(* Title: HOL/Tools/typecopy_package.ML
ID: $Id$
Author: Florian Haftmann, TU Muenchen
Introducing copies of types using trivial typedefs; datatype-like abstraction.
*)
signature TYPECOPY_PACKAGE =
sig
type info = {
vs: (string * sort) list,
constr: string,
typ: typ,
inject: thm,
proj: string * typ,
proj_def: thm
}
val add_typecopy: bstring * string list -> typ -> (bstring * bstring) option
-> theory -> (string * info) * theory
val get_typecopies: theory -> string list
val get_info: theory -> string -> info option
val interpretation: (string -> theory -> theory) -> theory -> theory
val print_typecopies: theory -> unit
val setup: theory -> theory
end;
structure TypecopyPackage: TYPECOPY_PACKAGE =
struct
(* theory data *)
type info = {
vs: (string * sort) list,
constr: string,
typ: typ,
inject: thm,
proj: string * typ,
proj_def: thm
};
structure TypecopyData = TheoryDataFun
(
type T = info Symtab.table;
val empty = Symtab.empty;
val copy = I;
val extend = I;
fun merge _ = Symtab.merge (K true);
);
fun print_typecopies thy =
let
val tab = TypecopyData.get thy;
fun mk (tyco, { vs, constr, typ, proj = (proj, _), ... } : info) =
(Pretty.block o Pretty.breaks) [
Syntax.pretty_typ_global thy (Type (tyco, map TFree vs)),
Pretty.str "=",
(Pretty.str o Sign.extern_const thy) constr,
Syntax.pretty_typ_global thy typ,
Pretty.block [Pretty.str "(", (Pretty.str o Sign.extern_const thy) proj, Pretty.str ")"]];
in
(Pretty.writeln o Pretty.block o Pretty.fbreaks)
(Pretty.str "type copies:" :: map mk (Symtab.dest tab))
end;
val get_typecopies = Symtab.keys o TypecopyData.get;
val get_info = Symtab.lookup o TypecopyData.get;
(* interpretation of type copies *)
structure TypecopyInterpretation = InterpretationFun(type T = string val eq = op =);
val interpretation = TypecopyInterpretation.interpretation;
(* add a type copy *)
local
fun gen_add_typecopy prep_typ (raw_tyco, raw_vs) raw_ty constr_proj thy =
let
val ty = prep_typ thy raw_ty;
val vs = AList.make (the_default HOLogic.typeS o AList.lookup (op =) (typ_tfrees ty)) raw_vs;
val tac = Tactic.rtac UNIV_witness 1;
fun add_info tyco ( { abs_type = ty_abs, rep_type = ty_rep, Abs_name = c_abs,
Rep_name = c_rep, Abs_inject = inject,
Abs_inverse = inverse, ... } : TypedefPackage.info ) thy =
let
val exists_thm =
UNIV_I
|> Drule.instantiate' [SOME (ctyp_of thy (Logic.varifyT ty_rep))] [];
val inject' = inject OF [exists_thm, exists_thm];
val proj_def = inverse OF [exists_thm];
val info = {
vs = vs,
constr = c_abs,
typ = ty_rep,
inject = inject',
proj = (c_rep, ty_abs --> ty_rep),
proj_def = proj_def
};
in
thy
|> (TypecopyData.map o Symtab.update_new) (tyco, info)
|> TypecopyInterpretation.data tyco
|> pair (tyco, info)
end
in
thy
|> TypedefPackage.add_typedef_i false (SOME raw_tyco) (raw_tyco, map fst vs, NoSyn)
(HOLogic.mk_UNIV ty) (Option.map swap constr_proj) tac
|-> (fn (tyco, info) => add_info tyco info)
end;
in
val add_typecopy = gen_add_typecopy Sign.certify_typ;
end;
(* code generator setup *)
fun add_typecopy_spec tyco thy =
let
val SOME { constr, proj_def, inject, vs, ... } = get_info thy tyco;
val vs' = (map o apsnd) (curry (Sorts.inter_sort (Sign.classes_of thy)) [HOLogic.class_eq]) vs;
val ty = Logic.unvarifyT (Sign.the_const_type thy constr);
fun add_def tyco lthy =
let
val ty = Type (tyco, map TFree vs');
fun mk_side const_name = Const (const_name, ty --> ty --> HOLogic.boolT)
$ Free ("x", ty) $ Free ("y", ty);
val def = HOLogic.mk_Trueprop (HOLogic.mk_eq
(mk_side @{const_name eq_class.eq}, mk_side @{const_name "op ="}));
val def' = Syntax.check_term lthy def;
val ((_, (_, thm)), lthy') = Specification.definition
(NONE, (("", []), def')) lthy;
val ctxt_thy = ProofContext.init (ProofContext.theory_of lthy);
val thm' = singleton (ProofContext.export lthy' ctxt_thy) thm;
in (thm', lthy') end;
fun tac thms = Class.intro_classes_tac []
THEN ALLGOALS (ProofContext.fact_tac thms);
fun add_eq_thm thy =
let
val eq = inject
|> CodeUnit.constrain_thm [HOLogic.class_eq]
|> Simpdata.mk_eq
|> MetaSimplifier.rewrite_rule [Thm.transfer thy @{thm equals_eq}];
in Code.add_func eq thy end;
in
thy
|> Code.add_datatype [(constr, ty)]
|> Code.add_func proj_def
|> TheoryTarget.instantiation ([tyco], vs', [HOLogic.class_eq])
|> add_def tyco
|-> (fn thm => Class.prove_instantiation_instance (K (tac [thm]))
#> LocalTheory.exit
#> ProofContext.theory_of
#> Code.del_func thm
#> add_eq_thm)
end;
val setup =
TypecopyInterpretation.init
#> interpretation add_typecopy_spec
end;