src/HOL/BNF/Tools/bnf_util.ML
author wenzelm
Fri Oct 12 21:22:35 2012 +0200 (2012-10-12)
changeset 49835 31f32ec4d766
parent 49833 1d80798e8d8a
child 51757 7babcb61aa5c
permissions -rw-r--r--
discontinued typedef with alternative name;
     1 (*  Title:      HOL/BNF/Tools/bnf_util.ML
     2     Author:     Dmitriy Traytel, TU Muenchen
     3     Copyright   2012
     4 
     5 Library for bounded natural functors.
     6 *)
     7 
     8 signature BNF_UTIL =
     9 sig
    10   val map3: ('a -> 'b -> 'c -> 'd) -> 'a list -> 'b list -> 'c list -> 'd list
    11   val map4: ('a -> 'b -> 'c -> 'd -> 'e) -> 'a list -> 'b list -> 'c list -> 'd list -> 'e list
    12   val map5: ('a -> 'b -> 'c -> 'd -> 'e -> 'f) ->
    13     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list
    14   val map6: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g) ->
    15     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list
    16   val map7: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h) ->
    17     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list
    18   val map8: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i) ->
    19     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list -> 'i list
    20   val map9: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j) ->
    21     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
    22     'i list -> 'j list
    23   val map10: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k) ->
    24     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
    25     'i list -> 'j list -> 'k list
    26   val map11: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k -> 'l) ->
    27     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
    28     'i list -> 'j list -> 'k list -> 'l list
    29   val map12: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k -> 'l -> 'm) ->
    30     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h list ->
    31     'i list -> 'j list -> 'k list -> 'l list -> 'm list
    32   val fold_map2: ('a -> 'b -> 'c -> 'd * 'c) -> 'a list -> 'b list -> 'c -> 'd list * 'c
    33   val fold_map3: ('a -> 'b -> 'c -> 'd -> 'e * 'd) ->
    34     'a list -> 'b list -> 'c list -> 'd -> 'e list * 'd
    35   val fold_map4: ('a -> 'b -> 'c -> 'd -> 'e -> 'f * 'e) ->
    36     'a list -> 'b list -> 'c list -> 'd list -> 'e -> 'f list * 'e
    37   val fold_map5: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g * 'f) ->
    38     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f -> 'g list * 'f
    39   val fold_map6: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h * 'g) ->
    40     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g -> 'h list * 'g
    41   val fold_map7: ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i * 'h) ->
    42     'a list -> 'b list -> 'c list -> 'd list -> 'e list -> 'f list -> 'g list -> 'h -> 'i list * 'h
    43   val splice: 'a list -> 'a list -> 'a list
    44   val transpose: 'a list list -> 'a list list
    45   val seq_conds: (bool -> 'a -> 'b) -> int -> int -> 'a list -> 'b list
    46 
    47   val mk_fresh_names: Proof.context -> int -> string -> string list * Proof.context
    48   val mk_TFrees: int -> Proof.context -> typ list * Proof.context
    49   val mk_TFreess: int list -> Proof.context -> typ list list * Proof.context
    50   val mk_TFrees': sort list -> Proof.context -> typ list * Proof.context
    51   val mk_Frees: string -> typ list -> Proof.context -> term list * Proof.context
    52   val mk_Freess: string -> typ list list -> Proof.context -> term list list * Proof.context
    53   val mk_Freesss: string -> typ list list list -> Proof.context ->
