src/HOL/Record.thy
author hoelzl
Thu Sep 02 10:14:32 2010 +0200 (2010-09-02)
changeset 39072 1030b1a166ef
parent 38539 3be65f879bcd
child 41229 d797baa3d57c
permissions -rw-r--r--
Add lessThan_Suc_eq_insert_0
     1 (*  Title:      HOL/Record.thy
     2     Author:     Wolfgang Naraschewski, TU Muenchen
     3     Author:     Markus Wenzel, TU Muenchen
     4     Author:     Norbert Schirmer, TU Muenchen
     5     Author:     Thomas Sewell, NICTA
     6     Author:     Florian Haftmann, TU Muenchen
     7 *)
     8 
     9 header {* Extensible records with structural subtyping *}
    10 
    11 theory Record
    12 imports Plain Quickcheck
    13 uses ("Tools/record.ML")
    14 begin
    15 
    16 subsection {* Introduction *}
    17 
    18 text {*
    19   Records are isomorphic to compound tuple types. To implement
    20   efficient records, we make this isomorphism explicit. Consider the
    21   record access/update simplification @{text "alpha (beta_update f
    22   rec) = alpha rec"} for distinct fields alpha and beta of some record
    23   rec with n fields. There are @{text "n ^ 2"} such theorems, which
    24   prohibits storage of all of them for large n. The rules can be
    25   proved on the fly by case decomposition and simplification in O(n)
    26   time. By creating O(n) isomorphic-tuple types while defining the
    27   record, however, we can prove the access/update simplification in
    28   @{text "O(log(n)^2)"} time.
    29 
    30   The O(n) cost of case decomposition is not because O(n) steps are
    31   taken, but rather because the resulting rule must contain O(n) new
    32   variables and an O(n) size concrete record construction. To sidestep
    33   this cost, we would like to avoid case decomposition in proving
    34   access/update theorems.
    35 
    36   Record types are defined as isomorphic to tuple types. For instance,
    37   a record type with fields @{text "'a"}, @{text "'b"}, @{text "'c"}
    38   and @{text "'d"} might be introduced as isomorphic to @{text "'a \<times>
    39   ('b \<times> ('c \<times> 'd))"}. If we balance the tuple tree to @{text "('a \<times>
    40   'b) \<times> ('c \<times> 'd)"} then accessors can be defined by converting to the
    41   underlying type then using O(log(n)) fst or snd operations.
    42   Updators can be defined similarly, if we introduce a @{text
    43   "fst_update"} and @{text "snd_update"} function. Furthermore, we can
    44   prove the access/update theorem in O(log(n)) steps by using simple
    45   rewrites on fst, snd, @{text "fst_update"} and @{text "snd_update"}.
    46 
    47   The catch is that, although O(log(n)) steps were taken, the
    48   underlying type we converted to is a tuple tree of size
    49   O(n). Processing this term type wastes performance. We avoid this
    50   for large n by taking each subtree of size K and defining a new type
    51   isomorphic to that tuple subtree. A record can now be defined as
    52   isomorphic to a tuple tree of these O(n/K) new types, or, if @{text
    53   "n > K*K"}, we can repeat the process, until the record can be
    54   defined in terms of a tuple tree of complexity less than the
    55   constant K.
    56 
    57   If we prove the access/update theorem on this type with the
    58   analagous steps to the tuple tree, we consume @{text "O(log(n)^2)"}
    59   time as the intermediate terms are @{text "O(log(n))"} in size and
    60   the types needed have size bounded by K.  To enable this analagous
    61   traversal, we define the functions seen below: @{text
    62   "iso_tuple_fst"}, @{text "iso_tuple_snd"}, @{text "iso_tuple_fst_update"}
    63   and @{text "iso_tuple_snd_update"}. These functions generalise tuple
    64   operations by taking a parameter that encapsulates a tuple
    65   isomorphism.  The rewrites needed on these functions now need an
    66   additional assumption which is that the isomorphism works.
    67 
    68   These rewrites are typically used in a structured way. They are here
    69   presented as the introduction rule @{text "isomorphic_tuple.intros"}
    70   rather than as a rewrite rule set. The introduction form is an
    71   optimisation, as net matching can be performed at one term location
    72   for each step rather than the simplifier searching the term for
    73   possible pattern matches. The rule set is used as it is viewed
    74   outside the locale, with the locale assumption (that the isomorphism
    75   is valid) left as a rule assumption. All rules are structured to aid
    76   net matching, using either a point-free form or an encapsulating
    77   predicate.
