src/HOL/Tools/BNF/bnf_fp_n2m.ML
author traytel
Wed Aug 06 10:20:50 2014 +0200 (2014-08-06)
changeset 57801 4adfa833072b
parent 57700 a2c4adb839a9
child 57802 9c065009cd8a
permissions -rw-r--r--
made tactic more robust
blanchet@55061
     1
(*  Title:      HOL/Tools/BNF/bnf_fp_n2m.ML
blanchet@53303
     2
    Author:     Dmitriy Traytel, TU Muenchen
blanchet@53303
     3
    Copyright   2013
blanchet@53303
     4
blanchet@53303
     5
Flattening of nested to mutual (co)recursion.
blanchet@53303
     6
*)
blanchet@53303
     7
blanchet@53303
     8
signature BNF_FP_N2M =
blanchet@53303
     9
sig
blanchet@56484
    10
  val construct_mutualized_fp: BNF_Util.fp_kind -> int list -> typ list ->
blanchet@56650
    11
    BNF_FP_Util.fp_sugar list -> binding list -> (string * sort) list ->
blanchet@56484
    12
    typ list * typ list list -> BNF_Def.bnf list -> BNF_Comp.absT_info list -> local_theory ->
blanchet@56484
    13
    BNF_FP_Util.fp_result * local_theory
blanchet@53303
    14
end;
blanchet@53303
    15
blanchet@53303
    16
structure BNF_FP_N2M : BNF_FP_N2M =
blanchet@53303
    17
struct
blanchet@53303
    18
blanchet@53303
    19
open BNF_Def
blanchet@53303
    20
open BNF_Util
traytel@55803
    21
open BNF_Comp
blanchet@53303
    22
open BNF_FP_Util
blanchet@53303
    23
open BNF_FP_Def_Sugar
blanchet@53303
    24
open BNF_Tactics
blanchet@53303
    25
open BNF_FP_N2M_Tactics
blanchet@53303
    26
blanchet@53303
    27
fun force_typ ctxt T =
blanchet@56638
    28
  Term.map_types Type_Infer.paramify_vars
blanchet@53303
    29
  #> Type.constraint T
blanchet@53303
    30
  #> Syntax.check_term ctxt
blanchet@53303
    31
  #> singleton (Variable.polymorphic ctxt);
blanchet@53303
    32
blanchet@53303
    33
fun mk_prod_map f g =
blanchet@53303
    34
  let
blanchet@53303
    35
    val ((fAT, fBT), fT) = `dest_funT (fastype_of f);
blanchet@53303
    36
    val ((gAT, gBT), gT) = `dest_funT (fastype_of g);
blanchet@53303
    37
  in
blanchet@55932
    38
    Const (@{const_name map_prod},
blanchet@53303
    39
      fT --> gT --> HOLogic.mk_prodT (fAT, gAT) --> HOLogic.mk_prodT (fBT, gBT)) $ f $ g
blanchet@53303
    40
  end;
blanchet@53303
    41
blanchet@55931
    42
fun mk_map_sum f g =
blanchet@53303
    43
  let
blanchet@53303
    44
    val ((fAT, fBT), fT) = `dest_funT (fastype_of f);
blanchet@53303
    45
    val ((gAT, gBT), gT) = `dest_funT (fastype_of g);
blanchet@53303
    46
  in
blanchet@55931
    47
    Const (@{const_name map_sum}, fT --> gT --> mk_sumT (fAT, gAT) --> mk_sumT (fBT, gBT)) $ f $ g
blanchet@53303
    48
  end;
blanchet@53303
    49
blanchet@56484
    50
fun construct_mutualized_fp fp cliques fpTs (fp_sugars : fp_sugar list) bs resBs (resDs, Dss) bnfs
traytel@55819
    51
    (absT_infos : absT_info list) lthy =
blanchet@53303
    52
  let
traytel@55803
    53
    fun of_fp_res get =
blanchet@55539
    54
      map (fn {fp_res, fp_res_index, ...} => nth (get fp_res) fp_res_index) fp_sugars;
blanchet@53303
    55
blanchet@55966
    56
    fun mk_co_algT T U = case_fp fp (T --> U) (U --> T);
blanchet@55966
    57
    fun co_swap pair = case_fp fp I swap pair;
traytel@55803
    58
    val mk_co_comp = HOLogic.mk_comp o co_swap;
blanchet@55966
    59
    val co_productC = BNF_FP_Rec_Sugar_Util.case_fp fp @{type_name prod} @{type_name sum};
traytel@55803
    60
blanchet@53303
    61
    val dest_co_algT = co_swap o dest_funT;
blanchet@55966
    62
    val co_alg_argT = case_fp fp range_type domain_type;
blanchet@55966
    63
    val co_alg_funT = case_fp fp domain_type range_type;
blanchet@55966
    64
    val mk_co_product = curry (case_fp fp mk_convol mk_case_sum);
blanchet@55966
    65
    val mk_map_co_product = case_fp fp mk_prod_map mk_map_sum;
blanchet@55966
    66
    val co_proj1_const = case_fp fp (fst_const o fst) (uncurry Inl_const o dest_sumT o snd);
