(* Title: HOL/typedef.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
Internal interface for typedefs.
*)
signature TYPEDEF =
sig
val prove_nonempty: cterm -> thm list -> tactic option -> thm
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
end;
structure Typedef: TYPEDEF =
struct
(* prove non-emptyness of a set *) (*exception ERROR*)
val is_def = Logic.is_equals o #prop o rep_thm;
fun prove_nonempty cset thms usr_tac =
let
val {T = setT, t = set, maxidx, sign} = rep_cterm cset;
val T = HOLogic.dest_setT setT;
val goal = cterm_of sign
(HOLogic.mk_Trueprop (HOLogic.mk_mem (Var (("x", maxidx + 1), T), set)));
val tac =
TRY (rewrite_goals_tac (filter is_def thms)) THEN
TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN
if_none usr_tac (TRY (ALLGOALS Fast_tac));
in
prove_goalw_cterm [] goal (K [tac])
end
handle ERROR =>
error ("Failed to prove nonemptiness of " ^ quote (string_of_cterm cset));
(* ext_typedef *)
fun ext_typedef prep_term name (t, vs, mx) raw_set axms thms usr_tac thy =
let
val _ = require_thy thy "Set" "typedefs";
val sign = sign_of thy;
val full_name = Sign.full_name sign;
(*rhs*)
val cset = prep_term sign raw_set;
val {T = setT, t = set, ...} = 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 tlen = length vs;
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);
(*axioms*)
val rep_type = HOLogic.mk_Trueprop (HOLogic.mk_mem (RepC $ x_new, setC));
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, setC)),
HOLogic.mk_Trueprop (HOLogic.mk_eq (RepC $ (AbsC $ y_old), y_old)));
(* 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);
writeln("Proving nonemptiness of " ^ quote name ^ " ...");
prove_nonempty cset (map (get_axiom thy) axms @ thms) usr_tac;
thy
|> Theory.add_types [(t, tlen, mx)]
|> Theory.add_arities_i
[(full_name tname, replicate tlen logicS, logicS),
(full_name tname, replicate tlen HOLogic.termS, HOLogic.termS)]
|> Theory.add_consts_i
[(name, setT, NoSyn),
(Rep_name, newT --> oldT, NoSyn),
(Abs_name, oldT --> newT, NoSyn)]
|> PureThy.add_store_defs_i
[(name ^ "_def", Logic.mk_equals (setC, set))]
|> PureThy.add_store_axioms_i
[(Rep_name, rep_type),
(Rep_name ^ "_inverse", rep_type_inv),
(Abs_name ^ "_inverse", abs_type_inv)]
end
handle ERROR =>
error ("The error(s) above occurred in typedef " ^ quote name);
(* external interfaces *)
fun read_term sg str =
read_cterm sg (str, HOLogic.termTVar);
fun cert_term sg tm =
cterm_of sg tm handle TERM (msg, _) => error msg;
val add_typedef = ext_typedef read_term;
val add_typedef_i = ext_typedef cert_term;
end;