src/HOL/BNF/Tools/bnf_ctr_sugar.ML
author blanchet
Thu Sep 26 13:42:13 2013 +0200 (2013-09-26)
changeset 53916 37c31a619eee
parent 53908 54afdc258272
child 53917 bf74357f91f8
permissions -rw-r--r--
generate "sel_exhaust" theorem
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(*  Title:      HOL/BNF/Tools/bnf_ctr_sugar.ML
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    Author:     Jasmin Blanchette, TU Muenchen
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    Copyright   2012
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Wrapping existing freely generated type's constructors.
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*)
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signature BNF_CTR_SUGAR =
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sig
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  type ctr_sugar =
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    {ctrs: term list,
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     casex: term,
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     discs: term list,
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     selss: term list list,
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     exhaust: thm,
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     nchotomy: thm,
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     injects: thm list,
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     distincts: thm list,
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     case_thms: thm list,
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     case_cong: thm,
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     weak_case_cong: thm,
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     split: thm,
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     split_asm: thm,
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     disc_thmss: thm list list,
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     discIs: thm list,
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     sel_thmss: thm list list,
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     disc_exhausts: thm list,
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     sel_exhausts: thm list,
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     collapses: thm list,
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     expands: thm list,
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     case_conv_ifs: thm list};
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  val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
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  val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
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  val ctr_sugars_of: Proof.context -> ctr_sugar list
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  val rep_compat_prefix: string
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  val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
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  val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
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  val mk_ctr: typ list -> term -> term
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  val mk_case: typ list -> typ -> term -> term
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  val mk_disc_or_sel: typ list -> term -> term
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  val name_of_ctr: term -> string
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  val name_of_disc: term -> string
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  val dest_ctr: Proof.context -> string -> term -> term * term list
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  val dest_case: Proof.context -> string -> typ list -> term -> (term list * term list) option
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  val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
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    (((bool * bool) * term list) * binding) *
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      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
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    ctr_sugar * local_theory
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  val parse_wrap_free_constructors_options: (bool * bool) parser
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  val parse_bound_term: (binding * string) parser
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end;
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structure BNF_Ctr_Sugar : BNF_CTR_SUGAR =
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struct
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open BNF_Util
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open BNF_Ctr_Sugar_Tactics
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type ctr_sugar =
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  {ctrs: term list,
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   casex: term,
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   discs: term list,
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   selss: term list list,
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   exhaust: thm,
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   nchotomy: thm,
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   injects: thm list,
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   distincts: thm list,
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   case_thms: thm list,
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   case_cong: thm,
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   weak_case_cong: thm,
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   split: thm,
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   split_asm: thm,
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   disc_thmss: thm list list,
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   discIs: thm list,
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   sel_thmss: thm list list,
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   disc_exhausts: thm list,
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   sel_exhausts: thm list,
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   collapses: thm list,
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   expands: thm list,
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   case_conv_ifs: thm list};
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fun eq_ctr_sugar ({ctrs = ctrs1, casex = case1, discs = discs1, selss = selss1, ...} : ctr_sugar,
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    {ctrs = ctrs2, casex = case2, discs = discs2, selss = selss2, ...} : ctr_sugar) =
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  ctrs1 = ctrs2 andalso case1 = case2 andalso discs1 = discs2 andalso selss1 = selss2;
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fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
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    case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
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    disc_exhausts, sel_exhausts, collapses, expands, case_conv_ifs} =
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  {ctrs = map (Morphism.term phi) ctrs,
