File ‹~~/src/HOL/Tools/BNF/bnf_axiomatization.ML›
signature BNF_AXIOMATIZATION =
sig
val bnf_axiomatization: (string -> bool) -> (binding option * (typ * sort)) list -> binding ->
mixfix -> binding -> binding -> binding -> typ list -> local_theory ->
BNF_Def.bnf * local_theory
end
structure BNF_Axiomatization : BNF_AXIOMATIZATION =
struct
open BNF_Util
open BNF_Def
fun prepare_decl prepare_plugins prepare_constraint prepare_typ
raw_plugins raw_vars b mx user_mapb user_relb user_predb user_witTs lthy =
let
val plugins = prepare_plugins lthy raw_plugins;
fun prepare_type_arg (set_opt, (ty, c)) =
let val s = fst (dest_TFree (prepare_typ lthy ty)) in
(set_opt, (s, prepare_constraint lthy c))
end;
val ((user_setbs, vars), raw_vars') =
map prepare_type_arg raw_vars
|> `split_list
|>> apfst (map_filter I);
val deads = map_filter (fn (NONE, x) => SOME x | _ => NONE) raw_vars';
fun mk_b name user_b =
(if Binding.is_empty user_b then Binding.prefix_name (name ^ "_") b else user_b)
|> Binding.qualify false (Binding.name_of b);
val (Tname, lthy) = Typedecl.basic_typedecl {final = true} (b, length vars, mx) lthy;
val (bd_type_Tname, lthy) = lthy
|> Typedecl.basic_typedecl {final = true} (mk_b "bd_type" Binding.empty, length deads, NoSyn);
val T = Type (Tname, map TFree vars);
val bd_type_T = Type (bd_type_Tname, map TFree deads);
val lives = map TFree (filter_out (member (op =) deads) vars);
val live = length lives;
val _ = "Trying to declare a BNF with no live variables" |> null lives ? error;
val (lives', _) = BNF_Util.mk_TFrees (length lives)
(fold Variable.declare_typ (map TFree vars) lthy);
val T' = Term.typ_subst_atomic (lives ~~ lives') T;
val mapT = map2 (curry op -->) lives lives' ---> T --> T';
val setTs = map (fn U => T --> HOLogic.mk_setT U) lives;
val bdT = BNF_Util.mk_relT (bd_type_T, bd_type_T);
val mapb = mk_b mapN user_mapb;
val bdb = mk_b "bd" Binding.empty;
val setbs = map2 (fn b => fn i => mk_b (mk_setN i) b) user_setbs
(if live = 1 then [0] else 1 upto live);
val witTs = map (prepare_typ lthy) user_witTs;
val nwits = length witTs;
val witbs = map (fn i => mk_b (mk_witN i) Binding.empty)
(if nwits = 1 then [0] else 1 upto nwits);
val lthy = Local_Theory.background_theory
(Sign.add_consts ((mapb, mapT, NoSyn) :: (bdb, bdT, NoSyn) ::
map2 (fn b => fn T => (b, T, NoSyn)) setbs setTs @
map2 (fn b => fn T => (b, T, NoSyn)) witbs witTs))
lthy;
val Fmap = Const (Local_Theory.full_name lthy mapb, mapT);
val Fsets = map2 (fn setb => fn setT =>
Const (Local_Theory.full_name lthy setb, setT)) setbs setTs;
val Fbd = Const (Local_Theory.full_name lthy bdb, bdT);
val Fwits = map2 (fn witb => fn witT =>
Const (Local_Theory.full_name lthy witb, witT)) witbs witTs;
val (key, goals, (triv_tac_opt, wit_goalss), after_qed, lthy, _) =
prepare_def Do_Inline (user_policy Note_Some) false I (K I) (K I) (SOME (map TFree deads))
user_mapb user_relb user_predb user_setbs
(((((((Binding.empty, T), Fmap), Fsets), Fbd), Fwits), NONE), NONE)
lthy;
fun mk_wits_tac ctxt set_maps = TRYALL Goal.conjunction_tac THEN the triv_tac_opt ctxt set_maps;
val wit_goals = map Logic.mk_conjunction_balanced wit_goalss;
val all_goalss = map single goals @ (if nwits > 0 then wit_goalss else []);
val (((_, raw_thms)), lthy) = Local_Theory.background_theory_result
(Specification.axiomatization [] [] []
(map_index (fn (i, ax) =>
((mk_b ("axiom" ^ string_of_int (i + 1)) Binding.empty, []), ax)) (flat all_goalss))) lthy;
fun mk_wit_thms set_maps =
Goal.prove_sorry lthy [] [] (Logic.mk_conjunction_balanced wit_goals)
(fn {context = ctxt, prems = _} => mk_wits_tac ctxt set_maps)
|> Thm.close_derivation ⌂
|> Conjunction.elim_balanced (length wit_goals)
|> map2 (Conjunction.elim_balanced o length) wit_goalss
|> (map o map) (Thm.forall_elim_vars 0);
val phi = Local_Theory.target_morphism lthy;
val thms = unflat all_goalss (Morphism.fact phi raw_thms);
val (bnf, lthy') = after_qed mk_wit_thms thms lthy
in
(bnf, register_bnf plugins key bnf lthy')
end;
val bnf_axiomatization = prepare_decl (K I) (K I) (K I);
fun read_constraint _ NONE = \<^sort>‹type›
| read_constraint ctxt (SOME s) = Syntax.read_sort ctxt s;
val bnf_axiomatization_cmd = prepare_decl Plugin_Name.make_filter read_constraint Syntax.read_typ;
val parse_witTs =
\<^keyword>‹[› |-- (Parse.name --| \<^keyword>‹:› -- Scan.repeat Parse.typ
>> (fn ("wits", Ts) => Ts
| (s, _) => error ("Unknown label " ^ quote s ^ " (expected \"wits\")"))) --|
\<^keyword>‹]› || Scan.succeed [];
val parse_bnf_axiomatization_options =
Scan.optional (\<^keyword>‹(› |-- Plugin_Name.parse_filter --| \<^keyword>‹)›) (K (K true));
val parse_bnf_axiomatization =
parse_bnf_axiomatization_options -- parse_type_args_named_constrained -- Parse.binding --
parse_witTs -- Parse.opt_mixfix -- parse_map_rel_pred_bindings;
val _ =
Outer_Syntax.local_theory \<^command_keyword>‹bnf_axiomatization› "bnf declaration"
(parse_bnf_axiomatization >>
(fn (((((plugins, bsTs), b), witTs), mx), (mapb, relb, predb)) =>
bnf_axiomatization_cmd plugins bsTs b mx mapb relb predb witTs #> snd));
end;