src/HOL/Tools/datatype_prop.ML
author nipkow
Thu Oct 12 18:38:23 2000 +0200 (2000-10-12)
changeset 10212 33fe2d701ddd
parent 9739 8470c4662685
child 10214 77349ed89f45
permissions -rw-r--r--
*** empty log message ***
     1 (*  Title:      HOL/Tools/datatype_prop.ML
     2     ID:         $Id$
     3     Author:     Stefan Berghofer
     4     Copyright   1998  TU Muenchen
     5 
     6 Characteristic properties of datatypes
     7 *)
     8 
     9 signature DATATYPE_PROP =
    10 sig
    11   val dtK : int ref
    12   val indexify_names: string list -> string list
    13   val make_injs : (int * (string * DatatypeAux.dtyp list *
    14     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    15       term list list
    16   val make_ind : (int * (string * DatatypeAux.dtyp list *
    17     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list -> term
    18   val make_casedists : (int * (string * DatatypeAux.dtyp list *
    19     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list -> term list
    20   val make_primrecs : string list -> (int * (string * DatatypeAux.dtyp list *
    21     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    22       theory -> term list
    23   val make_cases : string list -> (int * (string * DatatypeAux.dtyp list *
    24     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    25       theory -> term list list
    26   val make_distincts : string list -> (int * (string * DatatypeAux.dtyp list *
    27     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    28       theory -> term list list
    29   val make_splits : string list -> (int * (string * DatatypeAux.dtyp list *
    30     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    31       theory -> (term * term) list
    32   val make_case_trrules : string list -> (int * (string * DatatypeAux.dtyp list *
    33     (string * DatatypeAux.dtyp list) list)) list list -> ast Syntax.trrule list
    34   val make_size : (int * (string * DatatypeAux.dtyp list *
    35     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    36       theory -> term list
    37   val make_weak_case_congs : string list -> (int * (string * DatatypeAux.dtyp list *
    38     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    39       theory -> term list
    40   val make_case_congs : string list -> (int * (string * DatatypeAux.dtyp list *
    41     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list ->
    42       theory -> term list
    43   val make_nchotomys : (int * (string * DatatypeAux.dtyp list *
    44     (string * DatatypeAux.dtyp list) list)) list list -> (string * sort) list -> term list
    45 end;
    46 
    47 structure DatatypeProp : DATATYPE_PROP =
    48 struct
    49 
    50 open DatatypeAux;
    51 
    52 (*the kind of distinctiveness axioms depends on number of constructors*)
    53 val dtK = ref 7;
    54 
    55 fun indexify_names names =
    56   let
    57     fun index (x :: xs) tab =
    58       (case assoc (tab, x) of
    59         None => if x mem xs then (x ^ "1") :: index xs ((x, 2) :: tab) else x :: index xs tab
    60       | Some i => (x ^ Library.string_of_int i) :: index xs ((x, i + 1) :: tab))
    61     | index [] _ = [];
    62   in index names [] end;
    63 
    64 fun make_tnames Ts =
    65   let
    66     fun type_name (TFree (name, _)) = implode (tl (explode name))
    67       | type_name (Type (name, _)) = 
    68           let val name' = Sign.base_name name
    69           in if Syntax.is_identifier name' then name' else "x" end;
    70   in indexify_names (map type_name Ts) end;
    71 
    72 
    73 
    74 (************************* injectivity of constructors ************************)
    75 
    76 fun make_injs descr sorts =
    77   let
    78     val descr' = flat descr;
    79 
    80     fun make_inj T ((cname, cargs), injs) =
    81       if null cargs then injs else
    82         let
    83           val Ts = map (typ_of_dtyp descr' sorts) cargs;
    84           val constr_t = Const (cname, Ts ---> T);
    85           val tnames = make_tnames Ts;
    86           val frees = map Free (tnames ~~ Ts);
    87           val frees' = map Free ((map ((op ^) o (rpair "'")) tnames) ~~ Ts);