blanchet@55966
    67
    val mk_co_productT = curry (case_fp fp HOLogic.mk_prodT mk_sumT);
blanchet@55966
    68
    val dest_co_productT = case_fp fp HOLogic.dest_prodT dest_sumT;
blanchet@55966
    69
    val rewrite_comp_comp = case_fp fp @{thm rewriteL_comp_comp} @{thm rewriteR_comp_comp};
traytel@55803
    70
traytel@55803
    71
    val fp_absT_infos = map #absT_info fp_sugars;
traytel@55803
    72
    val fp_bnfs = of_fp_res #bnfs;
traytel@55803
    73
    val pre_bnfs = map #pre_bnf fp_sugars;
blanchet@57397
    74
    val nesting_bnfss =
blanchet@57397
    75
      map (fn sugar => #fp_nesting_bnfs sugar @ #live_nesting_bnfs sugar) fp_sugars;
blanchet@57397
    76
    val fp_or_nesting_bnfss = fp_bnfs :: nesting_bnfss;
blanchet@57397
    77
    val fp_or_nesting_bnfs = distinct (op = o pairself T_of_bnf) (flat fp_or_nesting_bnfss);
traytel@55803
    78
traytel@55803
    79
    val fp_absTs = map #absT fp_absT_infos;
traytel@55803
    80
    val fp_repTs = map #repT fp_absT_infos;
traytel@55803
    81
    val fp_abss = map #abs fp_absT_infos;
traytel@55803
    82
    val fp_reps = map #rep fp_absT_infos;
traytel@55803
    83
    val fp_type_definitions = map #type_definition fp_absT_infos;
traytel@55803
    84
traytel@55803
    85
    val absTs = map #absT absT_infos;
traytel@55803
    86
    val repTs = map #repT absT_infos;
traytel@55803
    87
    val absTs' = map (Logic.type_map (singleton (Variable.polymorphic lthy))) absTs;
traytel@55803
    88
    val repTs' = map (Logic.type_map (singleton (Variable.polymorphic lthy))) repTs;
traytel@55803
    89
    val abss = map #abs absT_infos;
traytel@55803
    90
    val reps = map #rep absT_infos;
traytel@55803
    91
    val abs_inverses = map #abs_inverse absT_infos;
traytel@55803
    92
    val type_definitions = map #type_definition absT_infos;
traytel@55803
    93
traytel@55803
    94
    val n = length bnfs;
traytel@55803
    95
    val deads = fold (union (op =)) Dss resDs;
traytel@55803
    96
    val As = subtract (op =) deads (map TFree resBs);
traytel@55803
    97
    val names_lthy = fold Variable.declare_typ (As @ deads) lthy;
traytel@55803
    98
    val m = length As;
traytel@55803
    99
    val live = m + n;
traytel@55803
   100
traytel@55803
   101
    val ((Xs, Bs), names_lthy) = names_lthy
traytel@55803
   102
      |> mk_TFrees n
traytel@55803
   103
      ||>> mk_TFrees m;
traytel@55803
   104
traytel@55803
   105
    val allAs = As @ Xs;
traytel@55803
   106
    val allBs = Bs @ Xs;
traytel@55803
   107
    val phiTs = map2 mk_pred2T As Bs;
traytel@55803
   108
    val thetaBs = As ~~ Bs;
traytel@55803
   109
    val fpTs' = map (Term.typ_subst_atomic thetaBs) fpTs;
traytel@55803
   110
    val fold_thetaAs = Xs ~~ fpTs;
traytel@55803
   111
    val fold_thetaBs = Xs ~~ fpTs';
traytel@55803
   112
    val rec_theta = Xs ~~ map2 mk_co_productT fpTs Xs;
traytel@55803
   113
    val pre_phiTs = map2 mk_pred2T fpTs fpTs';
blanchet@53303
   114
blanchet@53303
   115
    val ((ctors, dtors), (xtor's, xtors)) =
blanchet@53303
   116
      let
traytel@55803
   117
        val ctors = map2 (force_typ names_lthy o (fn T => dummyT --> T)) fpTs (of_fp_res #ctors);
traytel@55803
   118
        val dtors = map2 (force_typ names_lthy o (fn T => T --> dummyT)) fpTs (of_fp_res #dtors);
blanchet@53303
   119
      in
blanchet@55966
   120
        ((ctors, dtors), `(map (Term.subst_atomic_types thetaBs)) (case_fp fp ctors dtors))
blanchet@53303
   121
      end;
blanchet@53303
   122
traytel@55803
   123
    val absATs = map (domain_type o fastype_of) ctors;
traytel@55803
   124
    val absBTs = map (Term.typ_subst_atomic thetaBs) absATs;
blanchet@53303
   125
    val xTs = map (domain_type o fastype_of) xtors;
blanchet@53303
   126
    val yTs = map (domain_type o fastype_of) xtor's;
