blanchet@50089
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(* Title: HOL/Codatatype/Tools/bnf_wrap.ML
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Author: Jasmin Blanchette, TU Muenchen
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Copyright 2012
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blanchet@50089
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Wrapping existing datatypes.
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*)
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signature BNF_WRAP =
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sig
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val mk_half_pairss: 'a list -> ('a * 'a) list list
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val mk_ctr: typ list -> term -> term
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val base_name_of_ctr: term -> string
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val wrap_datatype: ({prems: thm list, context: Proof.context} -> tactic) list list ->
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((bool * term list) * term) *
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(binding list * (binding list list * (binding * term) list list)) -> local_theory ->
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(term list list * thm list * thm list * thm list * thm list * thm list list) * local_theory
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val parse_wrap_options: bool parser
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val parse_bound_term: (binding * string) parser
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end;
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structure BNF_Wrap : BNF_WRAP =
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struct
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open BNF_Util
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open BNF_Wrap_Tactics
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val isN = "is_";
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blanchet@50238
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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 case_congN = "case_cong";
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val case_eqN = "case_eq";
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val casesN = "cases";
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blanchet@50133
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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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blanchet@50090
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val exhaustN = "exhaust";
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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 split_asmN = "split_asm";
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val weak_case_cong_thmsN = "weak_case_cong";
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blanchet@50034
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val std_binding = @{binding _};
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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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blanchet@50061
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fun pad_list x n xs = xs @ replicate (n - length xs) x;
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blanchet@50274
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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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blanchet@50063
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fun mk_half_pairss' _ [] = []
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| mk_half_pairss' indent (y :: ys) =
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indent @ fold_rev (cons o single o pair y) ys (mk_half_pairss' ([] :: indent) ys);
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blanchet@50042
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blanchet@50063
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fun mk_half_pairss ys = mk_half_pairss' [[]] ys;
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blanchet@50042
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fun mk_undefined T = Const (@{const_name undefined}, T);
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blanchet@50070
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blanchet@50218
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fun mk_ctr Ts ctr =
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let val Type (_, Ts0) = body_type (fastype_of ctr) in
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Term.subst_atomic_types (Ts0 ~~ Ts) ctr
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end;
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blanchet@50218
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fun base_name_of_ctr c =
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Long_Name.base_name (case head_of c of
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Const (s, _) => s
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| Free (s, _) => s
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| _ => error "Cannot extract name of constructor");
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blanchet@50061
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fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
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blanchet@50452
