src/HOL/BNF/Tools/bnf_fp_n2m_sugar.ML
author blanchet
Mon Sep 09 14:22:11 2013 +0200 (2013-09-09)
changeset 53476 eb3865c3ee58
parent 53475 185ad6cf6576
child 53591 b6e2993fd0d3
permissions -rw-r--r--
include map theorems in datastructure for "primcorec"
     1 (*  Title:      HOL/BNF/Tools/bnf_fp_n2m_sugar.ML
     2     Author:     Jasmin Blanchette, TU Muenchen
     3     Copyright   2013
     4 
     5 Suggared flattening of nested to mutual (co)recursion.
     6 *)
     7 
     8 signature BNF_FP_N2M_SUGAR =
     9 sig
    10   val mutualize_fp_sugars: bool -> bool -> BNF_FP_Util.fp_kind -> binding list -> typ list ->
    11     (term -> int list) -> term list list list list -> BNF_FP_Def_Sugar.fp_sugar list ->
    12     local_theory -> (bool * BNF_FP_Def_Sugar.fp_sugar list) * local_theory
    13   val pad_and_indexify_calls: BNF_FP_Def_Sugar.fp_sugar list -> int ->
    14     (term * term list list) list list -> term list list list list
    15   val nested_to_mutual_fps: bool -> BNF_FP_Util.fp_kind -> binding list -> typ list ->
    16     (term -> int list) -> ((term * term list list) list) list -> local_theory ->
    17     (bool * typ list * int list * BNF_FP_Def_Sugar.fp_sugar list) * local_theory
    18 end;
    19 
    20 structure BNF_FP_N2M_Sugar : BNF_FP_N2M_SUGAR =
    21 struct
    22 
    23 open BNF_Util
    24 open BNF_Def
    25 open BNF_Ctr_Sugar
    26 open BNF_FP_Util
    27 open BNF_FP_Def_Sugar
    28 open BNF_FP_N2M
    29 
    30 val n2mN = "n2m_"
    31 
    32 (* TODO: test with sort constraints on As *)
    33 (* TODO: use right sorting order for "fp_sort" w.r.t. original BNFs (?) -- treat new variables
    34    as deads? *)
    35 fun mutualize_fp_sugars lose_co_rec mutualize fp bs fpTs get_indices callssss fp_sugars0
    36     no_defs_lthy0 =
    37   (* TODO: Also check whether there's any lost recursion? *)
    38   if mutualize orelse has_duplicates (op =) fpTs then
    39     let
    40       val thy = Proof_Context.theory_of no_defs_lthy0;
    41 
    42       val qsotm = quote o Syntax.string_of_term no_defs_lthy0;
    43 
    44       fun heterogeneous_call t = error ("Heterogeneous recursive call: " ^ qsotm t);
    45       fun incompatible_calls t1 t2 =
    46         error ("Incompatible recursive calls: " ^ qsotm t1 ^ " vs. " ^ qsotm t2);
    47 
    48       val b_names = map Binding.name_of bs;
    49       val fp_b_names = map base_name_of_typ fpTs;
    50 
    51       val nn = length fpTs;
    52 
    53       fun target_ctr_sugar_of_fp_sugar fpT {T, index, ctr_sugars, ...} =
    54         let
    55           val rho = Vartab.fold (cons o apsnd snd) (Sign.typ_match thy (T, fpT) Vartab.empty) [];
    56           val phi = Morphism.term_morphism (Term.subst_TVars rho);
    57         in
    58           morph_ctr_sugar phi (nth ctr_sugars index)
    59         end;
    60 
    61       val ctr_defss = map (of_fp_sugar #ctr_defss) fp_sugars0;
    62       val mapss = map (of_fp_sugar #mapss) fp_sugars0;
    63       val ctr_sugars0 = map2 target_ctr_sugar_of_fp_sugar fpTs fp_sugars0;
    64 
    65       val ctrss = map #ctrs ctr_sugars0;
    66       val ctr_Tss = map (map fastype_of) ctrss;
    67 
    68       val As' = fold (fold Term.add_tfreesT) ctr_Tss [];
    69       val As = map TFree As';
    70 