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   casex = Morphism.term phi casex,
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   discs = map (Morphism.term phi) discs,
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   selss = map (map (Morphism.term phi)) selss,
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   exhaust = Morphism.thm phi exhaust,
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   nchotomy = Morphism.thm phi nchotomy,
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   injects = map (Morphism.thm phi) injects,
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   distincts = map (Morphism.thm phi) distincts,
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   case_thms = map (Morphism.thm phi) case_thms,
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   case_cong = Morphism.thm phi case_cong,
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   weak_case_cong = Morphism.thm phi weak_case_cong,
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   split = Morphism.thm phi split,
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   split_asm = Morphism.thm phi split_asm,
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   disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
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   discIs = map (Morphism.thm phi) discIs,
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   sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
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   disc_exhausts = map (Morphism.thm phi) disc_exhausts,
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   sel_exhausts = map (Morphism.thm phi) sel_exhausts,
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   collapses = map (Morphism.thm phi) collapses,
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   expands = map (Morphism.thm phi) expands,
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   case_conv_ifs = map (Morphism.thm phi) case_conv_ifs};
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val transfer_ctr_sugar =
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  morph_ctr_sugar o Morphism.thm_morphism o Thm.transfer o Proof_Context.theory_of;
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structure Data = Generic_Data
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(
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  type T = ctr_sugar Symtab.table;
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  val empty = Symtab.empty;
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  val extend = I;
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  val merge = Symtab.merge eq_ctr_sugar;
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);
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fun ctr_sugar_of ctxt =
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  Symtab.lookup (Data.get (Context.Proof ctxt))
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  #> Option.map (transfer_ctr_sugar ctxt);
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fun ctr_sugars_of ctxt =
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  Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
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fun register_ctr_sugar key ctr_sugar =
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  Local_Theory.declaration {syntax = false, pervasive = true}
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    (fn phi => Data.map (Symtab.default (key, morph_ctr_sugar phi ctr_sugar)));
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val rep_compat_prefix = "new";
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val isN = "is_";
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val unN = "un_";
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fun mk_unN 1 1 suf = unN ^ suf
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  | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
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val caseN = "case";
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val case_congN = "case_cong";
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val case_conv_ifN = "case_conv_if";
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val collapseN = "collapse";
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val disc_excludeN = "disc_exclude";
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val disc_exhaustN = "disc_exhaust";
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val discN = "disc";
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val discIN = "discI";
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val distinctN = "distinct";
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val exhaustN = "exhaust";
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val expandN = "expand";
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val injectN = "inject";
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val nchotomyN = "nchotomy";
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val selN = "sel";
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val sel_exhaustN = "sel_exhaust";
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val splitN = "split";
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val splitsN = "splits";
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val split_asmN = "split_asm";
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val weak_case_cong_thmsN = "weak_case_cong";
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val cong_attrs = @{attributes [cong]};
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val dest_attrs = @{attributes [dest]};
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val safe_elim_attrs = @{attributes [elim!]};
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val iff_attrs = @{attributes [iff]};
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val induct_simp_attrs = @{attributes [induct_simp]};
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val nitpick_attrs = @{attributes [nitpick_simp]};
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val simp_attrs = @{attributes [simp]};
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val code_nitpick_simp_simp_attrs = Code.add_default_eqn_attrib :: nitpick_attrs @ simp_attrs;
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fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
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fun mk_half_pairss' _ ([], []) = []
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  | mk_half_pairss' indent (x :: xs, _ :: ys) =
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    indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
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fun mk_half_pairss p = mk_half_pairss' [[]] p;
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fun join_halves n half_xss other_half_xss =
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  let
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    val xsss =
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      map2 (map2 append) (Library.chop_groups n half_xss)
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        (transpose (Library.chop_groups n other_half_xss))