    88         in (HOLogic.mk_Trueprop (HOLogic.mk_eq
    89           (HOLogic.mk_eq (list_comb (constr_t, frees), list_comb (constr_t, frees')),
    90            foldr1 (HOLogic.mk_binop "op &")
    91              (map HOLogic.mk_eq (frees ~~ frees')))))::injs
    92         end;
    93 
    94   in map (fn (d, T) => foldr (make_inj T) (#3 (snd d), []))
    95     ((hd descr) ~~ take (length (hd descr), get_rec_types descr' sorts))
    96   end;
    97 
    98 (********************************* induction **********************************)
    99 
   100 fun make_ind descr sorts =
   101   let
   102     val descr' = flat descr;
   103     val recTs = get_rec_types descr' sorts;
   104     val pnames = if length descr' = 1 then ["P"]
   105       else map (fn i => "P" ^ string_of_int i) (1 upto length descr');
   106 
   107     fun make_pred i T =
   108       let val T' = T --> HOLogic.boolT
   109       in Free (nth_elem (i, pnames), T') end;
   110 
   111     fun make_ind_prem k T (cname, cargs) =
   112       let
   113         fun mk_prem ((DtRec k, s), T) = HOLogic.mk_Trueprop
   114               (make_pred k T $ Free (s, T))
   115           | mk_prem ((DtType ("fun", [_, DtRec k]), s), T' as Type ("fun", [T, U])) =
   116               HOLogic.mk_Trueprop (HOLogic.all_const T $
   117                 Abs ("x", T, make_pred k U $ (Free (s, T') $ Bound 0)));
   118 
   119         val recs = filter is_rec_type cargs;
   120         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   121         val recTs' = map (typ_of_dtyp descr' sorts) recs;
   122         val tnames = variantlist (make_tnames Ts, pnames);
   123         val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs));
   124         val frees = tnames ~~ Ts;
   125         val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs');
   126 
   127       in list_all_free (frees, Logic.list_implies (prems,
   128         HOLogic.mk_Trueprop (make_pred k T $ 
   129           list_comb (Const (cname, Ts ---> T), map Free frees))))
   130       end;
   131 
   132     val prems = flat (map (fn ((i, (_, _, constrs)), T) =>
   133       map (make_ind_prem i T) constrs) (descr' ~~ recTs));
   134     val tnames = make_tnames recTs;
   135     val concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop "op &")
   136       (map (fn (((i, _), T), tname) => make_pred i T $ Free (tname, T))
   137         (descr' ~~ recTs ~~ tnames)))
   138 
   139   in Logic.list_implies (prems, concl) end;
   140 
   141 (******************************* case distinction *****************************)
   142 
   143 fun make_casedists descr sorts =
   144   let
   145     val descr' = flat descr;
   146 
   147     fun make_casedist_prem T (cname, cargs) =
   148       let
   149         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   150         val frees = variantlist (make_tnames Ts, ["P", "y"]) ~~ Ts;
   151         val free_ts = map Free frees
   152       in list_all_free (frees, Logic.mk_implies (HOLogic.mk_Trueprop
   153         (HOLogic.mk_eq (Free ("y", T), list_comb (Const (cname, Ts ---> T), free_ts))),
   154           HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT))))
   155       end;
   156 
   157     fun make_casedist ((_, (_, _, constrs)), T) =
   158       let val prems = map (make_casedist_prem T) constrs
   159       in Logic.list_implies (prems, HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT)))
   160       end
   161 
   162   in map make_casedist
   163     ((hd descr) ~~ take (length (hd descr), get_rec_types descr' sorts))
   164   end;
   165 
   166 (*************** characteristic equations for primrec combinator **************)
   167 
   168 fun make_primrecs new_type_names descr sorts thy =
   169   let
   170     val o_name = Sign.intern_const (sign_of Fun.thy) "op o";
   171 
   172     val sign = Theory.sign_of thy;
   173 
   174     val descr' = flat descr;
   175     val recTs = get_rec_types descr' sorts;
   176     val used = foldr add_typ_tfree_names (recTs, []);
   177 
   178     val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
   179       replicate (length descr') HOLogic.termS);
