(* Title: HOL/Tools/typedef_package.ML
ID: $Id$
Author: Markus Wenzel, TU Muenchen
Gordon/HOL-style type definitions.
TODO:
- typedefP: elim witness;
*)
signature TYPEDEF_PACKAGE =
sig
val quiet_mode: bool ref
val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
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
val add_typedef_i_no_def: string -> bstring * string list * mixfix ->
term -> string list -> thm list -> tactic option -> theory -> theory
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
thy
|> PureThy.add_typedecls decls
|> Theory.add_arities_i (map arity_of decls)
end;
(** type definitions **)
(* messages *)
val quiet_mode = ref false;
fun message s = if ! quiet_mode then () else writeln s;
(* 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 (CLASET' blast_tac)));
in
prove_goalw_cterm [] goal (K [tac])
end handle ERROR => error ("Failed to prove nonemptiness of " ^ quote (string_of_cterm cset));
(* gen_add_typedef *)
fun gen_add_typedef prep_term no_def name (t, vs, mx) raw_set thm_names thms usr_tac thy =
let
val _ = Theory.requires 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 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)));
(* 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);
message ("Proving nonemptiness of " ^ quote name ^ " ...");
prove_nonempty cset (PureThy.get_thmss thy thm_names @ thms) usr_tac;
thy
|> PureThy.add_typedecls [(t, vs, mx)]
|> Theory.add_arities_i
[(full_name tname, replicate (length vs) HOLogic.termS, HOLogic.termS)]
|> 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 (PureThy.add_defs_i o map Thm.no_attributes)
[(name ^ "_def", Logic.mk_equals (setC, set))])
|> (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)]
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 = 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;
(* outer syntax *)
open OuterParse;
val typedeclP =
OuterSyntax.parser false "typedecl" "HOL type declaration"
((type_args -- name -- opt_mixfix) >> (fn ((vs, t), mx) =>
Toplevel.theory (add_typedecls [(t, vs, mx)])));
val opt_witness =
Scan.optional ($$$ "(" |-- !!! (list1 xname --| $$$ ")")) [];
val typedef_decl =
Scan.option ($$$ "(" |-- name --| $$$ ")") --
(type_args -- name) -- opt_infix -- ($$$ "=" |-- term -- opt_witness);
val typedefP =
OuterSyntax.parser false "typedef" "HOL type definition"
(typedef_decl >> (fn (((opt_name, (vs, t)), mx), (A, witn)) =>
Toplevel.theory (add_typedef (if_none opt_name t) (t, vs, mx) A witn [] None)));
val _ = OuterSyntax.add_parsers [typedeclP, typedefP];
end;