src/HOL/Tools/datatype_package.ML
author berghofe
Tue Jun 08 19:23:53 2004 +0200 (2004-06-08)
changeset 14887 4938ce4ef295
parent 14799 a405aadff16c
child 14981 e73f8140af78
permissions -rw-r--r--
Added exception Datatype_Empty.
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(*  Title:      HOL/Tools/datatype_package.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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Datatype package for Isabelle/HOL.
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*)
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signature BASIC_DATATYPE_PACKAGE =
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sig
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  val induct_tac : string -> int -> tactic
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  val induct_thm_tac : thm -> string -> int -> tactic
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  val case_tac : string -> int -> tactic
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  val distinct_simproc : simproc
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end;
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signature DATATYPE_PACKAGE =
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sig
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  include BASIC_DATATYPE_PACKAGE
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  val quiet_mode : bool ref
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  val add_datatype : bool -> string list -> (string list * bstring * mixfix *
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    (bstring * string list * mixfix) list) list -> theory -> theory *
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      {distinct : thm list list,
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       inject : thm list list,
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       exhaustion : thm list,
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       rec_thms : thm list,
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       case_thms : thm list list,
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       split_thms : (thm * thm) list,
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       induction : thm,
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       size : thm list,
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       simps : thm list}
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  val add_datatype_i : bool -> bool -> string list -> (string list * bstring * mixfix *
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    (bstring * typ list * mixfix) list) list -> theory -> theory *
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      {distinct : thm list list,
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       inject : thm list list,
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       exhaustion : thm list,
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       rec_thms : thm list,
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       case_thms : thm list list,
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       split_thms : (thm * thm) list,
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       induction : thm,
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       size : thm list,
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       simps : thm list}
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  val rep_datatype_i : string list option -> (thm list * theory attribute list) list list ->
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    (thm list * theory attribute list) list list -> (thm list * theory attribute list) ->
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    theory -> theory *
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      {distinct : thm list list,
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       inject : thm list list,
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       exhaustion : thm list,
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       rec_thms : thm list,
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       case_thms : thm list list,
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       split_thms : (thm * thm) list,
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       induction : thm,
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       size : thm list,
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       simps : thm list}
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  val rep_datatype : string list option -> (xstring * Args.src list) list list ->
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    (xstring * Args.src list) list list -> xstring * Args.src list -> theory -> theory *
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      {distinct : thm list list,
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       inject : thm list list,
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       exhaustion : thm list,
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       rec_thms : thm list,
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       case_thms : thm list list,
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       split_thms : (thm * thm) list,
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       induction : thm,
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       size : thm list,
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       simps : thm list}
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  val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
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  val get_datatypes_sg : Sign.sg -> DatatypeAux.datatype_info Symtab.table
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  val print_datatypes : theory -> unit
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  val datatype_info_sg : Sign.sg -> string -> DatatypeAux.datatype_info option
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  val datatype_info : theory -> string -> DatatypeAux.datatype_info option
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  val datatype_info_sg_err : Sign.sg -> string -> DatatypeAux.datatype_info
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  val datatype_info_err : theory -> string -> DatatypeAux.datatype_info
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  val constrs_of : theory -> string -> term list option
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  val constrs_of_sg : Sign.sg -> string -> term list option
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  val case_const_of : theory -> string -> term option
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  val weak_case_congs_of : theory -> thm list
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  val weak_case_congs_of_sg : Sign.sg -> thm list
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  val setup: (theory -> theory) list
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end;
