(* Title: HOL/Tools/typedef_package.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
License: GPL (GNU GENERAL PUBLIC LICENSE)
Gordon/HOL-style type definitions.
*)
signature TYPEDEF_PACKAGE =
sig
val quiet_mode: bool ref
val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
val add_typedef: string -> bstring * string list * mixfix ->
string -> string list -> thm list -> tactic option -> theory -> theory
val add_typedef_i: string -> bstring * string list * mixfix ->
term -> string list -> thm list -> tactic option -> theory -> theory
val add_typedef_i_no_def: string -> bstring * string list * mixfix ->
term -> string list -> thm list -> tactic option -> theory -> theory
val typedef_proof: (string * (bstring * string list * mixfix) * string) * Comment.text
-> bool -> theory -> ProofHistory.T
val typedef_proof_i: (string * (bstring * string list * mixfix) * term) * Comment.text
-> bool -> theory -> ProofHistory.T
end;
structure TypedefPackage: TYPEDEF_PACKAGE =
struct
(** type declarations **)
fun add_typedecls decls thy =
let
val full = Sign.full_name (Theory.sign_of thy);
fun arity_of (raw_name, args, mx) =
(full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.termS, HOLogic.termS);
in
if can (Theory.assert_super HOL.thy) thy then
thy
|> PureThy.add_typedecls decls
|> Theory.add_arities_i (map arity_of decls)
else thy |> PureThy.add_typedecls decls
end;
(** type definitions **)
(* messages *)
val quiet_mode = ref false;
fun message s = if ! quiet_mode then () else writeln s;
(* non-emptiness of set *) (*exception ERROR*)
fun check_nonempty cset thm =
let
val {t, sign, maxidx, ...} = Thm.rep_cterm cset;
val {prop, ...} = Thm.rep_thm (Thm.transfer_sg sign (Drule.standard thm));
val matches = Pattern.matches (Sign.tsig_of sign);
in
(case try (HOLogic.dest_mem o HOLogic.dest_Trueprop) prop of
None => raise ERROR
| Some (_, A) => if matches (Logic.incr_indexes ([], maxidx) A, t) then () else raise ERROR)
end handle ERROR => error ("Bad non-emptiness theorem " ^ Display.string_of_thm thm ^
"\nfor set " ^ quote (Display.string_of_cterm cset));
fun goal_nonempty ex cset =
let
val {T = setT, t = A, maxidx, sign} = Thm.rep_cterm cset;
val T = HOLogic.dest_setT setT;
val tm =
if ex then HOLogic.mk_exists ("x", T, HOLogic.mk_mem (Free ("x", T), A))
else HOLogic.mk_mem (Var (("x", maxidx + 1), T), A); (*old-style version*)
in Thm.cterm_of sign (HOLogic.mk_Trueprop tm) end;
fun prove_nonempty thy cset (witn_names, witn_thms, witn_tac) =
let
val is_def = Logic.is_equals o #prop o Thm.rep_thm;
val thms = PureThy.get_thmss thy witn_names @ witn_thms;
val tac =
TRY (rewrite_goals_tac (filter is_def thms)) THEN
TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
if_none witn_tac (TRY (ALLGOALS (CLASET' blast_tac)));
in
message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
prove_goalw_cterm [] (goal_nonempty false cset) (K [tac])
end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset));
(* prepare_typedef *)
fun read_term sg used s =
#1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.termT));
fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg;
fun err_in_typedef name =
error ("The error(s) above occurred in typedef " ^ quote name);
fun prepare_typedef prep_term no_def name (t, vs, mx) raw_set thy =
let
val _ = Theory.requires thy "Set" "typedefs";
val sign = Theory.sign_of thy;
val full_name = Sign.full_name sign;
(*rhs*)
val cset = prep_term sign 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 sign setT));
(*lhs*)
val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.termS)) vs;
val tname = Syntax.type_name t mx;
val newT = Type (full_name tname, map TFree lhs_tfrees);
val Rep_name = "Rep_" ^ name;
val Abs_name = "Abs_" ^ name;