    71       val ((Cs, Xs), no_defs_lthy) =
    72         no_defs_lthy0
    73         |> fold Variable.declare_typ As
    74         |> mk_TFrees nn
    75         ||>> variant_tfrees fp_b_names;
    76 
    77       (* If "lose_co_rec" is "true", the function "null" on "'a list" gives rise to
    78            'list = unit + 'a list
    79          instead of
    80            'list = unit + 'list
    81          resulting in a simpler (co)induction rule and (co)recursor. *)
    82       fun freeze_fp_default (T as Type (s, Ts)) =
    83           (case find_index (curry (op =) T) fpTs of
    84             ~1 => Type (s, map freeze_fp_default Ts)
    85           | kk => nth Xs kk)
    86         | freeze_fp_default T = T;
    87 
    88       fun get_indices_checked call =
    89         (case get_indices call of
    90           _ :: _ :: _ => heterogeneous_call call
    91         | kks => kks);
    92 
    93       fun freeze_fp calls (T as Type (s, Ts)) =
    94           (case map_filter (try (snd o dest_map no_defs_lthy s)) calls of
    95             [] =>
    96             (case union (op = o pairself fst)
    97                 (maps (fn call => map (rpair call) (get_indices_checked call)) calls) [] of
    98               [] => T |> not lose_co_rec ? freeze_fp_default
    99             | [(kk, _)] => nth Xs kk
   100             | (_, call1) :: (_, call2) :: _ => incompatible_calls call1 call2)
   101           | callss =>
   102             Type (s, map2 freeze_fp (flatten_type_args_of_bnf (the (bnf_of no_defs_lthy s)) []
   103               (transpose callss)) Ts))
   104         | freeze_fp _ T = T;
   105 
   106       val ctr_Tsss = map (map binder_types) ctr_Tss;
   107       val ctrXs_Tsss = map2 (map2 (map2 freeze_fp)) callssss ctr_Tsss;
   108       val ctrXs_sum_prod_Ts = map (mk_sumTN_balanced o map HOLogic.mk_tupleT) ctrXs_Tsss;
   109       val Ts = map (body_type o hd) ctr_Tss;
   110 
   111       val ns = map length ctr_Tsss;
   112       val kss = map (fn n => 1 upto n) ns;
   113       val mss = map (map length) ctr_Tsss;
   114 
   115       val fp_eqs = map dest_TFree Xs ~~ ctrXs_sum_prod_Ts;
   116 
   117       val base_fp_names = Name.variant_list [] fp_b_names;
   118       val fp_bs = map2 (fn b_name => fn base_fp_name =>
   119           Binding.qualify true b_name (Binding.name (n2mN ^ base_fp_name)))
   120         b_names base_fp_names;
   121 
   122       val (pre_bnfs, (fp_res as {xtor_co_iterss = xtor_co_iterss0, xtor_co_induct,
   123              dtor_injects, dtor_ctors, xtor_co_iter_thmss, ...}, lthy)) =
   124         fp_bnf (construct_mutualized_fp fp fpTs fp_sugars0) fp_bs As' fp_eqs no_defs_lthy;
   125 
   126       val nesting_bnfs = nesty_bnfs lthy ctrXs_Tsss As;
   127       val nested_bnfs = nesty_bnfs lthy ctrXs_Tsss Xs;
   128 
   129       val ((xtor_co_iterss, iters_args_types, coiters_args_types), _) =
   130         mk_co_iters_prelims fp fpTs Cs ns mss xtor_co_iterss0 lthy;
   131 
   132       fun mk_binding b suf = Binding.suffix_name ("_" ^ suf) b;
   133 
   134       val ((co_iterss, co_iter_defss), lthy) =
   135         fold_map2 (fn b =>
   136           (if fp = Least_FP then define_iters [foldN, recN] (the iters_args_types)
   137            else define_coiters [unfoldN, corecN] (the coiters_args_types))