   180 
   181     val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
   182       map (fn (_, cargs) =>
   183         let
   184           val Ts = map (typ_of_dtyp descr' sorts) cargs;
   185           val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
   186 
   187           fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
   188             | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
   189                T --> nth_elem (k, rec_result_Ts);
   190 
   191           val argTs = Ts @ map mk_argT recs
   192         in argTs ---> nth_elem (i, rec_result_Ts)
   193         end) constrs) descr');
   194 
   195     val rec_fns = map (uncurry (mk_Free "f"))
   196       (reccomb_fn_Ts ~~ (1 upto (length reccomb_fn_Ts)));
   197 
   198     val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
   199     val reccomb_names = map (Sign.intern_const sign)
   200       (if length descr' = 1 then [big_reccomb_name] else
   201         (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
   202           (1 upto (length descr'))));
   203     val reccombs = map (fn ((name, T), T') => list_comb
   204       (Const (name, reccomb_fn_Ts @ [T] ---> T'), rec_fns))
   205         (reccomb_names ~~ recTs ~~ rec_result_Ts);
   206 
   207     fun make_primrec T comb_t ((ts, f::fs), (cname, cargs)) =
   208       let
   209         val recs = filter is_rec_type cargs;
   210         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   211         val recTs' = map (typ_of_dtyp descr' sorts) recs;
   212         val tnames = make_tnames Ts;
   213         val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs));
   214         val frees = map Free (tnames ~~ Ts);
   215         val frees' = map Free (rec_tnames ~~ recTs');
   216 
   217         fun mk_reccomb (DtRec i, _) = nth_elem (i, reccombs)
   218           | mk_reccomb (DtType ("fun", [_, DtRec i]), Type ("fun", [T, U])) =
   219               let val T' = nth_elem (i, rec_result_Ts)
   220               in Const (o_name, [U --> T', T --> U, T] ---> T') $ nth_elem (i, reccombs)
   221               end;
   222 
   223         val reccombs' = map mk_reccomb (recs ~~ recTs')
   224 
   225       in (ts @ [HOLogic.mk_Trueprop (HOLogic.mk_eq
   226         (comb_t $ list_comb (Const (cname, Ts ---> T), frees),
   227          list_comb (f, frees @ (map (op $) (reccombs' ~~ frees')))))], fs)
   228       end
   229 
   230   in fst (foldl (fn (x, ((dt, T), comb_t)) =>
   231     foldl (make_primrec T comb_t) (x, #3 (snd dt)))
   232       (([], rec_fns), descr' ~~ recTs ~~ reccombs))
   233   end;
   234 
   235 (****************** make terms of form  t_case f1 ... fn  *********************)
   236 
   237 fun make_case_combs new_type_names descr sorts thy fname =
   238   let
   239     val descr' = flat descr;
   240     val recTs = get_rec_types descr' sorts;
   241     val used = foldr add_typ_tfree_names (recTs, []);
   242     val newTs = take (length (hd descr), recTs);
   243     val T' = TFree (variant used "'t", HOLogic.termS);
   244 
   245     val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
   246       map (fn (_, cargs) =>
   247         let val Ts = map (typ_of_dtyp descr' sorts) cargs
   248         in Ts ---> T' end) constrs) (hd descr);
   249 
   250     val case_names = map (fn s =>
   251       Sign.intern_const (Theory.sign_of thy) (s ^ "_case")) new_type_names
   252   in
   253     map (fn ((name, Ts), T) => list_comb
   254       (Const (name, Ts @ [T] ---> T'),
   255         map (uncurry (mk_Free fname)) (Ts ~~ (1 upto length Ts))))
   256           (case_names ~~ case_fn_Ts ~~ newTs)
   257   end;
   258 
   259 (**************** characteristic equations for case combinator ****************)
   260 
   261 fun make_cases new_type_names descr sorts thy =
   262   let
   263     val descr' = flat descr;
   264     val recTs = get_rec_types descr' sorts;
   265     val newTs = take (length (hd descr), recTs);
   266 
   267     fun make_case T comb_t ((cname, cargs), f) =
   268       let
   269         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   270         val frees = map Free ((make_tnames Ts) ~~ Ts)
