src/HOL/BNF/Tools/bnf_ctr_sugar.ML
author blanchet
Mon Apr 29 11:04:56 2013 +0200 (2013-04-29)
changeset 51809 d4c1abbb4095
parent 51798 ad3a241def73
child 51819 9df935196be9
permissions -rw-r--r--
code tuning
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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_wrap_result =
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    term list * term list list * thm * thm list * thm list * thm list * thm list list * thm list *
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    thm list 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_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) * term) *
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      (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
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    ctr_wrap_result * local_theory
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  val parse_wrap_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_wrap_result =
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  term list * term list list * thm * thm list * thm list * thm list * thm list list * thm list *
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  thm list list;
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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 ys zs = map (map (fn x => nth zs (find_index (curry eq x) 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_dests, rep_compat), raw_ctrs), raw_case),
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    (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 case0 = prep_term no_defs_lthy raw_case;
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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 case0T = fastype_of case0;
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    val Type (dataT_name, As0) =
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      domain_type (snd (strip_typeN (length (binder_types case0T) - 1) case0T));
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    val data_b = Binding.qualified_name dataT_name;
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    val data_b_name = Binding.name_of data_b;
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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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    val (As, B) =
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      no_defs_lthy
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      |> mk_TFrees' (map Type.sort_of_atyp 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 = qualify false o 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 casex = mk_case As B case0;
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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']), (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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      ||>> 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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    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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    (* 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 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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    val eta_ufcase = eta_fcase $ u;
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    val eta_vgcase = eta_gcase $ v;
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    fun mk_uu_eq () = HOLogic.mk_eq (u, u);
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    val uv_eq = mk_Trueprop_eq (u, v);
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    val exist_xs_u_eq_ctrs =
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      map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
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    val unique_disc_no_def = TrueI; (*arbitrary marker*)
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    val alternate_disc_no_def = FalseE; (*arbitrary marker*)
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    fun alternate_disc_lhs get_udisc k =
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      HOLogic.mk_not
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        (let val b = nth disc_bindings (k - 1) in
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           if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
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         end);
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    val (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
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         sel_defss, lthy') =
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      if no_dests then
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        (true, [], [], [], [], [], [], [], [], [], no_defs_lthy)
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      else
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        let
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          fun disc_free b = Free (Binding.name_of b, mk_pred1T dataT);
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          fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
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          fun alternate_disc k =
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            Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
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          fun mk_sel_case_args b proto_sels T =
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            map2 (fn Ts => fn k =>
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              (case AList.lookup (op =) proto_sels k of
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                NONE =>