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    val xs = splice (flat half_xss) (flat other_half_xss);
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  in (xs, xsss) end;
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fun mk_undefined T = Const (@{const_name undefined}, T);
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fun mk_ctr Ts t =
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  let val Type (_, Ts0) = body_type (fastype_of t) in
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    Term.subst_atomic_types (Ts0 ~~ Ts) t
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  end;
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fun mk_case Ts T t =
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  let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
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    Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
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  end;
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fun mk_disc_or_sel Ts t =
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  Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
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fun name_of_const what t =
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  (case head_of t of
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    Const (s, _) => s
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  | Free (s, _) => s
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  | _ => error ("Cannot extract name of " ^ what));
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val name_of_ctr = name_of_const "constructor";
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val notN = "not_";
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val eqN = "eq_";
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val neqN = "neq_";
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fun name_of_disc t =
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  (case head_of t of
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    Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
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    Long_Name.map_base_name (prefix notN) (name_of_disc t')
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  | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
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    Long_Name.map_base_name (prefix eqN) (name_of_disc t')
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  | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
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    Long_Name.map_base_name (prefix neqN) (name_of_disc t')
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  | t' => name_of_const "destructor" t');
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val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
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fun dest_ctr ctxt s t =
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  let
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    val (f, args) = Term.strip_comb t;
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  in
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    (case ctr_sugar_of ctxt s of
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      SOME {ctrs, ...} =>
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      (case find_first (can (fo_match ctxt f)) ctrs of
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        SOME f' => (f', args)
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      | NONE => raise Fail "dest_ctr")
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    | NONE => raise Fail "dest_ctr")
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  end;
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fun dest_case ctxt s Ts t =
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  (case Term.strip_comb t of
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    (Const (c, _), args as _ :: _) =>
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    (case ctr_sugar_of ctxt s of
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      SOME {casex = Const (case_name, _), discs = discs0, selss = selss0, ...} =>
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      if case_name = c then
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        let
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          val n = length discs0;
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          val (branches, obj :: leftovers) = chop n args;
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          val discs = map (mk_disc_or_sel Ts) discs0;
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          val selss = map (map (mk_disc_or_sel Ts)) selss0;
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          val conds = map (rapp obj) discs;
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          val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
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          val branches' = map2 (curry Term.betapplys) branches branch_argss;
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        in
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          SOME (conds, branches')
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        end
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      else
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        NONE
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    | _ => NONE)
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  | _ => NONE);
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fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
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fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, rep_compat), raw_ctrs),
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    raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
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  let
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    (* TODO: sanity checks on arguments *)
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    val n = length raw_ctrs;
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    val ks = 1 upto n;
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    val _ = if n > 0 then () else error "No constructors specified";
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    val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
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    val sel_defaultss =
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      pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
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    val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
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    val fc_b_name = Long_Name.base_name fcT_name;
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    val fc_b = Binding.name fc_b_name;
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    fun qualify mandatory =
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      Binding.qualify mandatory fc_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
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    fun dest_TFree_or_TVar (TFree p) = p