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structure DatatypePackage : DATATYPE_PACKAGE =
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struct
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open DatatypeAux;
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val quiet_mode = quiet_mode;
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(* data kind 'HOL/datatypes' *)
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structure DatatypesArgs =
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struct
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  val name = "HOL/datatypes";
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  type T = datatype_info Symtab.table;
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  val empty = Symtab.empty;
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  val copy = I;
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  val prep_ext = I;
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  val merge: T * T -> T = Symtab.merge (K true);
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  fun print sg tab =
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    Pretty.writeln (Pretty.strs ("datatypes:" ::
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      map #1 (Sign.cond_extern_table sg Sign.typeK tab)));
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end;
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structure DatatypesData = TheoryDataFun(DatatypesArgs);
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val get_datatypes_sg = DatatypesData.get_sg;
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val get_datatypes = DatatypesData.get;
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val put_datatypes = DatatypesData.put;
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val print_datatypes = DatatypesData.print;
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(** theory information about datatypes **)
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fun datatype_info_sg sg name = Symtab.lookup (get_datatypes_sg sg, name);
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fun datatype_info_sg_err sg name = (case datatype_info_sg sg name of
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      Some info => info
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    | None => error ("Unknown datatype " ^ quote name));
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val datatype_info = datatype_info_sg o Theory.sign_of;
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fun datatype_info_err thy name = (case datatype_info thy name of
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      Some info => info
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    | None => error ("Unknown datatype " ^ quote name));
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fun constrs_of_sg sg tname = (case datatype_info_sg sg tname of
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   Some {index, descr, ...} =>
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     let val (_, _, constrs) = the (assoc (descr, index))
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     in Some (map (fn (cname, _) => Const (cname, the (Sign.const_type sg cname))) constrs)
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     end
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 | _ => None);
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val constrs_of = constrs_of_sg o Theory.sign_of;
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fun case_const_of thy tname = (case datatype_info thy tname of
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   Some {case_name, ...} => Some (Const (case_name, the (Sign.const_type
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     (Theory.sign_of thy) case_name)))
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 | _ => None);
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val weak_case_congs_of_sg = map (#weak_case_cong o #2) o Symtab.dest o get_datatypes_sg;
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val weak_case_congs_of = weak_case_congs_of_sg o Theory.sign_of;
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fun find_tname var Bi =
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  let val frees = map dest_Free (term_frees Bi)
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      val params = rename_wrt_term Bi (Logic.strip_params Bi);
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  in case assoc (frees @ params, var) of
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       None => error ("No such variable in subgoal: " ^ quote var)
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     | Some(Type (tn, _)) => tn
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     | _ => error ("Cannot determine type of " ^ quote var)
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  end;
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fun infer_tname state i aterm =
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  let
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    val sign = Thm.sign_of_thm state;
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    val (_, _, Bi, _) = Thm.dest_state (state, i)
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    val params = Logic.strip_params Bi;   (*params of subgoal i*)
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    val params = rev (rename_wrt_term Bi params);   (*as they are printed*)
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    val (types, sorts) = types_sorts state;
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    fun types' (a, ~1) = (case assoc (params, a) of None => types(a, ~1) | sm => sm)
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      | types' ixn = types ixn;
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    val (ct, _) = read_def_cterm (sign, types', sorts) [] false (aterm, TypeInfer.logicT);
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  in case #T (rep_cterm ct) of
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       Type (tn, _) => tn
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     | _ => error ("Cannot determine type of " ^ quote aterm)
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  end;
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(*Warn if the (induction) variable occurs Free among the premises, which
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  usually signals a mistake.  But calls the tactic either way!*)
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fun occs_in_prems tacf vars =
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  SUBGOAL (fn (Bi, i) =>
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           (if  exists (fn Free (a, _) => a mem vars)
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                      (foldr add_term_frees (#2 (strip_context Bi), []))
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             then warning "Induction variable occurs also among premises!"
