src/HOL/Codatatype/Tools/bnf_fp_sugar.ML
author blanchet
Thu Sep 06 11:51:19 2012 +0200 (2012-09-06)
changeset 49179 f9d48d479c84
parent 49177 db8ce685073f
child 49180 592a81b4d413
permissions -rw-r--r--
don't throw away the context when hacking the theory (first step to localize the sugar code)
blanchet@49112
     1
(*  Title:      HOL/Codatatype/Tools/bnf_fp_sugar.ML
blanchet@49112
     2
    Author:     Jasmin Blanchette, TU Muenchen
blanchet@49112
     3
    Copyright   2012
blanchet@49112
     4
blanchet@49112
     5
Sugar for constructing LFPs and GFPs.
blanchet@49112
     6
*)
blanchet@49112
     7
blanchet@49112
     8
signature BNF_FP_SUGAR =
blanchet@49112
     9
sig
blanchet@49112
    10
end;
blanchet@49112
    11
blanchet@49112
    12
structure BNF_FP_Sugar : BNF_FP_SUGAR =
blanchet@49112
    13
struct
blanchet@49112
    14
blanchet@49119
    15
open BNF_Util
blanchet@49119
    16
open BNF_Wrap
blanchet@49119
    17
open BNF_FP_Util
blanchet@49119
    18
open BNF_LFP
blanchet@49119
    19
open BNF_GFP
blanchet@49123
    20
open BNF_FP_Sugar_Tactics
blanchet@49119
    21
blanchet@49129
    22
val caseN = "case";
blanchet@49129
    23
blanchet@49124
    24
fun cannot_merge_types () = error "Mutually recursive types must have the same type parameters";
blanchet@49119
    25
blanchet@49119
    26
fun merge_type_arg_constrained ctxt (T, c) (T', c') =
blanchet@49119
    27
  if T = T' then
blanchet@49119
    28
    (case (c, c') of
blanchet@49119
    29
      (_, NONE) => (T, c)
blanchet@49119
    30
    | (NONE, _) => (T, c')
blanchet@49119
    31
    | _ =>
blanchet@49119
    32
      if c = c' then
blanchet@49119
    33
        (T, c)
blanchet@49119
    34
      else
blanchet@49119
    35
        error ("Inconsistent sort constraints for type variable " ^
blanchet@49119
    36
          quote (Syntax.string_of_typ ctxt T)))
blanchet@49119
    37
  else
blanchet@49119
    38
    cannot_merge_types ();
blanchet@49119
    39
blanchet@49119
    40
fun merge_type_args_constrained ctxt (cAs, cAs') =
blanchet@49119
    41
  if length cAs = length cAs' then map2 (merge_type_arg_constrained ctxt) cAs cAs'
blanchet@49119
    42
  else cannot_merge_types ();
blanchet@49119
    43
blanchet@49121
    44
fun type_args_constrained_of (((cAs, _), _), _) = cAs;
blanchet@49121
    45
val type_args_of = map fst o type_args_constrained_of;
blanchet@49129
    46
fun type_binder_of (((_, b), _), _) = b;
blanchet@49121
    47
fun mixfix_of_typ ((_, mx), _) = mx;
blanchet@49121
    48
fun ctr_specs_of (_, ctr_specs) = ctr_specs;
blanchet@49119
    49
blanchet@49121
    50
fun disc_of (((disc, _), _), _) = disc;
blanchet@49121
    51
fun ctr_of (((_, ctr), _), _) = ctr;
blanchet@49121
    52
fun args_of ((_, args), _) = args;
blanchet@49121
    53
fun mixfix_of_ctr (_, mx) = mx;
blanchet@49119
    54
blanchet@49134
    55
fun prepare_data prepare_typ gfp specs fake_lthy lthy =
blanchet@49112
    56
  let
blanchet@49121
    57
    val constrained_As =
blanchet@49121
    58
      map (map (apfst (prepare_typ fake_lthy)) o type_args_constrained_of) specs
blanchet@49119
    59
      |> Library.foldr1 (merge_type_args_constrained lthy);
blanchet@49121
    60
    val As = map fst constrained_As;
blanchet@49134
    61
    val As' = map dest_TFree As;
blanchet@49119
    62
blanchet@49121
    63
    val _ = (case duplicates (op =) As of [] => ()
blanchet@49165
    64
      | A :: _ => error ("Duplicate type parameter " ^ quote (Syntax.string_of_typ lthy A)));
blanchet@49119
    65
blanchet@49119
    66
    (* TODO: use sort constraints on type args *)