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      | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
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      | dest_TFree_or_TVar _ = error "Invalid type argument";
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    val (unsorted_As, B) =
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      no_defs_lthy
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      |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
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      ||> the_single o fst o mk_TFrees 1;
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    val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
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    val fcT = Type (fcT_name, As);
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    val ctrs = map (mk_ctr As) ctrs0;
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    val ctr_Tss = map (binder_types o fastype_of) ctrs;
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    val ms = map length ctr_Tss;
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    val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
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    fun can_definitely_rely_on_disc k =
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      not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
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    fun can_rely_on_disc k =
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      can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
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    fun should_omit_disc_binding k =
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      n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
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    fun is_disc_binding_valid b =
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      not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
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blanchet@52322
   315
    val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
blanchet@49120
   316
blanchet@49336
   317
    val disc_bindings =
blanchet@49336
   318
      raw_disc_bindings'
blanchet@49120
   319
      |> map4 (fn k => fn m => fn ctr => fn disc =>
blanchet@51790
   320
        qualify false
blanchet@51787
   321
          (if Binding.is_empty disc then
blanchet@51790
   322
             if should_omit_disc_binding k then disc else standard_disc_binding ctr
blanchet@51790
   323
           else if Binding.eq_name (disc, equal_binding) then
blanchet@51790
   324
             if m = 0 then disc
blanchet@51790
   325
             else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
blanchet@51790
   326
           else if Binding.eq_name (disc, standard_binding) then
blanchet@51790
   327
             standard_disc_binding ctr
blanchet@49302
   328
           else
blanchet@51790
   329
             disc)) ks ms ctrs0;
blanchet@49056
   330
blanchet@51787
   331
    fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
blanchet@49120
   332
blanchet@49336
   333
    val sel_bindingss =
blanchet@49336
   334
      pad_list [] n raw_sel_bindingss
blanchet@49056
   335
      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
blanchet@49633
   336
        qualify false
blanchet@51790
   337
          (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
blanchet@51787
   338
            standard_sel_binding m l ctr
blanchet@49302
   339
          else
traytel@49434
   340
            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
blanchet@49020
   341
blanchet@49201
   342
    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
blanchet@49043
   343
blanchet@52968
   344
    val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
blanchet@49364
   345
      mk_Freess' "x" ctr_Tss
blanchet@49025
   346
      ||>> mk_Freess "y" ctr_Tss
blanchet@49201
   347
      ||>> mk_Frees "f" case_Ts
blanchet@49201
   348
      ||>> mk_Frees "g" case_Ts
blanchet@53908
   349
      ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
blanchet@52968
   350
      ||>> mk_Frees "z" [B]
blanchet@49043
   351
      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
blanchet@49043
   352
blanchet@49498
   353
    val u = Free u';
blanchet@49498
   354
    val v = Free v';
blanchet@49463
   355
    val q = Free (fst p', mk_pred1T B);
blanchet@49020
   356
blanchet@49025
   357
    val xctrs = map2 (curry Term.list_comb) ctrs xss;
blanchet@49025
   358
    val yctrs = map2 (curry Term.list_comb) ctrs yss;
blanchet@49032
   359
blanchet@49043
   360
    val xfs = map2 (curry Term.list_comb) fs xss;
blanchet@49043
   361
    val xgs = map2 (curry Term.list_comb) gs xss;
blanchet@49043
   362
blanchet@52968
   363
    (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
blanchet@52968
   364
       nicer names). Consider removing. *)
blanchet@52968
   365
    val eta_fs = map2 eta_expand_arg xss xfs;
blanchet@52968
   366
    val eta_gs = map2 eta_expand_arg xss xgs;
blanchet@52968
   367
blanchet@52968
   368
    val case_binding =
blanchet@52968
   369
      qualify false
blanchet@52968
   370
        (if Binding.is_empty raw_case_binding orelse
blanchet@52968
   371
            Binding.eq_name (raw_case_binding, standard_binding) then
blanchet@53908
   372
           Binding.suffix_name ("_" ^ caseN) fc_b
blanchet@52968
   373
         else
blanchet@52968
   374
           raw_case_binding);
blanchet@52968
   375
blanchet@52968
   376
    fun mk_case_disj xctr xf xs =
blanchet@52968
   377
      list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
blanchet@52968
   378
blanchet@52968
   379
    val case_rhs =
blanchet@52968
   380
      fold_rev (fold_rev Term.lambda) [fs, [u]]
blanchet@52968
   381
        (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
blanchet@52968
   382
           Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
blanchet@52968
   383
blanchet@52968
   384
    val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
blanchet@52968
   385
      |> Local_Theory.define ((case_binding, NoSyn), ((Thm.def_binding case_binding, []), case_rhs))
blanchet@52968
   386
      ||> `Local_Theory.restore;
blanchet@52968
   387
blanchet@52968
   388
    val phi = Proof_Context.export_morphism lthy lthy';
blanchet@52968
   389
blanchet@52968
   390
    val case_def = Morphism.thm phi raw_case_def;
blanchet@52968
   391
blanchet@52968
   392
    val case0 = Morphism.term phi raw_case;
blanchet@52968
   393
    val casex = mk_case As B case0;
blanchet@52968
   394
blanchet@51759
   395
    val fcase = Term.list_comb (casex, fs);
blanchet@51759
   396
blanchet@51759
   397
    val ufcase = fcase $ u;
blanchet@51759
   398
    val vfcase = fcase $ v;
blanchet@51759
   399
blanchet@51759
   400
    val eta_fcase = Term.list_comb (casex, eta_fs);
blanchet@51759
   401
    val eta_gcase = Term.list_comb (casex, eta_gs);
blanchet@49020
   402
blanchet@51759
   403
    val eta_ufcase = eta_fcase $ u;
blanchet@51759
   404
    val eta_vgcase = eta_gcase $ v;
blanchet@49486
   405
blanchet@49591
   406
    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
blanchet@49486
   407
blanchet@49591
   408
    val uv_eq = mk_Trueprop_eq (u, v);
blanchet@49486
   409
blanchet@49486
   410
    val exist_xs_u_eq_ctrs =