    78 *}
    79 
    80 subsection {* Operators and lemmas for types isomorphic to tuples *}
    81 
    82 datatype ('a, 'b, 'c) tuple_isomorphism =
    83   Tuple_Isomorphism "'a \<Rightarrow> 'b \<times> 'c" "'b \<times> 'c \<Rightarrow> 'a"
    84 
    85 primrec
    86   repr :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'c" where
    87   "repr (Tuple_Isomorphism r a) = r"
    88 
    89 primrec
    90   abst :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'b \<times> 'c \<Rightarrow> 'a" where
    91   "abst (Tuple_Isomorphism r a) = a"
    92 
    93 definition
    94   iso_tuple_fst :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'b" where
    95   "iso_tuple_fst isom = fst \<circ> repr isom"
    96 
    97 definition
    98   iso_tuple_snd :: "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'a \<Rightarrow> 'c" where
    99   "iso_tuple_snd isom = snd \<circ> repr isom"
   100 
   101 definition
   102   iso_tuple_fst_update ::
   103     "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)" where
   104   "iso_tuple_fst_update isom f = abst isom \<circ> apfst f \<circ> repr isom"
   105 
   106 definition
   107   iso_tuple_snd_update ::
   108     "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> ('c \<Rightarrow> 'c) \<Rightarrow> ('a \<Rightarrow> 'a)" where
   109   "iso_tuple_snd_update isom f = abst isom \<circ> apsnd f \<circ> repr isom"
   110 
   111 definition
   112   iso_tuple_cons ::
   113     "('a, 'b, 'c) tuple_isomorphism \<Rightarrow> 'b \<Rightarrow> 'c \<Rightarrow> 'a" where
   114   "iso_tuple_cons isom = curry (abst isom)"
   115 
   116 
   117 subsection {* Logical infrastructure for records *}
   118 
   119 definition
   120   iso_tuple_surjective_proof_assist :: "'a \<Rightarrow> 'b \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool" where
   121   "iso_tuple_surjective_proof_assist x y f \<longleftrightarrow> f x = y"
   122 
   123 definition
   124   iso_tuple_update_accessor_cong_assist ::
   125     "(('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> bool" where
   126   "iso_tuple_update_accessor_cong_assist upd ac \<longleftrightarrow>
   127      (\<forall>f v. upd (\<lambda>x. f (ac v)) v = upd f v) \<and> (\<forall>v. upd id v = v)"
   128 
   129 definition
   130   iso_tuple_update_accessor_eq_assist ::
   131     "(('b \<Rightarrow> 'b) \<Rightarrow> ('a \<Rightarrow> 'a)) \<Rightarrow> ('a \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> ('b \<Rightarrow> 'b) \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> bool" where
   132   "iso_tuple_update_accessor_eq_assist upd ac v f v' x \<longleftrightarrow>
   133      upd f v = v' \<and> ac v = x \<and> iso_tuple_update_accessor_cong_assist upd ac"
   134 
   135 lemma update_accessor_congruence_foldE:
   136   assumes uac: "iso_tuple_update_accessor_cong_assist upd ac"
   137     and r: "r = r'" and v: "ac r' = v'"
   138     and f: "\<And>v. v' = v \<Longrightarrow> f v = f' v"
   139   shows "upd f r = upd f' r'"
   140   using uac r v [symmetric]
   141   apply (subgoal_tac "upd (\<lambda>x. f (ac r')) r' = upd (\<lambda>x. f' (ac r')) r'")
   142    apply (simp add: iso_tuple_update_accessor_cong_assist_def)
   143   apply (simp add: f)
   144   done
   145 
   146 lemma update_accessor_congruence_unfoldE:
   147   "iso_tuple_update_accessor_cong_assist upd ac \<Longrightarrow>
   148     r = r' \<Longrightarrow> ac r' = v' \<Longrightarrow> (\<And>v. v = v' \<Longrightarrow> f v = f' v) \<Longrightarrow>
   149     upd f r = upd f' r'"
   150   apply (erule(2) update_accessor_congruence_foldE)
   151   apply simp
   152   done
   153 
   154 lemma iso_tuple_update_accessor_cong_assist_id:
   155   "iso_tuple_update_accessor_cong_assist upd ac \<Longrightarrow> upd id = id"
   156   by rule (simp add: iso_tuple_update_accessor_cong_assist_def)
   157 
   158 lemma update_accessor_noopE:
   159   assumes uac: "iso_tuple_update_accessor_cong_assist upd ac"
   160     and ac: "f (ac x) = ac x"
   161   shows "upd f x = x"
   162   using uac
   163   by (simp add: ac iso_tuple_update_accessor_cong_assist_id [OF uac, unfolded id_def]
   164     cong: update_accessor_congruence_unfoldE [OF uac])
   165 
   166 lemma update_accessor_noop_compE:
   167   assumes uac: "iso_tuple_update_accessor_cong_assist upd ac"
   168     and ac: "f (ac x) = ac x"
   169   shows "upd (g \<circ> f) x = upd g x"
   170   by (simp add: ac cong: update_accessor_congruence_unfoldE[OF uac])
   171 
   172 lemma update_accessor_cong_assist_idI:
   173   "iso_tuple_update_accessor_cong_assist id id"
   174   by (simp add: iso_tuple_update_accessor_cong_assist_def)
   175 
   176 lemma update_accessor_cong_assist_triv:
   177   "iso_tuple_update_accessor_cong_assist upd ac \<Longrightarrow>
   178     iso_tuple_update_accessor_cong_assist upd ac"
   179   by assumption
   180 
   181 lemma update_accessor_accessor_eqE:
   182   "iso_tuple_update_accessor_eq_assist upd ac v f v' x \<Longrightarrow> ac v = x"
   183   by (simp add: iso_tuple_update_accessor_eq_assist_def)
   184 
   185 lemma update_accessor_updator_eqE:
   186   "iso_tuple_update_accessor_eq_assist upd ac v f v' x \<Longrightarrow> upd f v = v'"
   187   by (simp add: iso_tuple_update_accessor_eq_assist_def)
   188 
   189 lemma iso_tuple_update_accessor_eq_assist_idI:
   190   "v' = f v \<Longrightarrow> iso_tuple_update_accessor_eq_assist id id v f v' v"
   191   by (simp add: iso_tuple_update_accessor_eq_assist_def update_accessor_cong_assist_idI)
   192 
   193 lemma iso_tuple_update_accessor_eq_assist_triv:
   194   "iso_tuple_update_accessor_eq_assist upd ac v f v' x \<Longrightarrow>
   195     iso_tuple_update_accessor_eq_assist upd ac v f v' x"
   196   by assumption
   197 
   198 lemma iso_tuple_update_accessor_cong_from_eq:
   199   "iso_tuple_update_accessor_eq_assist upd ac v f v' x \<Longrightarrow>
   200     iso_tuple_update_accessor_cong_assist upd ac"
   201   by (simp add: iso_tuple_update_accessor_eq_assist_def)
   202 
   203 lemma iso_tuple_surjective_proof_assistI:
   204   "f x = y \<Longrightarrow> iso_tuple_surjective_proof_assist x y f"
   205   by (simp add: iso_tuple_surjective_proof_assist_def)
   206 
   207 lemma iso_tuple_surjective_proof_assist_idE:
   208   "iso_tuple_surjective_proof_assist x y id \<Longrightarrow> x = y"
   209   by (simp add: iso_tuple_surjective_proof_assist_def)
   210 
   211 locale isomorphic_tuple =
   212   fixes isom :: "('a, 'b, 'c) tuple_isomorphism"
   213   assumes repr_inv: "\<And>x. abst isom (repr isom x) = x"
   214     and abst_inv: "\<And>y. repr isom (abst isom y) = y"
   215 begin
   216 
   217 lemma repr_inj: "repr isom x = repr isom y \<longleftrightarrow> x = y"
   218   by (auto dest: arg_cong [of "repr isom x" "repr isom y" "abst isom"]
   219     simp add: repr_inv)
   220 
   221 lemma abst_inj: "abst isom x = abst isom y \<longleftrightarrow> x = y"
   222   by (auto dest: arg_cong [of "abst isom x" "abst isom y" "repr isom"]
   223     simp add: abst_inv)
   224 
   225 lemmas simps = Let_def repr_inv abst_inv repr_inj abst_inj
   226 
   227 lemma iso_tuple_access_update_fst_fst:
   228   "f o h g = j o f \<Longrightarrow>
   229     (f o iso_tuple_fst isom) o (iso_tuple_fst_update isom o h) g =
   230       j o (f o iso_tuple_fst isom)"
   231   by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_fst_def simps
   232     intro!: ext elim!: o_eq_elim)