blanchet@49119
    67
blanchet@49119
    68
    val N = length specs;
blanchet@49119
    69
blanchet@49121
    70
    fun mk_T b =
blanchet@49121
    71
      Type (fst (Term.dest_Type (Proof_Context.read_type_name fake_lthy true (Binding.name_of b))),
blanchet@49121
    72
        As);
blanchet@49121
    73
blanchet@49129
    74
    val bs = map type_binder_of specs;
blanchet@49176
    75
    val fp_Ts = map mk_T bs;
blanchet@49121
    76
blanchet@49121
    77
    val mixfixes = map mixfix_of_typ specs;
blanchet@49119
    78
blanchet@49119
    79
    val _ = (case duplicates Binding.eq_name bs of [] => ()
blanchet@49119
    80
      | b :: _ => error ("Duplicate type name declaration " ^ quote (Binding.name_of b)));
blanchet@49119
    81
blanchet@49121
    82
    val ctr_specss = map ctr_specs_of specs;
blanchet@49119
    83
blanchet@49129
    84
    val disc_binderss = map (map disc_of) ctr_specss;
blanchet@49129
    85
    val ctr_binderss = map (map ctr_of) ctr_specss;
blanchet@49121
    86
    val ctr_argsss = map (map args_of) ctr_specss;
blanchet@49121
    87
    val ctr_mixfixess = map (map mixfix_of_ctr) ctr_specss;
blanchet@49119
    88
blanchet@49129
    89
    val sel_bindersss = map (map (map fst)) ctr_argsss;
blanchet@49121
    90
    val ctr_Tsss = map (map (map (prepare_typ fake_lthy o snd))) ctr_argsss;
blanchet@49121
    91
blanchet@49167
    92
    val rhs_As' = fold (fold (fold Term.add_tfreesT)) ctr_Tsss [];
blanchet@49167
    93
    val _ = (case subtract (op =) As' rhs_As' of
blanchet@49165
    94
        [] => ()
blanchet@49165
    95
      | A' :: _ => error ("Extra type variables on rhs: " ^
blanchet@49165
    96
          quote (Syntax.string_of_typ lthy (TFree A'))));
blanchet@49165
    97
blanchet@49176
    98
    val ((Cs, Xs), _) =
blanchet@49121
    99
      lthy
blanchet@49121
   100
      |> fold (fold (fn s => Variable.declare_typ (TFree (s, dummyS))) o type_args_of) specs
blanchet@49121
   101
      |> mk_TFrees N
blanchet@49176
   102
      ||>> mk_TFrees N;
blanchet@49119
   103
blanchet@49176
   104
    fun is_same_recT (T as Type (s, Us)) (Type (s', Us')) =
blanchet@49146
   105
        s = s' andalso (Us = Us' orelse error ("Illegal occurrence of recursive type " ^
blanchet@49146
   106
          quote (Syntax.string_of_typ fake_lthy T)))
blanchet@49176
   107
      | is_same_recT _ _ = false;
blanchet@49146
   108
blanchet@49176
   109
    fun freeze_recXs (T as Type (s, Us)) =
blanchet@49176
   110
        (case find_index (is_same_recT T) fp_Ts of
blanchet@49176
   111
          ~1 => Type (s, map freeze_recXs Us)
blanchet@49176
   112
        | i => nth Xs i)
blanchet@49176
   113
      | freeze_recXs T = T;
blanchet@49121
   114
blanchet@49176
   115
    val ctr_TsssXs = map (map (map freeze_recXs)) ctr_Tsss;
blanchet@49176
   116
    val sum_prod_TsXs = map (mk_sumTN o map HOLogic.mk_tupleT) ctr_TsssXs;
blanchet@49119
   117
blanchet@49176
   118
    val eqs = map dest_TFree Xs ~~ sum_prod_TsXs;
blanchet@49121
   119
blanchet@49176
   120
    val ((raw_unfs, raw_flds, raw_fp_iters, raw_fp_recs, unf_flds, fld_unfs, fld_injects), lthy') =
blanchet@49169
   121
      fp_bnf (if gfp then bnf_gfp else bnf_lfp) bs mixfixes As' eqs lthy;
blanchet@49121
   122
blanchet@49167
   123
    val timer = time (Timer.startRealTimer ());
blanchet@49167
   124
blanchet@49176
   125
    fun mk_unf_or_fld get_T Ts t =
blanchet@49176
   126
      let val Type (_, Ts0) = get_T (fastype_of t) in
blanchet@49124
   127
        Term.subst_atomic_types (Ts0 ~~ Ts) t