blanchet@53303
   127
traytel@55819
   128
    val absAs = map3 (fn Ds => mk_abs o mk_T_of_bnf Ds allAs) Dss bnfs abss;
traytel@55819
   129
    val absBs = map3 (fn Ds => mk_abs o mk_T_of_bnf Ds allBs) Dss bnfs abss;
traytel@55819
   130
    val fp_repAs = map2 mk_rep absATs fp_reps;
traytel@55819
   131
    val fp_repBs = map2 mk_rep absBTs fp_reps;
traytel@55803
   132
blanchet@53303
   133
    val (((((phis, phis'), pre_phis), xs), ys), names_lthy) = names_lthy
blanchet@53303
   134
      |> mk_Frees' "R" phiTs
blanchet@53303
   135
      ||>> mk_Frees "S" pre_phiTs
blanchet@53303
   136
      ||>> mk_Frees "x" xTs
blanchet@53303
   137
      ||>> mk_Frees "y" yTs;
blanchet@53303
   138
blanchet@53303
   139
    val rels =
blanchet@53303
   140
      let
blanchet@57397
   141
        fun find_rel T As Bs = fp_or_nesting_bnfss
blanchet@55394
   142
          |> map (filter_out (curry (op = o pairself name_of_bnf) BNF_Comp.DEADID_bnf))
blanchet@53303
   143
          |> get_first (find_first (fn bnf => Type.could_unify (T_of_bnf bnf, T)))
blanchet@53303
   144
          |> Option.map (fn bnf =>
blanchet@53303
   145
            let val live = live_of_bnf bnf;
blanchet@53303
   146
            in (mk_rel live As Bs (rel_of_bnf bnf), live) end)
blanchet@53303
   147
          |> the_default (HOLogic.eq_const T, 0);
blanchet@53303
   148
blanchet@53303
   149
        fun mk_rel (T as Type (_, Ts)) (Type (_, Us)) =
blanchet@53303
   150
              let
blanchet@53303
   151
                val (rel, live) = find_rel T Ts Us;
blanchet@53303
   152
                val (Ts', Us') = fastype_of rel |> strip_typeN live |> fst |> map_split dest_pred2T;
blanchet@53303
   153
                val rels = map2 mk_rel Ts' Us';
blanchet@53303
   154
              in
blanchet@53303
   155
                Term.list_comb (rel, rels)
blanchet@53303
   156
              end
traytel@54244
   157
          | mk_rel (T as TFree _) _ = (nth phis (find_index (curry op = T) As)
traytel@54244
   158
              handle General.Subscript => HOLogic.eq_const T)
blanchet@53303
   159
          | mk_rel _ _ = raise Fail "fpTs contains schematic type variables";
blanchet@53303
   160
      in
traytel@54298
   161
        map2 (fold_rev Term.absfree phis' oo mk_rel) fpTs fpTs'
blanchet@53303
   162
      end;
blanchet@53303
   163
blanchet@53303
   164
    val pre_rels = map2 (fn Ds => mk_rel_of_bnf Ds (As @ fpTs) (Bs @ fpTs')) Dss bnfs;
blanchet@53303
   165
blanchet@55539
   166
    val rel_unfolds = maps (no_refl o single o rel_def_of_bnf) pre_bnfs;
traytel@55803
   167
    val rel_xtor_co_inducts = of_fp_res (split_conj_thm o #rel_xtor_co_induct_thm)
blanchet@55539
   168
      |> map (unfold_thms lthy (id_apply :: rel_unfolds));
blanchet@53303
   169
blanchet@53303
   170
    val rel_defs = map rel_def_of_bnf bnfs;
blanchet@53303
   171
    val rel_monos = map rel_mono_of_bnf bnfs;
blanchet@53303
   172
traytel@55803
   173
    fun cast castA castB pre_rel =
traytel@55803
   174
      let
traytel@55803
   175
        val castAB = mk_vimage2p (Term.subst_atomic_types fold_thetaAs castA)
traytel@55803
   176
          (Term.subst_atomic_types fold_thetaBs castB);
traytel@55803
   177
      in
traytel@55803
   178
        fold_rev (fold_rev Term.absdummy) [phiTs, pre_phiTs]
traytel@55803
   179
          (castAB $ Term.list_comb (pre_rel, map Bound (live - 1 downto 0)))
traytel@55803
   180
      end;
traytel@55803
   181
traytel@55803
   182
    val castAs = map2 (curry HOLogic.mk_comp) absAs fp_repAs;
traytel@55803
   183
    val castBs = map2 (curry HOLogic.mk_comp) absBs fp_repBs;
traytel@55803
   184
blanchet@53303
   185
    val rel_xtor_co_induct_thm =
traytel@55803
   186
      mk_rel_xtor_co_induct_thm fp (map3 cast castAs castBs pre_rels) pre_phis rels phis xs ys xtors
