src/HOL/ex/Quickcheck.thy
 author haftmann Wed Mar 12 19:38:14 2008 +0100 (2008-03-12) changeset 26265 4b63b9e9b10d child 26267 ba710daf77a7 permissions -rw-r--r--
separated Random.thy from Quickcheck.thy
```     1 (*  ID:         \$Id\$
```
```     2     Author:     Florian Haftmann, TU Muenchen
```
```     3 *)
```
```     4
```
```     5 header {* A simple counterexample generator *}
```
```     6
```
```     7 theory Quickcheck
```
```     8 imports Random Eval
```
```     9 begin
```
```    10
```
```    11 subsection {* The @{text random} class *}
```
```    12
```
```    13 class random = type +
```
```    14   fixes random :: "index \<Rightarrow> seed \<Rightarrow> 'a \<times> seed"
```
```    15
```
```    16 print_classes
```
```    17
```
```    18 instantiation itself :: (type) random
```
```    19 begin
```
```    20
```
```    21 definition
```
```    22   "random _ = return TYPE('a)"
```
```    23
```
```    24 instance ..
```
```    25
```
```    26 end
```
```    27
```
```    28 lemma random_aux_if:
```
```    29   fixes random' :: "index \<Rightarrow> index \<Rightarrow> seed \<Rightarrow> 'a \<times> seed"
```
```    30   assumes "random' 0 j = undefined"
```
```    31     and "\<And>i. random' (Suc_index i) j = rhs2 i"
```
```    32   shows "random' i j s = (if i = 0 then undefined else rhs2 (i - 1) s)"
```
```    33   by (cases i rule: index.exhaust) (insert assms, simp_all add: undefined_fun)
```
```    34
```
```    35 setup {*
```
```    36 let
```
```    37   exception REC;
```
```    38   fun random_inst tyco thy =
```
```    39     let
```
```    40       val { descr, index, ... } = DatatypePackage.the_datatype thy tyco;
```
```    41       val _ = if length descr > 1 then raise REC else ();
```
```    42       val (raw_vs, _) = DatatypePackage.the_datatype_spec thy tyco;
```
```    43       val vs = (map o apsnd)
```
```    44         (curry (Sorts.inter_sort (Sign.classes_of thy)) @{sort random}) raw_vs;
```
```    45       val ty = Type (tyco, map TFree vs);
```
```    46       val typ_of = DatatypeAux.typ_of_dtyp descr vs;
```
```    47       val SOME (_, _, constrs) = AList.lookup (op =) descr index;
```
```    48       val randomN = NameSpace.base @{const_name random};
```
```    49       val random_aux_name = randomN ^ "_" ^ Class.type_name tyco ^ "'";
```
```    50       fun lift_ty ty = StateMonad.liftT ty @{typ seed};
```
```    51       val ty_aux = @{typ index} --> @{typ index} --> lift_ty ty;
```
```    52       fun random ty =
```
```    53         Const (@{const_name random}, @{typ index} --> lift_ty ty);
```
```    54       val random_aux = Free (random_aux_name, ty_aux);
```
```    55       fun add_cons_arg dty (is_rec, t) =
```
```    56         let
```
```    57           val ty' = typ_of dty;
```
```    58           val rec_call = case try DatatypeAux.dest_DtRec dty
```
```    59            of SOME index' => index = index'
```
```    60             | NONE => false
```
```    61           val random' = if rec_call
```
```    62             then random_aux \$ @{term "i\<Colon>index"} \$ @{term "j\<Colon>index"}
```
```    63             else random ty' \$ @{term "j\<Colon>index"}
```
```    64           val is_rec' = is_rec orelse DatatypeAux.is_rec_type dty;
```
```    65           val t' = StateMonad.mbind ty' ty @{typ seed} random' (Abs ("", ty', t))
```
```    66         in (is_rec', t') end;
```
```    67       fun mk_cons_t (c, dtys) =
```
```    68         let
```
```    69           val ty' = map typ_of dtys ---> ty;
```
```    70           val t = StateMonad.return ty @{typ seed} (list_comb (Const (c, ty'),
```
```    71             map Bound (length dtys - 1 downto 0)));
```
```    72           val (is_rec, t') = fold_rev add_cons_arg dtys (false, t);
```
```    73         in (is_rec, StateMonad.run ty @{typ seed} t') end;
```
```    74       fun check_empty [] = NONE
```
```    75         | check_empty xs = SOME xs;
```
```    76       fun bundle_cons_ts cons_ts =
```
```    77         let
```
```    78           val ts = map snd cons_ts;
```
```    79           val t = HOLogic.mk_list (lift_ty ty) ts;
```
```    80           val t' = Const (@{const_name select}, HOLogic.listT (lift_ty ty) --> lift_ty (lift_ty ty)) \$ t;
```
```    81           val t'' = Const (@{const_name collapse}, lift_ty (lift_ty ty) --> lift_ty ty) \$ t';
```
```    82         in t'' end;
```
```    83       fun bundle_conss (some_rec_t, nonrec_t) =
```
```    84         let
```
```    85           val t = case some_rec_t
```
```    86            of SOME rec_t => Const (@{const_name collapse}, lift_ty (lift_ty ty) --> lift_ty ty)
```