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                (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
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                  NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
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                | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term no_defs_lthy)
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              | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
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          fun sel_spec b proto_sels =
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            let
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              val _ =
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                (case duplicates (op =) (map fst proto_sels) of
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                   k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
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                     " for constructor " ^
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                     quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))
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                 | [] => ())
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              val T =
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                (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
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                  [T] => T
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                | T :: T' :: _ => error ("Inconsistent range type for selector " ^
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                    quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
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                    " vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));
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            in
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              mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ u,
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                Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
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            end;
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          val sel_bindings = flat sel_bindingss;
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          val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
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          val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
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          val sel_binding_index =
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            if all_sels_distinct then 1 upto length sel_bindings
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            else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
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          val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
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          val sel_infos =
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            AList.group (op =) (sel_binding_index ~~ proto_sels)
blanchet@49285
   311
            |> sort (int_ord o pairself fst)
blanchet@49336
   312
            |> map snd |> curry (op ~~) uniq_sel_bindings;
blanchet@49336
   313
          val sel_bindings = map fst sel_infos;
blanchet@49258
   314
blanchet@49336
   315
          fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
blanchet@49258
   316
blanchet@49278
   317
          val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
blanchet@49278
   318
            no_defs_lthy
blanchet@51809
   319
            |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
blanchet@51790
   320
                if Binding.is_empty b then
blanchet@51790
   321
                  if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
blanchet@51790
   322
                  else pair (alternate_disc k, alternate_disc_no_def)
blanchet@51790
   323
                else if Binding.eq_name (b, equal_binding) then
blanchet@51790
   324
                  pair (Term.lambda u exist_xs_u_eq_ctr, refl)
blanchet@51790
   325
                else
blanchet@51790
   326
                  Specification.definition (SOME (b, NONE, NoSyn),
blanchet@51790
   327
                    ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
blanchet@51809
   328
              ks exist_xs_u_eq_ctrs disc_bindings
blanchet@49278
   329
            ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
blanchet@49278
   330
              Specification.definition (SOME (b, NONE, NoSyn),
blanchet@49300
   331
                ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
blanchet@49278
   332
            ||> `Local_Theory.restore;
blanchet@49022
   333
blanchet@49278
   334
          val phi = Proof_Context.export_morphism lthy lthy';
blanchet@49025
   335
blanchet@49278
   336
          val disc_defs = map (Morphism.thm phi) raw_disc_defs;
blanchet@49281
   337
          val sel_defs = map (Morphism.thm phi) raw_sel_defs;
blanchet@49281
   338
          val sel_defss = unflat_selss sel_defs;
blanchet@49278
   339
blanchet@49278
   340
          val discs0 = map (Morphism.term phi) raw_discs;
blanchet@49278
   341
          val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
blanchet@49028
   342
blanchet@49278
   343
          val discs = map (mk_disc_or_sel As) discs0;
blanchet@49278
   344
          val selss = map (map (mk_disc_or_sel As)) selss0;
blanchet@49486
   345
blanchet@49500
   346
          val udiscs = map (rapp u) discs;
blanchet@49500
   347
          val uselss = map (map (rapp u)) selss;