    54     term list list list * Proof.context
    55   val mk_Freessss: string -> typ list list list list -> Proof.context ->
    56     term list list list list * Proof.context
    57   val mk_Frees': string -> typ list -> Proof.context ->
    58     (term list * (string * typ) list) * Proof.context
    59   val mk_Freess': string -> typ list list -> Proof.context ->
    60     (term list list * (string * typ) list list) * Proof.context
    61   val nonzero_string_of_int: int -> string
    62 
    63   val strip_typeN: int -> typ -> typ list * typ
    64 
    65   val mk_predT: typ list -> typ
    66   val mk_pred1T: typ -> typ
    67   val mk_pred2T: typ -> typ -> typ
    68   val mk_optionT: typ -> typ
    69   val mk_relT: typ * typ -> typ
    70   val dest_relT: typ -> typ * typ
    71   val mk_sumT: typ * typ -> typ
    72 
    73   val ctwo: term
    74   val fst_const: typ -> term
    75   val snd_const: typ -> term
    76   val Id_const: typ -> term
    77 
    78   val mk_Ball: term -> term -> term
    79   val mk_Bex: term -> term -> term
    80   val mk_Card_order: term -> term
    81   val mk_Field: term -> term
    82   val mk_Gr: term -> term -> term
    83   val mk_IfN: typ -> term list -> term list -> term
    84   val mk_Trueprop_eq: term * term -> term
    85   val mk_UNION: term -> term -> term
    86   val mk_Union: typ -> term
    87   val mk_card_binop: string -> (typ * typ -> typ) -> term -> term -> term
    88   val mk_card_of: term -> term
    89   val mk_card_order: term -> term
    90   val mk_ccexp: term -> term -> term
    91   val mk_cexp: term -> term -> term
    92   val mk_cinfinite: term -> term
    93   val mk_collect: term list -> typ -> term
    94   val mk_converse: term -> term
    95   val mk_cprod: term -> term -> term
    96   val mk_csum: term -> term -> term
    97   val mk_dir_image: term -> term -> term
    98   val mk_image: term -> term
    99   val mk_in: term list -> term list -> typ -> term
   100   val mk_ordLeq: term -> term -> term
   101   val mk_rel_comp: term * term -> term
   102   val mk_subset: term -> term -> term
   103   val mk_wpull: term -> term -> term -> term -> term -> (term * term) option -> term -> term -> term
   104 
   105   val rapp: term -> term -> term
   106 
   107   val list_all_free: term list -> term -> term
   108   val list_exists_free: term list -> term -> term
   109 
   110   (*parameterized terms*)
   111   val mk_nthN: int -> term -> int -> term
   112 
   113   (*parameterized thms*)
   114   val mk_Un_upper: int -> int -> thm
   115   val mk_conjIN: int -> thm
   116   val mk_conjunctN: int -> int -> thm
   117   val conj_dests: int -> thm -> thm list
   118   val mk_disjIN: int -> int -> thm
   119   val mk_nthI: int -> int -> thm
   120   val mk_nth_conv: int -> int -> thm
   121   val mk_ordLeq_csum: int -> int -> thm -> thm
   122   val mk_UnIN: int -> int -> thm
   123 
   124   val Pair_eqD: thm
   125   val Pair_eqI: thm
   126   val ctrans: thm
   127   val id_apply: thm
   128   val meta_mp: thm
   129   val meta_spec: thm
   130   val o_apply: thm
   131   val set_mp: thm
   132   val set_rev_mp: thm
   133   val subset_UNIV: thm
   134   val mk_sym: thm -> thm
   135   val mk_trans: thm -> thm -> thm
   136   val mk_unabs_def: int -> thm -> thm
   137 
   138   val is_triv_implies: thm -> bool
   139   val is_refl: thm -> bool
   140   val is_concl_refl: thm -> bool
   141   val no_refl: thm list -> thm list
   142   val no_reflexive: thm list -> thm list
   143 
   144   val cterm_instantiate_pos: cterm option list -> thm -> thm
   145   val fold_thms: Proof.context -> thm list -> thm -> thm
   146   val unfold_thms: Proof.context -> thm list -> thm -> thm
