src/HOL/BNF/Tools/bnf_ctr_sugar.ML
author blanchet
Mon Aug 26 18:08:54 2013 +0200 (2013-08-26)
changeset 53210 7219c61796c0
parent 53040 e6edd7abc4ce
child 53268 de1dc709f9d4
permissions -rw-r--r--
simplify code (now that ctr_sugar uses the same type variables as fp_sugar)
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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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  val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
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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_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 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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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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  {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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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_convN = "case_conv";
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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 discsN = "discs";
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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 selsN = "sels";
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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 induct_simp_attrs = @{attributes [induct_simp]};
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val cong_attrs = @{attributes [cong]};
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val iff_attrs = @{attributes [iff]};
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val safe_elim_attrs = @{attributes [elim!]};
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val simp_attrs = @{attributes [simp]};
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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_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 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 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 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 (dataT_name, As0) = body_type (fastype_of (hd ctrs0));
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    val data_b_name = Long_Name.base_name dataT_name;
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    val data_b = Binding.name data_b_name;
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    fun qualify mandatory =
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      Binding.qualify mandatory data_b_name o
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      (rep_compat ? Binding.qualify false rep_compat_prefix);
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    fun tfree_name_of (TFree (s, _)) = s
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      | tfree_name_of (TVar ((s, _), _)) = s
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      | tfree_name_of (Type (s, _)) = Long_Name.base_name s;
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    val (As, B) =
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      no_defs_lthy
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      |> variant_tfrees (map tfree_name_of As0)
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      ||> the_single o fst o mk_TFrees 1;
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    val dataT = Type (dataT_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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    val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
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    val disc_bindings =
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      raw_disc_bindings'
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      |> map4 (fn k => fn m => fn ctr => fn disc =>
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        qualify false
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          (if Binding.is_empty disc then
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             if should_omit_disc_binding k then disc else standard_disc_binding ctr
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           else if Binding.eq_name (disc, equal_binding) then
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             if m = 0 then disc
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             else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
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           else if Binding.eq_name (disc, standard_binding) then
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             standard_disc_binding ctr
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           else
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             disc)) ks ms ctrs0;
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    fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
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    val sel_bindingss =
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      pad_list [] n raw_sel_bindingss
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      |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
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        qualify false
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          (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
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            standard_sel_binding m l ctr
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          else
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            sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
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    val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
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    val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
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      mk_Freess' "x" ctr_Tss
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      ||>> mk_Freess "y" ctr_Tss
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      ||>> mk_Frees "f" case_Ts
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      ||>> mk_Frees "g" case_Ts
