f xtor s smap =
   308           ((f, xtor), (s, smap))
   309           |> pairself (HOLogic.mk_comp o co_swap)
   310           |> HOLogic.mk_eq;
   311 
   312         val fold_goals = map4 mk_goals folds xtors fold_strs pre_fold_maps
   313         val rec_goals = map4 mk_goals recs xtors rec_strs pre_rec_maps;
   314 
   315         fun mk_thms ss goals tac =
   316           Library.foldr1 HOLogic.mk_conj goals
   317           |> HOLogic.mk_Trueprop
   318           |> fold_rev Logic.all ss
   319           |> (fn goal => Goal.prove_sorry raw_lthy [] [] goal tac)
   320           |> Thm.close_derivation
   321           |> Morphism.thm phi
   322           |> split_conj_thm
   323           |> map (fn thm => thm RS @{thm comp_eq_dest});
   324 
   325         val pre_map_defs = no_refl (map map_def_of_bnf bnfs);
   326         val fp_pre_map_defs = no_refl (map map_def_of_bnf pre_bnfs);
   327 
   328         val map_unfoldss = map (maps (fn bnf => no_refl [map_def_of_bnf bnf])) pre_bnfss;
   329         val unfold_map = map2 (fn unfs => unfold_thms lthy (id_apply :: unfs)) map_unfoldss;
   330 
   331         val fp_xtor_co_iterss = steal #xtor_co_iter_thmss;
   332         val fp_xtor_un_folds = map (mk_pointfree lthy o un_fold_of) fp_xtor_co_iterss |> unfold_map;
   333         val fp_xtor_co_recs = map (mk_pointfree lthy o co_rec_of) fp_xtor_co_iterss |> unfold_map;
   334 
   335         val fp_co_iter_o_mapss = steal #xtor_co_iter_o_map_thmss;
   336         val fp_fold_o_maps = map un_fold_of fp_co_iter_o_mapss |> unfold_map;
   337         val fp_rec_o_maps = map co_rec_of fp_co_iter_o_mapss |> unfold_map;
   338         val fold_thms = fp_case fp @{thm comp_assoc} @{thm comp_assoc[symmetric]} :: @{thms id_apply
   339           o_apply comp_id id_comp map_pair.comp map_pair.id sum_map.comp sum_map.id};
   340         val rec_thms = fold_thms @ fp_case fp
   341           @{thms fst_convol map_pair_o_convol convol_o}
   342           @{thms case_sum_o_inj(1) case_sum_o_sum_map o_case_sum};
   343         val map_thms = no_refl (maps (fn bnf =>
   344           [map_comp0_of_bnf bnf RS sym, map_id0_of_bnf bnf]) fp_nesty_bnfs);
   345 
   346         fun mk_tac defs o_map_thms xtor_thms thms {context = ctxt, prems = _} =
   347           unfold_thms_tac ctxt
   348             (flat [thms, defs, pre_map_defs, fp_pre_map_defs, xtor_thms, o_map_thms, map_thms]) THEN
   349           CONJ_WRAP (K (HEADGOAL (rtac refl))) bnfs;
   350 
   351         val fold_tac = mk_tac raw_un_fold_defs fp_fold_o_maps fp_xtor_un_folds fold_thms;
   352         val rec_tac = mk_tac raw_co_rec_defs fp_rec_o_maps fp_xtor_co_recs rec_thms;
   353       in
   354         (mk_thms fold_strs fold_goals fold_tac, mk_thms rec_strs rec_goals rec_tac)
   355       end;
   356 
   357     (* These results are half broken. This is deliberate. We care only about those fields that are
   358        used by "primrec", "primcorecursive", and "datatype_new_compat". *)
   359     val fp_res =
   360       ({Ts = fpTs,
   361         bnfs = steal #bnfs,
   362         dtors = dtors,
   363         ctors = ctors,
   364         xtor_co_iterss = transpose [un_folds, co_recs],
   365         xtor_co_induct = xtor_co_induct_thm,
   366         dtor_ctors = steal #dtor_ctors (*too general types*),
   367         ctor_dtors = steal #ctor_dtors (*too general types*),
   368         ctor_injects = steal #ctor_injects (*too general types*),
   369         dtor_injects = steal #dtor_injects (*too general types*),
   370         xtor_map_thms = steal #xtor_map_thms (*too general types and terms*),
   371         xtor_set_thmss = steal #xtor_set_thmss (*too general types and terms*),
   372         xtor_rel_thms = steal #xtor_rel_thms (*too general types and terms*),
   373         xtor_co_iter_thmss = transpose [xtor_un_fold_thms, xtor_co_rec_thms],
   374         xtor_co_iter_o_map_thmss = steal #xtor_co_iter_o_map_thmss (*theorem about old constant*),
   375         rel_xtor_co_induct_thm = rel_xtor_co_induct_thm}
   376        |> morph_fp_result (Morphism.term_morphism "BNF" (singleton (Variable.polymorphic lthy))));
   377   in
   378     (fp_res, lthy)
   379   end;
   380 
   381 end;