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             else ();
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            tacf i));
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(* generic induction tactic for datatypes *)
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local
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fun prep_var (Var (ixn, _), Some x) = Some (implode (tl (explode (Syntax.string_of_vname ixn))), x)
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  | prep_var _ = None;
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fun prep_inst (concl, xs) =	(*exception LIST*)
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  let val vs = InductAttrib.vars_of concl
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  in mapfilter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
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in
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fun gen_induct_tac inst_tac (varss, opt_rule) i state =
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  let
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    val (_, _, Bi, _) = Thm.dest_state (state, i);
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    val {sign, ...} = Thm.rep_thm state;
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    val (rule, rule_name) =
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      (case opt_rule of
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        Some r => (r, "Induction rule")
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      | None =>
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          let val tn = find_tname (hd (mapfilter I (flat varss))) Bi
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          in (#induction (datatype_info_sg_err sign tn), "Induction rule for type " ^ tn) end);
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    val concls = HOLogic.dest_concls (Thm.concl_of rule);
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    val insts = flat (map prep_inst (concls ~~ varss)) handle LIST _ =>
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      error (rule_name ^ " has different numbers of variables");
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  in occs_in_prems (inst_tac insts rule) (map #2 insts) i state end;
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fun induct_tac s =
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  gen_induct_tac Tactic.res_inst_tac
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    (map (Library.single o Some) (Syntax.read_idents s), None);
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fun induct_thm_tac th s =
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  gen_induct_tac Tactic.res_inst_tac
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    ([map Some (Syntax.read_idents s)], Some th);
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end;
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(* generic case tactic for datatypes *)
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fun case_inst_tac inst_tac t rule i state =
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  let
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    val _ $ Var (ixn, _) $ _ = HOLogic.dest_Trueprop
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      (hd (Logic.strip_assums_hyp (hd (Thm.prems_of rule))));
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    val exh_vname = implode (tl (explode (Syntax.string_of_vname ixn)));
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  in inst_tac [(exh_vname, t)] rule i state end;
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fun gen_case_tac inst_tac (t, Some rule) i state =
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      case_inst_tac inst_tac t rule i state
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  | gen_case_tac inst_tac (t, None) i state =
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      let val tn = infer_tname state i t in
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        if tn = HOLogic.boolN then inst_tac [("P", t)] case_split_thm i state
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        else case_inst_tac inst_tac t
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               (#exhaustion (datatype_info_sg_err (Thm.sign_of_thm state) tn))
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               i state
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      end handle THM _ => Seq.empty;
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fun case_tac t = gen_case_tac Tactic.res_inst_tac (t, None);
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(** Isar tactic emulations **)
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local
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val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
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val opt_rule = Scan.option (rule_spec |-- Attrib.local_thm);
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val varss = Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift Args.name_dummy)));
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fun mk_ixn (vars, s) = (fst (Term.dest_Var (Syntax.read_var ("?" ^ vars))), s)
