src/HOLCF/pcpodef_package.ML

avoid 'as' as identifier;

(*  Title:      HOLCF/pcpodef_package.ML
    ID:         $Id$
    Author:     Brian Huffman

Gordon/HOL-style type definitions for HOLCF.
*)

signature PCPODEF_PACKAGE =
sig
  val quiet_mode: bool ref
  val pcpodef_proof: (bool * string) * (bstring * string list * mixfix) * string
    * (string * string) option -> theory -> Proof.state
  val pcpodef_proof_i: (bool * string) * (bstring * string list * mixfix) * term
    * (string * string) option -> theory -> Proof.state
  val cpodef_proof: (bool * string) * (bstring * string list * mixfix) * string
    * (string * string) option -> theory -> Proof.state
  val cpodef_proof_i: (bool * string) * (bstring * string list * mixfix) * term
    * (string * string) option -> theory -> Proof.state
end;

structure PcpodefPackage: PCPODEF_PACKAGE =
struct


(** theory context references **)

val typedef_po = thm "typedef_po";
val typedef_cpo = thm "typedef_cpo";
val typedef_pcpo = thm "typedef_pcpo";
val typedef_lub = thm "typedef_lub";
val typedef_thelub = thm "typedef_thelub";
val typedef_compact = thm "typedef_compact";
val cont_Rep = thm "typedef_cont_Rep";
val cont_Abs = thm "typedef_cont_Abs";
val Rep_strict = thm "typedef_Rep_strict";
val Abs_strict = thm "typedef_Abs_strict";
val Rep_defined = thm "typedef_Rep_defined";
val Abs_defined = thm "typedef_Abs_defined";


(** type definitions **)

(* messages *)

val quiet_mode = ref false;
fun message s = if ! quiet_mode then () else writeln s;


(* prepare_cpodef *)

fun read_term thy used s =
  #1 (Thm.read_def_cterm (thy, K NONE, K NONE) used true (s, HOLogic.typeT));

fun cert_term thy _ t = Thm.cterm_of thy t handle TERM (msg, _) => error msg;

fun err_in_cpodef name =
  error ("The error(s) above occurred in cpodef " ^ quote name);

fun adm_const T = Const ("Adm.adm", (T --> HOLogic.boolT) --> HOLogic.boolT);
fun mk_adm (x, T, P) = adm_const T $ absfree (x, T, P);

fun gen_prepare_pcpodef prep_term pcpo def name (t, vs, mx) raw_set opt_morphs thy =
  let
    val full = Sign.full_name thy;

    (*rhs*)
    val full_name = full name;
    val cset = prep_term thy vs raw_set;
    val {T = setT, t = set, ...} = Thm.rep_cterm cset;
    val rhs_tfrees = term_tfrees set;
    val oldT = HOLogic.dest_setT setT handle TYPE _ =>
      error ("Not a set type: " ^ quote (Sign.string_of_typ thy setT));
    fun mk_nonempty A =
      HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A));
    fun mk_admissible A =
      mk_adm ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A));
    fun mk_UU_mem A = HOLogic.mk_mem (Const ("Pcpo.UU", oldT), A);
    val goal = if pcpo
      then HOLogic.mk_Trueprop (HOLogic.mk_conj (mk_UU_mem set, mk_admissible set))
      else HOLogic.mk_Trueprop (HOLogic.mk_conj (mk_nonempty set, mk_admissible set));
  
    (*lhs*)
    val lhs_tfrees = map (fn v => (v, AList.lookup (op =) rhs_tfrees v |> the_default HOLogic.typeS)) vs;
    val lhs_sorts = map snd lhs_tfrees;
    val tname = Syntax.type_name t mx;
    val full_tname = full tname;
    val newT = Type (full_tname, map TFree lhs_tfrees);

    val (Rep_name, Abs_name) = getOpt (opt_morphs, ("Rep_" ^ name, "Abs_" ^ name));
    val RepC = Const (full Rep_name, newT --> oldT);
    fun lessC T = Const ("Porder.<<", T --> T --> HOLogic.boolT);
    val less_def = ("less_" ^ name ^ "_def", Logic.mk_equals (lessC newT,
      Abs ("x", newT, Abs ("y", newT, lessC oldT $ (RepC $ Bound 1) $ (RepC $ Bound 0)))));

    fun option_fold_rule NONE = I
      | option_fold_rule (SOME def) = fold_rule [def];
    
    fun make_po tac theory =
      theory
      |> TypedefPackage.add_typedef_i def (SOME name) (t, vs, mx) set opt_morphs tac
      |>> AxClass.add_inst_arity_i (full_tname, lhs_sorts, ["Porder.sq_ord"])
          (AxClass.intro_classes_tac [])
      |>>> PureThy.add_defs_i true [Thm.no_attributes less_def]
      |> (fn (theory', ({type_definition, set_def, ...}, [less_definition])) =>
        theory'
        |> AxClass.add_inst_arity_i (full_tname, lhs_sorts, ["Porder.po"])
            (Tactic.rtac (typedef_po OF [type_definition, less_definition]) 1)
        |> rpair (type_definition, less_definition, set_def));
    