   147 
   148   val mk_permute: ''a list -> ''a list -> 'b list -> 'b list
   149   val find_indices: ''a list -> ''a list -> int list
   150 
   151   val certifyT: Proof.context -> typ -> ctyp
   152   val certify: Proof.context -> term -> cterm
   153 
   154   val parse_binding_colon: Token.T list -> binding * Token.T list
   155   val parse_opt_binding_colon: Token.T list -> binding * Token.T list
   156 
   157   val typedef: binding * (string * sort) list * mixfix -> term ->
   158     (binding * binding) option -> tactic -> local_theory -> (string * Typedef.info) * local_theory
   159 
   160   val WRAP: ('a -> tactic) -> ('a -> tactic) -> 'a list -> tactic -> tactic
   161   val WRAP': ('a -> int -> tactic) -> ('a -> int -> tactic) -> 'a list -> (int -> tactic) -> int ->
   162     tactic
   163   val CONJ_WRAP_GEN: tactic -> ('a -> tactic) -> 'a list -> tactic
   164   val CONJ_WRAP_GEN': (int -> tactic) -> ('a -> int -> tactic) -> 'a list -> int -> tactic
   165   val CONJ_WRAP: ('a -> tactic) -> 'a list -> tactic
   166   val CONJ_WRAP': ('a -> int -> tactic) -> 'a list -> int -> tactic
   167 end;
   168 
   169 structure BNF_Util : BNF_UTIL =
   170 struct
   171 
   172 (* Library proper *)
   173 
   174 fun map3 _ [] [] [] = []
   175   | map3 f (x1::x1s) (x2::x2s) (x3::x3s) = f x1 x2 x3 :: map3 f x1s x2s x3s
   176   | map3 _ _ _ _ = raise ListPair.UnequalLengths;
   177 
   178 fun map4 _ [] [] [] [] = []
   179   | map4 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) = f x1 x2 x3 x4 :: map4 f x1s x2s x3s x4s
   180   | map4 _ _ _ _ _ = raise ListPair.UnequalLengths;
   181 
   182 fun map5 _ [] [] [] [] [] = []
   183   | map5 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) =
   184     f x1 x2 x3 x4 x5 :: map5 f x1s x2s x3s x4s x5s
   185   | map5 _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   186 
   187 fun map6 _ [] [] [] [] [] [] = []
   188   | map6 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) =
   189     f x1 x2 x3 x4 x5 x6 :: map6 f x1s x2s x3s x4s x5s x6s
   190   | map6 _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   191 
   192 fun map7 _ [] [] [] [] [] [] [] = []
   193   | map7 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) (x7::x7s) =
   194     f x1 x2 x3 x4 x5 x6 x7 :: map7 f x1s x2s x3s x4s x5s x6s x7s
   195   | map7 _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   196 
   197 fun map8 _ [] [] [] [] [] [] [] [] = []
   198   | map8 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) (x7::x7s) (x8::x8s) =
   199     f x1 x2 x3 x4 x5 x6 x7 x8 :: map8 f x1s x2s x3s x4s x5s x6s x7s x8s
   200   | map8 _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   201 
   202 fun map9 _ [] [] [] [] [] [] [] [] [] = []
   203   | map9 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
   204       (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) =
   205     f x1 x2 x3 x4 x5 x6 x7 x8 x9 :: map9 f x1s x2s x3s x4s x5s x6s x7s x8s x9s
   206   | map9 _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   207 
   208 fun map10 _ [] [] [] [] [] [] [] [] [] [] = []
   209   | map10 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
   210       (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) (x10::x10s) =
   211     f x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 :: map10 f x1s x2s x3s x4s x5s x6s x7s x8s x9s x10s
   212   | map10 _ _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   213 
   214 fun map11 _ [] [] [] [] [] [] [] [] [] [] [] = []
   215   | map11 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
   216       (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) (x10::x10s) (x11::x11s) =