blanchet@49486
   348
blanchet@49500
   349
          val vdiscs = map (rapp v) discs;
blanchet@49500
   350
          val vselss = map (map (rapp v)) selss;
blanchet@49278
   351
        in
blanchet@49486
   352
          (all_sels_distinct, discs, selss, udiscs, uselss, vdiscs, vselss, disc_defs, sel_defs,
blanchet@49486
   353
           sel_defss, lthy')
blanchet@49278
   354
        end;
blanchet@49025
   355
blanchet@49032
   356
    fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
blanchet@49029
   357
blanchet@49458
   358
    val exhaust_goal =
blanchet@49486
   359
      let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
blanchet@49486
   360
        fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
blanchet@49020
   361
      end;
blanchet@49019
   362
blanchet@49484
   363
    val inject_goalss =
blanchet@49017
   364
      let
blanchet@49034
   365
        fun mk_goal _ _ [] [] = []
blanchet@49025
   366
          | mk_goal xctr yctr xs ys =
blanchet@49121
   367
            [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
blanchet@49121
   368
              Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
blanchet@49017
   369
      in
blanchet@49034
   370
        map4 mk_goal xctrs yctrs xss yss
blanchet@49017
   371
      end;
blanchet@49017
   372
blanchet@49484
   373
    val half_distinct_goalss =
blanchet@49121
   374
      let
blanchet@49203
   375
        fun mk_goal ((xs, xc), (xs', xc')) =
blanchet@49121
   376
          fold_rev Logic.all (xs @ xs')
blanchet@49203
   377
            (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
blanchet@49121
   378
      in
blanchet@49585
   379
        map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
blanchet@49121
   380
      end;
blanchet@49019
   381
blanchet@49458
   382
    val cases_goal =
blanchet@49121
   383
      map3 (fn xs => fn xctr => fn xf =>
blanchet@51770
   384
        fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;
blanchet@49025
   385
blanchet@49484
   386
    val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss @ [cases_goal];
blanchet@49019
   387
blanchet@49019
   388
    fun after_qed thmss lthy =
blanchet@49019
   389
      let
blanchet@49048
   390
        val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
blanchet@49048
   391
          (hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
blanchet@49019
   392
blanchet@49438
   393
        val inject_thms = flat inject_thmss;
blanchet@49438
   394
blanchet@49486
   395
        val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
blanchet@49486
   396
blanchet@49486
   397
        fun inst_thm t thm =
blanchet@49486
   398
          Drule.instantiate' [] [SOME (certify lthy t)]
blanchet@49486
   399
            (Thm.instantiate (Tinst, []) (Drule.zero_var_indexes thm));
blanchet@49486
   400
blanchet@49486
   401
        val uexhaust_thm = inst_thm u exhaust_thm;
blanchet@49032
   402
blanchet@49300
   403
        val exhaust_cases = map base_name_of_ctr ctrs;
blanchet@49300
   404
blanchet@49048
   405
        val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
blanchet@49048
   406
blanchet@49486
   407
        val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
blanchet@49585
   408
          join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
blanchet@49019
   409
blanchet@49020
   410
        val nchotomy_thm =
blanchet@49020
   411
          let
blanchet@49020
   412
            val goal =
blanchet@49486
   413
              HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
blanchet@49486
   414
                Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
blanchet@49020
   415
          in
wenzelm@51551
   416
            Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
traytel@49667
   417
            |> Thm.close_derivation
blanchet@49020
   418
          end;
blanchet@49020
   419
blanchet@49484
   420
        val (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49594
   421
             disc_exhaust_thms, collapse_thms, expand_thms, case_conv_thms) =
blanchet@49278
   422
          if no_dests then
blanchet@49486
   423
            ([], [], [], [], [], [], [], [], [], [])
blanchet@49116
   424
          else
blanchet@49116
   425
            let
blanchet@49364
   426
              fun make_sel_thm xs' case_thm sel_def =
blanchet@49364
   427
                zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
blanchet@49364
   428
                    (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
blanchet@49281
   429
blanchet@49281
   430
              fun has_undefined_rhs thm =
blanchet@49281
   431
                (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
blanchet@49281
   432
                  Const (@{const_name undefined}, _) => true
blanchet@49281
   433
                | _ => false);
blanchet@49281
   434
blanchet@49364
   435
              val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
blanchet@49281
   436
blanchet@49281
   437
              val all_sel_thms =
blanchet@49285
   438
                (if all_sels_distinct andalso forall null sel_defaultss then
blanchet@49285
   439
                   flat sel_thmss
blanchet@49285
   440
                 else
blanchet@49364
   441
                   map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
blanchet@49364
   442
                     (xss' ~~ case_thms))
blanchet@49285
   443
                |> filter_out has_undefined_rhs;
blanchet@49278
   444
blanchet@49278
   445
              fun mk_unique_disc_def () =
blanchet@49278
   446
                let
blanchet@49278
   447
                  val m = the_single ms;
blanchet@49591
   448
                  val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
blanchet@49278
   449
                in
wenzelm@51551