blanchet@49486
   411
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   412
blanchet@51743
   413
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@51743
   414
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@51743
   415
blanchet@49486
   416
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   417
      HOLogic.mk_not
blanchet@51790
   418
        (let val b = nth disc_bindings (k - 1) in
blanchet@51790
   419
           if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
blanchet@51790
   420
         end);
blanchet@49116
   421
blanchet@53916
   422
    val (all_sels_distinct, discs, selss, udiscs, uselss, usel_ctrs, vdiscs, vselss, disc_defs,
blanchet@53916
   423
         sel_defs, sel_defss, lthy') =
blanchet@52969
   424
      if no_discs_sels then
blanchet@53916
   425
        (true, [], [], [], [], [], [], [], [], [], [], lthy)
blanchet@49278
   426
      else
blanchet@49278
   427
        let
blanchet@53908
   428
          fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
blanchet@49025
   429
blanchet@49486
   430
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@49278
   431
blanchet@49500
   432
          fun alternate_disc k =
blanchet@49500
   433
            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
blanchet@49278
   434
blanchet@49280
   435
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   436
            map2 (fn Ts => fn k =>
blanchet@49280
   437
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   438
                NONE =>
blanchet@49364
   439
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   440
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@52968
   441
                | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
blanchet@49280
   442
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   443
blanchet@49278
   444
          fun sel_spec b proto_sels =
blanchet@49278
   445
            let
blanchet@49278
   446
              val _ =
blanchet@49278
   447
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   448
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   449
                     " for constructor " ^
blanchet@52968
   450
                     quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
blanchet@49278
   451
                 | [] => ())
blanchet@49278
   452
              val T =
blanchet@49278
   453
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   454
                  [T] => T
blanchet@49278
   455
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@52968
   456
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
blanchet@52968
   457
                    ^ quote (Syntax.string_of_typ lthy T')));
blanchet@49278
   458
            in
blanchet@53908
   459
              mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
blanchet@49536
   460
                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   461
            end;
blanchet@49116
   462
blanchet@49336
   463
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   464
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   465
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   466
blanchet@49336
   467
          val sel_binding_index =
blanchet@49336
   468
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   469
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   470
blanchet@49285
   471
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   472
          val sel_infos =
blanchet@49336
   473
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   474
            |> sort (int_ord o pairself fst)
blanchet@49336
   475
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   476
          val sel_bindings = map fst sel_infos;
blanchet@49258
   477
blanchet@49336
   478
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   479
blanchet@49278
   480
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@52968
   481
            lthy
blanchet@51809
   482
            |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
blanchet@51790
   483
                if Binding.is_empty b then
blanchet@51790
   484
                  if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@51790
   485
                  else pair (alternate_disc k, alternate_disc_no_def)
blanchet@51790
   486
                else if Binding.eq_name (b, equal_binding) then
blanchet@51790
   487
                  pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@51790
   488
                else
blanchet@51790
   489
                  Specification.definition (SOME (b, NONE, NoSyn),
blanchet@51790
   490
                    ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@51809
   491
              ks exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   492
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   493
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   494
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   495
            ||> `Local_Theory.restore;
blanchet@49022
   496
blanchet@49278
   497
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   498
blanchet@49278
   499
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   500
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   501
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   502
blanchet@49278
   503
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   504
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   505
blanchet@49278
   506
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   507
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49486
   508
blanchet@49500
   509
          val udiscs = map (rapp u) discs;
blanchet@49500
   510
          val uselss = map (map (rapp u)) selss;
blanchet@53916
   511
          val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
blanchet@49486
   512
blanchet@49500
   513
          val vdiscs = map (rapp v) discs;
blanchet@49500
   514
          val vselss = map (map (rapp v)) selss;
blanchet@49278
   515
        in
blanchet@53916
   516
          (all_sels_distinct, discs, selss, udiscs, uselss, usel_ctrs, vdiscs, vselss, disc_defs,
blanchet@53916
   517
           sel_defs, sel_defss, lthy')
blanchet@49278
   518
        end;
blanchet@49025
   519
blanchet@49032
   520
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   521
blanchet@49458
   522
    val exhaust_goal =
blanchet@49486
   523
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   524
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   525
      end;
blanchet@49019
   526
blanchet@49484
   527
    val inject_goalss =
blanchet@49017
   528
      let
blanchet@49034
   529
        fun mk_goal _ _ [] [] = []
blanchet@49025
   530
          | mk_goal xctr yctr xs ys =
blanchet@49121
   531
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   532
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   533
      in
blanchet@49034
   534
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   535
      end;
blanchet@49017
   536
blanchet@49484
   537
    val half_distinct_goalss =
blanchet@49121
   538
      let
blanchet@49203
   539
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   540
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   541
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   542
      in
blanchet@49585
   543
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   544
      end;
