(* 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 msg name =
cat_error msg ("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 thy =
thy
|> TypedefPackage.add_typedef_i def (SOME name) (t, vs, mx) set opt_morphs tac
|>> AxClass.prove_arity (full_tname, lhs_sorts, ["Porder.sq_ord"])
(ClassPackage.intro_classes_tac [])
|>>> (PureThy.add_defs_i true [Thm.no_attributes less_def] #> Library.swap)
|> (fn (thy', ({type_definition, set_def, ...}, [less_definition])) =>
thy'
|> AxClass.prove_arity (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.prove_arity (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.prove_arity (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 (context, UUmem_admissible) =
let
val theory = Context.the_theory context;
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, _, _)) => (Context.Theory theory', type_def))
end;
fun cpodef_result (context, nonempty_admissible) =
let
val theory = Context.the_theory context;
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, _, _)) => (Context.Theory theory', type_def))
end;
in (goal, if pcpo then pcpodef_result else cpodef_result) end
handle ERROR msg => err_in_cpodef msg 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 PureThy.internalK ("", [att]) (goal, ([], [])) thy end;
fun pcpodef_proof x = gen_pcpodef_proof read_term true x;
fun pcpodef_proof_i x = gen_pcpodef_proof cert_term true x;
fun cpodef_proof x = gen_pcpodef_proof read_term false x;
fun cpodef_proof_i x = gen_pcpodef_proof cert_term false x;
(** 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;