```    87                \$ (Const (@{const_name select_default},
```
```    88                    @{typ index} --> lift_ty ty --> lift_ty ty --> lift_ty (lift_ty ty))
```
```    89                   \$ @{term "i\<Colon>index"} \$ rec_t \$ nonrec_t)
```
```    90             | NONE => nonrec_t
```
```    91         in t end;
```
```    92       val random_rhs = constrs
```
```    93         |> map mk_cons_t
```
```    94         |> List.partition fst
```
```    95         |> apfst (Option.map bundle_cons_ts o check_empty)
```
```    96         |> apsnd bundle_cons_ts
```
```    97         |> bundle_conss;
```
```    98       val random_aux_undef = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
```
```    99         (random_aux \$ @{term "0\<Colon>index"} \$ @{term "j\<Colon>index"}, Const (@{const_name undefined}, lift_ty ty))
```
```   100       val random_aux_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
```
```   101         (random_aux \$ @{term "Suc_index i"} \$ @{term "j\<Colon>index"}, random_rhs);
```
```   102       val random_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq) (Const (@{const_name random},
```
```   103         @{typ index} --> lift_ty ty) \$ @{term "i\<Colon>index"},
```
```   104           random_aux \$ @{term "i\<Colon>index"} \$ @{term "i\<Colon>index"});
```
```   105       val del_func = Attrib.internal (fn _ => Thm.declaration_attribute
```
```   106         (fn thm => Context.mapping (Code.del_func thm) I));
```
```   107       fun add_code simps lthy =
```
```   108         let
```
```   109           val thy = ProofContext.theory_of lthy;
```
```   110           val thm = @{thm random_aux_if}
```
```   111             |> Drule.instantiate' [SOME (Thm.ctyp_of thy ty)] [SOME (Thm.cterm_of thy random_aux)]
```
```   112             |> (fn thm => thm OF simps)
```
```   113             |> singleton (ProofContext.export lthy (ProofContext.init thy))
```
```   114         in
```
```   115           lthy
```
```   116           |> LocalTheory.theory (PureThy.note Thm.internalK (random_aux_name ^ "_code", thm)
```
```   117                #-> Code.add_func)
```
```   118         end;
```
```   119     in
```
```   120       thy
```
```   121       |> TheoryTarget.instantiation ([tyco], vs, @{sort random})
```
```   122       |> PrimrecPackage.add_primrec [(random_aux_name, SOME ty_aux, NoSyn)]
```
```   123            [(("", [del_func]), random_aux_undef), (("", [del_func]), random_aux_eq)]
```
```   124       |-> add_code
```
```   125       |> `(fn lthy => Syntax.check_term lthy random_eq)
```
```   126       |-> (fn eq => Specification.definition (NONE, (("", []), eq)))
```
```   127       |> snd
```
```   128       |> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
```
```   129       |> LocalTheory.exit
```
```   130       |> ProofContext.theory_of
```
```   131     end;
```
```   132   fun add_random_inst [tyco] = (fn thy => random_inst tyco thy handle REC =>
```
```   133         (warning ("Will not generated random elements for mutual recursive type " ^ quote tyco); thy))
```
```   134     | add_random_inst tycos = tap (fn _ => warning
```
```   135         ("Will not generated random elements for mutual recursive type(s) " ^ commas (map quote tycos)));
```
```   136 in DatatypePackage.interpretation add_random_inst end
```
```   137 *}
```
```   138
```
```   139 instantiation int :: random
```
```   140 begin
```
```   141
```
```   142 definition
```
```   143   "random n = (do
```
```   144      (b, m) \<leftarrow> random n;
```
```   145      return (if b then int m else - int m)
```
```   146    done)"
```
```   147
```
```   148 instance ..
```
```   149
```
```   150 end
```
```   151
```
```   152 instantiation set :: (random) random
```
```   153 begin
```
```   154
```
```   155 primrec random_set' :: "index \<Rightarrow> index \<Rightarrow> seed \<Rightarrow> 'a set \<times> seed" where
```
```   156   "random_set' 0 j = undefined"
```
```   157   | "random_set' (Suc_index i) j = collapse (select_default i
```
```   158        (do x \<leftarrow> random i; xs \<leftarrow> random_set' i j; return (insert x xs) done)
```
```   159        (return {}))"
```
```   160
```
```   161 lemma random_set'_code [code func]:
```
```   162   "random_set' i j s = (if i = 0 then undefined else collapse (select_default (i - 1)
```
```   163        (do x \<leftarrow> random (i - 1); xs \<leftarrow> random_set' (i - 1) j; return (insert x xs) done)
```
```   164        (return {})) s)"
```
```   165   by (rule random_aux_if random_set'.simps)+
```
```   166
```
```   167 definition
```
```   168   "random i = random_set' i i"
```
```   169
```
```   170 instance ..