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      ||>> (apfst (map (rpair dataT)) oo Variable.variant_fixes) [data_b_name, data_b_name ^ "'"]
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      ||>> mk_Frees "z" [B]
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      ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
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    val u = Free u';
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    val v = Free v';
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    val q = Free (fst p', mk_pred1T B);
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    val xctrs = map2 (curry Term.list_comb) ctrs xss;
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    val yctrs = map2 (curry Term.list_comb) ctrs yss;
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    val xfs = map2 (curry Term.list_comb) fs xss;
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    val xgs = map2 (curry Term.list_comb) gs xss;
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    (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
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       nicer names). Consider removing. *)
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    val eta_fs = map2 eta_expand_arg xss xfs;
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    val eta_gs = map2 eta_expand_arg xss xgs;
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    val case_binding =
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      qualify false
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        (if Binding.is_empty raw_case_binding orelse
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            Binding.eq_name (raw_case_binding, standard_binding) then
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           Binding.suffix_name ("_" ^ caseN) data_b
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         else
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           raw_case_binding);
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    fun mk_case_disj xctr xf xs =
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      list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
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    val case_rhs =
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      fold_rev (fold_rev Term.lambda) [fs, [u]]
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        (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
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           Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
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    val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
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      |> Local_Theory.define ((case_binding, NoSyn), ((Thm.def_binding case_binding, []), case_rhs))
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      ||> `Local_Theory.restore;
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    val phi = Proof_Context.export_morphism lthy lthy';
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    val case_def = Morphism.thm phi raw_case_def;
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    val case0 = Morphism.term phi raw_case;
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    val casex = mk_case As B case0;
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    val fcase = Term.list_comb (casex, fs);
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    val ufcase = fcase $ u;
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    val vfcase = fcase $ v;
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    val eta_fcase = Term.list_comb (casex, eta_fs);
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    val eta_gcase = Term.list_comb (casex, eta_gs);
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   317
    val eta_ufcase = eta_fcase $ u;
blanchet@51759
   318
    val eta_vgcase = eta_gcase $ v;
blanchet@49486
   319
blanchet@49591
   320
    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
blanchet@49486
   321
blanchet@49591
   322
    val uv_eq = mk_Trueprop_eq (u, v);
blanchet@49486
   323
blanchet@49486
   324
    val exist_xs_u_eq_ctrs =
blanchet@49486
   325
      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
blanchet@49022
   326
blanchet@51743
   327
    val unique_disc_no_def = TrueI; (*arbitrary marker*)
blanchet@51743
   328
    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
blanchet@51743
   329
blanchet@49486
   330
    fun alternate_disc_lhs get_udisc k =
blanchet@49116
   331
      HOLogic.mk_not
blanchet@51790
   332
        (let val b = nth disc_bindings (k - 1) in
blanchet@51790
   333
           if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
blanchet@51790
   334
         end);
blanchet@49116
   335
blanchet@49486
   336
    val (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   337
         sel_defss, lthy') =
blanchet@52969
   338
      if no_discs_sels then
blanchet@52968
   339
        (true, [], [], [], [], [], [], [], [], [], lthy)
blanchet@49278
   340
      else
blanchet@49278
   341
        let
blanchet@49463
   342
          fun disc_free b = Free (Binding.name_of b, mk_pred1T dataT);
blanchet@49025
   343
blanchet@49486
   344
          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
blanchet@49278
   345
blanchet@49500
   346
          fun alternate_disc k =
blanchet@49500
   347
            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
blanchet@49278
   348
blanchet@49280
   349
          fun mk_sel_case_args b proto_sels T =
blanchet@49280
   350
            map2 (fn Ts => fn k =>
blanchet@49280
   351
              (case AList.lookup (op =) proto_sels k of
blanchet@49280
   352
                NONE =>
blanchet@49364
   353
                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
blanchet@49364
   354
                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
blanchet@52968
   355
                | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
blanchet@49280
   356
              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
blanchet@49258
   357
blanchet@49278
   358
          fun sel_spec b proto_sels =
blanchet@49278
   359
            let
blanchet@49278
   360
              val _ =
blanchet@49278
   361