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  handle _ => error (vars ^ " not a variable name");
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fun inst_tac ctxt sinsts =
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  Method.bires_inst_tac false ctxt (map mk_ixn sinsts);
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fun induct_meth ctxt (varss, opt_rule) =
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  gen_induct_tac (inst_tac ctxt) (varss, opt_rule);
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fun case_meth ctxt (varss, opt_rule) =
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  gen_case_tac (inst_tac ctxt) (varss, opt_rule);
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in
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val tactic_emulations =
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 [("induct_tac", Method.goal_args_ctxt' (varss -- opt_rule) induct_meth,
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    "induct_tac emulation (dynamic instantiation)"),
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  ("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name -- opt_rule) case_meth,
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    "case_tac emulation (dynamic instantiation)")];
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end;
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(** induct method setup **)
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(* case names *)
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local
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fun dt_recs (DtTFree _) = []
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  | dt_recs (DtType (_, dts)) = flat (map dt_recs dts)
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  | dt_recs (DtRec i) = [i];
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fun dt_cases (descr: descr) (_, args, constrs) =
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  let
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    fun the_bname i = Sign.base_name (#1 (the (assoc (descr, i))));
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    val bnames = map the_bname (distinct (flat (map dt_recs args)));
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  in map (fn (c, _) => space_implode "_" (Sign.base_name c :: bnames)) constrs end;
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fun induct_cases descr =
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  DatatypeProp.indexify_names (flat (map (dt_cases descr) (map #2 descr)));
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fun exhaust_cases descr i = dt_cases descr (the (assoc (descr, i)));
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in
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fun mk_case_names_induct descr = RuleCases.case_names (induct_cases descr);
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fun mk_case_names_exhausts descr new =
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  map (RuleCases.case_names o exhaust_cases descr o #1)
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    (filter (fn ((_, (name, _, _))) => name mem_string new) descr);
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end;
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fun add_rules simps case_thms size_thms rec_thms inject distinct
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                  weak_case_congs cong_att =
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  (#1 o PureThy.add_thmss [(("simps", simps), []),
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    (("", flat case_thms @ size_thms @ 
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          flat distinct  @ rec_thms), [Simplifier.simp_add_global]),
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    (("", size_thms @ rec_thms), [RecfunCodegen.add]),
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    (("", flat inject),               [iff_add_global]),
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    (("", flat distinct RL [notE]),   [Classical.safe_elim_global]),
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    (("", weak_case_congs),           [cong_att])]);
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(* add_cases_induct *)
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fun add_cases_induct infos induction =
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  let
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    val n = length (HOLogic.dest_concls (Thm.concl_of induction));
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    fun proj i thm =
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      if n = 1 then thm
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      else (if i + 1 < n then (fn th => th RS conjunct1) else I)
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        (Library.funpow i (fn th => th RS conjunct2) thm)
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        |> Drule.zero_var_indexes
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        |> RuleCases.save thm;
wenzelm@8405
   327
wenzelm@11805
   328
    fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
wenzelm@11805
   329