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fun prepare_wrap_datatype prep_term (((no_dests, 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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(* TODO: attributes (simp, case_names, etc.) *)
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(* TODO: case syntax *)
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(* TODO: integration with function package ("size") *)
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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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blanchet@50136
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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 Type (dataT_name, As0) = body_type (fastype_of (hd ctrs0));
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val data_b = Binding.qualified_name dataT_name;
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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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blanchet@50070
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val ctr_Tss = map (binder_types o fastype_of) ctrs;
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blanchet@50070
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val ms = map length ctr_Tss;
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blanchet@50070
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traytel@50449
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val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
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blanchet@50135
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fun can_really_rely_on_disc k =
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traytel@50449
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not (Binding.eq_name (nth raw_disc_bindings' (k - 1), Binding.empty)) orelse
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nth ms (k - 1) = 0;
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blanchet@50167
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fun can_rely_on_disc k =
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can_really_rely_on_disc k orelse (k = 1 andalso not (can_really_rely_on_disc 2));
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fun can_omit_disc_binding k m =
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n = 1 orelse m = 0 orelse (n = 2 andalso can_rely_on_disc (3 - k));
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val std_disc_binding =
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Binding.qualify false (Binding.name_of data_b) 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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Option.map (Binding.qualify false (Binding.name_of data_b))
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(if Binding.eq_name (disc, Binding.empty) then
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if can_omit_disc_binding k m then NONE else SOME (std_disc_binding ctr)
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else if Binding.eq_name (disc, std_binding) then
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SOME (std_disc_binding ctr)
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else
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SOME disc)) ks ms ctrs0;
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val no_discs = map is_none disc_bindings;
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blanchet@50152
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val no_discs_at_all = forall I no_discs;
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blanchet@50131
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fun std_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
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blanchet@50135
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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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Binding.qualify false (Binding.name_of data_b)
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(if Binding.eq_name (sel, Binding.empty) orelse Binding.eq_name (sel, std_binding) then
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std_sel_binding m l ctr
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else
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traytel@50449
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sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
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blanchet@50035
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blanchet@50145
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fun mk_case Ts T =
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blanchet@50136
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let
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val (bindings, body) = strip_type (fastype_of case0)
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val Type (_, Ts0) = List.last bindings
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in Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) case0 end;
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blanchet@50037
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blanchet@50216
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val casex = mk_case As B;
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blanchet@50216
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val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
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blanchet@50058
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blanchet@50379