                (case duplicates (op =) (map fst proto_sels) of
blanchet@49278
   362
                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
blanchet@49278
   363
                     " for constructor " ^
blanchet@52968
   364
                     quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
blanchet@49278
   365
                 | [] => ())
blanchet@49278
   366
              val T =
blanchet@49278
   367
                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
blanchet@49278
   368
                  [T] => T
blanchet@49278
   369
                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
blanchet@52968
   370
                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
blanchet@52968
   371
                    ^ quote (Syntax.string_of_typ lthy T')));
blanchet@49278
   372
            in
blanchet@49486
   373
              mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ u,
blanchet@49536
   374
                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
blanchet@49278
   375
            end;
blanchet@49116
   376
blanchet@49336
   377
          val sel_bindings = flat sel_bindingss;
blanchet@49336
   378
          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
blanchet@49336
   379
          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
blanchet@49285
   380
blanchet@49336
   381
          val sel_binding_index =
blanchet@49336
   382
            if all_sels_distinct then 1 upto length sel_bindings
blanchet@49336
   383
            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
blanchet@49285
   384
blanchet@49285
   385
          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
blanchet@49300
   386
          val sel_infos =
blanchet@49336
   387
            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   388
            |> sort (int_ord o pairself fst)
blanchet@49336
   389
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   390
          val sel_bindings = map fst sel_infos;
blanchet@49258
   391
blanchet@49336
   392
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   393
blanchet@49278
   394
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@52968
   395
            lthy
blanchet@51809
   396
            |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
blanchet@51790
   397
                if Binding.is_empty b then
blanchet@51790
   398
                  if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@51790
   399
                  else pair (alternate_disc k, alternate_disc_no_def)
blanchet@51790
   400
                else if Binding.eq_name (b, equal_binding) then
blanchet@51790
   401
                  pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@51790
   402
                else
blanchet@51790
   403
                  Specification.definition (SOME (b, NONE, NoSyn),
blanchet@51790
   404
                    ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@51809
   405
              ks exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   406
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   407
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   408
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   409
            ||> `Local_Theory.restore;
blanchet@49022
   410
blanchet@49278
   411
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   412
blanchet@49278
   413
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   414
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   415
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   416
blanchet@49278
   417
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   418
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   419
blanchet@49278
   420
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   421
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49486
   422
blanchet@49500
   423
          val udiscs = map (rapp u) discs;
blanchet@49500
   424
          val uselss = map (map (rapp u)) selss;
blanchet@49486
   425
blanchet@49500
   426
          val vdiscs = map (rapp v) discs;
blanchet@49500
   427
          val vselss = map (map (rapp v)) selss;
blanchet@49278
   428
        in
blanchet@49486
   429
          (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   430
           sel_defss, lthy')
blanchet@49278
   431
        end;
blanchet@49025
   432
blanchet@49032
   433
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   434
blanchet@49458
   435
    val exhaust_goal =
blanchet@49486
   436
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   437
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   438
      end;
blanchet@49019
   439
blanchet@49484
   440
    val inject_goalss =
blanchet@49017
   441
      let
blanchet@49034
   442
        fun mk_goal _ _ [] [] = []
blanchet@49025
   443
          | mk_goal xctr yctr xs ys =
blanchet@49121
   444
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   445
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   446
      in
blanchet@49034
   447
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   448
      end;
blanchet@49017
   449
blanchet@49484
   450
    val half_distinct_goalss =
blanchet@49121
   451
      let
blanchet@49203
   452
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   453
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   454
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   455
      in
blanchet@49585
   456
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   457
      end;
blanchet@49019
   458
blanchet@52968
   459
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
blanchet@49019
   460
blanchet@49019
   461
    fun after_qed thmss lthy =
blanchet@49019
   462
      let
blanchet@52968
   463
        val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
blanchet@49019
   464
blanchet@49438
   465
        val inject_thms = flat inject_thmss;
blanchet@49438
   466
blanchet@53210
   467
        val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   468
blanchet@49486
   469
        fun inst_thm t thm =
blanchet@49486
   470
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@53210
   471
            (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
blanchet@49486
   472
blanchet@49486
   473
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   474
blanchet@49300
   475