blanchet@49121
   128
      end;
blanchet@49119
   129
blanchet@49126
   130
    val mk_unf = mk_unf_or_fld domain_type;
blanchet@49126
   131
    val mk_fld = mk_unf_or_fld range_type;
blanchet@49121
   132
blanchet@49126
   133
    val unfs = map (mk_unf As) raw_unfs;
blanchet@49124
   134
    val flds = map (mk_fld As) raw_flds;
blanchet@49124
   135
blanchet@49176
   136
    fun mk_fp_iter_or_rec Ts Us t =
blanchet@49121
   137
      let
blanchet@49176
   138
        val (binders, body) = strip_type (fastype_of t);
blanchet@49176
   139
        val Type (_, Ts0) = if gfp then body else List.last binders;
blanchet@49176
   140
        val Us0 = map (if gfp then domain_type else body_type) (fst (split_last binders));
blanchet@49176
   141
      in
blanchet@49176
   142
        Term.subst_atomic_types (Ts0 @ Us0 ~~ Ts @ Us) t
blanchet@49176
   143
      end;
blanchet@49176
   144
blanchet@49176
   145
    val fp_iters = map (mk_fp_iter_or_rec As Cs) raw_fp_iters;
blanchet@49176
   146
    val fp_recs = map (mk_fp_iter_or_rec As Cs) raw_fp_recs;
blanchet@49176
   147
blanchet@49176
   148
    fun pour_sugar_on_type ((((((((((((((b, fp_T), C), fld), unf), fp_iter), fp_rec), fld_unf),
blanchet@49176
   149
          unf_fld), fld_inject), ctr_binders), ctr_mixfixes), ctr_Tss), disc_binders), sel_binderss)
blanchet@49176
   150
        no_defs_lthy =
blanchet@49176
   151
      let
blanchet@49176
   152
        val n = length ctr_Tss;
blanchet@49121
   153
        val ks = 1 upto n;
blanchet@49121
   154
        val ms = map length ctr_Tss;
blanchet@49121
   155
blanchet@49124
   156
        val unf_T = domain_type (fastype_of fld);
blanchet@49121
   157
        val prod_Ts = map HOLogic.mk_tupleT ctr_Tss;
blanchet@49134
   158
        val case_Ts = map (fn Ts => Ts ---> C) ctr_Tss;
blanchet@49119
   159
blanchet@49176
   160
        val ((((u, v), fs), xss), _) =
blanchet@49124
   161
          lthy
blanchet@49176
   162
          |> yield_singleton (mk_Frees "u") unf_T
blanchet@49176
   163
          ||>> yield_singleton (mk_Frees "v") fp_T
blanchet@49176
   164
          ||>> mk_Frees "f" case_Ts
blanchet@49124
   165
          ||>> mk_Freess "x" ctr_Tss;
blanchet@49121
   166
blanchet@49129
   167
        val ctr_rhss =
blanchet@49121
   168
          map2 (fn k => fn xs =>
blanchet@49121
   169
            fold_rev Term.lambda xs (fld $ mk_InN prod_Ts (HOLogic.mk_tuple xs) k)) ks xss;
blanchet@49121
   170
blanchet@49130
   171
        val case_binder = Binding.suffix_name ("_" ^ caseN) b;
blanchet@49129
   172
blanchet@49134
   173
        val case_rhs =
blanchet@49176
   174
          fold_rev Term.lambda (fs @ [v]) (mk_sum_caseN (map2 mk_uncurried_fun fs xss) $ (unf $ v));
blanchet@49129
   175
blanchet@49130
   176
        val (((raw_ctrs, raw_ctr_defs), (raw_case, raw_case_def)), (lthy', lthy)) = no_defs_lthy
blanchet@49169
   177
          |> apfst split_list o fold_map3 (fn b => fn mx => fn rhs =>
blanchet@49169
   178
               Local_Theory.define ((b, mx), ((Thm.def_binding b, []), rhs)) #>> apsnd snd)
blanchet@49169
   179
             ctr_binders ctr_mixfixes ctr_rhss
blanchet@49130
   180
          ||>> (Local_Theory.define ((case_binder, NoSyn), ((Thm.def_binding case_binder, []),
blanchet@49130
   181
             case_rhs)) #>> apsnd snd)
blanchet@49121
   182
          ||> `Local_Theory.restore;
blanchet@49121
   183
blanchet@49121
   184
        (*transforms defined frees into consts (and more)*)
blanchet@49121
   185
        val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49121