    fun make_cpo admissible (theory, defs as (type_def, less_def, set_def)) =
      let
        val admissible' = option_fold_rule set_def admissible;
        val cpo_thms = [type_def, less_def, admissible'];
        val (theory', _) =
          theory
          |> AxClass.add_inst_arity_i (full_tname, lhs_sorts, ["Pcpo.cpo"])
            (Tactic.rtac (typedef_cpo OF cpo_thms) 1)
          |> Theory.add_path name
          |> PureThy.add_thms
            ([(("adm_" ^ name, admissible'), []),
              (("cont_" ^ Rep_name, cont_Rep OF cpo_thms), []),
              (("cont_" ^ Abs_name, cont_Abs OF cpo_thms), []),
              (("lub_"     ^ name, typedef_lub     OF cpo_thms), []),
              (("thelub_"  ^ name, typedef_thelub  OF cpo_thms), []),
              (("compact_" ^ name, typedef_compact OF cpo_thms), [])])
          |>> Theory.parent_path;
      in (theory', defs) end;

    fun make_pcpo UUmem (theory, defs as (type_def, less_def, set_def)) =
      let
        val UUmem' = option_fold_rule set_def UUmem;
        val pcpo_thms = [type_def, less_def, UUmem'];
        val (theory', _) =
          theory
          |> AxClass.add_inst_arity_i (full_tname, lhs_sorts, ["Pcpo.pcpo"])
            (Tactic.rtac (typedef_pcpo OF pcpo_thms) 1)
          |> Theory.add_path name
          |> PureThy.add_thms
            ([((Rep_name ^ "_strict", Rep_strict OF pcpo_thms), []),
              ((Abs_name ^ "_strict", Abs_strict OF pcpo_thms), []),
              ((Rep_name ^ "_defined", Rep_defined OF pcpo_thms), []),
              ((Abs_name ^ "_defined", Abs_defined OF pcpo_thms), [])
              ])
          |>> Theory.parent_path;
      in (theory', defs) end;
    
    fun pcpodef_result (theory, UUmem_admissible) =
      let
        val UUmem = UUmem_admissible RS conjunct1;
        val admissible = UUmem_admissible RS conjunct2;
      in
        theory
        |> make_po (Tactic.rtac exI 1 THEN Tactic.rtac UUmem 1)
        |> make_cpo admissible
        |> make_pcpo UUmem
        |> (fn (theory', (type_def, _, _)) => (theory', type_def))
      end;
  
    fun cpodef_result (theory, nonempty_admissible) =
      let
        val nonempty = nonempty_admissible RS conjunct1;
        val admissible = nonempty_admissible RS conjunct2;
      in
        theory
        |> make_po (Tactic.rtac nonempty 1)
        |> make_cpo admissible
        |> (fn (theory', (type_def, _, _)) => (theory', type_def))
      end;
  
  in (goal, if pcpo then pcpodef_result else cpodef_result) end
  handle ERROR => err_in_cpodef name;

(* cpodef_proof interface *)

fun gen_pcpodef_proof prep_term pcpo ((def, name), typ, set, opt_morphs) thy =
  let
    val (goal, att) =
      gen_prepare_pcpodef prep_term pcpo def name typ set opt_morphs thy;
  in IsarThy.theorem_i Drule.internalK ("", [att]) (goal, ([], [])) thy end;

val pcpodef_proof = gen_pcpodef_proof read_term true;
val pcpodef_proof_i = gen_pcpodef_proof cert_term true;

val cpodef_proof = gen_pcpodef_proof read_term false;
val cpodef_proof_i = gen_pcpodef_proof cert_term false;


(** outer syntax **)

local structure P = OuterParse and K = OuterKeyword in

(* copied from HOL/Tools/typedef_package.ML *)
val typedef_proof_decl =
  Scan.optional (P.$$$ "(" |--
      ((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, SOME s)))
        --| P.$$$ ")") (true, NONE) --
    (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) --
    Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name));

fun mk_pcpodef_proof pcpo ((((((def, opt_name), (vs, t)), mx), A), morphs)) =
  (if pcpo then pcpodef_proof else cpodef_proof)
    ((def, getOpt (opt_name, Syntax.type_name t mx)), (t, vs, mx), A, morphs);

val pcpodefP =
  OuterSyntax.command "pcpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal
    (typedef_proof_decl >>
      (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof true)));

val cpodefP =
  OuterSyntax.command "cpodef" "HOLCF type definition (requires admissibility proof)" K.thy_goal
    (typedef_proof_decl >>
      (Toplevel.print oo (Toplevel.theory_to_proof o mk_pcpodef_proof false)));

val _ = OuterSyntax.add_parsers [pcpodefP, cpodefP];

end;

end;