(* Title: HOL/Library/RType.thy
ID: $Id$
Author: Florian Haftmann, TU Muenchen
*)
header {* Reflecting Pure types into HOL *}
theory RType
imports Main Code_Message Code_Index (* import all 'special code' types *)
begin
datatype "rtype" = RType message_string "rtype list"
class rtype =
fixes rtype :: "'a\<Colon>{} itself \<Rightarrow> rtype"
begin
definition
rtype_of :: "'a \<Rightarrow> rtype"
where
[simp]: "rtype_of x = rtype TYPE('a)"
end
setup {*
let
fun rtype_tr (*"_RTYPE"*) [ty] =
Lexicon.const @{const_syntax rtype} $ (Lexicon.const "_constrain" $ Lexicon.const "TYPE" $
(Lexicon.const "itself" $ ty))
| rtype_tr (*"_RTYPE"*) ts = raise TERM ("rtype_tr", ts);
fun rtype_tr' show_sorts (*"rtype"*)
(Type ("fun", [Type ("itself", [T]), _])) (Const (@{const_syntax TYPE}, _) :: ts) =
Term.list_comb (Lexicon.const "_RTYPE" $ Syntax.term_of_typ show_sorts T, ts)
| rtype_tr' _ T ts = raise Match;
in
Sign.add_syntax_i
[("_RTYPE", SimpleSyntax.read_typ "type => logic", Delimfix "(1RTYPE/(1'(_')))")]
#> Sign.add_trfuns ([], [("_RTYPE", rtype_tr)], [], [])
#> Sign.add_trfunsT [(@{const_syntax rtype}, rtype_tr')]
end
*}
ML {*
structure RType =
struct
fun mk f (Type (tyco, tys)) =
@{term RType} $ Message_String.mk tyco
$ HOLogic.mk_list @{typ rtype} (map (mk f) tys)
| mk f (TFree v) =
f v;
fun rtype ty =
Const (@{const_name rtype}, Term.itselfT ty --> @{typ rtype})
$ Logic.mk_type ty;
fun add_def tyco thy =
let
val sorts = replicate (Sign.arity_number thy tyco) @{sort rtype};
val vs = Name.names Name.context "'a" sorts;
val ty = Type (tyco, map TFree vs);
val lhs = Const (@{const_name rtype}, Term.itselfT ty --> @{typ rtype})
$ Free ("T", Term.itselfT ty);
val rhs = mk (rtype o TFree) ty;
val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs));
in
thy
|> TheoryTarget.instantiation ([tyco], vs, @{sort rtype})
|> `(fn lthy => Syntax.check_term lthy eq)
|-> (fn eq => Specification.definition (NONE, (("", []), eq)))
|> snd
|> Class.prove_instantiation_instance (K (Class.intro_classes_tac []))
|> LocalTheory.exit
|> ProofContext.theory_of
end;
fun perhaps_add_def tyco thy =
let
val inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort rtype}
in if inst then thy else add_def tyco thy end;
end;
*}
setup {*
RType.add_def @{type_name prop}
#> RType.add_def @{type_name fun}
#> RType.add_def @{type_name itself}
#> RType.add_def @{type_name bool}
#> RType.add_def @{type_name set}
#> TypedefPackage.interpretation RType.perhaps_add_def
*}
lemma [code func]:
"RType tyco1 tys1 = RType tyco2 tys2 \<longleftrightarrow> tyco1 = tyco2
\<and> list_all2 (op =) tys1 tys2"
by (auto simp add: list_all2_eq [symmetric])
code_type rtype
(SML "Term.typ")
code_const RType
(SML "Term.Type/ (_, _)")
code_reserved SML Term
hide (open) const rtype RType
end