```
```   171
```
```   172 end
```
```   173
```
```   174 code_reserved SML Quickcheck
```
```   175
```
```   176
```
```   177 subsection {* Quickcheck generator *}
```
```   178
```
```   179 ML {*
```
```   180 structure Quickcheck =
```
```   181 struct
```
```   182
```
```   183 val eval_ref : (unit -> int -> int * int -> term list option * (int * int)) option ref = ref NONE;
```
```   184
```
```   185 fun mk_generator_expr prop tys =
```
```   186   let
```
```   187     val bounds = map_index (fn (i, ty) => (i, ty)) tys;
```
```   188     val result = list_comb (prop, map (fn (i, _) => Bound (length tys - i - 1)) bounds);
```
```   189     val terms = map (fn (i, ty) => Const (@{const_name Eval.term_of}, ty --> @{typ term}) \$ Bound (length tys - i - 1)) bounds;
```
```   190     val check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"}
```
```   191       \$ result \$ @{term "None \<Colon> term list option"} \$ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} \$ HOLogic.mk_list @{typ term} terms);
```
```   192     val return = @{term "Pair \<Colon> term list option \<Rightarrow> seed \<Rightarrow> term list option \<times> seed"};
```
```   193     fun mk_bindtyp ty = @{typ seed} --> HOLogic.mk_prodT (ty, @{typ seed});
```
```   194     fun mk_bindclause (i, ty) t = Const (@{const_name mbind}, mk_bindtyp ty
```
```   195       --> (ty --> mk_bindtyp @{typ "term list option"}) --> mk_bindtyp @{typ "term list option"})
```
```   196       \$ (Const (@{const_name random}, @{typ index} --> mk_bindtyp ty)
```
```   197         \$ Bound i) \$ Abs ("a", ty, t);
```
```   198     val t = fold_rev mk_bindclause bounds (return \$ check);
```
```   199   in Abs ("n", @{typ index}, t) end;
```
```   200
```
```   201 fun compile_generator_expr thy prop tys =
```
```   202   let
```
```   203     val f = CodePackage.eval_term ("Quickcheck.eval_ref", eval_ref) thy
```
```   204       (mk_generator_expr prop tys) [];
```
```   205   in f #> Random_Engine.run #> (Option.map o map) (Code.postprocess_term thy) end;
```
```   206
```
```   207 fun VALUE prop tys thy =
```
```   208   let
```
```   209     val t = mk_generator_expr prop tys;
```
```   210     val eq = Logic.mk_equals (Free ("VALUE", fastype_of t), t)
```
```   211   in
```
```   212     thy
```
```   213     |> TheoryTarget.init NONE
```
```   214     |> Specification.definition (NONE, (("", []), eq))
```
```   215     |> snd
```
```   216     |> LocalTheory.exit
```
```   217     |> ProofContext.theory_of
```
```   218   end;
```
```   219
```
```   220 end
```
```   221 *}
```
```   222
```
```   223 (*setup {* Quickcheck.VALUE @{term "\<lambda>(n::nat) (m::nat) (q::nat). n = m + q + 1"} [@{typ nat}, @{typ nat}, @{typ nat}] *}
```
```   224 export_code VALUE in SML module_name QuickcheckExample file "~~/../../gen_code/quickcheck.ML"
```
```   225 use "~~/../../gen_code/quickcheck.ML"
```
```   226 ML {* Random_Engine.run (QuickcheckExample.range 1) *}*)
```
```   227
```
```   228 ML {* val f = Quickcheck.compile_generator_expr @{theory}
```
```   229   @{term "\<lambda>(n::nat) (m::nat) (q::nat). n = m + q + 1"} [@{typ nat}, @{typ nat}, @{typ nat}] *}
```
```   230
```
```   231 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   232 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   233 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   234 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   235 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   236 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   237 ML {* f 25 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   238 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   239 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   240 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   241 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   242
```
```   243 ML {* val f = Quickcheck.compile_generator_expr @{theory}
```
```   244   @{term "\<lambda>(n::int) (m::int) (q::int). n = m + q + 1"} [@{typ int}, @{typ int}, @{typ int}] *}
```
```   245
```
```   246 (*definition "FOO = (True, Suc 0)"
```
```   247
```
```   248 code_module (test) QuickcheckExample
```
```   249   file "~~/../../gen_code/quickcheck'.ML"
```
```   250   contains FOO*)
```
```   251
```
```   252 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   253 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   254 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   255 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   256 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   257 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   258 ML {* f 25 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   259 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   260 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   261 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   262 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   263 ML {* f 3 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   264 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   265 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   266
```
```   267 ML {* val f = Quickcheck.compile_generator_expr @{theory}
```
```   268   @{term "\<lambda>(xs\<Colon>int list) ys. rev (xs @ ys) = rev xs @ rev ys"}
```
```   269   [@{typ "int list"}, @{typ "int list"}] *}
```
```   270
```