blanchet@49019
   545
blanchet@52968
   546
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
blanchet@49019
   547
blanchet@49019
   548
    fun after_qed thmss lthy =
blanchet@49019
   549
      let
blanchet@52968
   550
        val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
blanchet@49019
   551
blanchet@49438
   552
        val inject_thms = flat inject_thmss;
blanchet@49438
   553
blanchet@53210
   554
        val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   555
blanchet@49486
   556
        fun inst_thm t thm =
blanchet@49486
   557
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@53210
   558
            (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
blanchet@49486
   559
blanchet@49486
   560
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   561
blanchet@49300
   562
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   563
blanchet@49048
   564
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   565
blanchet@49486
   566
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   567
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   568
blanchet@49020
   569
        val nchotomy_thm =
blanchet@49020
   570
          let
blanchet@49020
   571
            val goal =
blanchet@49486
   572
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   573
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   574
          in
wenzelm@51551
   575
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
traytel@49667
   576
            |> Thm.close_derivation
blanchet@49020
   577
          end;
blanchet@49020
   578
blanchet@52968
   579
        val case_thms =
blanchet@52968
   580
          let
blanchet@52968
   581
            val goals =
blanchet@52968
   582
              map3 (fn xctr => fn xf => fn xs =>
blanchet@52968
   583
                fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
blanchet@52968
   584
          in
blanchet@52968
   585
            map4 (fn k => fn goal => fn injects => fn distinctss =>
blanchet@52968
   586
                Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@52968
   587
                  mk_case_tac ctxt n k case_def injects distinctss)
blanchet@52968
   588
                |> Thm.close_derivation)
blanchet@52968
   589
              ks goals inject_thmss distinct_thmsss
blanchet@52968
   590
          end;
blanchet@52968
   591
blanchet@53704
   592
        val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
blanchet@53916
   593
             disc_exclude_thms, disc_exhaust_thms, sel_exhaust_thms, all_collapse_thms,
blanchet@53916
   594
             safe_collapse_thms, expand_thms, case_conv_if_thms) =
blanchet@52969
   595
          if no_discs_sels then
blanchet@53916
   596
            ([], [], [], [], [], [], [], [], [], [], [], [], [])
blanchet@49116
   597
          else
blanchet@49116
   598
            let
blanchet@49364
   599
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   600
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   601
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   602
blanchet@53704
   603
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@53704
   604
blanchet@49281
   605
              fun has_undefined_rhs thm =
blanchet@49281
   606
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   607
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   608
                | _ => false);
blanchet@49281
   609
blanchet@49281
   610
              val all_sel_thms =
blanchet@49285
   611
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   612
                   flat sel_thmss
blanchet@49285
   613
                 else
blanchet@49364
   614
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   615
                     (xss' ~~ case_thms))
blanchet@49285
   616
                |> filter_out has_undefined_rhs;
blanchet@49278
   617
blanchet@49278
   618
              fun mk_unique_disc_def () =
blanchet@49278
   619
                let
blanchet@49278
   620
                  val m = the_single ms;
blanchet@49591
   621
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   622
                in
wenzelm@51551
   623
                  Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49692
   624
                  |> Thm.close_derivation
blanchet@49278
   625
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   626
                end;
blanchet@49278
   627
blanchet@49278
   628
              fun mk_alternate_disc_def k =
blanchet@49278
   629
                let
blanchet@49278
   630
                  val goal =
blanchet@49486
   631
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   632
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   633
                in
wenzelm@51551
   634
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   635
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   636
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49692
   637
                  |> Thm.close_derivation
blanchet@49278
   638
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   639
                end;
blanchet@49028
   640
blanchet@49278
   641
              val has_alternate_disc_def =
blanchet@49278
   642
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   643
blanchet@49278
   644
              val disc_defs' =
blanchet@49278
   645
                map2 (fn k => fn def =>
blanchet@49278
   646
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   647
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   648
                  else def) ks disc_defs;
blanchet@49278
   649
blanchet@49278
   650
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   651
              val discI_thms =
blanchet@49278
   652
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   653
                  disc_defs';
blanchet@49278
   654
              val not_discI_thms =
blanchet@49278
   655
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   656
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   657
                  ms disc_defs';
blanchet@49278
   658
blanchet@49278
   659
              val (disc_thmss', disc_thmss) =
blanchet@49278
   660
                let
blanchet@49278
   661
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   662
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   663
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   664
                in
blanchet@49278
   665
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   666
                end;
blanchet@49278
   667
blanchet@53704
   668
              val nontriv_disc_thms =
blanchet@53704
   669
                flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
blanchet@53704
   670
                  disc_bindings disc_thmss);
blanchet@53704
   671
blanchet@53704
   672
              fun is_discI_boring b =
blanchet@53704
   673
                (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
blanchet@53704
   674
blanchet@53704
   675
              val nontriv_discI_thms =
blanchet@53704
   676
                flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
blanchet@53704
   677
                  discI_thms);
blanchet@49028
   678
blanchet@49486
   679
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   680
                let
blanchet@49486
   681
                  fun mk_goal [] = []
blanchet@49486
   682
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   683