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   476
blanchet@49048
   477
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   478
blanchet@49486
   479
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   480
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   481
blanchet@49020
   482
        val nchotomy_thm =
blanchet@49020
   483
          let
blanchet@49020
   484
            val goal =
blanchet@49486
   485
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   486
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   487
          in
wenzelm@51551
   488
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
traytel@49667
   489
            |> Thm.close_derivation
blanchet@49020
   490
          end;
blanchet@49020
   491
blanchet@52968
   492
        val case_thms =
blanchet@52968
   493
          let
blanchet@52968
   494
            val goals =
blanchet@52968
   495
              map3 (fn xctr => fn xf => fn xs =>
blanchet@52968
   496
                fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
blanchet@52968
   497
          in
blanchet@52968
   498
            map4 (fn k => fn goal => fn injects => fn distinctss =>
blanchet@52968
   499
                Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@52968
   500
                  mk_case_tac ctxt n k case_def injects distinctss)
blanchet@52968
   501
                |> Thm.close_derivation)
blanchet@52968
   502
              ks goals inject_thmss distinct_thmsss
blanchet@52968
   503
          end;
blanchet@52968
   504
blanchet@49484
   505
        val (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49594
   506
             disc_exhaust_thms, collapse_thms, expand_thms, case_conv_thms) =
blanchet@52969
   507
          if no_discs_sels then
blanchet@49486
   508
            ([], [], [], [], [], [], [], [], [], [])
blanchet@49116
   509
          else
blanchet@49116
   510
            let
blanchet@49364
   511
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   512
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   513
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   514
blanchet@49281
   515
              fun has_undefined_rhs thm =
blanchet@49281
   516
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   517
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   518
                | _ => false);
blanchet@49281
   519
blanchet@49364
   520
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@49281
   521
blanchet@49281
   522
              val all_sel_thms =
blanchet@49285
   523
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   524
                   flat sel_thmss
blanchet@49285
   525
                 else
blanchet@49364
   526
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   527
                     (xss' ~~ case_thms))
blanchet@49285
   528
                |> filter_out has_undefined_rhs;
blanchet@49278
   529
blanchet@49278
   530
              fun mk_unique_disc_def () =
blanchet@49278
   531
                let
blanchet@49278
   532
                  val m = the_single ms;
blanchet@49591
   533
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   534
                in
wenzelm@51551
   535
                  Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49692
   536
                  |> Thm.close_derivation
blanchet@49278
   537
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   538
                end;
blanchet@49278
   539
blanchet@49278
   540
              fun mk_alternate_disc_def k =
blanchet@49278
   541
                let
blanchet@49278
   542
                  val goal =
blanchet@49486
   543
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   544
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   545
                in
wenzelm@51551
   546
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   547
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   548
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49692
   549
                  |> Thm.close_derivation
blanchet@49278
   550
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   551
                end;
blanchet@49028
   552
blanchet@49278
   553
              val has_alternate_disc_def =
blanchet@49278
   554
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   555
blanchet@49278
   556
              val disc_defs' =
blanchet@49278
   557
                map2 (fn k => fn def =>
blanchet@49278
   558
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   559
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   560
                  else def) ks disc_defs;
blanchet@49278
   561
blanchet@49278
   562
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   563
              val discI_thms =
blanchet@49278
   564
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   565
                  disc_defs';
blanchet@49278
   566
              val not_discI_thms =
blanchet@49278
   567
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   568
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   569
                  ms disc_defs';
blanchet@49278
   570
blanchet@49278
   571
              val (disc_thmss', disc_thmss) =
blanchet@49278
   572
                let
blanchet@49278
   573
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   574
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   575
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   576
                in
blanchet@49278
   577
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   578
                end;
blanchet@49278
   579
blanchet@51790
   580
              val disc_thms = flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
blanchet@51790
   581
                disc_bindings disc_thmss);
blanchet@49028
   582
blanchet@49486
   583
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   584
                let
blanchet@49486
   585
                  fun mk_goal [] = []
blanchet@49486
   586
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   587
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   588
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   589
traytel@49667
   590
                  fun prove tac goal =
wenzelm@51551
   591
                    Goal.prove_sorry lthy [] [] goal (K tac)
traytel@49667
   592
                    |> Thm.close_derivation;
blanchet@49486
   593
blanchet@49585
   594