traytel@55803
   187
        xtor's (mk_rel_xtor_co_induct_tactic fp abs_inverses rel_xtor_co_inducts rel_defs rel_monos)
traytel@55803
   188
        lthy;
blanchet@53303
   189
blanchet@57397
   190
    val rel_eqs = no_refl (map rel_eq_of_bnf fp_or_nesting_bnfs);
blanchet@53303
   191
    val map_id0s = no_refl (map map_id0_of_bnf bnfs);
blanchet@53303
   192
blanchet@53303
   193
    val xtor_co_induct_thm =
blanchet@53303
   194
      (case fp of
blanchet@53303
   195
        Least_FP =>
blanchet@53303
   196
          let
blanchet@53303
   197
            val (Ps, names_lthy) = names_lthy
blanchet@53303
   198
              |> mk_Frees "P" (map (fn T => T --> HOLogic.boolT) fpTs);
blanchet@53303
   199
            fun mk_Grp_id P =
blanchet@53303
   200
              let val T = domain_type (fastype_of P);
blanchet@53303
   201
              in mk_Grp (HOLogic.Collect_const T $ P) (HOLogic.id_const T) end;
blanchet@53303
   202
            val cts = map (SOME o certify lthy) (map HOLogic.eq_const As @ map mk_Grp_id Ps);
traytel@55803
   203
            fun mk_fp_type_copy_thms thm = map (curry op RS thm)
traytel@55803
   204
              @{thms type_copy_Abs_o_Rep type_copy_vimage2p_Grp_Rep};
traytel@55803
   205
            fun mk_type_copy_thms thm = map (curry op RS thm)
traytel@55803
   206
              @{thms type_copy_Rep_o_Abs type_copy_vimage2p_Grp_Abs};
blanchet@53303
   207
          in
blanchet@53303
   208
            cterm_instantiate_pos cts rel_xtor_co_induct_thm
blanchet@53303
   209
            |> singleton (Proof_Context.export names_lthy lthy)
blanchet@53303
   210
            |> unfold_thms lthy (@{thms eq_le_Grp_id_iff all_simps(1,2)[symmetric]} @ rel_eqs)
blanchet@53303
   211
            |> funpow n (fn thm => thm RS spec)
blanchet@53303
   212
            |> unfold_thms lthy (@{thm eq_alt} :: map rel_Grp_of_bnf bnfs @ map_id0s)
blanchet@55854
   213
            |> unfold_thms lthy (@{thms vimage2p_id vimage2p_comp comp_apply comp_id
traytel@55803
   214
               Grp_id_mono_subst eqTrueI[OF subset_UNIV] simp_thms(22)} @
traytel@55803
   215
               maps mk_fp_type_copy_thms fp_type_definitions @
traytel@55803
   216
               maps mk_type_copy_thms type_definitions)
blanchet@53303
   217
            |> unfold_thms lthy @{thms subset_iff mem_Collect_eq
blanchet@53303
   218
               atomize_conjL[symmetric] atomize_all[symmetric] atomize_imp[symmetric]}
blanchet@53303
   219
          end
blanchet@53303
   220
      | Greatest_FP =>
blanchet@53303
   221
          let
blanchet@53303
   222
            val cts = NONE :: map (SOME o certify lthy) (map HOLogic.eq_const As);
blanchet@53303
   223
          in
blanchet@53303
   224
            cterm_instantiate_pos cts rel_xtor_co_induct_thm
blanchet@53303
   225
            |> unfold_thms lthy (@{thms le_fun_def le_bool_def all_simps(1,2)[symmetric]} @ rel_eqs)
blanchet@53303
   226
            |> funpow (2 * n) (fn thm => thm RS spec)
wenzelm@54742
   227
            |> Conv.fconv_rule (Object_Logic.atomize lthy)
blanchet@53303
   228
            |> funpow n (fn thm => thm RS mp)
blanchet@53303
   229
          end);
blanchet@53303
   230
blanchet@53303
   231
    val fold_preTs = map2 (fn Ds => mk_T_of_bnf Ds allAs) Dss bnfs;
blanchet@53303
   232
    val rec_preTs = map (Term.typ_subst_atomic rec_theta) fold_preTs;
blanchet@53303
   233
blanchet@53303
   234
    val rec_strTs = map2 mk_co_algT rec_preTs Xs;
blanchet@53303
   235
    val resTs = map2 mk_co_algT fpTs Xs;
blanchet@53303
   236
blanchet@55894
   237
    val ((rec_strs, rec_strs'), names_lthy) = names_lthy
blanchet@55894
   238
      |> mk_Frees' "s" rec_strTs;
blanchet@53303
   239
blanchet@55868
   240
    val co_recs = of_fp_res #xtor_co_recs;
blanchet@55539
   241