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val ((((((((xss, xss'), yss), fs), gs), (v, v')), w), (p, p')), names_lthy) = no_defs_lthy |>
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blanchet@50379
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mk_Freess' "x" ctr_Tss
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||>> mk_Freess "y" ctr_Tss
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blanchet@50216
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||>> mk_Frees "f" case_Ts
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blanchet@50216
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||>> mk_Frees "g" case_Ts
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blanchet@50315
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "v") dataT
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blanchet@50315
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||>> yield_singleton (mk_Frees "w") dataT
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blanchet@50058
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||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
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blanchet@50058
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blanchet@50058
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val q = Free (fst p', B --> HOLogic.boolT);
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blanchet@50035
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blanchet@50225
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fun ap_v t = t $ v;
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blanchet@50152
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fun mk_v_eq_v () = HOLogic.mk_eq (v, v);
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blanchet@50152
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blanchet@50040
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val xctrs = map2 (curry Term.list_comb) ctrs xss;
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blanchet@50040
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val yctrs = map2 (curry Term.list_comb) ctrs yss;
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blanchet@50047
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blanchet@50058
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val xfs = map2 (curry Term.list_comb) fs xss;
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blanchet@50058
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val xgs = map2 (curry Term.list_comb) gs xss;
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blanchet@50058
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blanchet@50452
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val eta_fs = map2 eta_expand_arg xss xfs;
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blanchet@50452
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val eta_gs = map2 eta_expand_arg xss xgs;
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blanchet@50058
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blanchet@50216
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val fcase = Term.list_comb (casex, eta_fs);
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blanchet@50216
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val gcase = Term.list_comb (casex, eta_gs);
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blanchet@50035
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blanchet@50040
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val exist_xs_v_eq_ctrs =
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blanchet@50040
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map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (v, xctr))) xctrs xss;
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blanchet@50037
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blanchet@50293
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val unique_disc_no_def = TrueI; (*arbitrary marker*)
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blanchet@50293
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val alternate_disc_no_def = FalseE; (*arbitrary marker*)
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blanchet@50131
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blanchet@50293
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fun alternate_disc_lhs get_disc k =
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blanchet@50131
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HOLogic.mk_not
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blanchet@50351
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(case nth disc_bindings (k - 1) of
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blanchet@50167
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NONE => nth exist_xs_v_eq_ctrs (k - 1)
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blanchet@50293
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| SOME b => get_disc b (k - 1) $ v);
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blanchet@50131
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blanchet@50300
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val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
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blanchet@50293
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if no_dests then
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blanchet@50300
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(true, [], [], [], [], [], no_defs_lthy)
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blanchet@50293