      [(("", proj index induction), [InductAttrib.induct_type_global name]),
wenzelm@11805
   330
       (("", exhaustion), [InductAttrib.cases_type_global name])];
wenzelm@11805
   331
    fun unnamed_rule i =
wenzelm@11805
   332
      (("", proj i induction), [InductAttrib.induct_type_global ""]);
wenzelm@11805
   333
    val rules = flat (map named_rules infos) @ map unnamed_rule (length infos upto n - 1);
wenzelm@11805
   334
  in #1 o PureThy.add_thms rules end;
wenzelm@8306
   335
berghofe@5177
   336
wenzelm@8405
   337
berghofe@7015
   338
(**** simplification procedure for showing distinctness of constructors ****)
berghofe@7015
   339
berghofe@7060
   340
fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
berghofe@7060
   341
  | stripT p = p;
berghofe@7060
   342
berghofe@7060
   343
fun stripC (i, f $ x) = stripC (i + 1, f)
berghofe@7060
   344
  | stripC p = p;
berghofe@7060
   345
berghofe@7015
   346
val distinctN = "constr_distinct";
berghofe@7015
   347
berghofe@7015
   348
exception ConstrDistinct of term;
berghofe@7015
   349
berghofe@7015
   350
fun distinct_proc sg _ (t as Const ("op =", _) $ t1 $ t2) =
berghofe@7060
   351
  (case (stripC (0, t1), stripC (0, t2)) of
berghofe@7060
   352
     ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
berghofe@7060
   353
         (case (stripT (0, T1), stripT (0, T2)) of
berghofe@7060
   354
            ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
berghofe@7060
   355
                if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
berghofe@7015
   356
                   (case (constrs_of_sg sg tname1) of
berghofe@7015
   357
                      Some constrs => let val cnames = map (fst o dest_Const) constrs
berghofe@7015
   358
                        in if cname1 mem cnames andalso cname2 mem cnames then
berghofe@7015
   359
                             let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
berghofe@7015
   360
                                 val eq_ct = cterm_of sg eq_t;
berghofe@7015
   361
                                 val Datatype_thy = theory "Datatype";
berghofe@7015
   362
                                 val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
berghofe@7015
   363
                                   map (get_thm Datatype_thy)
berghofe@7015
   364
                                     ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
berghofe@7015
   365
                             in (case (#distinct (datatype_info_sg_err sg tname1)) of
berghofe@7015
   366
                                 QuickAndDirty => Some (Thm.invoke_oracle
berghofe@7015
   367
                                   Datatype_thy distinctN (sg, ConstrDistinct eq_t))
wenzelm@13480
   368
                               | FewConstrs thms => Some (Tactic.prove sg [] [] eq_t (K
wenzelm@13480
   369
                                   (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
wenzelm@13480
   370
                                    atac 2, resolve_tac thms 1, etac FalseE 1])))
wenzelm@13480
   371
                               | ManyConstrs (thm, ss) => Some (Tactic.prove sg [] [] eq_t (K
wenzelm@13480
   372
                                   (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
berghofe@7015
   373
                                    full_simp_tac ss 1,
berghofe@7015
   374
                                    REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
berghofe@7015
   375
                                    eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
wenzelm@13480
   376
                                    etac FalseE 1]))))
berghofe@7015
   377
                             end
berghofe@7015
   378
                           else None
berghofe@7015
   379
                        end
berghofe@7015
   380
                    | None => None)
berghofe@7015
   381
                else None
berghofe@7015
   382
          | _ => None)
berghofe@7015
   383
   | _ => None)
berghofe@7015
   384
  | distinct_proc sg _ _ = None;
berghofe@7015
   385
wenzelm@13462
   386
val distinct_simproc =
wenzelm@13462
   387
  Simplifier.simproc (Theory.sign_of HOL.thy) distinctN ["s = t"] distinct_proc;
berghofe@7015
   388
berghofe@7015
   389
val dist_ss = HOL_ss addsimprocs [distinct_simproc];
berghofe@7015
   390
berghofe@7015
   391
val simproc_setup =
berghofe@7015
   392
  [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
berghofe@7015
   393
   fn thy => (simpset_ref_of thy := simpset_of thy addsimprocs [distinct_simproc]; thy)];
berghofe@7015
   394
berghofe@7015
   395
berghofe@14799
   396
(**** translation rules for case ****)
berghofe@14799
   397
berghofe@14799
   398
fun case_tr sg [t, u] =
berghofe@14799
   399
    let
berghofe@14799
   400
      fun case_error s name ts = raise TERM ("Error in case expression" ^
berghofe@14799
   401
        if_none (apsome (curry op ^ " for datatype ") name) "" ^ ":\n" ^ s, ts);
berghofe@14799
   402
      fun dest_case1 (Const ("_case1", _) $ t $ u) = (case strip_comb t of
berghofe@14799
   403
            (Const (s, _), ts) => (Sign.intern_const sg s, ts)
berghofe@14799
   404
          | (Free (s, _), ts) => (Sign.intern_const sg s, ts)
berghofe@14799
   405
          | _ => case_error "Head is not a constructor" None [t, u], u)