    val ns = map (length o #Ts o #fp_res) fp_sugars;
blanchet@55539
   242
blanchet@56640
   243
    fun substT rho (Type (@{type_name fun}, [T, U])) = substT rho T --> substT rho U
blanchet@53303
   244
      | substT rho (Type (s, Ts)) = Type (s, map (typ_subst_nonatomic rho) Ts)
blanchet@53303
   245
      | substT _ T = T;
blanchet@55539
   246
traytel@55803
   247
    val typ_subst_nonatomic_sorted = fold_rev (typ_subst_nonatomic o single);
traytel@55803
   248
traytel@55899
   249
    fun foldT_of_recT recT =
traytel@55899
   250
      let
traytel@55899
   251
        val ((FTXs, Xs), TX) = strip_fun_type recT |>> map_split dest_co_algT;
traytel@55899
   252
        fun subst (Type (C, Ts as [_, X])) =
traytel@55899
   253
            if C = co_productC andalso member op = Xs X then X else Type (C, map subst Ts)
traytel@55899
   254
          | subst (Type (C, Ts)) = Type (C, map subst Ts)
traytel@55899
   255
          | subst T = T;
traytel@55899
   256
      in
traytel@55899
   257
        map2 (mk_co_algT o subst) FTXs Xs ---> TX
traytel@55899
   258
      end;
traytel@55899
   259
traytel@55899
   260
    fun force_rec i TU TU_rec raw_rec =
blanchet@53303
   261
      let
traytel@55803
   262
        val thy = Proof_Context.theory_of lthy;
traytel@55803
   263
traytel@55899
   264
        val approx_rec = raw_rec
blanchet@55894
   265
          |> force_typ names_lthy (replicate (nth ns i) dummyT ---> TU_rec);
traytel@55803
   266
        val subst = Term.typ_subst_atomic fold_thetaAs;
traytel@55803
   267
traytel@55803
   268
        fun mk_fp_absT_repT fp_repT fp_absT = mk_absT thy fp_repT fp_absT ooo mk_repT;
traytel@55803
   269
        val mk_fp_absT_repTs = map5 mk_fp_absT_repT fp_repTs fp_absTs absTs repTs;
traytel@55803
   270
traytel@55803
   271
        val fold_preTs' = mk_fp_absT_repTs (map subst fold_preTs);
traytel@55803
   272
traytel@55803
   273
        val fold_pre_deads_only_Ts =
traytel@55803
   274
          map (typ_subst_nonatomic_sorted (map (rpair dummyT) (As @ fpTs))) fold_preTs';
traytel@55803
   275
traytel@56487
   276
        val (clique, TUs) =
traytel@56487
   277
          map_split dest_co_algT (binder_fun_types (foldT_of_recT (fastype_of approx_rec)))
traytel@55478
   278
          |>> map subst
traytel@56487
   279
          |> `(fn (_, Ys) =>
traytel@56487
   280
            nth cliques (find_index (fn X => X = the (find_first (can dest_TFree) Ys)) Xs))
traytel@56487
   281
          ||> uncurry (map2 mk_co_algT);
traytel@56487
   282
        val cands = cliques ~~ map2 mk_co_algT fold_preTs' Xs;
traytel@56487
   283
        val js = find_indices (fn ((cl, cand), TU) =>
traytel@56487
   284
          cl = clique andalso Type.could_unify (TU, cand)) TUs cands;
blanchet@53303
   285
        val Tpats = map (fn j => mk_co_algT (nth fold_pre_deads_only_Ts j) (nth Xs j)) js;
blanchet@53303
   286
      in
blanchet@55894
   287
        force_typ names_lthy (Tpats ---> TU) raw_rec
blanchet@53303
   288
      end;
blanchet@53303
   289
traytel@55803
   290
    fun mk_co_comp_abs_rep fp_absT absT fp_abs fp_rep abs rep t =
blanchet@55966
   291
      case_fp fp (HOLogic.mk_comp (HOLogic.mk_comp (t, mk_abs absT abs), mk_rep fp_absT fp_rep))
traytel@55803
   292
        (HOLogic.mk_comp (mk_abs fp_absT fp_abs, HOLogic.mk_comp (mk_rep absT rep, t)));
traytel@55803
   293
blanchet@55894
   294
    fun mk_rec b_opt recs lthy TU =
blanchet@53303
   295
      let
traytel@55803
   296
        val thy = Proof_Context.theory_of lthy;
traytel@55803
   297
blanchet@53303
   298
        val x = co_alg_argT TU;
blanchet@53303
   299
        val i = find_index (fn T => x = T) Xs;
blanchet@55894
   300
        val TUrec =
blanchet@55894
   301
          (case find_first (fn f => body_fun_type (fastype_of f) = TU) recs of
desharna@57527
   302
            NONE =>