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   595
blanchet@49486
   596
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   597
                  val half_thmss =
blanchet@49486
   598
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
wenzelm@51798
   599
                        fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
blanchet@49486
   600
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   601
blanchet@49486
   602
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   603
                  val other_half_thmss =
blanchet@49486
   604
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   605
                      other_half_goalss;
blanchet@49486
   606
                in
blanchet@49585
   607
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   608
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   609
                end;
blanchet@49278
   610
blanchet@49486
   611
              val disc_exhaust_thm =
blanchet@49486
   612
                let
blanchet@49486
   613
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   614
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   615
                in
wenzelm@51551
   616
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@49486
   617
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
traytel@49667
   618
                  |> Thm.close_derivation
blanchet@49486
   619
                end;
blanchet@49028
   620
blanchet@49486
   621
              val (collapse_thms, collapse_thm_opts) =
blanchet@49486
   622
                let
blanchet@49486
   623
                  fun mk_goal ctr udisc usels =
blanchet@49486
   624
                    let
blanchet@49486
   625
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@49486
   626
                      val concl =
blanchet@49486
   627
                        mk_Trueprop_eq ((null usels ? swap) (Term.list_comb (ctr, usels), u));
blanchet@49486
   628
                    in
blanchet@49486
   629
                      if prem aconv concl then NONE
blanchet@49486
   630
                      else SOME (Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   631
                    end;
blanchet@49486
   632
                  val goals = map3 mk_goal ctrs udiscs uselss;
blanchet@49486
   633
                in
blanchet@49486
   634
                  map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
wenzelm@51551
   635
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49486
   636
                      mk_collapse_tac ctxt m discD sel_thms)
traytel@49667
   637
                    |> Thm.close_derivation
blanchet@49486
   638
                    |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
blanchet@49486
   639
                  |> `(map_filter I)
blanchet@49486
   640
                end;
blanchet@49025
   641
blanchet@49486
   642
              val expand_thms =
blanchet@49486
   643
                let
blanchet@49486
   644
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   645
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   646
                    (if null usels then
blanchet@49486
   647
                       []
blanchet@49486
   648
                     else
blanchet@49486
   649
                       [Logic.list_implies
blanchet@49486
   650
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   651
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   652
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   653
blanchet@49591
   654
                  val goal =
blanchet@49591
   655
                    Library.foldr Logic.list_implies
blanchet@49591
   656
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49486
   657
                  val uncollapse_thms =
blanchet@51742
   658
                    map2 (fn NONE => K asm_rl | SOME thm => fn [] => thm | _ => thm RS sym)
blanchet@51742
   659
                      collapse_thm_opts uselss;
blanchet@49486
   660
                in
wenzelm@51551
   661
                  [Goal.prove_sorry lthy [] [] goal (fn _ =>
wenzelm@51717
   662
                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
blanchet@49486
   663
                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@49486
   664
                       disc_exclude_thmsss')]
blanchet@49692
   665
                  |> map Thm.close_derivation
blanchet@49486
   666
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   667
                end;
blanchet@49278
   668
blanchet@49594
   669
              val case_conv_thms =
blanchet@49486
   670
                let
blanchet@49486
   671
                  fun mk_body f usels = Term.list_comb (f, usels);
blanchet@51770
   672
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
blanchet@49486
   673
                in
wenzelm@51551
   674
                  [Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49594
   675
                     mk_case_conv_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
blanchet@49692
   676
                  |> map Thm.close_derivation
blanchet@49486
   677
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   678
                end;
blanchet@49116
   679
            in
blanchet@49484
   680
              (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49594
   681
               [disc_exhaust_thm], collapse_thms, expand_thms, case_conv_thms)
blanchet@49116
   682
            end;
blanchet@49025
   683
blanchet@49033
   684
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   685
          let
blanchet@51763
   686
            fun mk_prem xctr xs xf xg =
blanchet@49486
   687
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@51763
   688
                mk_Trueprop_eq (xf, xg)));
blanchet@49033
   689
blanchet@49032
   690
            val goal =
blanchet@51763
   691
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
blanchet@51759
   692
                 mk_Trueprop_eq (eta_ufcase, eta_vgcase));
blanchet@49591
   693
            val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
blanchet@49032
   694
          in
wenzelm@51717
   695
            (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
wenzelm@51551
   696
             Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@49692
   697
            |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   698
          end;
blanchet@49025
   699
blanchet@49044