   233 
   234 lemma iso_tuple_access_update_snd_snd:
   235   "f o h g = j o f \<Longrightarrow>
   236     (f o iso_tuple_snd isom) o (iso_tuple_snd_update isom o h) g =
   237       j o (f o iso_tuple_snd isom)"
   238   by (clarsimp simp: iso_tuple_snd_update_def iso_tuple_snd_def simps
   239     intro!: ext elim!: o_eq_elim)
   240 
   241 lemma iso_tuple_access_update_fst_snd:
   242   "(f o iso_tuple_fst isom) o (iso_tuple_snd_update isom o h) g =
   243     id o (f o iso_tuple_fst isom)"
   244   by (clarsimp simp: iso_tuple_snd_update_def iso_tuple_fst_def simps
   245     intro!: ext elim!: o_eq_elim)
   246 
   247 lemma iso_tuple_access_update_snd_fst:
   248   "(f o iso_tuple_snd isom) o (iso_tuple_fst_update isom o h) g =
   249     id o (f o iso_tuple_snd isom)"
   250   by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_snd_def simps
   251     intro!: ext elim!: o_eq_elim)
   252 
   253 lemma iso_tuple_update_swap_fst_fst:
   254   "h f o j g = j g o h f \<Longrightarrow>
   255     (iso_tuple_fst_update isom o h) f o (iso_tuple_fst_update isom o j) g =
   256       (iso_tuple_fst_update isom o j) g o (iso_tuple_fst_update isom o h) f"
   257   by (clarsimp simp: iso_tuple_fst_update_def simps apfst_compose intro!: ext)
   258 
   259 lemma iso_tuple_update_swap_snd_snd:
   260   "h f o j g = j g o h f \<Longrightarrow>
   261     (iso_tuple_snd_update isom o h) f o (iso_tuple_snd_update isom o j) g =
   262       (iso_tuple_snd_update isom o j) g o (iso_tuple_snd_update isom o h) f"
   263   by (clarsimp simp: iso_tuple_snd_update_def simps apsnd_compose intro!: ext)
   264 
   265 lemma iso_tuple_update_swap_fst_snd:
   266   "(iso_tuple_snd_update isom o h) f o (iso_tuple_fst_update isom o j) g =
   267     (iso_tuple_fst_update isom o j) g o (iso_tuple_snd_update isom o h) f"
   268   by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_snd_update_def
   269     simps intro!: ext)
   270 
   271 lemma iso_tuple_update_swap_snd_fst:
   272   "(iso_tuple_fst_update isom o h) f o (iso_tuple_snd_update isom o j) g =
   273     (iso_tuple_snd_update isom o j) g o (iso_tuple_fst_update isom o h) f"
   274   by (clarsimp simp: iso_tuple_fst_update_def iso_tuple_snd_update_def simps intro!: ext)
   275 
   276 lemma iso_tuple_update_compose_fst_fst:
   277   "h f o j g = k (f o g) \<Longrightarrow>
   278     (iso_tuple_fst_update isom o h) f o (iso_tuple_fst_update isom o j) g =
   279       (iso_tuple_fst_update isom o k) (f o g)"
   280   by (clarsimp simp: iso_tuple_fst_update_def simps apfst_compose intro!: ext)
   281 
   282 lemma iso_tuple_update_compose_snd_snd:
   283   "h f o j g = k (f o g) \<Longrightarrow>
   284     (iso_tuple_snd_update isom o h) f o (iso_tuple_snd_update isom o j) g =
   285       (iso_tuple_snd_update isom o k) (f o g)"
   286   by (clarsimp simp: iso_tuple_snd_update_def simps apsnd_compose intro!: ext)
   287 
   288 lemma iso_tuple_surjective_proof_assist_step:
   289   "iso_tuple_surjective_proof_assist v a (iso_tuple_fst isom o f) \<Longrightarrow>
   290     iso_tuple_surjective_proof_assist v b (iso_tuple_snd isom o f) \<Longrightarrow>
   291     iso_tuple_surjective_proof_assist v (iso_tuple_cons isom a b) f"
   292   by (clarsimp simp: iso_tuple_surjective_proof_assist_def simps
   293     iso_tuple_fst_def iso_tuple_snd_def iso_tuple_cons_def)
   294 
   295 lemma iso_tuple_fst_update_accessor_cong_assist:
   296   assumes "iso_tuple_update_accessor_cong_assist f g"
   297   shows "iso_tuple_update_accessor_cong_assist
   298     (iso_tuple_fst_update isom o f) (g o iso_tuple_fst isom)"
   299 proof -
   300   from assms have "f id = id"
   301     by (rule iso_tuple_update_accessor_cong_assist_id)