   271       in HOLogic.mk_Trueprop (HOLogic.mk_eq
   272         (comb_t $ list_comb (Const (cname, Ts ---> T), frees),
   273          list_comb (f, frees)))
   274       end
   275 
   276   in map (fn (((_, (_, _, constrs)), T), comb_t) =>
   277     map (make_case T comb_t) (constrs ~~ (snd (strip_comb comb_t))))
   278       ((hd descr) ~~ newTs ~~ (make_case_combs new_type_names descr sorts thy "f"))
   279   end;
   280 
   281 (************************* distinctness of constructors ***********************)
   282 
   283 fun make_distincts new_type_names descr sorts thy =
   284   let
   285     val descr' = flat descr;
   286     val recTs = get_rec_types descr' sorts;
   287     val newTs = take (length (hd descr), recTs);
   288 
   289     (**** number of constructors < dtK : C_i ... ~= C_j ... ****)
   290 
   291     fun make_distincts_1 _ [] = []
   292       | make_distincts_1 T ((cname, cargs)::constrs) =
   293           let
   294             val Ts = map (typ_of_dtyp descr' sorts) cargs;
   295             val frees = map Free ((make_tnames Ts) ~~ Ts);
   296             val t = list_comb (Const (cname, Ts ---> T), frees);
   297 
   298             fun make_distincts' [] = []
   299               | make_distincts' ((cname', cargs')::constrs') =
   300                   let
   301                     val Ts' = map (typ_of_dtyp descr' sorts) cargs';
   302                     val frees' = map Free ((map ((op ^) o (rpair "'"))
   303                       (make_tnames Ts')) ~~ Ts');
   304                     val t' = list_comb (Const (cname', Ts' ---> T), frees')
   305                   in
   306                     (HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t, t')))::
   307                     (HOLogic.mk_Trueprop (HOLogic.Not $ HOLogic.mk_eq (t', t)))::
   308                       (make_distincts' constrs')
   309                   end
   310 
   311           in (make_distincts' constrs) @ (make_distincts_1 T constrs)
   312           end;
   313 
   314   in map (fn (((_, (_, _, constrs)), T), tname) =>
   315       if length constrs < !dtK then make_distincts_1 T constrs else [])
   316         ((hd descr) ~~ newTs ~~ new_type_names)
   317   end;
   318 
   319 
   320 (*************************** the "split" - equations **************************)
   321 
   322 fun make_splits new_type_names descr sorts thy =
   323   let
   324     val descr' = flat descr;
   325     val recTs = get_rec_types descr' sorts;
   326     val used' = foldr add_typ_tfree_names (recTs, []);
   327     val newTs = take (length (hd descr), recTs);
   328     val T' = TFree (variant used' "'t", HOLogic.termS);
   329     val P = Free ("P", T' --> HOLogic.boolT);
   330 
   331     fun make_split (((_, (_, _, constrs)), T), comb_t) =
   332       let
   333         val (_, fs) = strip_comb comb_t;
   334         val used = ["P", "x"] @ (map (fst o dest_Free) fs);
   335 
   336         fun process_constr (((cname, cargs), f), (t1s, t2s)) =
   337           let
   338             val Ts = map (typ_of_dtyp descr' sorts) cargs;
   339             val frees = map Free (variantlist (make_tnames Ts, used) ~~ Ts);
   340             val eqn = HOLogic.mk_eq (Free ("x", T),
   341               list_comb (Const (cname, Ts ---> T), frees));
   342             val P' = P $ list_comb (f, frees)
   343           in ((foldr (fn (Free (s, T), t) => HOLogic.mk_all (s, T, t))
   344                 (frees, HOLogic.imp $ eqn $ P'))::t1s,
   345               (foldr (fn (Free (s, T), t) => HOLogic.mk_exists (s, T, t))
   346                 (frees, HOLogic.conj $ eqn $ (HOLogic.Not $ P')))::t2s)
   347           end;
   348 
   349         val (t1s, t2s) = foldr process_constr (constrs ~~ fs, ([], []));
   350         val lhs = P $ (comb_t $ Free ("x", T))
   351       in
   352         (HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, mk_conj t1s)),
   353          HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, HOLogic.Not $ mk_disj t2s)))
   354       end
   355 
   356   in map make_split ((hd descr) ~~ newTs ~~
   357     (make_case_combs new_type_names descr sorts thy "f"))
   358   end;
   359 
   360 (************************ translation rules for case **************************)