   217     f x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 :: map11 f x1s x2s x3s x4s x5s x6s x7s x8s x9s x10s x11s
   218   | map11 _ _ _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   219 
   220 fun map12 _ [] [] [] [] [] [] [] [] [] [] [] [] = []
   221   | map12 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s)
   222       (x6::x6s) (x7::x7s) (x8::x8s) (x9::x9s) (x10::x10s) (x11::x11s) (x12::x12s) =
   223     f x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 ::
   224       map12 f x1s x2s x3s x4s x5s x6s x7s x8s x9s x10s x11s x12s
   225   | map12 _ _ _ _ _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   226 
   227 fun fold_map2 _ [] [] acc = ([], acc)
   228   | fold_map2 f (x1::x1s) (x2::x2s) acc =
   229     let
   230       val (x, acc') = f x1 x2 acc;
   231       val (xs, acc'') = fold_map2 f x1s x2s acc';
   232     in (x :: xs, acc'') end
   233   | fold_map2 _ _ _ _ = raise ListPair.UnequalLengths;
   234 
   235 fun fold_map3 _ [] [] [] acc = ([], acc)
   236   | fold_map3 f (x1::x1s) (x2::x2s) (x3::x3s) acc =
   237     let
   238       val (x, acc') = f x1 x2 x3 acc;
   239       val (xs, acc'') = fold_map3 f x1s x2s x3s acc';
   240     in (x :: xs, acc'') end
   241   | fold_map3 _ _ _ _ _ = raise ListPair.UnequalLengths;
   242 
   243 fun fold_map4 _ [] [] [] [] acc = ([], acc)
   244   | fold_map4 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) acc =
   245     let
   246       val (x, acc') = f x1 x2 x3 x4 acc;
   247       val (xs, acc'') = fold_map4 f x1s x2s x3s x4s acc';
   248     in (x :: xs, acc'') end
   249   | fold_map4 _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   250 
   251 fun fold_map5 _ [] [] [] [] [] acc = ([], acc)
   252   | fold_map5 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) acc =
   253     let
   254       val (x, acc') = f x1 x2 x3 x4 x5 acc;
   255       val (xs, acc'') = fold_map5 f x1s x2s x3s x4s x5s acc';
   256     in (x :: xs, acc'') end
   257   | fold_map5 _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   258 
   259 fun fold_map6 _ [] [] [] [] [] [] acc = ([], acc)
   260   | fold_map6 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) acc =
   261     let
   262       val (x, acc') = f x1 x2 x3 x4 x5 x6 acc;
   263       val (xs, acc'') = fold_map6 f x1s x2s x3s x4s x5s x6s acc';
   264     in (x :: xs, acc'') end
   265   | fold_map6 _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   266 
   267 fun fold_map7 _ [] [] [] [] [] [] [] acc = ([], acc)
   268   | fold_map7 f (x1::x1s) (x2::x2s) (x3::x3s) (x4::x4s) (x5::x5s) (x6::x6s) (x7::x7s) acc =
   269     let
   270       val (x, acc') = f x1 x2 x3 x4 x5 x6 x7 acc;
   271       val (xs, acc'') = fold_map7 f x1s x2s x3s x4s x5s x6s x7s acc';
   272     in (x :: xs, acc'') end
   273   | fold_map7 _ _ _ _ _ _ _ _ _ = raise ListPair.UnequalLengths;
   274 
   275 (*stolen from ~~/src/HOL/Tools/SMT/smt_utils.ML*)
   276 fun certify ctxt = Thm.cterm_of (Proof_Context.theory_of ctxt);
   277 fun certifyT ctxt = Thm.ctyp_of (Proof_Context.theory_of ctxt);
   278 
   279 val parse_binding_colon = Parse.binding --| @{keyword ":"};
   280 val parse_opt_binding_colon = Scan.optional parse_binding_colon Binding.empty;
   281 
   282 (*TODO: is this really different from Typedef.add_typedef_global?*)
   283 fun typedef typ set opt_morphs tac lthy =
   284   let
   285     val ((name, info), (lthy, lthy_old)) =
   286       lthy
   287       |> Typedef.add_typedef typ set opt_morphs tac
   288       ||> `Local_Theory.restore;
   289     val phi = Proof_Context.export_morphism lthy_old lthy;
   290   in
   291     ((name, Typedef.transform_info phi info), lthy)
   292   end;
   293 