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   684
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   685
traytel@49667
   686
                  fun prove tac goal =
wenzelm@51551
   687
                    Goal.prove_sorry lthy [] [] goal (K tac)
traytel@49667
   688
                    |> Thm.close_derivation;
blanchet@49486
   689
blanchet@49585
   690
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   691
blanchet@49486
   692
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   693
                  val half_thmss =
blanchet@49486
   694
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
wenzelm@51798
   695
                        fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
blanchet@49486
   696
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   697
blanchet@49486
   698
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   699
                  val other_half_thmss =
blanchet@49486
   700
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   701
                      other_half_goalss;
blanchet@49486
   702
                in
blanchet@49585
   703
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   704
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   705
                end;
blanchet@49278
   706
blanchet@49486
   707
              val disc_exhaust_thm =
blanchet@49486
   708
                let
blanchet@49486
   709
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   710
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   711
                in
wenzelm@51551
   712
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@49486
   713
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
traytel@49667
   714
                  |> Thm.close_derivation
blanchet@49486
   715
                end;
blanchet@49028
   716
blanchet@53740
   717
              val (safe_collapse_thms, all_collapse_thms) =
blanchet@49486
   718
                let
blanchet@53916
   719
                  fun mk_goal m ctr udisc usel_ctr =
blanchet@49486
   720
                    let
blanchet@49486
   721
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@53916
   722
                      val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
blanchet@49486
   723
                    in
blanchet@53740
   724
                      (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   725
                    end;
blanchet@53916
   726
                  val (trivs, goals) = map4 mk_goal ms ctrs udiscs usel_ctrs |> split_list;
blanchet@53740
   727
                  val thms =
blanchet@53740
   728
                    map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
blanchet@53740
   729
                        Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@53740
   730
                          mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
blanchet@53740
   731
                        |> Thm.close_derivation
blanchet@53740
   732
                        |> not triv ? perhaps (try (fn thm => refl RS thm)))
blanchet@53740
   733
                      ms discD_thms sel_thmss trivs goals;
blanchet@49486
   734
                in
blanchet@53740
   735
                  (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
blanchet@53740
   736
                   thms)
blanchet@49486
   737
                end;
blanchet@49025
   738
blanchet@53916
   739
              val swapped_all_collapse_thms =
blanchet@53916
   740
                map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
blanchet@53916
   741
blanchet@53916
   742
              val sel_exhaust_thm =
blanchet@53916
   743
                let
blanchet@53916
   744
                  fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
blanchet@53916
   745
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
blanchet@53916
   746
                in
blanchet@53916
   747
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@53916
   748
                    mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
blanchet@53916
   749
                  |> Thm.close_derivation
blanchet@53916
   750
                end;
blanchet@53916
   751
blanchet@49486
   752
              val expand_thms =
blanchet@49486
   753
                let
blanchet@49486
   754
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   755
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   756
                    (if null usels then
blanchet@49486
   757
                       []
blanchet@49486
   758
                     else
blanchet@49486
   759
                       [Logic.list_implies
blanchet@49486
   760
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   761
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   762
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   763
blanchet@49591
   764
                  val goal =
blanchet@49591
   765
                    Library.foldr Logic.list_implies
blanchet@49591
   766
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49486
   767
                  val uncollapse_thms =
blanchet@53740
   768
                    map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
blanchet@49486
   769
                in
wenzelm@51551
   770
                  [Goal.prove_sorry lthy [] [] goal (fn _ =>
wenzelm@51717
   771
                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
blanchet@49486
   772
                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@49486
   773
                       disc_exclude_thmsss')]
blanchet@49692
   774
                  |> map Thm.close_derivation
blanchet@49486
   775
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   776
                end;
blanchet@49278
   777
blanchet@53857
   778
              val case_conv_if_thms =
blanchet@49486
   779
                let
blanchet@49486
   780
                  fun mk_body f usels = Term.list_comb (f, usels);
blanchet@51770
   781
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
blanchet@49486
   782
                in
wenzelm@51551
   783
                  [Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@53857
   784
                     mk_case_conv_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
blanchet@49692
   785
                  |> map Thm.close_derivation
blanchet@49486
   786
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   787
                end;
blanchet@49116
   788
            in
blanchet@53704
   789
              (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
blanchet@53916
   790
               nontriv_discI_thms, disc_exclude_thms, [disc_exhaust_thm], [sel_exhaust_thm],
blanchet@53916
   791
               all_collapse_thms, safe_collapse_thms, expand_thms, case_conv_if_thms)
blanchet@49116
   792
            end;
blanchet@49025
   793
blanchet@49033
   794
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   795
          let
blanchet@51763
   796
            fun mk_prem xctr xs xf xg =
blanchet@49486
   797
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@51763
   798
                mk_Trueprop_eq (xf, xg)));
blanchet@49033
   799
blanchet@49032
   800
            val goal =
blanchet@51763
   801
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
blanchet@51759
   802
                 mk_Trueprop_eq (eta_ufcase, eta_vgcase));
blanchet@49591
   803