val setC = Const (full_name name, setT);
val RepC = Const (full_name Rep_name, newT --> oldT);
val AbsC = Const (full_name Abs_name, oldT --> newT);
val x_new = Free ("x", newT);
val y_old = Free ("y", oldT);
val set' = if no_def then set else setC;
(*axioms*)
val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, set'));
val rep_type_inv = HOLogic.mk_Trueprop (HOLogic.mk_eq (AbsC $ (RepC $ x_new), x_new));
val abs_type_inv = Logic.mk_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (y_old, set')),
HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
(*theory extender*)
fun do_typedef theory =
theory
|> Theory.assert_super thy
|> add_typedecls [(t, vs, mx)]
|> Theory.add_consts_i
((if no_def then [] else [(name, setT, NoSyn)]) @
[(Rep_name, newT --> oldT, NoSyn),
(Abs_name, oldT --> newT, NoSyn)])
|> (if no_def then I else (#1 oo (PureThy.add_defs_i false o map Thm.no_attributes))
[Logic.mk_defpair (setC, set)])
|> (#1 oo (PureThy.add_axioms_i o map Thm.no_attributes))
[(Rep_name, rep_type),
(Rep_name ^ "_inverse", rep_type_inv),
(Abs_name ^ "_inverse", abs_type_inv)]
handle ERROR => err_in_typedef name;
(* errors *)
fun show_names pairs = commas_quote (map fst pairs);
val illegal_vars =
if null (term_vars set) andalso null (term_tvars set) then []
else ["Illegal schematic variable(s) on rhs"];
val dup_lhs_tfrees =
(case duplicates lhs_tfrees of [] => []
| dups => ["Duplicate type variables on lhs: " ^ show_names dups]);
val extra_rhs_tfrees =
(case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => []
| extras => ["Extra type variables on rhs: " ^ show_names extras]);
val illegal_frees =
(case term_frees set of [] => []
| xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]);
val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees;
in
if null errs then () else error (cat_lines errs);
(cset, do_typedef)
end handle ERROR => err_in_typedef name;
(* add_typedef interfaces *)
fun gen_add_typedef prep_term no_def name typ set names thms tac thy =
let
val (cset, do_typedef) = prepare_typedef prep_term no_def name typ set thy;
val result = prove_nonempty thy cset (names, thms, tac);
in check_nonempty cset result; thy |> do_typedef end;
val add_typedef = gen_add_typedef read_term false;
val add_typedef_i = gen_add_typedef cert_term false;
val add_typedef_i_no_def = gen_add_typedef cert_term true;
(* typedef_proof interface *)
fun typedef_attribute cset do_typedef (thy, thm) =
(check_nonempty cset (thm RS (select_eq_Ex RS iffD2)); (thy |> do_typedef, thm));
fun gen_typedef_proof prep_term ((name, typ, set), comment) int thy =
let
val (cset, do_typedef) = prepare_typedef prep_term false name typ set thy;
val goal = Thm.term_of (goal_nonempty true cset);
in
thy
|> IsarThy.theorem_i (("", [typedef_attribute cset do_typedef], (goal, ([], []))), comment) int
end;
val typedef_proof = gen_typedef_proof read_term;
val typedef_proof_i = gen_typedef_proof cert_term;
(** outer syntax **)
local structure P = OuterParse and K = OuterSyntax.Keyword in
val typedeclP =
OuterSyntax.command "typedecl" "HOL type declaration" K.thy_decl
(P.type_args -- P.name -- P.opt_infix --| P.marg_comment >> (fn ((vs, t), mx) =>
Toplevel.theory (add_typedecls [(t, vs, mx)])));
val typedef_proof_decl =
Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") --
(P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- P.marg_comment;
fun mk_typedef_proof ((((opt_name, (vs, t)), mx), A), comment) =
typedef_proof ((if_none opt_name (Syntax.type_name t mx), (t, vs, mx), A), comment);
val typedefP =
OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal
(typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof)));
val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
end;
end;