(* Title: HOL/Library/bnf_decl.ML
Author: Dmitriy Traytel, TU Muenchen
Copyright 2013
Axiomatic declaration of bounded natural functors.
*)
signature BNF_DECL =
sig
val bnf_decl: (binding option * (typ * sort)) list -> binding -> mixfix -> binding -> binding ->
typ list -> local_theory -> BNF_Def.bnf * local_theory
end
structure BNF_Decl : BNF_DECL =
struct
open BNF_Util
open BNF_Def
fun prepare_decl prepare_constraint prepare_typ raw_vars b mx user_mapb user_relb user_witTs lthy =
let
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 (b, length vars, mx) lthy;
val (bd_type_Tname, lthy) =
Typedecl.basic_typedecl (mk_b "bd_type" Binding.empty, length deads, NoSyn) lthy;
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 BNF_Def.mapN user_mapb;
val bdb = mk_b "bd" Binding.empty;
val setbs = map2 (fn b => fn i => mk_b (BNF_Def.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 (BNF_Def.mk_witN i) Binding.empty)
(if nwits = 1 then [0] else 1 upto nwits);
val lthy = Local_Theory.background_theory
(Sign.add_consts_i ((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) I (K I) (K I) (SOME (map TFree deads))
user_mapb user_relb user_setbs ((((((Binding.empty, T), Fmap), Fsets), Fbd), Fwits), 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_old, lthy)) = Local_Theory.background_theory_result
(Specification.axiomatization [] [((mk_b "axioms" Binding.empty, []), flat all_goalss)]) lthy
||> `Local_Theory.restore;
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)
|> Conjunction.elim_balanced (length wit_goals)
|> map2 (Conjunction.elim_balanced o length) wit_goalss
|> map (map (Thm.close_derivation o Thm.forall_elim_vars 0));
val phi = Proof_Context.export_morphism lthy_old lthy;
val thms = unflat all_goalss (Morphism.fact phi raw_thms);
in
BNF_Def.register_bnf key (after_qed mk_wit_thms thms lthy)
end;
val bnf_decl = prepare_decl (K I) (K I);
fun read_constraint _ NONE = HOLogic.typeS
| read_constraint ctxt (SOME s) = Syntax.read_sort ctxt s;
val bnf_decl_cmd = prepare_decl read_constraint Syntax.read_typ;
val parse_witTs =
@{keyword "["} |-- (Parse.short_ident --| @{keyword ":"} -- Scan.repeat Parse.typ
>> (fn ("wits", Ts) => Ts
| (s, _) => error ("Unknown label " ^ quote s ^ " (expected \"wits\")"))) --|
@{keyword "]"} || Scan.succeed [];
val parse_bnf_decl =
parse_type_args_named_constrained -- parse_binding -- parse_map_rel_bindings --
parse_witTs -- Parse.opt_mixfix;
val _ =
Outer_Syntax.local_theory @{command_spec "bnf_decl"} "bnf declaration"
(parse_bnf_decl >>
(fn ((((bsTs, b), (mapb, relb)), witTs), mx) =>
bnf_decl_cmd bsTs b mx mapb relb witTs #> snd));
end;