   186
blanchet@49121
   187
        val ctr_defs = map (Morphism.thm phi) raw_ctr_defs;
blanchet@49130
   188
        val case_def = Morphism.thm phi raw_case_def;
blanchet@49130
   189
blanchet@49123
   190
        val ctrs = map (Morphism.term phi) raw_ctrs;
blanchet@49130
   191
        val casex = Morphism.term phi raw_case;
blanchet@49121
   192
blanchet@49135
   193
        fun exhaust_tac {context = ctxt, ...} =
blanchet@49123
   194
          let
blanchet@49135
   195
            val fld_iff_unf_thm =
blanchet@49135
   196
              let
blanchet@49135
   197
                val goal =
blanchet@49135
   198
                  fold_rev Logic.all [u, v]
blanchet@49135
   199
                    (mk_Trueprop_eq (HOLogic.mk_eq (v, fld $ u), HOLogic.mk_eq (unf $ v, u)));
blanchet@49135
   200
              in
blanchet@49135
   201
                Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49176
   202
                  mk_fld_iff_unf_tac ctxt (map (SOME o certifyT lthy) [unf_T, fp_T])
blanchet@49176
   203
                    (certify lthy fld) (certify lthy unf) fld_unf unf_fld)
blanchet@49135
   204
                |> Thm.close_derivation
blanchet@49135
   205
                |> Morphism.thm phi
blanchet@49135
   206
              end;
blanchet@49135
   207
blanchet@49135
   208
            val sumEN_thm' =
blanchet@49135
   209
              Local_Defs.unfold lthy @{thms all_unit_eq}
blanchet@49135
   210
                (Drule.instantiate' (map (SOME o certifyT lthy) prod_Ts) [] (mk_sumEN n))
blanchet@49135
   211
              |> Morphism.thm phi;
blanchet@49123
   212
          in
blanchet@49161
   213
            mk_exhaust_tac ctxt n ctr_defs fld_iff_unf_thm sumEN_thm'
blanchet@49123
   214
          end;
blanchet@49121
   215
blanchet@49126
   216
        val inject_tacss =
blanchet@49126
   217
          map2 (fn 0 => K []
blanchet@49126
   218
                 | _ => fn ctr_def => [fn {context = ctxt, ...} =>
blanchet@49126
   219
                     mk_inject_tac ctxt ctr_def fld_inject])
blanchet@49126
   220
            ms ctr_defs;
blanchet@49126
   221
blanchet@49127
   222
        val half_distinct_tacss =
blanchet@49127
   223
          map (map (fn (def, def') => fn {context = ctxt, ...} =>
blanchet@49127
   224
            mk_half_distinct_tac ctxt fld_inject [def, def'])) (mk_half_pairss ctr_defs);
blanchet@49127
   225
blanchet@49130
   226
        val case_tacs =
blanchet@49130
   227
          map3 (fn k => fn m => fn ctr_def => fn {context = ctxt, ...} =>
blanchet@49130
   228
            mk_case_tac ctxt n k m case_def ctr_def unf_fld) ks ms ctr_defs;
blanchet@49121
   229
blanchet@49121
   230
        val tacss = [exhaust_tac] :: inject_tacss @ half_distinct_tacss @ [case_tacs];
blanchet@49134
   231
blanchet@49176
   232
        (* (co)iterators, (co)recursors, (co)induction *)
blanchet@49176
   233
blanchet@49176
   234
        val is_recT = member (op =) fp_Ts;
blanchet@49176
   235
blanchet@49176
   236
        val ns = map length ctr_Tsss;
blanchet@49176
   237
        val mss = map (map length) ctr_Tsss;
blanchet@49176
   238
        val Css = map2 replicate ns Cs;
blanchet@49176
   239
blanchet@49134
   240
        fun sugar_lfp lthy =
blanchet@49134
   241
          let
blanchet@49176
   242
            val fp_y_Ts = map domain_type (fst (split_last (binder_types (fastype_of fp_iter))));
blanchet@49176
   243
            val y_prod_Tss = map2 dest_sumTN ns fp_y_Ts;
blanchet@49176
   244
            val y_Tsss = map2 (map2 dest_tupleT) mss y_prod_Tss;