   361 
   362 fun make_case_trrules new_type_names descr =
   363   let
   364     fun mk_asts i j ((cname, cargs)::constrs) =
   365       let
   366         val k = length cargs;
   367         val xs = map (fn i => Variable ("x" ^ string_of_int i)) (i upto i + k - 1);
   368         val t = Variable ("t" ^ string_of_int j);
   369         val ast = Syntax.mk_appl (Constant "_case1")
   370           [Syntax.mk_appl (Constant (Sign.base_name cname)) xs, t];
   371         val ast' = foldr (fn (x, y) =>
   372           Syntax.mk_appl (Constant "_abs") [x, y]) (xs, t)
   373       in
   374         (case constrs of
   375             [] => (ast, [ast'])
   376           | cs => let val (ast'', asts) = mk_asts (i + k) (j + 1) cs
   377               in (Syntax.mk_appl (Constant "_case2") [ast, ast''],
   378                   ast'::asts)
   379               end)
   380       end;
   381 
   382     fun mk_trrule ((_, (_, _, constrs)), tname) =
   383       let val (ast, asts) = mk_asts 1 1 constrs
   384       in Syntax.ParsePrintRule
   385         (Syntax.mk_appl (Constant "_case_syntax") [Variable "t", ast],
   386          Syntax.mk_appl (Constant (tname ^ "_case"))
   387            (asts @ [Variable "t"]))
   388       end
   389 
   390   in
   391     map mk_trrule (hd descr ~~ new_type_names)
   392   end;
   393 
   394 (******************************* size functions *******************************)
   395 
   396 fun make_size descr sorts thy =
   397   let
   398     val descr' = flat descr;
   399     val recTs = get_rec_types descr' sorts;
   400 
   401     val size_name = Sign.intern_const (Theory.sign_of (theory "Arithmetic")) "size";
   402     val size_names = replicate (length (hd descr)) size_name @
   403       map (Sign.intern_const (Theory.sign_of thy)) (indexify_names
   404         (map (fn T => name_of_typ T ^ "_size") (drop (length (hd descr), recTs))));
   405     val size_consts = map (fn (s, T) =>
   406       Const (s, T --> HOLogic.natT)) (size_names ~~ recTs);
   407 
   408     fun plus (t1, t2) = Const ("op +", [HOLogic.natT, HOLogic.natT] ---> HOLogic.natT) $ t1 $ t2;
   409 
   410     fun make_size_eqn size_const T (cname, cargs) =
   411       let
   412         val recs = filter is_rec_type cargs;
   413         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   414         val recTs = map (typ_of_dtyp descr' sorts) recs;
   415         val tnames = make_tnames Ts;
   416         val rec_tnames = map fst (filter (is_rec_type o snd) (tnames ~~ cargs));
   417         val ts = map (fn ((r, s), T) => nth_elem (dest_DtRec r, size_consts) $
   418           Free (s, T)) (recs ~~ rec_tnames ~~ recTs);
   419         val t = if ts = [] then HOLogic.zero else
   420           foldl1 plus (ts @ [HOLogic.mk_nat 1])
   421       in
   422         HOLogic.mk_Trueprop (HOLogic.mk_eq (size_const $
   423           list_comb (Const (cname, Ts ---> T), map Free (tnames ~~ Ts)), t))
   424       end
   425 
   426   in
   427     flat (map (fn (((_, (_, _, constrs)), size_const), T) =>
   428       map (make_size_eqn size_const T) constrs) (descr' ~~ size_consts ~~ recTs))
   429   end;
   430 
   431 (************************* additional rules for TFL ***************************)
   432 
   433 fun make_weak_case_congs new_type_names descr sorts thy =
   434   let
   435     val case_combs = make_case_combs new_type_names descr sorts thy "f";
   436 
   437     fun mk_case_cong comb =
   438       let 
   439         val Type ("fun", [T, _]) = fastype_of comb;
   440         val M = Free ("M", T);
   441         val M' = Free ("M'", T);
   442       in
   443         Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')),
   444           HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb $ M')))
   445       end
   446   in
   447     map mk_case_cong case_combs
   448   end;
   449  
   450 
   451 (*---------------------------------------------------------------------------
   452  * Structure of case congruence theorem looks like this:
   453  *
   454  *    (M = M') 
   455  *    ==> (!!x1,...,xk. (M' = C1 x1..xk) ==> (f1 x1..xk = g1 x1..xk)) 
   456  *    ==> ... 