   700
        val (split_thm, split_asm_thm) =
blanchet@49043
   701
          let
blanchet@49044
   702
            fun mk_conjunct xctr xs f_xs =
blanchet@49486
   703
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@49044
   704
            fun mk_disjunct xctr xs f_xs =
blanchet@49486
   705
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@49044
   706
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   707
blanchet@51770
   708
            val lhs = q $ ufcase;
blanchet@49044
   709
blanchet@49043
   710
            val goal =
blanchet@49044
   711
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49458
   712
            val asm_goal =
blanchet@49044
   713
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   714
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   715
blanchet@49044
   716
            val split_thm =
wenzelm@51551
   717
              Goal.prove_sorry lthy [] [] goal
wenzelm@51717
   718
                (fn _ => mk_split_tac lthy uexhaust_thm case_thms inject_thmss distinct_thmsss)
blanchet@49692
   719
              |> Thm.close_derivation
blanchet@49692
   720
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49044
   721
            val split_asm_thm =
wenzelm@51551
   722
              Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@49044
   723
                mk_split_asm_tac ctxt split_thm)
blanchet@49692
   724
              |> Thm.close_derivation
blanchet@49692
   725
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49043
   726
          in
blanchet@49044
   727
            (split_thm, split_asm_thm)
blanchet@49043
   728
          end;
blanchet@49025
   729
blanchet@49437
   730
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@49300
   731
        val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));
blanchet@49300
   732
blanchet@49052
   733
        val notes =
blanchet@49594
   734
          [(caseN, case_thms, simp_attrs),
blanchet@49594
   735
           (case_congN, [case_cong_thm], []),
blanchet@49594
   736
           (case_convN, case_conv_thms, []),
blanchet@49300
   737
           (collapseN, collapse_thms, simp_attrs),
blanchet@49300
   738
           (discsN, disc_thms, simp_attrs),
blanchet@49300
   739
           (disc_excludeN, disc_exclude_thms, []),
blanchet@49300
   740
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@49300
   741
           (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
blanchet@49300
   742
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   743
           (expandN, expand_thms, []),
blanchet@49438
   744
           (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
blanchet@49300
   745
           (nchotomyN, [nchotomy_thm], []),
blanchet@49300
   746
           (selsN, all_sel_thms, simp_attrs),
blanchet@49300
   747
           (splitN, [split_thm], []),
blanchet@49300
   748
           (split_asmN, [split_asm_thm], []),
blanchet@49633
   749
           (splitsN, [split_thm, split_asm_thm], []),
blanchet@49300
   750
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   751
          |> filter_out (null o #2)
blanchet@49300
   752
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   753
            ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   754
blanchet@49300
   755
        val notes' =
blanchet@49300
   756
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
blanchet@49300
   757
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49019
   758
      in
blanchet@52375
   759
        ({ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
blanchet@52375
   760
          nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
blanchet@52375
   761
          case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
blanchet@52375
   762
          split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
blanchet@51819
   763
          discIs = discI_thms, sel_thmss = sel_thmss},
blanchet@51819
   764
         lthy
blanchet@51819
   765
         |> not rep_compat ?
blanchet@51819
   766
            (Local_Theory.declaration {syntax = false, pervasive = true}
traytel@51697
   767
               (fn phi => Case_Translation.register
blanchet@51819
   768
                  (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
blanchet@51819
   769
         |> Local_Theory.notes (notes' @ notes) |> snd)
blanchet@49019
   770
      end;
blanchet@49017
   771
  in
blanchet@49121
   772
    (goalss, after_qed, lthy')
blanchet@49017
   773
  end;
blanchet@49017
   774
blanchet@51781
   775
fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
wenzelm@51551
   776
  map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
blanchet@51781
   777
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
blanchet@49280
   778
blanchet@51781
   779
val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   780
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@51781
   781
  prepare_wrap_free_constructors Syntax.read_term;
blanchet@49297
   782
blanchet@49280
   783
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   784
blanchet@51790
   785
val parse_bindings = parse_bracket_list parse_binding;
blanchet@49280
   786
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   787
blanchet@51790
   788
val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   789
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   790
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   791
blanchet@52823
   792
val parse_wrap_free_constructors_options =
blanchet@52969
   793
  Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_discs_sels"} >> K (true, false)) ||
blanchet@49633
   794
      (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
blanchet@49633
   795
    >> (pairself (exists I) o split_list)) (false, false);
blanchet@49278
   796
blanchet@49017
   797
val _ =
blanchet@51781
   798
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
blanchet@51797
   799
    "wrap an existing freely generated type's constructors"
blanchet@52823
   800
    ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
blanchet@52823
   801
        @{keyword "]"}) --
blanchet@52968
   802
      parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   803
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@51781
   804
     >> wrap_free_constructors_cmd);
blanchet@49017
   805
blanchet@49017
   806
end;