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else
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blanchet@50293
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let
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blanchet@50315
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fun disc_free b = Free (Binding.name_of b, dataT --> HOLogic.boolT);
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blanchet@50040
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blanchet@50293
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fun disc_spec b exist_xs_v_eq_ctr = mk_Trueprop_eq (disc_free b $ v, exist_xs_v_eq_ctr);
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blanchet@50273
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blanchet@50293
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fun alternate_disc k = Term.lambda v (alternate_disc_lhs (K o disc_free) (3 - k));
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blanchet@50037
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blanchet@50379
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fun mk_default T t =
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blanchet@50379
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let
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blanchet@50379
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val Ts0 = map TFree (Term.add_tfreesT (fastype_of t) []);
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blanchet@50379
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val Ts = map TFree (Term.add_tfreesT T []);
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blanchet@50379
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in Term.subst_atomic_types (Ts0 ~~ Ts) t end;
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blanchet@50379
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blanchet@50295
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fun mk_sel_case_args b proto_sels T =
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blanchet@50295
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map2 (fn Ts => fn k =>
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blanchet@50295
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217 |
(case AList.lookup (op =) proto_sels k of
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blanchet@50295
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NONE =>
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blanchet@50379
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(case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
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blanchet@50379
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NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
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blanchet@50379
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221 |
| SOME t => mk_default (Ts ---> T) t)
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blanchet@50295
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222 |
| SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
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blanchet@50131
|
223 |
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blanchet@50293
|
224 |
fun sel_spec b proto_sels =
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blanchet@50293
|
225 |
let
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blanchet@50293
|
226 |
val _ =
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blanchet@50293
|
227 |
(case duplicates (op =) (map fst proto_sels) of
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blanchet@50293
|
228 |
k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
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blanchet@50293
|
229 |
" for constructor " ^
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blanchet@50293
|
230 |
quote (Syntax.string_of_term no_defs_lthy (nth ctrs (k - 1))))
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blanchet@50293
|
231 |
| [] => ())
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blanchet@50293
|
232 |
val T =
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blanchet@50293
|
233 |
(case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
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blanchet@50293
|
234 |
[T] => T
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blanchet@50293
|
235 |
| T :: T' :: _ => error ("Inconsistent range type for selector " ^
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blanchet@50293
|
236 |
quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ no_defs_lthy T) ^
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blanchet@50293
|
237 |
" vs. " ^ quote (Syntax.string_of_typ no_defs_lthy T')));
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blanchet@50293
|
238 |
in
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blanchet@50315
|
239 |
mk_Trueprop_eq (Free (Binding.name_of b, dataT --> T) $ v,
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blanchet@50295
|
240 |
Term.list_comb (mk_case As T, mk_sel_case_args b proto_sels T) $ v)
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blanchet@50293
|
241 |
end;
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blanchet@50273
|
242 |
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blanchet@50351
|
243 |
val sel_bindings = flat sel_bindingss;
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blanchet@50351
|
244 |
val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
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blanchet@50351
|
