(*  Title:      HOL/Tools/typedef_package.ML

    ID:         $Id$

    Author:     Markus Wenzel, TU Muenchen

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 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 axms 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 (map (get_axiom thy) axms @ 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 Attribute.none)

     [(name ^ "_def", Logic.mk_equals (setC, set))])

    |> (PureThy.add_axioms_i o map Attribute.none)

     [(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;

end;