            val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
blanchet@49032
   804
          in
wenzelm@51717
   805
            (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
wenzelm@51551
   806
             Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@49692
   807
            |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   808
          end;
blanchet@49025
   809
blanchet@49044
   810
        val (split_thm, split_asm_thm) =
blanchet@49043
   811
          let
blanchet@49044
   812
            fun mk_conjunct xctr xs f_xs =
blanchet@49486
   813
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@49044
   814
            fun mk_disjunct xctr xs f_xs =
blanchet@49486
   815
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@49044
   816
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   817
blanchet@51770
   818
            val lhs = q $ ufcase;
blanchet@49044
   819
blanchet@49043
   820
            val goal =
blanchet@49044
   821
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49458
   822
            val asm_goal =
blanchet@49044
   823
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   824
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   825
blanchet@49044
   826
            val split_thm =
wenzelm@51551
   827
              Goal.prove_sorry lthy [] [] goal
wenzelm@51717
   828
                (fn _ => mk_split_tac lthy uexhaust_thm case_thms inject_thmss distinct_thmsss)
blanchet@49692
   829
              |> Thm.close_derivation
blanchet@49692
   830
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49044
   831
            val split_asm_thm =
wenzelm@51551
   832
              Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@49044
   833
                mk_split_asm_tac ctxt split_thm)
blanchet@49692
   834
              |> Thm.close_derivation
blanchet@49692
   835
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49043
   836
          in
blanchet@49044
   837
            (split_thm, split_asm_thm)
blanchet@49043
   838
          end;
blanchet@49025
   839
blanchet@49437
   840
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@53908
   841
        val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
blanchet@49300
   842
blanchet@49052
   843
        val notes =
blanchet@53810
   844
          [(caseN, case_thms, code_nitpick_simp_simp_attrs),
blanchet@49594
   845
           (case_congN, [case_cong_thm], []),
blanchet@53857
   846
           (case_conv_ifN, case_conv_if_thms, []),
blanchet@53740
   847
           (collapseN, safe_collapse_thms, simp_attrs),
blanchet@53704
   848
           (discN, nontriv_disc_thms, simp_attrs),
blanchet@53700
   849
           (discIN, nontriv_discI_thms, []),
blanchet@53836
   850
           (disc_excludeN, disc_exclude_thms, dest_attrs),
blanchet@49300
   851
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@49300
   852
           (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
blanchet@49300
   853
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   854
           (expandN, expand_thms, []),
blanchet@49438
   855
           (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
blanchet@49300
   856
           (nchotomyN, [nchotomy_thm], []),
blanchet@53810
   857
           (selN, all_sel_thms, code_nitpick_simp_simp_attrs),
blanchet@53916
   858
           (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
blanchet@49300
   859
           (splitN, [split_thm], []),
blanchet@49300
   860
           (split_asmN, [split_asm_thm], []),
blanchet@49633
   861
           (splitsN, [split_thm, split_asm_thm], []),
blanchet@49300
   862
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   863
          |> filter_out (null o #2)
blanchet@49300
   864
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   865
            ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   866
blanchet@49300
   867
        val notes' =
blanchet@49300
   868
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
blanchet@49300
   869
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@53867
   870
blanchet@53867
   871
        val ctr_sugar =
blanchet@53867
   872
          {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
blanchet@53867
   873
           nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
blanchet@53867
   874
           case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
blanchet@53867
   875
           split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
blanchet@53867
   876
           discIs = discI_thms, sel_thmss = sel_thmss, disc_exhausts = disc_exhaust_thms,
blanchet@53916
   877
           sel_exhausts = sel_exhaust_thms, collapses = all_collapse_thms, expands = expand_thms,
blanchet@53916
   878
           case_conv_ifs = case_conv_if_thms};
blanchet@49019
   879
      in
blanchet@53867
   880
        (ctr_sugar,
blanchet@51819
   881
         lthy
blanchet@51819
   882
         |> not rep_compat ?
blanchet@51819
   883
            (Local_Theory.declaration {syntax = false, pervasive = true}
traytel@51697
   884
               (fn phi => Case_Translation.register
blanchet@51819
   885
                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
blanchet@53867
   886
         |> Local_Theory.notes (notes' @ notes) |> snd
blanchet@53908
   887
         |> register_ctr_sugar fcT_name ctr_sugar)
blanchet@49019
   888
      end;
blanchet@49017
   889
  in
blanchet@49121
   890
    (goalss, after_qed, lthy')
blanchet@49017
   891
  end;
blanchet@49017
   892
blanchet@51781
   893
fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
wenzelm@51551
   894
  map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
blanchet@51781
   895
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
blanchet@49280
   896
blanchet@51781
   897
val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   898
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@51781
   899
  prepare_wrap_free_constructors Syntax.read_term;
blanchet@49297
   900
blanchet@49280
   901
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   902
blanchet@51790
   903
val parse_bindings = parse_bracket_list parse_binding;
blanchet@49280
   904
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   905
blanchet@51790
   906
val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   907
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   908
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   909
blanchet@52823
   910
val parse_wrap_free_constructors_options =
blanchet@52969
   911
  Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_discs_sels"} >> K (true, false)) ||
blanchet@49633
   912
      (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
blanchet@49633
   913
    >> (pairself (exists I) o split_list)) (false, false);
blanchet@49278
   914
blanchet@49017
   915
val _ =
blanchet@51781
   916
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
blanchet@51797
   917
    "wrap an existing freely generated type's constructors"
blanchet@52823
   918
    ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
blanchet@52823
   919
        @{keyword "]"}) --
blanchet@52968
   920
      parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   921
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@51781
   922
     >> wrap_free_constructors_cmd);
blanchet@49017
   923
blanchet@49017
   924
end;