245 |
val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
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blanchet@50300
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246 |
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blanchet@50351
|
247 |
val sel_binding_index =
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blanchet@50351
|
248 |
if all_sels_distinct then 1 upto length sel_bindings
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blanchet@50351
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249 |
else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
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blanchet@50300
|
250 |
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blanchet@50300
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251 |
val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
|
blanchet@50315
|
252 |
val sel_infos =
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blanchet@50351
|
253 |
AList.group (op =) (sel_binding_index ~~ proto_sels)
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blanchet@50300
|
254 |
|> sort (int_ord o pairself fst)
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blanchet@50351
|
255 |
|> map snd |> curry (op ~~) uniq_sel_bindings;
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blanchet@50351
|
256 |
val sel_bindings = map fst sel_infos;
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blanchet@50273
|
257 |
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blanchet@50351
|
258 |
fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
|
blanchet@50037
|
259 |
|
blanchet@50293
|
260 |
val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
|
blanchet@50293
|
261 |
no_defs_lthy
|
blanchet@50293
|
262 |
|> apfst split_list o fold_map4 (fn k => fn m => fn exist_xs_v_eq_ctr =>
|
blanchet@50293
|
263 |
fn NONE =>
|
blanchet@50293
|
264 |
if n = 1 then pair (Term.lambda v (mk_v_eq_v ()), unique_disc_no_def)
|
blanchet@50293
|
265 |
else if m = 0 then pair (Term.lambda v exist_xs_v_eq_ctr, refl)
|
blanchet@50293
|
266 |
else pair (alternate_disc k, alternate_disc_no_def)
|
blanchet@50293
|
267 |
| SOME b => Specification.definition (SOME (b, NONE, NoSyn),
|
blanchet@50293
|
268 |
((Thm.def_binding b, []), disc_spec b exist_xs_v_eq_ctr)) #>> apsnd snd)
|
blanchet@50351
|
269 |
ks ms exist_xs_v_eq_ctrs disc_bindings
|
blanchet@50293
|
270 |
||>> apfst split_list o fold_map (fn (b, proto_sels) =>
|
blanchet@50293
|
271 |
Specification.definition (SOME (b, NONE, NoSyn),
|
blanchet@50315
|
272 |
((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
|
blanchet@50293
|
273 |
||> `Local_Theory.restore;
|
blanchet@50040
|
274 |
|
blanchet@50293
|
275 |
val phi = Proof_Context.export_morphism lthy lthy';
|
blanchet@50040
|
276 |
|
blanchet@50293
|
277 |
val disc_defs = map (Morphism.thm phi) raw_disc_defs;
|
blanchet@50296
|
278 |
val sel_defs = map (Morphism.thm phi) raw_sel_defs;
|
blanchet@50296
|
279 |
val sel_defss = unflat_selss sel_defs;
|
blanchet@50043
|
280 |
|
blanchet@50293
|
281 |
val discs0 = map (Morphism.term phi) raw_discs;
|
blanchet@50293
|
282 |
val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
|
blanchet@50043
|
283 |
|
blanchet@50293
|
284 |
fun mk_disc_or_sel Ts c =
|
blanchet@50293
|
285 |
Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of c))) ~~ Ts) c;
|
blanchet@50293
|
286 |
|
blanchet@50293
|
287 |
val discs = map (mk_disc_or_sel As) discs0;
|
blanchet@50293
|
288 |
val selss = map (map (mk_disc_or_sel As)) selss0;
|
blanchet@50293
|
289 |
in
|
blanchet@50300
|
290 |
(all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
|
blanchet@50293
|
291 |
end;
|
blanchet@50040
|
292 |
|
blanchet@50047
|
293 |
fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
|
blanchet@50044
|
294 |
|
blanchet@50035
|
295 |
val goal_exhaust =
|
blanchet@50047
|
296 |
let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (v, xctr)]) in
|
blanchet@50136
|
297 |
fold_rev Logic.all [p, v] (mk_imp_p (map2 mk_prem xctrs xss))
|
blanchet@50035
|
298 |
end;
|
blanchet@50032
|
299 |
|
blanchet@50049
|
300 |
val goal_injectss =
|
blanchet@50032
|
301 |
let
|
blanchet@50049
|
302 |
fun mk_goal _ _ [] [] = []
|
blanchet@50040
|
303 |
| mk_goal xctr yctr xs ys =
|
blanchet@50136
|
304 |
[fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
|
blanchet@50136
|
305 |
Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
|
blanchet@50032
|
306 |
in
|
blanchet@50049
|
307 |
map4 mk_goal xctrs yctrs xss yss
|
blanchet@50032
|
308 |
end;
|
blanchet@50032
|
309 |
|
blanchet@50063
|
310 |
val goal_half_distinctss =
|
blanchet@50136
|
311 |
let
|
blanchet@50218
|
312 |
fun mk_goal ((xs, xc), (xs', xc')) =
|
blanchet@50136
|
313 |
fold_rev Logic.all (xs @ xs')
|
blanchet@50218
|
314 |
(HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
|
blanchet@50136
|
315 |
in
|
blanchet@50136
|
316 |
map (map mk_goal) (mk_half_pairss (xss ~~ xctrs))
|
blanchet@50136
|
317 |
end;
|
blanchet@50034
|
318 |
|
blanchet@50136
|
319 |
val goal_cases =
|
blanchet@50136
|
320 |
map3 (fn xs => fn xctr => fn xf =>
|
blanchet@50216
|
321 |
fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xss xctrs xfs;
|
blanchet@50040
|
322 |
|
blanchet@50136
|
323 |
val goalss = [goal_exhaust] :: goal_injectss @ goal_half_distinctss @ [goal_cases];
|
blanchet@50034
|
324 |
|
blanchet@50034
|
325 |
fun after_qed thmss lthy =
|
blanchet@50034
|
326 |
let
|
blanchet@50063
|
327 |
val ([exhaust_thm], (inject_thmss, (half_distinct_thmss, [case_thms]))) =
|
blanchet@50063
|
328 |
(hd thmss, apsnd (chop (n * n)) (chop n (tl thmss)));
|