   450
                  Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
blanchet@49692
   451
                  |> Thm.close_derivation
blanchet@49278
   452
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   453
                end;
blanchet@49278
   454
blanchet@49278
   455
              fun mk_alternate_disc_def k =
blanchet@49278
   456
                let
blanchet@49278
   457
                  val goal =
blanchet@49486
   458
                    mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
blanchet@49486
   459
                      nth exist_xs_u_eq_ctrs (k - 1));
blanchet@49278
   460
                in
wenzelm@51551
   461
                  Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49278
   462
                    mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
blanchet@49486
   463
                      (nth distinct_thms (2 - k)) uexhaust_thm)
blanchet@49692
   464
                  |> Thm.close_derivation
blanchet@49278
   465
                  |> singleton (Proof_Context.export names_lthy lthy)
blanchet@49278
   466
                end;
blanchet@49028
   467
blanchet@49278
   468
              val has_alternate_disc_def =
blanchet@49278
   469
                exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
blanchet@49278
   470
blanchet@49278
   471
              val disc_defs' =
blanchet@49278
   472
                map2 (fn k => fn def =>
blanchet@49278
   473
                  if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
blanchet@49278
   474
                  else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
blanchet@49278
   475
                  else def) ks disc_defs;
blanchet@49278
   476
blanchet@49278
   477
              val discD_thms = map (fn def => def RS iffD1) disc_defs';
blanchet@49278
   478
              val discI_thms =
blanchet@49278
   479
                map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
blanchet@49278
   480
                  disc_defs';
blanchet@49278
   481
              val not_discI_thms =
blanchet@49278
   482
                map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
blanchet@49504
   483
                    (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
blanchet@49278
   484
                  ms disc_defs';
blanchet@49278
   485
blanchet@49278
   486
              val (disc_thmss', disc_thmss) =
blanchet@49278
   487
                let
blanchet@49278
   488
                  fun mk_thm discI _ [] = refl RS discI
blanchet@49278
   489
                    | mk_thm _ not_discI [distinct] = distinct RS not_discI;
blanchet@49278
   490
                  fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
blanchet@49278
   491
                in
blanchet@49278
   492
                  map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
blanchet@49278
   493
                end;
blanchet@49278
   494
blanchet@51790
   495
              val disc_thms = flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
blanchet@51790
   496
                disc_bindings disc_thmss);
blanchet@49028
   497
blanchet@49486
   498
              val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
blanchet@49486
   499
                let
blanchet@49486
   500
                  fun mk_goal [] = []
blanchet@49486
   501
                    | mk_goal [((_, udisc), (_, udisc'))] =
blanchet@49486
   502
                      [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
blanchet@49486
   503
                         HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
blanchet@49486
   504
traytel@49667
   505
                  fun prove tac goal =
wenzelm@51551
   506
                    Goal.prove_sorry lthy [] [] goal (K tac)
traytel@49667
   507
                    |> Thm.close_derivation;
blanchet@49486
   508
blanchet@49585
   509
                  val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
blanchet@49486
   510
blanchet@49486
   511
                  val half_goalss = map mk_goal half_pairss;
blanchet@49486
   512
                  val half_thmss =
blanchet@49486
   513
                    map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
wenzelm@51798
   514
                        fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
blanchet@49486
   515
                      half_goalss half_pairss (flat disc_thmss');
blanchet@49278
   516
blanchet@49486
   517
                  val other_half_goalss = map (mk_goal o map swap) half_pairss;
blanchet@49486
   518
                  val other_half_thmss =
blanchet@49486
   519
                    map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
blanchet@49486
   520
                      other_half_goalss;
blanchet@49486
   521
                in
blanchet@49585
   522
                  join_halves n half_thmss other_half_thmss ||> `transpose
blanchet@49486
   523
                  |>> has_alternate_disc_def ? K []
blanchet@49486
   524
                end;
blanchet@49278
   525
blanchet@49486
   526
              val disc_exhaust_thm =
blanchet@49486
   527
                let
blanchet@49486
   528
                  fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
blanchet@49486
   529
                  val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
blanchet@49486
   530
                in
wenzelm@51551
   531
                  Goal.prove_sorry lthy [] [] goal (fn _ =>
blanchet@49486
   532
                    mk_disc_exhaust_tac n exhaust_thm discI_thms)
traytel@49667
   533
                  |> Thm.close_derivation
blanchet@49486
   534
                end;
blanchet@49028
   535
blanchet@49486
   536
              val (collapse_thms, collapse_thm_opts) =
blanchet@49486
   537
                let
blanchet@49486
   538
                  fun mk_goal ctr udisc usels =
blanchet@49486
   539
