header {* Reflecting Pure types into HOL *}
theory Typerep
imports Plain String
begin
datatype typerep = Typerep String.literal "typerep list"
class typerep =
fixes typerep :: "'a itself => typerep"
begin
definition typerep_of :: "'a => typerep" where
[simp]: "typerep_of x = typerep TYPE('a)"
end
syntax
"_TYPEREP" :: "type => logic" ("(1TYPEREP/(1'(_')))")
parse_translation {*
let
fun typerep_tr (*"_TYPEREP"*) [ty] =
Syntax.const @{const_syntax typerep} $
(Syntax.const @{syntax_const "_constrain"} $ Syntax.const @{const_syntax "TYPE"} $
(Syntax.const @{type_syntax itself} $ ty))
| typerep_tr (*"_TYPEREP"*) ts = raise TERM ("typerep_tr", ts);
in [(@{syntax_const "_TYPEREP"}, typerep_tr)] end
*}
typed_print_translation (advanced) {*
let
fun typerep_tr' ctxt (*"typerep"*)
(Type (@{type_name fun}, [Type (@{type_name itself}, [T]), _]))
(Const (@{const_syntax TYPE}, _) :: ts) =
Term.list_comb
(Syntax.const @{syntax_const "_TYPEREP"} $ Syntax_Phases.term_of_typ ctxt T, ts)
| typerep_tr' _ T ts = raise Match;
in [(@{const_syntax typerep}, typerep_tr')] end
*}
setup {*
let
fun add_typerep tyco thy =
let
val sorts = replicate (Sign.arity_number thy tyco) @{sort typerep};
val vs = Name.invent_names Name.context "'a" sorts;
val ty = Type (tyco, map TFree vs);
val lhs = Const (@{const_name typerep}, Term.itselfT ty --> @{typ typerep})
$ Free ("T", Term.itselfT ty);
val rhs = @{term Typerep} $ HOLogic.mk_literal tyco
$ HOLogic.mk_list @{typ typerep} (map (HOLogic.mk_typerep o TFree) vs);
val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
in
thy
|> Class.instantiation ([tyco], vs, @{sort typerep})
|> `(fn lthy => Syntax.check_term lthy eq)
|-> (fn eq => Specification.definition (NONE, (Attrib.empty_binding, eq)))
|> snd
|> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
end;
fun ensure_typerep tyco thy = if not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep})
andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort type}
then add_typerep tyco thy else thy;
in
add_typerep @{type_name fun}
#> Typedef.interpretation ensure_typerep
#> Code.datatype_interpretation (ensure_typerep o fst)
#> Code.abstype_interpretation (ensure_typerep o fst)
end
*}
lemma [code]:
"HOL.equal (Typerep tyco1 tys1) (Typerep tyco2 tys2) <-> HOL.equal tyco1 tyco2
∧ list_all2 HOL.equal tys1 tys2"
by (auto simp add: eq_equal [symmetric] list_all2_eq [symmetric])
lemma [code nbe]:
"HOL.equal (x :: typerep) x <-> True"
by (fact equal_refl)
code_type typerep
(Eval "Term.typ")
code_const Typerep
(Eval "Term.Type/ (_, _)")
code_reserved Eval Term
hide_const (open) typerep Typerep
end