   294 (*Tactical WRAP surrounds a static given tactic (core) with two deterministic chains of tactics*)
   295 fun WRAP gen_before gen_after xs core_tac =
   296   fold_rev (fn x => fn tac => gen_before x THEN tac THEN gen_after x) xs core_tac;
   297 
   298 fun WRAP' gen_before gen_after xs core_tac =
   299   fold_rev (fn x => fn tac => gen_before x THEN' tac THEN' gen_after x) xs core_tac;
   300 
   301 fun CONJ_WRAP_GEN conj_tac gen_tac xs =
   302   let val (butlast, last) = split_last xs;
   303   in WRAP (fn thm => conj_tac THEN gen_tac thm) (K all_tac) butlast (gen_tac last) end;
   304 
   305 fun CONJ_WRAP_GEN' conj_tac gen_tac xs =
   306   let val (butlast, last) = split_last xs;
   307   in WRAP' (fn thm => conj_tac THEN' gen_tac thm) (K (K all_tac)) butlast (gen_tac last) end;
   308 
   309 (*not eta-converted because of monotype restriction*)
   310 fun CONJ_WRAP gen_tac = CONJ_WRAP_GEN (rtac conjI 1) gen_tac;
   311 fun CONJ_WRAP' gen_tac = CONJ_WRAP_GEN' (rtac conjI) gen_tac;
   312 
   313 
   314 
   315 (* Term construction *)
   316 
   317 (** Fresh variables **)
   318 
   319 fun nonzero_string_of_int 0 = ""
   320   | nonzero_string_of_int n = string_of_int n;
   321 
   322 val mk_TFrees' = apfst (map TFree) oo Variable.invent_types;
   323 
   324 fun mk_TFrees n = mk_TFrees' (replicate n HOLogic.typeS);
   325 val mk_TFreess = fold_map mk_TFrees;
   326 
   327 fun mk_names n x = if n = 1 then [x] else map (fn i => x ^ string_of_int i) (1 upto n);
   328 
   329 fun mk_fresh_names ctxt = (fn xs => Variable.variant_fixes xs ctxt) oo mk_names;
   330 fun mk_Frees x Ts ctxt = mk_fresh_names ctxt (length Ts) x |>> (fn xs => map2 (curry Free) xs Ts);
   331 fun mk_Freess x Tss = fold_map2 mk_Frees (mk_names (length Tss) x) Tss;
   332 fun mk_Freesss x Tsss = fold_map2 mk_Freess (mk_names (length Tsss) x) Tsss;
   333 fun mk_Freessss x Tssss = fold_map2 mk_Freesss (mk_names (length Tssss) x) Tssss;
   334 fun mk_Frees' x Ts ctxt = mk_fresh_names ctxt (length Ts) x |>> (fn xs => `(map Free) (xs ~~ Ts));
   335 fun mk_Freess' x Tss = fold_map2 mk_Frees' (mk_names (length Tss) x) Tss #>> split_list;
   336 
   337 
   338 (** Types **)
   339 
   340 fun strip_typeN 0 T = ([], T)
   341   | strip_typeN n (Type (@{type_name fun}, [T, T'])) = strip_typeN (n - 1) T' |>> cons T
   342   | strip_typeN _ T = raise TYPE ("strip_typeN", [T], []);
   343 
   344 fun mk_predT Ts = Ts ---> HOLogic.boolT;
   345 fun mk_pred1T T = mk_predT [T];
   346 fun mk_pred2T T U = mk_predT [T, U];
   347 fun mk_optionT T = Type (@{type_name option}, [T]);
   348 val mk_relT = HOLogic.mk_setT o HOLogic.mk_prodT;
   349 val dest_relT = HOLogic.dest_prodT o HOLogic.dest_setT;
   350 fun mk_sumT (LT, RT) = Type (@{type_name Sum_Type.sum}, [LT, RT]);
   351 fun mk_partial_funT (ranT, domT) = domT --> mk_optionT ranT;
   352 
   353 
   354 (** Constants **)
   355 
   356 fun fst_const T = Const (@{const_name fst}, T --> fst (HOLogic.dest_prodT T));
   357 fun snd_const T = Const (@{const_name snd}, T --> snd (HOLogic.dest_prodT T));
   358 fun Id_const T = Const (@{const_name Id}, mk_relT (T, T));
   359 
   360 
   361 (** Operators **)
   362 
   363 val mk_Trueprop_eq = HOLogic.mk_Trueprop o HOLogic.mk_eq;
   364 
   365 fun mk_IfN _ _ [t] = t
   366   | mk_IfN T (c :: cs) (t :: ts) =
   367     Const (@{const_name If}, HOLogic.boolT --> T --> T --> T) $ c $ t $ mk_IfN T cs ts;
   368 
   369 fun mk_converse R =
   370   let
   371     val RT = dest_relT (fastype_of R);
   372     val RST = mk_relT (snd RT, fst RT);
   373   in Const (@{const_name converse}, fastype_of R --> RST) $ R end;
   374 
   375 fun mk_rel_comp (R, S) =
   376   let