blanchet@55894
   303
              force_rec i TU
traytel@55899
   304
                (TU |> is_none b_opt ? substT (map2 mk_co_productT fpTs Xs ~~ Xs)) (nth co_recs i)
blanchet@53303
   305
          | SOME f => f);
traytel@55803
   306
blanchet@55894
   307
        val TUs = binder_fun_types (fastype_of TUrec);
traytel@55803
   308
blanchet@53303
   309
        fun mk_s TU' =
blanchet@53303
   310
          let
traytel@55803
   311
            fun mk_absT_fp_repT repT absT = mk_absT thy repT absT ooo mk_repT;
traytel@55803
   312
blanchet@53303
   313
            val i = find_index (fn T => co_alg_argT TU' = T) Xs;
traytel@55803
   314
            val fp_abs = nth fp_abss i;
traytel@55803
   315
            val fp_rep = nth fp_reps i;
traytel@55803
   316
            val abs = nth abss i;
traytel@55803
   317
            val rep = nth reps i;
blanchet@54233
   318
            val sF = co_alg_funT TU';
traytel@55803
   319
            val sF' =
traytel@55803
   320
              mk_absT_fp_repT (nth repTs' i) (nth absTs' i) (nth fp_absTs i) (nth fp_repTs i) sF
traytel@55803
   321
                handle Term.TYPE _ => sF;
blanchet@55894
   322
            val F = nth rec_preTs i;
blanchet@55894
   323
            val s = nth rec_strs i;
blanchet@53303
   324
          in
traytel@55803
   325
            if sF = F then s
traytel@55803
   326
            else if sF' = F then mk_co_comp_abs_rep sF sF' fp_abs fp_rep abs rep s
blanchet@53303
   327
            else
blanchet@53303
   328
              let
traytel@55803
   329
                val smapT = replicate live dummyT ---> mk_co_algT sF' F;
blanchet@53303
   330
                fun hidden_to_unit t =
blanchet@53303
   331
                  Term.subst_TVars (map (rpair HOLogic.unitT) (Term.add_tvar_names t [])) t;
blanchet@53303
   332
                val smap = map_of_bnf (nth bnfs i)
blanchet@53303
   333
                  |> force_typ names_lthy smapT
blanchet@53303
   334
                  |> hidden_to_unit;
blanchet@53303
   335
                val smap_argTs = strip_typeN live (fastype_of smap) |> fst;
blanchet@54233
   336
                fun mk_smap_arg TU =
blanchet@53303
   337
                  (if domain_type TU = range_type TU then
blanchet@53303
   338
                    HOLogic.id_const (domain_type TU)
blanchet@55894
   339
                  else
blanchet@53303
   340
                    let
blanchet@53303
   341
                      val (TY, (U, X)) = TU |> dest_co_algT ||> dest_co_productT;
blanchet@53303
   342
                      val T = mk_co_algT TY U;
blanchet@53303
   343
                    in
desharna@57303
   344
                      (case try (force_typ names_lthy T o build_map lthy [] co_proj1_const o dest_funT) T of
blanchet@53303
   345
                        SOME f => mk_co_product f
blanchet@55894
   346
                          (fst (fst (mk_rec NONE recs lthy (mk_co_algT TY X))))
blanchet@53303
   347
                      | NONE => mk_map_co_product
desharna@57303
   348
                          (build_map lthy [] co_proj1_const
blanchet@53303
   349
                            (dest_funT (mk_co_algT (dest_co_productT TY |> fst) U)))
blanchet@53303
   350
                          (HOLogic.id_const X))
blanchet@55894
   351
                    end)
blanchet@53303
   352
                val smap_args = map mk_smap_arg smap_argTs;
blanchet@53303
   353
              in
traytel@55803
   354
                mk_co_comp_abs_rep sF sF' fp_abs fp_rep abs rep
traytel@55803
   355
                  (mk_co_comp (s, Term.list_comb (smap, smap_args)))
traytel@55803
   356
              end
blanchet@53303
   357
          end;
blanchet@55894
   358
        val t = Term.list_comb (TUrec, map mk_s TUs);
blanchet@53303
   359
      in
blanchet@53303
   360
        (case b_opt of