blanchet@50034
|
329 |
|
blanchet@50453
|
330 |
val inject_thms = flat inject_thmss;
|
blanchet@50453
|
331 |
|
blanchet@50047
|
332 |
val exhaust_thm' =
|
blanchet@50047
|
333 |
let val Tinst = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As) in
|
blanchet@50047
|
334 |
Drule.instantiate' [] [SOME (certify lthy v)]
|
blanchet@50047
|
335 |
(Thm.instantiate (Tinst, []) (Drule.zero_var_indexes exhaust_thm))
|
blanchet@50047
|
336 |
end;
|
blanchet@50047
|
337 |
|
blanchet@50315
|
338 |
val exhaust_cases = map base_name_of_ctr ctrs;
|
blanchet@50315
|
339 |
|
blanchet@50063
|
340 |
val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
|
blanchet@50063
|
341 |
|
blanchet@50067
|
342 |
val (distinct_thmsss', distinct_thmsss) =
|
blanchet@50063
|
343 |
map2 (map2 append) (Library.chop_groups n half_distinct_thmss)
|
blanchet@50067
|
344 |
(transpose (Library.chop_groups n other_half_distinct_thmss))
|
blanchet@50067
|
345 |
|> `transpose;
|
blanchet@50063
|
346 |
val distinct_thms = interleave (flat half_distinct_thmss) (flat other_half_distinct_thmss);
|
blanchet@50034
|
347 |
|
blanchet@50035
|
348 |
val nchotomy_thm =
|
blanchet@50035
|
349 |
let
|
blanchet@50035
|
350 |
val goal =
|
blanchet@50037
|
351 |
HOLogic.mk_Trueprop (HOLogic.mk_all (fst v', snd v',
|
blanchet@50044
|
352 |
Library.foldr1 HOLogic.mk_disj exist_xs_v_eq_ctrs));
|
blanchet@50035
|
353 |
in
|
blanchet@50035
|
354 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
|
blanchet@50035
|
355 |
end;
|
blanchet@50035
|
356 |
|
blanchet@50296
|
357 |
val (all_sel_thms, sel_thmss, disc_thms, discI_thms, disc_exclude_thms, disc_exhaust_thms,
|
blanchet@50296
|
358 |
collapse_thms, case_eq_thms) =
|
blanchet@50293
|
359 |
if no_dests then
|
blanchet@50296
|
360 |
([], [], [], [], [], [], [], [])
|
blanchet@50131
|
361 |
else
|
blanchet@50131
|
362 |
let
|
blanchet@50379
|
363 |
fun make_sel_thm xs' case_thm sel_def =
|
blanchet@50379
|
364 |
zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
|
blanchet@50379
|
365 |
(Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
|
blanchet@50296
|
366 |
|
blanchet@50296
|
367 |
fun has_undefined_rhs thm =
|
blanchet@50296
|
368 |
(case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
|
blanchet@50296
|
369 |
Const (@{const_name undefined}, _) => true
|
blanchet@50296
|
370 |
| _ => false);
|
blanchet@50296
|
371 |
|
blanchet@50379
|
372 |
val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
|
blanchet@50296
|
373 |
|
blanchet@50296
|
374 |
val all_sel_thms =
|
blanchet@50300
|
375 |
(if all_sels_distinct andalso forall null sel_defaultss then
|
blanchet@50300
|
376 |
flat sel_thmss
|
blanchet@50300
|
377 |
else
|
blanchet@50379
|
378 |
map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
|
blanchet@50379
|
379 |
(xss' ~~ case_thms))
|
blanchet@50300
|
380 |
|> filter_out has_undefined_rhs;
|
blanchet@50043
|
381 |
|
blanchet@50293
|
382 |
fun mk_unique_disc_def () =
|
blanchet@50293
|
383 |
let
|
blanchet@50293
|
384 |
val m = the_single ms;
|
blanchet@50293
|
385 |
val goal = mk_Trueprop_eq (mk_v_eq_v (), the_single exist_xs_v_eq_ctrs);
|
blanchet@50293
|
386 |
in
|
blanchet@50293
|
387 |
Skip_Proof.prove lthy [] [] goal (fn _ => mk_unique_disc_def_tac m exhaust_thm')
|
blanchet@50293
|
388 |
|> singleton (Proof_Context.export names_lthy lthy)
|
blanchet@50293
|
389 |
|> Thm.close_derivation
|
blanchet@50293
|
390 |
end;
|
blanchet@50043
|
391 |
|
blanchet@50293
|
392 |
fun mk_alternate_disc_def k =
|
blanchet@50293
|
393 |
let
|
blanchet@50293
|
394 |
val goal =
|
blanchet@50293
|
395 |
mk_Trueprop_eq (alternate_disc_lhs (K (nth discs)) (3 - k),
|
blanchet@50293
|
396 |
nth exist_xs_v_eq_ctrs (k - 1));
|
blanchet@50293
|
397 |
in
|
blanchet@50293
|
398 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
|
blanchet@50293
|
399 |
mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
|
blanchet@50293
|
400 |
(nth distinct_thms (2 - k)) exhaust_thm')
|
blanchet@50293
|
401 |
|> singleton (Proof_Context.export names_lthy lthy)
|
blanchet@50293
|
402 |
|> Thm.close_derivation
|
blanchet@50293
|
403 |
end;
|
blanchet@50043
|
404 |
|
blanchet@50293
|
405 |
val has_alternate_disc_def =
|
blanchet@50293
|
406 |
exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
|
blanchet@50293
|
407 |
|
blanchet@50293
|
408 |
val disc_defs' =
|
blanchet@50293
|
409 |
map2 (fn k => fn def =>
|
blanchet@50293
|
410 |
if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
|
blanchet@50293
|
411 |
else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
|
blanchet@50293
|
412 |
else def) ks disc_defs;
|
blanchet@50293
|
413 |
|
blanchet@50293
|
414 |
val discD_thms = map (fn def => def RS iffD1) disc_defs';
|
blanchet@50293
|
415 |
val discI_thms =
|
blanchet@50293
|
416 |
map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
|
blanchet@50293
|
417 |
disc_defs';
|
blanchet@50293
|
418 |
val not_discI_thms =
|
blanchet@50293
|
419 |
map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
|
blanchet@50293
|
420 |
(Local_Defs.unfold lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
|
blanchet@50293
|
421 |
ms disc_defs';
|
blanchet@50293
|
422 |
|
blanchet@50293
|
423 |
val (disc_thmss', disc_thmss) =
|
blanchet@50293
|
424 |
let
|
blanchet@50293
|
425 |
fun mk_thm discI _ [] = refl RS discI
|
blanchet@50293
|
426 |
| mk_thm _ not_discI [distinct] = distinct RS not_discI;
|
blanchet@50293
|
427 |
fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
|
blanchet@50293
|
428 |
in
|
blanchet@50293
|
429 |
map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
|
blanchet@50293
|
430 |
end;
|