   377     val RT = fastype_of R;
   378     val ST = fastype_of S;
   379     val RST = mk_relT (fst (dest_relT RT), snd (dest_relT ST));
   380   in Const (@{const_name relcomp}, RT --> ST --> RST) $ R $ S end;
   381 
   382 fun mk_Gr A f =
   383   let val ((AT, BT), FT) = `dest_funT (fastype_of f);
   384   in Const (@{const_name Gr}, HOLogic.mk_setT AT --> FT --> mk_relT (AT, BT)) $ A $ f end;
   385 
   386 fun mk_image f =
   387   let val (T, U) = dest_funT (fastype_of f);
   388   in Const (@{const_name image},
   389     (T --> U) --> (HOLogic.mk_setT T) --> (HOLogic.mk_setT U)) $ f end;
   390 
   391 fun mk_Ball X f =
   392   Const (@{const_name Ball}, fastype_of X --> fastype_of f --> HOLogic.boolT) $ X $ f;
   393 
   394 fun mk_Bex X f =
   395   Const (@{const_name Bex}, fastype_of X --> fastype_of f --> HOLogic.boolT) $ X $ f;
   396 
   397 fun mk_UNION X f =
   398   let val (T, U) = dest_funT (fastype_of f);
   399   in Const (@{const_name SUPR}, fastype_of X --> (T --> U) --> U) $ X $ f end;
   400 
   401 fun mk_Union T =
   402   Const (@{const_name Sup}, HOLogic.mk_setT (HOLogic.mk_setT T) --> HOLogic.mk_setT T);
   403 
   404 fun mk_Field r =
   405   let val T = fst (dest_relT (fastype_of r));
   406   in Const (@{const_name Field}, mk_relT (T, T) --> HOLogic.mk_setT T) $ r end;
   407 
   408 fun mk_card_order bd =
   409   let
   410     val T = fastype_of bd;
   411     val AT = fst (dest_relT T);
   412   in
   413     Const (@{const_name card_order_on}, HOLogic.mk_setT AT --> T --> HOLogic.boolT) $
   414       (HOLogic.mk_UNIV AT) $ bd
   415   end;
   416 
   417 fun mk_Card_order bd =
   418   let
   419     val T = fastype_of bd;
   420     val AT = fst (dest_relT T);
   421   in
   422     Const (@{const_name card_order_on}, HOLogic.mk_setT AT --> T --> HOLogic.boolT) $
   423       mk_Field bd $ bd
   424   end;
   425 
   426 fun mk_cinfinite bd =
   427   Const (@{const_name cinfinite}, fastype_of bd --> HOLogic.boolT) $ bd;
   428 
   429 fun mk_ordLeq t1 t2 =
   430   HOLogic.mk_mem (HOLogic.mk_prod (t1, t2),
   431     Const (@{const_name ordLeq}, mk_relT (fastype_of t1, fastype_of t2)));
   432 
   433 fun mk_card_of A =
   434   let
   435     val AT = fastype_of A;
   436     val T = HOLogic.dest_setT AT;
   437   in
   438     Const (@{const_name card_of}, AT --> mk_relT (T, T)) $ A
   439   end;
   440 
   441 fun mk_dir_image r f =
   442   let val (T, U) = dest_funT (fastype_of f);
   443   in Const (@{const_name dir_image}, mk_relT (T, T) --> (T --> U) --> mk_relT (U, U)) $ r $ f end;
   444 
   445 (*FIXME: "x"?*)
   446 (*(nth sets i) must be of type "T --> 'ai set"*)
   447 fun mk_in As sets T =
   448   let
   449     fun in_single set A =
   450       let val AT = fastype_of A;
   451       in Const (@{const_name less_eq},
   452         AT --> AT --> HOLogic.boolT) $ (set $ Free ("x", T)) $ A end;
   453   in
   454     if length sets > 0
   455     then HOLogic.mk_Collect ("x", T, foldr1 (HOLogic.mk_conj) (map2 in_single sets As))
   456     else HOLogic.mk_UNIV T
   457   end;
   458 
   459 fun mk_wpull A B1 B2 f1 f2 pseudo p1 p2 =
   460   let
   461     val AT = fastype_of A;
   462     val BT1 = fastype_of B1;
   463     val BT2 = fastype_of B2;
   464     val FT1 = fastype_of f1;
   465     val FT2 = fastype_of f2;
   466     val PT1 = fastype_of p1;
   467     val PT2 = fastype_of p2;
   468     val T1 = HOLogic.dest_setT BT1;
   469     val T2 = HOLogic.dest_setT BT2;
   470     val domP = domain_type PT1;
   471     val ranF = range_type FT1;
   472     val _ = if is_some pseudo orelse
   473                (HOLogic.dest_setT AT = domP andalso
   474                domain_type FT1 = T1 andalso