   138             (mk_binding b) fpTs Cs) fp_bs xtor_co_iterss lthy
   139         |>> split_list;
   140 
   141       val rho = tvar_subst thy Ts fpTs;
   142       val ctr_sugar_phi =
   143         Morphism.compose (Morphism.typ_morphism (Term.typ_subst_TVars rho))
   144           (Morphism.term_morphism (Term.subst_TVars rho));
   145       val inst_ctr_sugar = morph_ctr_sugar ctr_sugar_phi;
   146 
   147       val ctr_sugars = map inst_ctr_sugar ctr_sugars0;
   148 
   149       val (co_inducts, un_fold_thmss, co_rec_thmss, disc_unfold_thmss, disc_corec_thmss,
   150            sel_unfold_thmsss, sel_corec_thmsss) =
   151         if fp = Least_FP then
   152           derive_induct_iters_thms_for_types pre_bnfs (the iters_args_types) xtor_co_induct
   153             xtor_co_iter_thmss nesting_bnfs nested_bnfs fpTs Cs Xs ctrXs_Tsss ctrss ctr_defss
   154             co_iterss co_iter_defss lthy
   155           |> (fn ((_, induct, _), (fold_thmss, _), (rec_thmss, _)) =>
   156             ([induct], fold_thmss, rec_thmss, [], [], [], []))
   157         else
   158           derive_coinduct_coiters_thms_for_types pre_bnfs (the coiters_args_types) xtor_co_induct
   159             dtor_injects dtor_ctors xtor_co_iter_thmss nesting_bnfs fpTs Cs kss mss ns ctr_defss
   160             ctr_sugars co_iterss co_iter_defss (Proof_Context.export lthy no_defs_lthy) lthy
   161           |> (fn ((coinduct_thms_pairs, _), (unfold_thmss, corec_thmss, _), _, _,
   162                   (disc_unfold_thmss, disc_corec_thmss, _),
   163                   (sel_unfold_thmsss, sel_corec_thmsss, _)) =>
   164             (map snd coinduct_thms_pairs, unfold_thmss, corec_thmss, disc_unfold_thmss,
   165              disc_corec_thmss, sel_unfold_thmsss, sel_corec_thmsss));
   166 
   167       val phi = Proof_Context.export_morphism no_defs_lthy no_defs_lthy0;
   168 
   169       fun mk_target_fp_sugar (kk, T) =
   170         {T = T, fp = fp, index = kk, pre_bnfs = pre_bnfs, nested_bnfs = nested_bnfs,
   171          nesting_bnfs = nesting_bnfs, fp_res = fp_res, ctr_defss = ctr_defss,
   172          ctr_sugars = ctr_sugars, co_iterss = co_iterss, mapss = mapss, co_inducts = co_inducts,
   173          co_iter_thmsss = transpose [un_fold_thmss, co_rec_thmss],
   174          disc_co_itersss = transpose [disc_unfold_thmss, disc_corec_thmss],
   175          sel_co_iterssss = transpose [sel_unfold_thmsss, sel_corec_thmsss]}
   176         |> morph_fp_sugar phi;
   177     in
   178       ((true, map_index mk_target_fp_sugar fpTs), lthy)
   179     end
   180   else
   181     (* TODO: reorder hypotheses and predicates in (co)induction rules? *)
   182     ((false, fp_sugars0), no_defs_lthy0);
   183 
   184 fun indexify_callsss fp_sugar callsss =
   185   let
   186     val {ctrs, ...} = of_fp_sugar #ctr_sugars fp_sugar;
   187     fun do_ctr ctr =
   188       (case AList.lookup Term.aconv_untyped callsss ctr of
   189         NONE => replicate (num_binder_types (fastype_of ctr)) []
   190       | SOME callss => map (map Envir.beta_eta_contract) callss);
   191   in
   192     map do_ctr ctrs
   193   end;
   194 
   195 fun pad_and_indexify_calls fp_sugars0 = map2 indexify_callsss fp_sugars0 oo pad_list [];
   196 
   197 fun nested_to_mutual_fps lose_co_rec fp actual_bs actual_Ts get_indices actual_callssss0 lthy =
