(* Title: HOL/Types_To_Sets/internalize_sort.ML
Author: Ondřej Kunčar, TU München
A derived rule (by using Thm.unconstrainT) that internalizes
type class annotations.
*)
(*
\<phi>['a::{c_1, ..., c_n} / 'a]
---------------------------------------------------------------------
class.c_1 ops_1 \<Longrightarrow> ... \<Longrightarrow> class.c_n ops_n \<Longrightarrow> \<phi>['a::type / 'a]
where class.c is the locale predicate associated with type class c and
ops are operations associated with type class c. For example:
If c = semigroup_add, then ops = op-, op+, 0, uminus.
If c = finite, then ops = TYPE('a::type).
*)
signature INTERNALIZE_SORT =
sig
val internalize_sort: ctyp -> thm -> typ * thm
val internalize_sort_attr: typ -> attribute
end;
structure Internalize_Sort : INTERNALIZE_SORT =
struct
fun internalize_sort ctvar thm =
let
val thy = Thm.theory_of_thm thm;
val tvar = Thm.typ_of ctvar;
val ((_, assms, classes),_) = Logic.unconstrainT [] (Thm.prop_of thm);
fun is_proper_class thy = can (Axclass.get_info thy); (* trick by FH *)
fun reduce_to_non_proper_sort (TVar (name, sort)) =
TVar (name, Sign.minimize_sort thy (filter_out (is_proper_class thy) (Sign.complete_sort thy sort)))
| reduce_to_non_proper_sort _ = error "not supported";
val data = (map fst classes) ~~ assms;
val new_tvar = get_first (fn (tvar', ((ren_tvar, _), _)) => if tvar = tvar'
then SOME (reduce_to_non_proper_sort ren_tvar) else NONE) data
|> the_default tvar;
fun localify class = Class.rules thy class |> snd |> Thm.transfer thy;
fun discharge_of_class tvar class = Thm.of_class (Thm.global_ctyp_of thy tvar, class);
val rules = map (fn (tvar', ((ren_tvar, class), _)) => if tvar = tvar'
then (if Class.is_class thy class then localify class else discharge_of_class ren_tvar class)
else discharge_of_class ren_tvar class) data;
in
(new_tvar, (Thm.unconstrainT (Thm.strip_shyps thm) OF rules) |> Drule.zero_var_indexes)
end;
val tvar = Args.context -- Args.typ >> (fn (_, v as TFree _) => Logic.varifyT_global v
| (ctxt, t) => error ("Not a type variable: " ^ Syntax.string_of_typ ctxt t));
fun internalize_sort_attr tvar =
Thm.rule_attribute [] (fn context => fn thm =>
(snd (internalize_sort (Thm.ctyp_of (Context.proof_of context) tvar) thm)));
val _ = Context.>> (Context.map_theory (Attrib.setup \<^binding>\<open>internalize_sort\<close>
(tvar >> internalize_sort_attr) "internalize a sort"));
end;