   302   with assms show ?thesis
   303     by (clarsimp simp: iso_tuple_update_accessor_cong_assist_def simps
   304       iso_tuple_fst_update_def iso_tuple_fst_def)
   305 qed
   306 
   307 lemma iso_tuple_snd_update_accessor_cong_assist:
   308   assumes "iso_tuple_update_accessor_cong_assist f g"
   309   shows "iso_tuple_update_accessor_cong_assist
   310     (iso_tuple_snd_update isom o f) (g o iso_tuple_snd isom)"
   311 proof -
   312   from assms have "f id = id"
   313     by (rule iso_tuple_update_accessor_cong_assist_id)
   314   with assms show ?thesis
   315     by (clarsimp simp: iso_tuple_update_accessor_cong_assist_def simps
   316       iso_tuple_snd_update_def iso_tuple_snd_def)
   317 qed
   318 
   319 lemma iso_tuple_fst_update_accessor_eq_assist:
   320   assumes "iso_tuple_update_accessor_eq_assist f g a u a' v"
   321   shows "iso_tuple_update_accessor_eq_assist
   322     (iso_tuple_fst_update isom o f) (g o iso_tuple_fst isom)
   323     (iso_tuple_cons isom a b) u (iso_tuple_cons isom a' b) v"
   324 proof -
   325   from assms have "f id = id"
   326     by (auto simp add: iso_tuple_update_accessor_eq_assist_def
   327       intro: iso_tuple_update_accessor_cong_assist_id)
   328   with assms show ?thesis
   329     by (clarsimp simp: iso_tuple_update_accessor_eq_assist_def
   330       iso_tuple_fst_update_def iso_tuple_fst_def
   331       iso_tuple_update_accessor_cong_assist_def iso_tuple_cons_def simps)
   332 qed
   333 
   334 lemma iso_tuple_snd_update_accessor_eq_assist:
   335   assumes "iso_tuple_update_accessor_eq_assist f g b u b' v"
   336   shows "iso_tuple_update_accessor_eq_assist
   337     (iso_tuple_snd_update isom o f) (g o iso_tuple_snd isom)
   338     (iso_tuple_cons isom a b) u (iso_tuple_cons isom a b') v"
   339 proof -
   340   from assms have "f id = id"
   341     by (auto simp add: iso_tuple_update_accessor_eq_assist_def
   342       intro: iso_tuple_update_accessor_cong_assist_id)
   343   with assms show ?thesis
   344     by (clarsimp simp: iso_tuple_update_accessor_eq_assist_def
   345       iso_tuple_snd_update_def iso_tuple_snd_def
   346       iso_tuple_update_accessor_cong_assist_def iso_tuple_cons_def simps)
   347 qed
   348 
   349 lemma iso_tuple_cons_conj_eqI:
   350   "a = c \<and> b = d \<and> P \<longleftrightarrow> Q \<Longrightarrow>
   351     iso_tuple_cons isom a b = iso_tuple_cons isom c d \<and> P \<longleftrightarrow> Q"
   352   by (clarsimp simp: iso_tuple_cons_def simps)
   353 
   354 lemmas intros =
   355   iso_tuple_access_update_fst_fst
   356   iso_tuple_access_update_snd_snd
   357   iso_tuple_access_update_fst_snd
   358   iso_tuple_access_update_snd_fst
   359   iso_tuple_update_swap_fst_fst
   360   iso_tuple_update_swap_snd_snd
   361   iso_tuple_update_swap_fst_snd
   362   iso_tuple_update_swap_snd_fst
   363   iso_tuple_update_compose_fst_fst
   364   iso_tuple_update_compose_snd_snd
   365   iso_tuple_surjective_proof_assist_step
   366   iso_tuple_fst_update_accessor_eq_assist
   367   iso_tuple_snd_update_accessor_eq_assist
   368   iso_tuple_fst_update_accessor_cong_assist
   369   iso_tuple_snd_update_accessor_cong_assist
   370   iso_tuple_cons_conj_eqI
   371 
   372 end
   373 
   374 lemma isomorphic_tuple_intro:
   375   fixes repr abst
   376   assumes repr_inj: "\<And>x y. repr x = repr y \<longleftrightarrow> x = y"
   377     and abst_inv: "\<And>z. repr (abst z) = z"
   378     and v: "v \<equiv> Tuple_Isomorphism repr abst"
   379   shows "isomorphic_tuple v"
   380 proof
   381   fix x have "repr (abst (repr x)) = repr x"
   382     by (simp add: abst_inv)
   383   then show "Record.abst v (Record.repr v x) = x"
   384     by (simp add: v repr_inj)
