src/HOL/Tools/typecopy_package.ML
author wenzelm
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use long names for old-style fold combinators;
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(*  Title:      HOL/Tools/typecopy_package.ML
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    Author:     Florian Haftmann, TU Muenchen
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Introducing copies of types using trivial typedefs; datatype-like abstraction.
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*)
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signature TYPECOPY_PACKAGE =
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sig
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  type info = {
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    vs: (string * sort) list,
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    constr: string,
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    typ: typ,
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    inject: thm,
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    proj: string * typ,
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    proj_def: thm
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  }
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  val add_typecopy: bstring * string list -> typ -> (bstring * bstring) option
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    -> theory -> (string * info) * theory
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  val get_typecopies: theory -> string list
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  val get_info: theory -> string -> info option
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  val interpretation: (string -> theory -> theory) -> theory -> theory
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  val add_typecopy_default_code: string -> theory -> theory
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  val print_typecopies: theory -> unit
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  val setup: theory -> theory
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end;
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structure TypecopyPackage: TYPECOPY_PACKAGE =
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struct
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(* theory data *)
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type info = {
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  vs: (string * sort) list,
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  constr: string,
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  typ: typ,
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  inject: thm,
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  proj: string * typ,
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  proj_def: thm
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};
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structure TypecopyData = TheoryDataFun
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(
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  type T = info Symtab.table;
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  val empty = Symtab.empty;
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  val copy = I;
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  val extend = I;
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  fun merge _ = Symtab.merge (K true);
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);
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fun print_typecopies thy =
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  let
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    val tab = TypecopyData.get thy;
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    fun mk (tyco, { vs, constr, typ, proj = (proj, _), ... } : info) =
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      (Pretty.block o Pretty.breaks) [
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        Syntax.pretty_typ_global thy (Type (tyco, map TFree vs)),
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        Pretty.str "=",
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        (Pretty.str o Sign.extern_const thy) constr,
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        Syntax.pretty_typ_global thy typ,
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        Pretty.block [Pretty.str "(", (Pretty.str o Sign.extern_const thy) proj, Pretty.str  ")"]];
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    in
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      (Pretty.writeln o Pretty.block o Pretty.fbreaks)
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        (Pretty.str "type copies:" :: map mk (Symtab.dest tab))
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    end;
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val get_typecopies = Symtab.keys o TypecopyData.get;
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val get_info = Symtab.lookup o TypecopyData.get;
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(* interpretation of type copies *)
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structure TypecopyInterpretation = InterpretationFun(type T = string val eq = op =);
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val interpretation = TypecopyInterpretation.interpretation;
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fun add_typecopy (raw_tyco, raw_vs) raw_ty constr_proj thy =
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  let
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    val ty = Sign.certify_typ thy raw_ty;
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    val vs =
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      AList.make (the_default HOLogic.typeS o AList.lookup (op =) (Term.add_tfreesT ty [])) raw_vs;
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    val tac = Tactic.rtac UNIV_witness 1;
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    fun add_info tyco ( { abs_type = ty_abs, rep_type = ty_rep, Abs_name = c_abs,
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      Rep_name = c_rep, Abs_inject = inject,
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      Abs_inverse = inverse, ... } : TypedefPackage.info ) thy =
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        let
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          val exists_thm =
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            UNIV_I
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            |> Drule.instantiate' [SOME (ctyp_of thy (Logic.varifyT ty_rep))] [];
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          val inject' = inject OF [exists_thm, exists_thm];
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          val proj_def = inverse OF [exists_thm];
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          val info = {
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            vs = vs,
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            constr = c_abs,
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            typ = ty_rep,
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            inject = inject',
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            proj = (c_rep, ty_abs --> ty_rep),
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            proj_def = proj_def
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          };
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        in
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          thy
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          |> (TypecopyData.map o Symtab.update_new) (tyco, info)
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          |> TypecopyInterpretation.data tyco
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          |> pair (tyco, info)
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        end
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  in
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    thy
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    |> TypedefPackage.add_typedef false (SOME raw_tyco) (raw_tyco, map fst vs, NoSyn)
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      (HOLogic.mk_UNIV ty) (Option.map swap constr_proj) tac
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    |-> (fn (tyco, info) => add_info tyco info)
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  end;
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(* code generator setup *)
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fun add_typecopy_default_code tyco thy =
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  let
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    val SOME { constr = constr_name, proj = (proj, _), proj_def = proj_eq, vs = raw_vs,
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      typ = raw_ty_rep, ... } =  get_info thy tyco;
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    val inst_meet = Sorts.meet_sort_typ (Sign.classes_of thy)
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      (Logic.varifyT raw_ty_rep, [HOLogic.class_eq]) handle Sorts.CLASS_ERROR _ => I;
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    val ty_inst = Logic.unvarifyT o inst_meet o Logic.varifyT;
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    val vs = (map dest_TFree o snd o dest_Type o ty_inst)
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      (Type (tyco, map TFree raw_vs));
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    val ty_rep = ty_inst raw_ty_rep;
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    val SOME { Rep_inject = proj_inject, ... } = TypedefPackage.get_info thy tyco;
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    val ty_constr = Logic.unvarifyT (Sign.the_const_type thy constr_name);
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    val constr = (constr_name, ty_constr)
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    val ty = Type (tyco, map TFree vs);
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    fun mk_eq ty t_x t_y = Const (@{const_name eq_class.eq}, ty --> ty --> HOLogic.boolT)
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      $ t_x $ t_y;
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    fun mk_proj t = Const (proj, ty --> ty_rep) $ t;
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    val (t_x, t_y) = (Free ("x", ty), Free ("y", ty));
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    val def_eq = (HOLogic.mk_Trueprop o HOLogic.mk_eq)
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      (mk_eq ty t_x t_y, HOLogic.mk_eq (mk_proj t_x, mk_proj t_y));
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    fun mk_eq_refl thy = @{thm HOL.eq_refl}
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      |> Thm.instantiate
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         ([pairself (Thm.ctyp_of thy) (TVar (("'a", 0), @{sort eq}), Logic.varifyT ty)], [])
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      |> AxClass.unoverload thy;
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  in
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    thy
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    |> Code.add_datatype [constr]
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    |> Code.add_eqn proj_eq
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    |> TheoryTarget.instantiation ([tyco], vs, [HOLogic.class_eq])
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    |> `(fn lthy => Syntax.check_term lthy def_eq)
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    |-> (fn def_eq => Specification.definition
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         (NONE, (Attrib.empty_binding, def_eq)))
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    |-> (fn (_, (_, def_thm)) =>
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       Class.prove_instantiation_exit_result Morphism.thm
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         (fn _ => fn def_thm => Class.intro_classes_tac []
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            THEN (Simplifier.rewrite_goals_tac
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              (map Simpdata.mk_eq [def_thm, @{thm eq}, proj_inject]))
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                THEN ALLGOALS (rtac @{thm refl})) def_thm)
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    |-> (fn def_thm => Code.add_eqn def_thm)
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    |> `(fn thy => mk_eq_refl thy)
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    |-> (fn refl_thm => Code.add_nonlinear_eqn refl_thm)
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  end;
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val setup =
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  TypecopyInterpretation.init
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  #> interpretation add_typecopy_default_code
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end;