blanchet@53303
   361
          NONE => ((t, Drule.dummy_thm), lthy)
blanchet@54233
   362
        | SOME b => Local_Theory.define ((b, NoSyn), ((Binding.conceal (Thm.def_binding b), []),
blanchet@55894
   363
            fold_rev Term.absfree rec_strs' t)) lthy |>> apsnd snd)
blanchet@53303
   364
      end;
blanchet@53303
   365
blanchet@55966
   366
    val recN = case_fp fp ctor_recN dtor_corecN;
blanchet@55894
   367
    fun mk_recs lthy =
blanchet@55894
   368
      fold2 (fn TU => fn b => fn ((recs, defs), lthy) =>
blanchet@55894
   369
        mk_rec (SOME b) recs lthy TU |>> (fn (f, d) => (f :: recs, d :: defs)))
blanchet@55894
   370
      resTs (map (Binding.suffix_name ("_" ^ recN)) bs) (([], []), lthy)
desharna@57527
   371
      |>> map_prod rev rev;
blanchet@55894
   372
    val ((raw_co_recs, raw_co_rec_defs), (lthy, raw_lthy)) = lthy
blanchet@55894
   373
      |> mk_recs
traytel@53331
   374
      ||> `Local_Theory.restore;
blanchet@53303
   375
traytel@53331
   376
    val phi = Proof_Context.export_morphism raw_lthy lthy;
blanchet@53303
   377
blanchet@53303
   378
    val co_recs = map (Morphism.term phi) raw_co_recs;
blanchet@53303
   379
traytel@56486
   380
    val fp_rec_o_maps = of_fp_res #xtor_co_rec_o_map_thms
traytel@56486
   381
      |> maps (fn thm => [thm, thm RS rewrite_comp_comp]);
blanchet@55868
   382
blanchet@55894
   383
    val xtor_co_rec_thms =
blanchet@53303
   384
      let
blanchet@53303
   385
        val recs = map (fn r => Term.list_comb (r, rec_strs)) raw_co_recs;
blanchet@53303
   386
        val rec_mapTs = co_swap (As @ fpTs, As @ map2 mk_co_productT fpTs Xs);
blanchet@53303
   387
        val pre_rec_maps =
blanchet@53303
   388
          map2 (fn Ds => fn bnf =>
blanchet@53303
   389
            Term.list_comb (uncurry (mk_map_of_bnf Ds) rec_mapTs bnf,
blanchet@53303
   390
              map HOLogic.id_const As @ map2 (mk_co_product o HOLogic.id_const) fpTs recs))
blanchet@53303
   391
          Dss bnfs;
blanchet@53303
   392
traytel@55803
   393
        fun mk_goals f xtor s smap fp_abs fp_rep abs rep =
traytel@55803
   394
          let
traytel@55803
   395
            val lhs = mk_co_comp (f, xtor);
traytel@55803
   396
            val rhs = mk_co_comp (s, smap);
traytel@55803
   397
          in
traytel@55803
   398
            HOLogic.mk_eq (lhs,
traytel@55803
   399
              mk_co_comp_abs_rep (co_alg_funT (fastype_of lhs)) (co_alg_funT (fastype_of rhs))
traytel@55803
   400
                fp_abs fp_rep abs rep rhs)
traytel@55803
   401
          end;
blanchet@53303
   402
blanchet@55894
   403
        val goals = map8 mk_goals recs xtors rec_strs pre_rec_maps fp_abss fp_reps abss reps;
blanchet@53303
   404
blanchet@53303
   405
        val pre_map_defs = no_refl (map map_def_of_bnf bnfs);
blanchet@53303
   406
        val fp_pre_map_defs = no_refl (map map_def_of_bnf pre_bnfs);
blanchet@53303
   407
traytel@55803
   408
        val unfold_map = map (unfold_thms lthy (id_apply :: pre_map_defs));
traytel@55803
   409
blanchet@55868
   410
        val fp_xtor_co_recs = map (mk_pointfree lthy) (of_fp_res #xtor_co_rec_thms);
blanchet@53303
   411
blanchet@55966
   412
        val fold_thms = case_fp fp @{thm comp_assoc} @{thm comp_assoc[symmetric]} ::
blanchet@55932
   413
          map (fn thm => thm RS rewrite_comp_comp) @{thms map_prod.comp map_sum.comp} @
blanchet@55932
   414
          @{thms id_apply comp_id id_comp map_prod.comp map_prod.id map_sum.comp map_sum.id};
blanchet@55966
   415
        val rec_thms = fold_thms @ case_fp fp
blanchet@55932
   416
          @{thms fst_convol map_prod_o_convol convol_o}
blanchet@55931
   417
          @{thms case_sum_o_inj(1) case_sum_o_map_sum o_case_sum};
traytel@55803
   418
traytel@55810
   419
        val eq_thm_prop_untyped = Term.aconv_untyped o pairself Thm.full_prop_of;