   475                domain_type FT2 = T2 andalso
   476                domain_type PT2 = domP andalso
   477                range_type PT1 = T1 andalso
   478                range_type PT2 = T2 andalso
   479                range_type FT2 = ranF)
   480       then () else raise TYPE ("mk_wpull", [BT1, BT2, FT1, FT2, PT1, PT2], []);
   481   in
   482     (case pseudo of
   483       NONE => Const (@{const_name wpull},
   484         AT --> BT1 --> BT2 --> FT1 --> FT2 --> PT1 --> PT2 --> HOLogic.boolT) $
   485         A $ B1 $ B2 $ f1 $ f2 $ p1 $ p2
   486     | SOME (e1, e2) => Const (@{const_name wppull},
   487         AT --> BT1 --> BT2 --> FT1 --> FT2 --> fastype_of e1 --> fastype_of e2 -->
   488           PT1 --> PT2 --> HOLogic.boolT) $
   489         A $ B1 $ B2 $ f1 $ f2 $ e1 $ e2 $ p1 $ p2)
   490   end;
   491 
   492 fun mk_subset t1 t2 =
   493   Const (@{const_name less_eq}, (fastype_of t1) --> (fastype_of t2) --> HOLogic.boolT) $ t1 $ t2;
   494 
   495 fun mk_card_binop binop typop t1 t2 =
   496   let
   497     val (T1, relT1) = `(fst o dest_relT) (fastype_of t1);
   498     val (T2, relT2) = `(fst o dest_relT) (fastype_of t2);
   499   in
   500     Const (binop, relT1 --> relT2 --> mk_relT (typop (T1, T2), typop (T1, T2))) $ t1 $ t2
   501   end;
   502 
   503 val mk_csum = mk_card_binop @{const_name csum} mk_sumT;
   504 val mk_cprod = mk_card_binop @{const_name cprod} HOLogic.mk_prodT;
   505 val mk_cexp = mk_card_binop @{const_name cexp} mk_partial_funT;
   506 val mk_ccexp = mk_card_binop @{const_name ccexp} mk_partial_funT;
   507 val ctwo = @{term ctwo};
   508 
   509 fun mk_collect xs defT =
   510   let val T = (case xs of [] => defT | (x::_) => fastype_of x);
   511   in Const (@{const_name collect}, HOLogic.mk_setT T --> T) $ (HOLogic.mk_set T xs) end;
   512 
   513 fun mk_permute src dest xs = map (nth xs o (fn x => find_index ((curry op =) x) src)) dest;
   514 
   515 fun rapp u t = betapply (t, u);
   516 
   517 val list_all_free =
   518   fold_rev (fn free => fn P =>
   519     let val (x, T) = Term.dest_Free free;
   520     in HOLogic.all_const T $ Term.absfree (x, T) P end);
   521 
   522 val list_exists_free =
   523   fold_rev (fn free => fn P =>
   524     let val (x, T) = Term.dest_Free free;
   525     in HOLogic.exists_const T $ Term.absfree (x, T) P end);
   526 
   527 fun find_indices xs ys = map_filter I
   528   (map_index (fn (i, y) => if member (op =) xs y then SOME i else NONE) ys);
   529 
   530 fun mk_trans thm1 thm2 = trans OF [thm1, thm2];
   531 fun mk_sym thm = sym OF [thm];
   532 
   533 (*TODO: antiquote heavily used theorems once*)
   534 val Pair_eqD = @{thm iffD1[OF Pair_eq]};
   535 val Pair_eqI = @{thm iffD2[OF Pair_eq]};
   536 val ctrans = @{thm ordLeq_transitive};
   537 val id_apply = @{thm id_apply};
   538 val meta_mp = @{thm meta_mp};
   539 val meta_spec = @{thm meta_spec};
   540 val o_apply = @{thm o_apply};
   541 val set_mp = @{thm set_mp};
   542 val set_rev_mp = @{thm set_rev_mp};
   543 val subset_UNIV = @{thm subset_UNIV};
   544 
   545 fun mk_nthN 1 t 1 = t
   546   | mk_nthN _ t 1 = HOLogic.mk_fst t
   547   | mk_nthN 2 t 2 = HOLogic.mk_snd t
   548   | mk_nthN n t m = mk_nthN (n - 1) (HOLogic.mk_snd t) (m - 1);
   549 
   550 fun mk_nth_conv n m =
   551   let
   552     fun thm b = if b then @{thm fst_snd} else @{thm snd_snd}
   553     fun mk_nth_conv _ 1 1 = refl
   554       | mk_nth_conv _ _ 1 = @{thm fst_conv}
   555       | mk_nth_conv _ 2 2 = @{thm snd_conv}
   556       | mk_nth_conv b _ 2 = @{thm snd_conv} RS thm b
   557       | mk_nth_conv b n m = mk_nth_conv false (n - 1) (m - 1) RS thm b;
   558   in mk_nth_conv (not (m = n)) n m end;