   457  *    ==> (!!x1,...,xj. (M' = Cn x1..xj) ==> (fn x1..xj = gn x1..xj)) 
   458  *    ==>
   459  *      (ty_case f1..fn M = ty_case g1..gn M')
   460  *---------------------------------------------------------------------------*)
   461 
   462 fun make_case_congs new_type_names descr sorts thy =
   463   let
   464     val case_combs = make_case_combs new_type_names descr sorts thy "f";
   465     val case_combs' = make_case_combs new_type_names descr sorts thy "g";
   466 
   467     fun mk_case_cong ((comb, comb'), (_, (_, _, constrs))) =
   468       let
   469         val Type ("fun", [T, _]) = fastype_of comb;
   470         val (_, fs) = strip_comb comb;
   471         val (_, gs) = strip_comb comb';
   472         val used = ["M", "M'"] @ map (fst o dest_Free) (fs @ gs);
   473         val M = Free ("M", T);
   474         val M' = Free ("M'", T);
   475 
   476         fun mk_clause ((f, g), (cname, _)) =
   477           let
   478             val (Ts, _) = strip_type (fastype_of f);
   479             val tnames = variantlist (make_tnames Ts, used);
   480             val frees = map Free (tnames ~~ Ts)
   481           in
   482             list_all_free (tnames ~~ Ts, Logic.mk_implies
   483               (HOLogic.mk_Trueprop
   484                 (HOLogic.mk_eq (M', list_comb (Const (cname, Ts ---> T), frees))),
   485                HOLogic.mk_Trueprop
   486                 (HOLogic.mk_eq (list_comb (f, frees), list_comb (g, frees)))))
   487           end
   488 
   489       in
   490         Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (M, M')) ::
   491           map mk_clause (fs ~~ gs ~~ constrs),
   492             HOLogic.mk_Trueprop (HOLogic.mk_eq (comb $ M, comb' $ M')))
   493       end
   494 
   495   in
   496     map mk_case_cong (case_combs ~~ case_combs' ~~ hd descr)
   497   end;
   498 
   499 (*---------------------------------------------------------------------------
   500  * Structure of exhaustion theorem looks like this:
   501  *
   502  *    !v. (? y1..yi. v = C1 y1..yi) | ... | (? y1..yj. v = Cn y1..yj)
   503  *---------------------------------------------------------------------------*)
   504 
   505 fun make_nchotomys descr sorts =
   506   let
   507     val descr' = flat descr;
   508     val recTs = get_rec_types descr' sorts;
   509     val newTs = take (length (hd descr), recTs);
   510 
   511     fun mk_eqn T (cname, cargs) =
   512       let
   513         val Ts = map (typ_of_dtyp descr' sorts) cargs;
   514         val tnames = variantlist (make_tnames Ts, ["v"]);
   515         val frees = tnames ~~ Ts
   516       in
   517         foldr (fn ((s, T'), t) => HOLogic.mk_exists (s, T', t))
   518           (frees, HOLogic.mk_eq (Free ("v", T),
   519             list_comb (Const (cname, Ts ---> T), map Free frees)))
   520       end
   521 
   522   in map (fn ((_, (_, _, constrs)), T) =>
   523     HOLogic.mk_Trueprop (HOLogic.mk_all ("v", T, mk_disj (map (mk_eqn T) constrs))))
   524       (hd descr ~~ newTs)
   525   end;
   526 
   527 end;