```   271 ML {* f 15 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   272 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   273 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   274 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   275 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   276 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   277 ML {* f 25 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   278 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   279 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   280 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   281 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   282 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   283 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   284 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   285 ML {* f 8 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   286 ML {* f 8 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   287 ML {* f 8 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   288 ML {* f 88 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   289
```
```   290 subsection {* Incremental function generator *}
```
```   291
```
```   292 ML {*
```
```   293 structure Quickcheck =
```
```   294 struct
```
```   295
```
```   296 open Quickcheck;
```
```   297
```
```   298 fun random_fun (eq : 'a -> 'a -> bool)
```
```   299     (random : Random_Engine.seed -> 'b * Random_Engine.seed)
```
```   300     (random_split : Random_Engine.seed -> Random_Engine.seed * Random_Engine.seed)
```
```   301     (seed : Random_Engine.seed) =
```
```   302   let
```
```   303     val (seed', seed'') = random_split seed;
```
```   304     val state = ref (seed', []);
```
```   305     fun random_fun' x =
```
```   306       let
```
```   307         val (seed, fun_map) = ! state;
```
```   308       in case AList.lookup (uncurry eq) fun_map x
```
```   309        of SOME y => y
```
```   310         | NONE => let
```
```   311               val (y, seed') = random seed;
```
```   312               val _ = state := (seed', (x, y) :: fun_map);
```
```   313             in y end
```
```   314       end;
```
```   315   in (random_fun', seed'') end;
```
```   316
```
```   317 end
```
```   318 *}
```
```   319
```
```   320 axiomatization
```
```   321   random_fun_aux :: "('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> (seed \<Rightarrow> 'b \<times> seed)
```
```   322     \<Rightarrow> (seed \<Rightarrow> seed \<times> seed) \<Rightarrow> seed \<Rightarrow> ('a \<Rightarrow> 'b) \<times> seed"
```
```   323
```
```   324 code_const random_fun_aux (SML "Quickcheck.random'_fun")
```
```   325
```
```   326 instantiation "fun" :: (term_of, term_of) term_of
```
```   327 begin
```
```   328
```
```   329 instance ..
```
```   330
```
```   331 end
```
```   332
```
```   333 code_const "Eval.term_of :: ('a\<Colon>term_of \<Rightarrow> 'b\<Colon>term_of) \<Rightarrow> _"
```
```   334   (SML "(fn '_ => Const (\"arbitrary\", dummyT))")
```
```   335
```
```   336 instantiation "fun" :: (eq, "{type, random}") random
```
```   337 begin
```
```   338
```
```   339 definition
```
```   340   "random n = random_fun_aux (op =) (random n) split_seed"
```
```   341
```
```   342 instance ..
```
```   343
```
```   344 end
```
```   345
```
```   346 ML {* val f = Quickcheck.compile_generator_expr @{theory}
```
```   347   @{term "\<lambda>f k. int (f k) = k"} [@{typ "int \<Rightarrow> nat"}, @{typ int}] *}
```
```   348
```
```   349 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   350 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   351 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   352 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   353 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   354 ML {* f 20 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   355
```
```   356 ML {* val f = Quickcheck.compile_generator_expr @{theory}
```
```   357   @{term "\<lambda>(A \<Colon> nat set) B. card (A \<union> B) = card A + card B"} [@{typ "nat set"}, @{typ "nat set"}] *}
```
```   358
```
```   359 ML {* f 1 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   360 ML {* f 2 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   361 ML {* f 3 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   362 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   363 ML {* f 5 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   364 ML {* f 6 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   365 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   366 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   367
```
```   368 ML {* val f = Quickcheck.compile_generator_expr @{theory}
```
```   369   @{term "\<lambda>(s \<Colon> string). s \<noteq> rev s"} [@{typ string}] *}
```
```   370
```
```   371 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   372 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   373 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   374 ML {* f 4 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   375 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   376 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   377 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   378 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   379 ML {* f 10 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   380 ML {* f 8 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   381 ML {* f 8 |> (Option.map o map) (Sign.string_of_term @{theory}) *}
```
```   382
```
```   383 end
```