   198   let
   199     val qsoty = quote o Syntax.string_of_typ lthy;
   200     val qsotys = space_implode " or " o map qsoty;
   201 
   202     fun not_co_datatype0 T = error (qsoty T ^ " is not a " ^ co_prefix fp ^ "datatype");
   203     fun not_co_datatype (T as Type (s, _)) =
   204         if fp = Least_FP andalso
   205            is_some (Datatype_Data.get_info (Proof_Context.theory_of lthy) s) then
   206           error (qsoty T ^ " is not a new-style datatype (cf. \"datatype_new\")")
   207         else
   208           not_co_datatype0 T
   209       | not_co_datatype T = not_co_datatype0 T;
   210     fun not_mutually_nested_rec Ts1 Ts2 =
   211       error (qsotys Ts1 ^ " is neither mutually recursive with nor nested recursive via " ^
   212         qsotys Ts2);
   213 
   214     val perm_actual_Ts as Type (_, ty_args0) :: _ =
   215       sort (int_ord o pairself Term.size_of_typ) actual_Ts;
   216 
   217     fun check_enrich_with_mutuals _ [] = []
   218       | check_enrich_with_mutuals seen ((T as Type (T_name, ty_args)) :: Ts) =
   219         (case fp_sugar_of lthy T_name of
   220           SOME ({fp = fp', fp_res = {Ts = Ts', ...}, ...}) =>
   221           if fp = fp' then
   222             let
   223               val mutual_Ts = map (fn Type (s, _) => Type (s, ty_args)) Ts';
   224               val _ =
   225                 seen = [] orelse exists (exists_subtype_in seen) mutual_Ts orelse
   226                 not_mutually_nested_rec mutual_Ts seen;
   227               val (seen', Ts') = List.partition (member (op =) mutual_Ts) Ts;
   228             in
   229               mutual_Ts @ check_enrich_with_mutuals (seen @ T :: seen') Ts'
   230             end
   231           else
   232             not_co_datatype T
   233         | NONE => not_co_datatype T)
   234       | check_enrich_with_mutuals _ (T :: _) = not_co_datatype T;
   235 
   236     val perm_Ts = check_enrich_with_mutuals [] perm_actual_Ts;
   237 
   238     val missing_Ts = perm_Ts |> subtract (op =) actual_Ts;
   239     val Ts = actual_Ts @ missing_Ts;
   240 
   241     val nn = length Ts;
   242     val kks = 0 upto nn - 1;
   243 
   244     val common_name = mk_common_name (map Binding.name_of actual_bs);
   245     val bs = pad_list (Binding.name common_name) nn actual_bs;
   246 
   247     fun permute xs = permute_like (op =) Ts perm_Ts xs;
   248     fun unpermute perm_xs = permute_like (op =) perm_Ts Ts perm_xs;
   249 
   250     val perm_bs = permute bs;
   251     val perm_kks = permute kks;
   252     val perm_fp_sugars0 = map (the o fp_sugar_of lthy o fst o dest_Type) perm_Ts;
   253 
   254     val mutualize = exists (fn Type (_, ty_args) => ty_args <> ty_args0) Ts;
   255     val perm_callssss = pad_and_indexify_calls perm_fp_sugars0 nn actual_callssss0;
   256 
   257     val get_perm_indices = map (fn kk => find_index (curry (op =) kk) perm_kks) o get_indices;
   258 
   259     val ((nontriv, perm_fp_sugars), lthy) =
   260       mutualize_fp_sugars lose_co_rec mutualize fp perm_bs perm_Ts get_perm_indices perm_callssss
   261         perm_fp_sugars0 lthy;
   262 
   263     val fp_sugars = unpermute perm_fp_sugars;
   264   in
   265     ((nontriv, missing_Ts, perm_kks, fp_sugars), lthy)
   266   end;
   267 
   268 end;