blanchet@49176
   245
            val g_Tss = map2 (map2 (curry (op --->))) y_Tsss Css;
blanchet@49176
   246
            val iter_T = flat g_Tss ---> fp_T --> C;
blanchet@49146
   247
blanchet@49176
   248
            val ((gss, ysss), _) =
blanchet@49176
   249
              lthy
blanchet@49176
   250
              |> mk_Freess "f" g_Tss
blanchet@49177
   251
              ||>> mk_Freesss "x" y_Tsss;
blanchet@49134
   252
blanchet@49146
   253
            val iter_rhs =
blanchet@49176
   254
              fold_rev (fold_rev Term.lambda) gss
blanchet@49176
   255
                (Term.list_comb (fp_iter, map2 (mk_sum_caseN oo map2 mk_uncurried_fun) gss ysss));
blanchet@49134
   256
          in
blanchet@49134
   257
            lthy
blanchet@49134
   258
          end;
blanchet@49134
   259
blanchet@49134
   260
        fun sugar_gfp lthy = lthy;
blanchet@49119
   261
      in
blanchet@49130
   262
        wrap_data tacss ((ctrs, casex), (disc_binders, sel_binderss)) lthy'
blanchet@49134
   263
        |> (if gfp then sugar_gfp else sugar_lfp)
blanchet@49119
   264
      end;
blanchet@49167
   265
blanchet@49167
   266
    val lthy'' =
blanchet@49176
   267
      fold pour_sugar_on_type (bs ~~ fp_Ts ~~ Cs ~~ flds ~~ unfs ~~ fp_iters ~~ fp_recs ~~
blanchet@49176
   268
        fld_unfs ~~ unf_flds ~~ fld_injects ~~ ctr_binderss ~~ ctr_mixfixess ~~ ctr_Tsss ~~
blanchet@49176
   269
        disc_binderss ~~ sel_bindersss) lthy';
blanchet@49167
   270
blanchet@49167
   271
    val timer = time (timer ("Constructors, discriminators, selectors, etc., for the new " ^
blanchet@49167
   272
      (if gfp then "co" else "") ^ "datatype"));
blanchet@49112
   273
  in
blanchet@49167
   274
    (timer; lthy'')
blanchet@49112
   275
  end;
blanchet@49112
   276
blanchet@49121
   277
fun data_cmd info specs lthy =
blanchet@49121
   278
  let
blanchet@49179
   279
    val fake_thy = Theory.copy
blanchet@49179
   280
      #> Sign.add_types_global (map (fn spec =>
blanchet@49179
   281
        (type_binder_of spec, length (type_args_constrained_of spec), mixfix_of_typ spec)) specs);
blanchet@49179
   282
    val fake_lthy = Proof_Context.background_theory fake_thy lthy;
blanchet@49121
   283
  in
blanchet@49121
   284
    prepare_data Syntax.read_typ info specs fake_lthy lthy
blanchet@49121
   285
  end;
blanchet@49119
   286
blanchet@49129
   287
val parse_opt_binding_colon = Scan.optional (Parse.binding --| Parse.$$$ ":") no_binder
blanchet@49119
   288
blanchet@49112
   289
val parse_ctr_arg =
blanchet@49119
   290
  Parse.$$$ "(" |-- parse_opt_binding_colon -- Parse.typ --| Parse.$$$ ")" ||
blanchet@49129
   291
  (Parse.typ >> pair no_binder);
blanchet@49112
   292
blanchet@49112
   293
val parse_single_spec =
blanchet@49112
   294
  Parse.type_args_constrained -- Parse.binding -- Parse.opt_mixfix --
blanchet@49119
   295
  (@{keyword "="} |-- Parse.enum1 "|" (parse_opt_binding_colon -- Parse.binding --
blanchet@49119
   296
    Scan.repeat parse_ctr_arg -- Parse.opt_mixfix));
blanchet@49112
   297
blanchet@49112
   298
val _ =
blanchet@49112
   299
  Outer_Syntax.local_theory @{command_spec "data"} "define BNF-based inductive datatypes"
blanchet@49134
   300
    (Parse.and_list1 parse_single_spec >> data_cmd false);
blanchet@49112
   301
blanchet@49112
   302
val _ =
blanchet@49112
   303
  Outer_Syntax.local_theory @{command_spec "codata"} "define BNF-based coinductive datatypes"
blanchet@49134
   304
    (Parse.and_list1 parse_single_spec >> data_cmd true);
blanchet@49112
   305
blanchet@49112
   306
end;