                    let
blanchet@49486
   540
                      val prem = HOLogic.mk_Trueprop udisc;
blanchet@49486
   541
                      val concl =
blanchet@49486
   542
                        mk_Trueprop_eq ((null usels ? swap) (Term.list_comb (ctr, usels), u));
blanchet@49486
   543
                    in
blanchet@49486
   544
                      if prem aconv concl then NONE
blanchet@49486
   545
                      else SOME (Logic.all u (Logic.mk_implies (prem, concl)))
blanchet@49486
   546
                    end;
blanchet@49486
   547
                  val goals = map3 mk_goal ctrs udiscs uselss;
blanchet@49486
   548
                in
blanchet@49486
   549
                  map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
wenzelm@51551
   550
                    Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49486
   551
                      mk_collapse_tac ctxt m discD sel_thms)
traytel@49667
   552
                    |> Thm.close_derivation
blanchet@49486
   553
                    |> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
blanchet@49486
   554
                  |> `(map_filter I)
blanchet@49486
   555
                end;
blanchet@49025
   556
blanchet@49486
   557
              val expand_thms =
blanchet@49486
   558
                let
blanchet@49486
   559
                  fun mk_prems k udisc usels vdisc vsels =
blanchet@49486
   560
                    (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
blanchet@49486
   561
                    (if null usels then
blanchet@49486
   562
                       []
blanchet@49486
   563
                     else
blanchet@49486
   564
                       [Logic.list_implies
blanchet@49486
   565
                          (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
blanchet@49486
   566
                             HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
blanchet@49486
   567
                               (map2 (curry HOLogic.mk_eq) usels vsels)))]);
blanchet@49486
   568
blanchet@49591
   569
                  val goal =
blanchet@49591
   570
                    Library.foldr Logic.list_implies
blanchet@49591
   571
                      (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
blanchet@49486
   572
                  val uncollapse_thms =
blanchet@51742
   573
                    map2 (fn NONE => K asm_rl | SOME thm => fn [] => thm | _ => thm RS sym)
blanchet@51742
   574
                      collapse_thm_opts uselss;
blanchet@49486
   575
                in
wenzelm@51551
   576
                  [Goal.prove_sorry lthy [] [] goal (fn _ =>
wenzelm@51717
   577
                     mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
blanchet@49486
   578
                       (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
blanchet@49486
   579
                       disc_exclude_thmsss')]
blanchet@49692
   580
                  |> map Thm.close_derivation
blanchet@49486
   581
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   582
                end;
blanchet@49278
   583
blanchet@49594
   584
              val case_conv_thms =
blanchet@49486
   585
                let
blanchet@49486
   586
                  fun mk_body f usels = Term.list_comb (f, usels);
blanchet@51770
   587
                  val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs (map2 mk_body fs uselss));
blanchet@49486
   588
                in
wenzelm@51551
   589
                  [Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
blanchet@49594
   590
                     mk_case_conv_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)]
blanchet@49692
   591
                  |> map Thm.close_derivation
blanchet@49486
   592
                  |> Proof_Context.export names_lthy lthy
blanchet@49486
   593
                end;
blanchet@49116
   594
            in
blanchet@49484
   595
              (all_sel_thms, sel_thmss, disc_thmss, disc_thms, discI_thms, disc_exclude_thms,
blanchet@49594
   596
               [disc_exhaust_thm], collapse_thms, expand_thms, case_conv_thms)
blanchet@49116
   597
            end;
blanchet@49025
   598
blanchet@49033
   599
        val (case_cong_thm, weak_case_cong_thm) =
blanchet@49032
   600
          let
blanchet@51763
   601
            fun mk_prem xctr xs xf xg =
blanchet@49486
   602
              fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
blanchet@51763
   603
                mk_Trueprop_eq (xf, xg)));
blanchet@49033
   604
blanchet@49032
   605
            val goal =
blanchet@51763
   606
              Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
blanchet@51759
   607
                 mk_Trueprop_eq (eta_ufcase, eta_vgcase));
blanchet@49591
   608
            val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
blanchet@49032
   609
          in
wenzelm@51717
   610
            (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
wenzelm@51551
   611
             Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
blanchet@49692
   612
            |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
blanchet@49032
   613
          end;
blanchet@49025
   614
blanchet@49044
   615
        val (split_thm, split_asm_thm) =
blanchet@49043
   616
          let
blanchet@49044
   617
            fun mk_conjunct xctr xs f_xs =
blanchet@49486
   618
              list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
blanchet@49044
   619
            fun mk_disjunct xctr xs f_xs =
blanchet@49486
   620
              list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
blanchet@49044
   621
                HOLogic.mk_not (q $ f_xs)));
blanchet@49044
   622
blanchet@51770
   623
            val lhs = q $ ufcase;
blanchet@49044
   624
blanchet@49043
   625
            val goal =
blanchet@49044
   626
              mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
blanchet@49458
   627
            val asm_goal =
blanchet@49044
   628
              mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
blanchet@49044
   629
                (map3 mk_disjunct xctrs xss xfs)));
blanchet@49044
   630
blanchet@49044
   631
            val split_thm =
wenzelm@51551
   632
              Goal.prove_sorry lthy [] [] goal
wenzelm@51717
   633
                (fn _ => mk_split_tac lthy uexhaust_thm case_thms inject_thmss distinct_thmsss)
blanchet@49692
   634
              |> Thm.close_derivation
blanchet@49692
   635
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49044
   636
            val split_asm_thm =
wenzelm@51551
   637
              Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
blanchet@49044
   638
                mk_split_asm_tac ctxt split_thm)
blanchet@49692
   639
              |> Thm.close_derivation
blanchet@49692
   640
              |> singleton (Proof_Context.export names_lthy lthy);
blanchet@49043
   641
          in
blanchet@49044
   642
            (split_thm, split_asm_thm)
blanchet@49043
   643
          end;
blanchet@49025
   644
blanchet@49437
   645
        val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
blanchet@49300
   646
        val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));
blanchet@49300
   647
blanchet@49052
   648
        val notes =
blanchet@49594
   649
          [(caseN, case_thms, simp_attrs),
blanchet@49594
   650
           (case_congN, [case_cong_thm], []),
blanchet@49594
   651
           (case_convN, case_conv_thms, []),
blanchet@49300
   652
           (collapseN, collapse_thms, simp_attrs),
blanchet@49300
   653
           (discsN, disc_thms, simp_attrs),
blanchet@49300
   654
           (disc_excludeN, disc_exclude_thms, []),
blanchet@49300
   655
           (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
blanchet@49300
   656
           (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
blanchet@49300
   657
           (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
blanchet@49486
   658
           (expandN, expand_thms, []),
blanchet@49438
   659
           (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
blanchet@49300
   660
           (nchotomyN, [nchotomy_thm], []),
blanchet@49300
   661
           (selsN, all_sel_thms, simp_attrs),
blanchet@49300
   662
           (splitN, [split_thm], []),
blanchet@49300
   663
           (split_asmN, [split_asm_thm], []),
blanchet@49633
   664
           (splitsN, [split_thm, split_asm_thm], []),
blanchet@49300
   665
           (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
blanchet@49300
   666
          |> filter_out (null o #2)
blanchet@49300
   667
          |> map (fn (thmN, thms, attrs) =>
blanchet@49633
   668
            ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
blanchet@49300
   669
blanchet@49300
   670
        val notes' =
blanchet@49300
   671
          [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
blanchet@49300
   672
          |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
blanchet@49019
   673
      in
blanchet@49591
   674
        ((discs, selss, exhaust_thm, inject_thms, distinct_thms, case_thms, disc_thmss, discI_thms,
traytel@51695
   675
          sel_thmss),
traytel@51695
   676
          lthy
traytel@51697
   677
          |> not rep_compat ?
traytel@51697
   678
             (Local_Theory.declaration {syntax = false, pervasive = true}
traytel@51697
   679
               (fn phi => Case_Translation.register
traytel@51697
   680
                 (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
traytel@51695
   681
          |> Local_Theory.notes (notes' @ notes) |> snd)
blanchet@49019
   682
      end;
blanchet@49017
   683
  in
blanchet@49121
   684
    (goalss, after_qed, lthy')
blanchet@49017
   685
  end;
blanchet@49017
   686
blanchet@51781
   687
fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
wenzelm@51551
   688
  map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
blanchet@51781
   689
  |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
blanchet@49280
   690
blanchet@51781
   691
val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
blanchet@49297
   692
  Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
blanchet@51781
   693
  prepare_wrap_free_constructors Syntax.read_term;
blanchet@49297
   694
blanchet@49280
   695
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --|  @{keyword "]"};
blanchet@49111
   696
blanchet@51790
   697
val parse_bindings = parse_bracket_list parse_binding;
blanchet@49280
   698
val parse_bindingss = parse_bracket_list parse_bindings;
blanchet@49280
   699
blanchet@51790
   700
val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
blanchet@49280
   701
val parse_bound_terms = parse_bracket_list parse_bound_term;
blanchet@49280
   702
val parse_bound_termss = parse_bracket_list parse_bound_terms;
blanchet@49017
   703
blanchet@49278
   704
val parse_wrap_options =
blanchet@49633
   705
  Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_dests"} >> K (true, false)) ||
blanchet@49633
   706
      (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
blanchet@49633
   707
    >> (pairself (exists I) o split_list)) (false, false);
blanchet@49278
   708
blanchet@49017
   709
val _ =
blanchet@51781
   710
  Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
blanchet@51797
   711
    "wrap an existing freely generated type's constructors"
blanchet@49278
   712
    ((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --
blanchet@49280
   713
      Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
blanchet@49280
   714
        Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
blanchet@51781
   715
     >> wrap_free_constructors_cmd);
blanchet@49017
   716
blanchet@49017
   717
end;