traytel@55803
   420
blanchet@53303
   421
        val map_thms = no_refl (maps (fn bnf =>
traytel@55803
   422
           let val map_comp0 = map_comp0_of_bnf bnf RS sym
blanchet@57397
   423
           in [map_comp0, map_comp0 RS rewrite_comp_comp, map_id0_of_bnf bnf] end)
blanchet@57397
   424
          fp_or_nesting_bnfs) @
blanchet@55966
   425
          remove eq_thm_prop_untyped (case_fp fp @{thm comp_assoc[symmetric]} @{thm comp_assoc})
traytel@55803
   426
          (map2 (fn thm => fn bnf =>
traytel@55803
   427
            @{thm type_copy_map_comp0_undo} OF
traytel@55803
   428
              (replicate 3 thm @ unfold_map [map_comp0_of_bnf bnf]) RS
traytel@55803
   429
              rewrite_comp_comp)
traytel@55803
   430
          type_definitions bnfs);
traytel@55803
   431
traytel@57801
   432
        fun mk_Rep_o_Abs thm = (thm RS @{thm type_copy_Rep_o_Abs})
traytel@57801
   433
          |> (fn thm => [thm, thm RS rewrite_comp_comp]);
traytel@55803
   434
traytel@57801
   435
        val fp_Rep_o_Abss = maps mk_Rep_o_Abs fp_type_definitions;
traytel@57801
   436
        val Rep_o_Abss = maps mk_Rep_o_Abs type_definitions;
blanchet@53303
   437
blanchet@55894
   438
        fun tac {context = ctxt, prems = _} =
blanchet@55894
   439
          unfold_thms_tac ctxt (flat [rec_thms, raw_co_rec_defs, pre_map_defs, fp_pre_map_defs,
blanchet@55894
   440
            fp_xtor_co_recs, fp_rec_o_maps, map_thms, fp_Rep_o_Abss, Rep_o_Abss]) THEN
blanchet@53303
   441
          CONJ_WRAP (K (HEADGOAL (rtac refl))) bnfs;
blanchet@53303
   442
      in
blanchet@55894
   443
        Library.foldr1 HOLogic.mk_conj goals
blanchet@55894
   444
        |> HOLogic.mk_Trueprop
blanchet@55894
   445
        |> fold_rev Logic.all rec_strs
blanchet@55894
   446
        |> (fn goal => Goal.prove_sorry raw_lthy [] [] goal tac)
blanchet@55894
   447
        |> Thm.close_derivation
blanchet@55894
   448
        |> Morphism.thm phi
blanchet@55894
   449
        |> split_conj_thm
blanchet@55894
   450
        |> map (fn thm => thm RS @{thm comp_eq_dest})
blanchet@53303
   451
      end;
blanchet@53303
   452
blanchet@53303
   453
    (* These results are half broken. This is deliberate. We care only about those fields that are
blanchet@55531
   454
       used by "primrec", "primcorecursive", and "datatype_compat". *)
blanchet@53303
   455
    val fp_res =
blanchet@55894
   456
      ({Ts = fpTs, bnfs = of_fp_res #bnfs, dtors = dtors, ctors = ctors,
blanchet@55868
   457
        xtor_co_recs = co_recs, xtor_co_induct = xtor_co_induct_thm,
traytel@55803
   458
        dtor_ctors = of_fp_res #dtor_ctors (*too general types*),
traytel@55803
   459
        ctor_dtors = of_fp_res #ctor_dtors (*too general types*),
traytel@55803
   460
        ctor_injects = of_fp_res #ctor_injects (*too general types*),
traytel@55803
   461
        dtor_injects = of_fp_res #dtor_injects (*too general types*),
traytel@55803
   462
        xtor_map_thms = of_fp_res #xtor_map_thms (*too general types and terms*),
traytel@55803
   463
        xtor_set_thmss = of_fp_res #xtor_set_thmss (*too general types and terms*),
traytel@55803
   464
        xtor_rel_thms = of_fp_res #xtor_rel_thms (*too general types and terms*),
blanchet@55868
   465
        xtor_co_rec_thms = xtor_co_rec_thms,
blanchet@55868
   466
        xtor_co_rec_o_map_thms = fp_rec_o_maps (*theorems about old constants*),
desharna@57700
   467
        rel_xtor_co_induct_thm = rel_xtor_co_induct_thm,
desharna@57700
   468
        dtor_set_induct_thms = []}
wenzelm@54740
   469
       |> morph_fp_result (Morphism.term_morphism "BNF" (singleton (Variable.polymorphic lthy))));
blanchet@53303
   470
  in
blanchet@53303
   471
    (fp_res, lthy)
blanchet@54242
   472
  end;
blanchet@53303
   473
blanchet@53303
   474
end;