   559 
   560 fun mk_nthI 1 1 = @{thm TrueE[OF TrueI]}
   561   | mk_nthI n m = fold (curry op RS) (replicate (m - 1) @{thm sndI})
   562     (if m = n then @{thm TrueE[OF TrueI]} else @{thm fstI});
   563 
   564 fun mk_conjunctN 1 1 = @{thm TrueE[OF TrueI]}
   565   | mk_conjunctN _ 1 = conjunct1
   566   | mk_conjunctN 2 2 = conjunct2
   567   | mk_conjunctN n m = conjunct2 RS (mk_conjunctN (n - 1) (m - 1));
   568 
   569 fun conj_dests n thm = map (fn k => thm RS mk_conjunctN n k) (1 upto n);
   570 
   571 fun mk_conjIN 1 = @{thm TrueE[OF TrueI]}
   572   | mk_conjIN n = mk_conjIN (n - 1) RSN (2, conjI);
   573 
   574 fun mk_disjIN 1 1 = @{thm TrueE[OF TrueI]}
   575   | mk_disjIN _ 1 = disjI1
   576   | mk_disjIN 2 2 = disjI2
   577   | mk_disjIN n m = (mk_disjIN (n - 1) (m - 1)) RS disjI2;
   578 
   579 fun mk_ordLeq_csum 1 1 thm = thm
   580   | mk_ordLeq_csum _ 1 thm = @{thm ordLeq_transitive} OF [thm, @{thm ordLeq_csum1}]
   581   | mk_ordLeq_csum 2 2 thm = @{thm ordLeq_transitive} OF [thm, @{thm ordLeq_csum2}]
   582   | mk_ordLeq_csum n m thm = @{thm ordLeq_transitive} OF
   583     [mk_ordLeq_csum (n - 1) (m - 1) thm, @{thm ordLeq_csum2[OF Card_order_csum]}];
   584 
   585 local
   586   fun mk_Un_upper' 0 = subset_refl
   587     | mk_Un_upper' 1 = @{thm Un_upper1}
   588     | mk_Un_upper' k = Library.foldr (op RS o swap)
   589       (replicate (k - 1) @{thm subset_trans[OF Un_upper1]}, @{thm Un_upper1});
   590 in
   591   fun mk_Un_upper 1 1 = subset_refl
   592     | mk_Un_upper n 1 = mk_Un_upper' (n - 2) RS @{thm subset_trans[OF Un_upper1]}
   593     | mk_Un_upper n m = mk_Un_upper' (n - m) RS @{thm subset_trans[OF Un_upper2]};
   594 end;
   595 
   596 local
   597   fun mk_UnIN' 0 = @{thm UnI2}
   598     | mk_UnIN' m = mk_UnIN' (m - 1) RS @{thm UnI1};
   599 in
   600   fun mk_UnIN 1 1 = @{thm TrueE[OF TrueI]}
   601     | mk_UnIN n 1 = Library.foldr1 (op RS o swap) (replicate (n - 1) @{thm UnI1})
   602     | mk_UnIN n m = mk_UnIN' (n - m)
   603 end;
   604 
   605 fun splice xs ys = flat (map2 (fn x => fn y => [x, y]) xs ys);
   606 
   607 fun transpose [] = []
   608   | transpose ([] :: xss) = transpose xss
   609   | transpose xss = map hd xss :: transpose (map tl xss);
   610 
   611 fun seq_conds f n k xs =
   612   if k = n then
   613     map (f false) (take (k - 1) xs)
   614   else
   615     let val (negs, pos) = split_last (take k xs) in
   616       map (f false) negs @ [f true pos]
   617     end;
   618 
   619 fun mk_unabs_def n = funpow n (fn thm => thm RS fun_cong);
   620 
   621 fun is_triv_implies thm =
   622   op aconv (Logic.dest_implies (Thm.prop_of thm))
   623   handle TERM _ => false;
   624 
   625 fun is_refl_prop t =
   626   op aconv (HOLogic.dest_eq (HOLogic.dest_Trueprop t))
   627   handle TERM _ => false;
   628 
   629 val is_refl = is_refl_prop o Thm.prop_of;
   630 val is_concl_refl = is_refl_prop o Logic.strip_imp_concl o Thm.prop_of;
   631 
   632 val no_refl = filter_out is_refl;
   633 val no_reflexive = filter_out Thm.is_reflexive;
   634 
   635 fun cterm_instantiate_pos cts thm =
   636   let
   637     val cert = Thm.cterm_of (Thm.theory_of_thm thm);
   638     val vars = Term.add_vars (prop_of thm) [];
   639     val vars' = rev (drop (length vars - length cts) vars);
   640     val ps = map_filter (fn (_, NONE) => NONE
   641       | (var, SOME ct) => SOME (cert (Var var), ct)) (vars' ~~ cts);
   642   in
   643     Drule.cterm_instantiate ps thm
   644   end;
   645 
   646 fun fold_thms ctxt thms = Local_Defs.fold ctxt (distinct Thm.eq_thm_prop thms);
   647 fun unfold_thms ctxt thms = Local_Defs.unfold ctxt (distinct Thm.eq_thm_prop thms);
   648 
   649 end;