blanchet@50293
|
431 |
|
blanchet@50293
|
432 |
val disc_thms = flat (map2 (fn true => K [] | false => I) no_discs disc_thmss);
|
blanchet@50293
|
433 |
|
blanchet@50293
|
434 |
val disc_exclude_thms =
|
blanchet@50293
|
435 |
if has_alternate_disc_def then
|
blanchet@50293
|
436 |
[]
|
blanchet@50293
|
437 |
else
|
blanchet@50293
|
438 |
let
|
blanchet@50293
|
439 |
fun mk_goal [] = []
|
blanchet@50293
|
440 |
| mk_goal [((_, true), (_, true))] = []
|
blanchet@50293
|
441 |
| mk_goal [(((_, disc), _), ((_, disc'), _))] =
|
blanchet@50293
|
442 |
[Logic.all v (Logic.mk_implies (HOLogic.mk_Trueprop (betapply (disc, v)),
|
blanchet@50293
|
443 |
HOLogic.mk_Trueprop (HOLogic.mk_not (betapply (disc', v)))))];
|
blanchet@50293
|
444 |
fun prove tac goal = Skip_Proof.prove lthy [] [] goal (K tac);
|
blanchet@50293
|
445 |
|
blanchet@50315
|
446 |
val infos = ms ~~ discD_thms ~~ discs ~~ no_discs;
|
blanchet@50315
|
447 |
val half_pairss = mk_half_pairss infos;
|
blanchet@50293
|
448 |
|
blanchet@50293
|
449 |
val goal_halvess = map mk_goal half_pairss;
|
blanchet@50293
|
450 |
val half_thmss =
|
blanchet@50293
|
451 |
map3 (fn [] => K (K []) | [goal] => fn [((((m, discD), _), _), _)] =>
|
blanchet@50293
|
452 |
fn disc_thm => [prove (mk_half_disc_exclude_tac m discD disc_thm) goal])
|
blanchet@50293
|
453 |
goal_halvess half_pairss (flat disc_thmss');
|
blanchet@50293
|
454 |
|
blanchet@50293
|
455 |
val goal_other_halvess = map (mk_goal o map swap) half_pairss;
|
blanchet@50293
|
456 |
val other_half_thmss =
|
blanchet@50293
|
457 |
map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
|
blanchet@50293
|
458 |
goal_other_halvess;
|
blanchet@50293
|
459 |
in
|
blanchet@50293
|
460 |
interleave (flat half_thmss) (flat other_half_thmss)
|
blanchet@50293
|
461 |
end;
|
blanchet@50293
|
462 |
|
blanchet@50293
|
463 |
val disc_exhaust_thms =
|
blanchet@50293
|
464 |
if has_alternate_disc_def orelse no_discs_at_all then
|
blanchet@50293
|
465 |
[]
|
blanchet@50293
|
466 |
else
|
blanchet@50293
|
467 |
let
|
blanchet@50293
|
468 |
fun mk_prem disc = mk_imp_p [HOLogic.mk_Trueprop (betapply (disc, v))];
|
blanchet@50293
|
469 |
val goal = fold_rev Logic.all [p, v] (mk_imp_p (map mk_prem discs));
|
blanchet@50293
|
470 |
in
|
blanchet@50293
|
471 |
[Skip_Proof.prove lthy [] [] goal (fn _ =>
|
blanchet@50293
|
472 |
mk_disc_exhaust_tac n exhaust_thm discI_thms)]
|
blanchet@50293
|
473 |
end;
|
blanchet@50293
|
474 |
|
blanchet@50293
|
475 |
val collapse_thms =
|
blanchet@50293
|
476 |
if no_dests then
|
blanchet@50293
|
477 |
[]
|
blanchet@50293
|
478 |
else
|
blanchet@50293
|
479 |
let
|
blanchet@50293
|
480 |
fun mk_goal ctr disc sels =
|
blanchet@50293
|
481 |
let
|
blanchet@50293
|
482 |
val prem = HOLogic.mk_Trueprop (betapply (disc, v));
|
blanchet@50293
|
483 |
val concl =
|
blanchet@50293
|
484 |
mk_Trueprop_eq ((null sels ? swap)
|
blanchet@50293
|
485 |
(Term.list_comb (ctr, map ap_v sels), v));
|
blanchet@50293
|
486 |
in
|
blanchet@50293
|
487 |
if prem aconv concl then NONE
|
blanchet@50293
|
488 |
else SOME (Logic.all v (Logic.mk_implies (prem, concl)))
|
blanchet@50293
|
489 |
end;
|
blanchet@50293
|
490 |
val goals = map3 mk_goal ctrs discs selss;
|
blanchet@50293
|
491 |
in
|
blanchet@50293
|
492 |
map4 (fn m => fn discD => fn sel_thms => Option.map (fn goal =>
|
blanchet@50293
|
493 |
Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
|
blanchet@50293
|
494 |
mk_collapse_tac ctxt m discD sel_thms)
|
blanchet@50293
|
495 |
|> perhaps (try (fn thm => refl RS thm)))) ms discD_thms sel_thmss goals
|
blanchet@50293
|
496 |
|> map_filter I
|
blanchet@50293
|
497 |
end;
|
blanchet@50293
|
498 |
|
blanchet@50293
|
499 |
val case_eq_thms =
|
blanchet@50293
|
500 |
if no_dests then
|
blanchet@50293
|
501 |
[]
|
blanchet@50293
|
502 |
else
|
blanchet@50293
|
503 |
let
|
blanchet@50293
|
504 |
fun mk_body f sels = Term.list_comb (f, map ap_v sels);
|
blanchet@50293
|
505 |
val goal =
|
blanchet@50293
|
506 |
mk_Trueprop_eq (fcase $ v, mk_IfN B (map ap_v discs) (map2 mk_body fs selss));
|
blanchet@50293
|
507 |
in
|
blanchet@50293
|
508 |
[Skip_Proof.prove lthy [] [] goal (fn {context = ctxt, ...} =>
|
blanchet@50293
|
509 |
mk_case_eq_tac ctxt n exhaust_thm' case_thms disc_thmss' sel_thmss)]
|
blanchet@50293
|
510 |
|> Proof_Context.export names_lthy lthy
|
blanchet@50293
|
511 |
end;
|
blanchet@50131
|
512 |
in
|
blanchet@50296
|
513 |
(all_sel_thms, sel_thmss, disc_thms, discI_thms, disc_exclude_thms, disc_exhaust_thms,
|
blanchet@50293
|
514 |
collapse_thms, case_eq_thms)
|
blanchet@50131
|
515 |
end;
|
blanchet@50040
|
516 |
|
blanchet@50048
|
517 |
val (case_cong_thm, weak_case_cong_thm) =
|
blanchet@50047
|
518 |
let
|
blanchet@50047
|
519 |
fun mk_prem xctr xs f g =
|
blanchet@50060
|
520 |
fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (w, xctr),
|
blanchet@50047
|
521 |
mk_Trueprop_eq (f, g)));
|
blanchet@50048
|
522 |
|
blanchet@50048
|
523 |
val v_eq_w = mk_Trueprop_eq (v, w);
|
blanchet@50047
|
524 |
|
blanchet@50047
|
525 |
val goal =
|
blanchet@50048
|
526 |
Logic.list_implies (v_eq_w :: map4 mk_prem xctrs xss fs gs,
|
blanchet@50216
|
527 |
mk_Trueprop_eq (fcase $ v, gcase $ w));
|
blanchet@50216
|
528 |
val goal_weak = Logic.mk_implies (v_eq_w, mk_Trueprop_eq (fcase $ v, fcase $ w));
|
blanchet@50047
|
529 |
in
|
blanchet@50064
|
530 |
(Skip_Proof.prove lthy [] [] goal (fn _ => mk_case_cong_tac exhaust_thm' case_thms),
|
blanchet@50048
|
531 |
Skip_Proof.prove lthy [] [] goal_weak (K (etac arg_cong 1)))
|
blanchet@50048
|
532 |
|> pairself (singleton (Proof_Context.export names_lthy lthy))
|