   385 next
   386   fix y
   387   show "Record.repr v (Record.abst v y) = y"
   388     by (simp add: v) (fact abst_inv)
   389 qed
   390 
   391 definition
   392   "tuple_iso_tuple \<equiv> Tuple_Isomorphism id id"
   393 
   394 lemma tuple_iso_tuple:
   395   "isomorphic_tuple tuple_iso_tuple"
   396   by (simp add: isomorphic_tuple_intro [OF _ _ reflexive] tuple_iso_tuple_def)
   397 
   398 lemma refl_conj_eq: "Q = R \<Longrightarrow> P \<and> Q \<longleftrightarrow> P \<and> R"
   399   by simp
   400 
   401 lemma iso_tuple_UNIV_I: "x \<in> UNIV \<equiv> True"
   402   by simp
   403 
   404 lemma iso_tuple_True_simp: "(True \<Longrightarrow> PROP P) \<equiv> PROP P"
   405   by simp
   406 
   407 lemma prop_subst: "s = t \<Longrightarrow> PROP P t \<Longrightarrow> PROP P s"
   408   by simp
   409 
   410 lemma K_record_comp: "(\<lambda>x. c) \<circ> f = (\<lambda>x. c)"
   411   by (simp add: comp_def)
   412 
   413 lemma o_eq_dest_lhs: "a o b = c \<Longrightarrow> a (b v) = c v"
   414   by clarsimp
   415 
   416 lemma o_eq_id_dest: "a o b = id o c \<Longrightarrow> a (b v) = c v"
   417   by clarsimp
   418 
   419 
   420 subsection {* Concrete record syntax *}
   421 
   422 nonterminals
   423   ident field_type field_types field fields field_update field_updates
   424 syntax
   425   "_constify"           :: "id => ident"                        ("_")
   426   "_constify"           :: "longid => ident"                    ("_")
   427 
   428   "_field_type"         :: "ident => type => field_type"        ("(2_ ::/ _)")
   429   ""                    :: "field_type => field_types"          ("_")
   430   "_field_types"        :: "field_type => field_types => field_types"    ("_,/ _")
   431   "_record_type"        :: "field_types => type"                ("(3'(| _ |'))")
   432   "_record_type_scheme" :: "field_types => type => type"        ("(3'(| _,/ (2... ::/ _) |'))")
   433 
   434   "_field"              :: "ident => 'a => field"               ("(2_ =/ _)")
   435   ""                    :: "field => fields"                    ("_")
   436   "_fields"             :: "field => fields => fields"          ("_,/ _")
   437   "_record"             :: "fields => 'a"                       ("(3'(| _ |'))")
   438   "_record_scheme"      :: "fields => 'a => 'a"                 ("(3'(| _,/ (2... =/ _) |'))")
   439 
   440   "_field_update"       :: "ident => 'a => field_update"        ("(2_ :=/ _)")
   441   ""                    :: "field_update => field_updates"      ("_")
   442   "_field_updates"      :: "field_update => field_updates => field_updates"  ("_,/ _")
   443   "_record_update"      :: "'a => field_updates => 'b"          ("_/(3'(| _ |'))" [900, 0] 900)
   444 
   445 syntax (xsymbols)
   446   "_record_type"        :: "field_types => type"                ("(3\<lparr>_\<rparr>)")
   447   "_record_type_scheme" :: "field_types => type => type"        ("(3\<lparr>_,/ (2\<dots> ::/ _)\<rparr>)")
   448   "_record"             :: "fields => 'a"                       ("(3\<lparr>_\<rparr>)")
   449   "_record_scheme"      :: "fields => 'a => 'a"                 ("(3\<lparr>_,/ (2\<dots> =/ _)\<rparr>)")
   450   "_record_update"      :: "'a => field_updates => 'b"          ("_/(3\<lparr>_\<rparr>)" [900, 0] 900)
   451 
   452 
   453 subsection {* Record package *}
   454 
   455 use "Tools/record.ML" setup Record.setup
   456 
   457 hide_const (open) Tuple_Isomorphism repr abst iso_tuple_fst iso_tuple_snd
   458   iso_tuple_fst_update iso_tuple_snd_update iso_tuple_cons
   459   iso_tuple_surjective_proof_assist iso_tuple_update_accessor_cong_assist
   460   iso_tuple_update_accessor_eq_assist tuple_iso_tuple
   461 
   462 end