(* Title: HOLCF/pcpodef_package.ML ID: $Id: pcpodef_package.ML,v 1.5 2005/09/13 20:21:46 wenzelm Exp $ 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 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.op <<", 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), [])]) |>> 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;