blanchet@50047
|
533 |
end;
|
blanchet@50040
|
534 |
|
blanchet@50059
|
535 |
val (split_thm, split_asm_thm) =
|
blanchet@50058
|
536 |
let
|
blanchet@50059
|
537 |
fun mk_conjunct xctr xs f_xs =
|
blanchet@50058
|
538 |
list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (v, xctr), q $ f_xs));
|
blanchet@50059
|
539 |
fun mk_disjunct xctr xs f_xs =
|
blanchet@50059
|
540 |
list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (v, xctr),
|
blanchet@50059
|
541 |
HOLogic.mk_not (q $ f_xs)));
|
blanchet@50059
|
542 |
|
blanchet@50216
|
543 |
val lhs = q $ (fcase $ v);
|
blanchet@50059
|
544 |
|
blanchet@50058
|
545 |
val goal =
|
blanchet@50059
|
546 |
mk_Trueprop_eq (lhs, Library.foldr1 HOLogic.mk_conj (map3 mk_conjunct xctrs xss xfs));
|
blanchet@50059
|
547 |
val goal_asm =
|
blanchet@50059
|
548 |
mk_Trueprop_eq (lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
|
blanchet@50059
|
549 |
(map3 mk_disjunct xctrs xss xfs)));
|
blanchet@50059
|
550 |
|
blanchet@50059
|
551 |
val split_thm =
|
blanchet@50064
|
552 |
Skip_Proof.prove lthy [] [] goal
|
blanchet@50067
|
553 |
(fn _ => mk_split_tac exhaust_thm' case_thms inject_thmss distinct_thmsss)
|
blanchet@50059
|
554 |
|> singleton (Proof_Context.export names_lthy lthy)
|
blanchet@50059
|
555 |
val split_asm_thm =
|
blanchet@50059
|
556 |
Skip_Proof.prove lthy [] [] goal_asm (fn {context = ctxt, ...} =>
|
blanchet@50059
|
557 |
mk_split_asm_tac ctxt split_thm)
|
blanchet@50059
|
558 |
|> singleton (Proof_Context.export names_lthy lthy)
|
blanchet@50058
|
559 |
in
|
blanchet@50059
|
560 |
(split_thm, split_asm_thm)
|
blanchet@50058
|
561 |
end;
|
blanchet@50040
|
562 |
|
blanchet@50452
|
563 |
val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
|
blanchet@50315
|
564 |
val cases_type_attr = Attrib.internal (K (Induct.cases_type dataT_name));
|
blanchet@50315
|
565 |
|
blanchet@50067
|
566 |
val notes =
|
blanchet@50315
|
567 |
[(case_congN, [case_cong_thm], []),
|
blanchet@50315
|
568 |
(case_eqN, case_eq_thms, []),
|
blanchet@50315
|
569 |
(casesN, case_thms, simp_attrs),
|
blanchet@50315
|
570 |
(collapseN, collapse_thms, simp_attrs),
|
blanchet@50315
|
571 |
(discsN, disc_thms, simp_attrs),
|
blanchet@50315
|
572 |
(disc_excludeN, disc_exclude_thms, []),
|
blanchet@50315
|
573 |
(disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
|
blanchet@50315
|
574 |
(distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
|
blanchet@50315
|
575 |
(exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
|
blanchet@50453
|
576 |
(injectN, inject_thms, iff_attrs @ induct_simp_attrs),
|
blanchet@50315
|
577 |
(nchotomyN, [nchotomy_thm], []),
|
blanchet@50315
|
578 |
(selsN, all_sel_thms, simp_attrs),
|
blanchet@50315
|
579 |
(splitN, [split_thm], []),
|
blanchet@50315
|
580 |
(split_asmN, [split_asm_thm], []),
|
blanchet@50315
|
581 |
(weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
|
blanchet@50315
|
582 |
|> filter_out (null o #2)
|
blanchet@50315
|
583 |
|> map (fn (thmN, thms, attrs) =>
|
blanchet@50317
|
584 |
((Binding.qualify true (Binding.name_of data_b) (Binding.name thmN), attrs),
|
blanchet@50317
|
585 |
[(thms, [])]));
|
blanchet@50315
|
586 |
|
blanchet@50315
|
587 |
val notes' =
|
blanchet@50315
|
588 |
[(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
|
blanchet@50315
|
589 |
|> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
|
blanchet@50034
|
590 |
in
|
blanchet@50453
|
591 |
((selss, inject_thms, distinct_thms, case_thms, discI_thms, sel_thmss),
|
blanchet@50453
|
592 |
lthy |> Local_Theory.notes (notes' @ notes) |> snd)
|
blanchet@50034
|
593 |
end;
|
blanchet@50032
|
594 |
in
|
blanchet@50136
|
595 |
(goalss, after_qed, lthy')
|
blanchet@50032
|
596 |
end;
|
blanchet@50032
|
597 |
|
blanchet@50214
|
598 |
fun wrap_datatype tacss = (fn (goalss, after_qed, lthy) =>
|
blanchet@50126
|
599 |
map2 (map2 (Skip_Proof.prove lthy [] [])) goalss tacss
|
blanchet@50295
|
600 |
|> (fn thms => after_qed thms lthy)) oo prepare_wrap_datatype (K I);
|
blanchet@50126
|
601 |
|
blanchet@50312
|
602 |
val wrap_datatype_cmd = (fn (goalss, after_qed, lthy) =>
|
blanchet@50312
|
603 |
Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
|
blanchet@50312
|
604 |
prepare_wrap_datatype Syntax.read_term;
|
blanchet@50312
|
605 |
|
blanchet@50295
|
606 |
fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --| @{keyword "]"};
|
blanchet@50295
|
607 |
|
blanchet@50295
|
608 |
val parse_bindings = parse_bracket_list Parse.binding;
|
blanchet@50295
|
609 |
val parse_bindingss = parse_bracket_list parse_bindings;
|
blanchet@50295
|
610 |
|
blanchet@50295
|
611 |
val parse_bound_term = (Parse.binding --| @{keyword ":"}) -- Parse.term;
|
blanchet@50295
|
612 |
val parse_bound_terms = parse_bracket_list parse_bound_term;
|
blanchet@50295
|
613 |
val parse_bound_termss = parse_bracket_list parse_bound_terms;
|
blanchet@50032
|
614 |
|
blanchet@50293
|
615 |
val parse_wrap_options =
|
blanchet@50293
|
616 |
Scan.optional (@{keyword "("} |-- (@{keyword "no_dests"} >> K true) --| @{keyword ")"}) false;
|
blanchet@50293
|
617 |
|
blanchet@50032
|
618 |
val _ =
|
blanchet@50089
|
619 |
Outer_Syntax.local_theory_to_proof @{command_spec "wrap_data"} "wraps an existing datatype"
|
blanchet@50293
|
620 |
((parse_wrap_options -- (@{keyword "["} |-- Parse.list Parse.term --| @{keyword "]"}) --
|
blanchet@50295
|
621 |
Parse.term -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
|
blanchet@50295
|
622 |
Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
|
blanchet@50214
|
623 |
>> wrap_datatype_cmd);
|
blanchet@50032
|
624 |
|
blanchet@50032
|
625 |
end;
|