berghofe@14799
   406
        | dest_case1 t = raise TERM ("dest_case1", [t]);
berghofe@14799
   407
      fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
berghofe@14799
   408
        | dest_case2 t = [t];
berghofe@14799
   409
      val cases as ((cname, _), _) :: _ = map dest_case1 (dest_case2 u);
berghofe@14799
   410
      val tab = Symtab.dest (get_datatypes_sg sg);
berghofe@14799
   411
      val (cases', default) = (case split_last cases of
berghofe@14799
   412
          (cases', (("dummy_pattern", []), t)) => (cases', Some t)
berghofe@14799
   413
        | _ => (cases, None))
berghofe@14799
   414
      fun abstr (Free (x, T), body) = Term.absfree (x, T, body)
berghofe@14799
   415
        | abstr (Const ("_constrain", _) $ Free (x, T) $ tT, body) =
berghofe@14799
   416
            Syntax.const Syntax.constrainAbsC $ Term.absfree (x, T, body) $ tT
berghofe@14799
   417
        | abstr (Const ("Pair", _) $ x $ y, body) =
berghofe@14799
   418
            Syntax.const "split" $ abstr (x, abstr (y, body))
berghofe@14799
   419
        | abstr (t, _) = case_error "Illegal pattern" None [t];
berghofe@14799
   420
    in case find_first (fn (_, {descr, index, ...}) =>
berghofe@14799
   421
      exists (equal cname o fst) (#3 (snd (nth_elem (index, descr))))) tab of
berghofe@14799
   422
        None => case_error ("Not a datatype constructor: " ^ cname) None [u]
berghofe@14799
   423
      | Some (tname, {descr, case_name, index, ...}) =>
berghofe@14799
   424
        let
berghofe@14799
   425
          val _ = if exists (equal "dummy_pattern" o fst o fst) cases' then
berghofe@14799
   426
            case_error "Illegal occurrence of '_' dummy pattern" (Some tname) [u] else ();
berghofe@14799
   427
          val (_, (_, dts, constrs)) = nth_elem (index, descr);
berghofe@14799
   428
          val sorts = map (rpair [] o dest_DtTFree) dts;
berghofe@14799
   429
          fun find_case (cases, (s, dt)) =
berghofe@14799
   430
            (case find_first (equal s o fst o fst) cases' of
berghofe@14799
   431
               None => (case default of
berghofe@14799
   432
                   None => case_error ("No clause for constructor " ^ s) (Some tname) [u]
berghofe@14799
   433
                 | Some t => (cases, list_abs (map (rpair dummyT) (DatatypeProp.make_tnames
berghofe@14799
   434
                     (map (typ_of_dtyp descr sorts) dt)), t)))
berghofe@14799
   435
             | Some (c as ((_, vs), t)) =>
berghofe@14799
   436
                 if length dt <> length vs then
berghofe@14799
   437
                    case_error ("Wrong number of arguments for constructor " ^ s)
berghofe@14799
   438
                      (Some tname) vs
berghofe@14799
   439
                 else (cases \ c, foldr abstr (vs, t)))
berghofe@14799
   440
          val (cases'', fs) = foldl_map find_case (cases', constrs)
berghofe@14799
   441
        in case (cases'', length constrs = length cases', default) of
berghofe@14799
   442
            ([], true, Some _) =>
berghofe@14799
   443
              case_error "Extra '_' dummy pattern" (Some tname) [u]
berghofe@14799
   444
          | (_ :: _, _, _) =>
berghofe@14799
   445
              let val extra = distinct (map (fst o fst) cases'')
berghofe@14799
   446
              in case extra \\ map fst constrs of
berghofe@14799
   447
                  [] => case_error ("More than one clause for constructor(s) " ^
berghofe@14799
   448
                    commas extra) (Some tname) [u]
berghofe@14799
   449
                | extra' => case_error ("Illegal constructor(s): " ^ commas extra')
berghofe@14799
   450
                    (Some tname) [u]
berghofe@14799
   451
              end
berghofe@14799
   452
          | _ => list_comb (Syntax.const case_name, fs) $ t
berghofe@14799
   453
        end
berghofe@14799
   454
    end
berghofe@14799
   455
  | case_tr sg ts = raise TERM ("case_tr", ts);
berghofe@14799
   456
berghofe@14799
   457
fun case_tr' constrs sg ts =
berghofe@14799
   458
  if length ts <> length constrs + 1 then raise Match else
berghofe@14799
   459
  let
berghofe@14799
   460
    val (fs, x) = split_last ts;
berghofe@14799
   461
    fun strip_abs 0 t = ([], t)
berghofe@14799
   462
      | strip_abs i (Abs p) =
berghofe@14799
   463
        let val (x, u) = Syntax.atomic_abs_tr' p
berghofe@14799
   464
        in apfst (cons x) (strip_abs (i-1) u) end
berghofe@14799
   465
      | strip_abs i (Const ("split", _) $ t) = (case strip_abs (i+1) t of
berghofe@14799
   466
          (v :: v' :: vs, u) => (Syntax.const "Pair" $ v $ v' :: vs, u));
berghofe@14799
   467
    fun is_dependent i t =
berghofe@14799
   468
      let val k = length (strip_abs_vars t) - i
berghofe@14799
   469
      in k < 0 orelse exists (fn j => j >= k)
berghofe@14799
   470
        (loose_bnos (strip_abs_body t))
berghofe@14799
   471
      end;
berghofe@14799
   472
    val cases = map (fn ((cname, dts), t) =>
berghofe@14799
   473
      (Sign.cond_extern sg Sign.constK cname,
berghofe@14799
   474
       strip_abs (length dts) t, is_dependent (length dts) t))
berghofe@14799
   475
      (constrs ~~ fs);
berghofe@14799
   476
    fun count_cases (cs, (_, _, true)) = cs
berghofe@14799
   477
      | count_cases (cs, (cname, (_, body), false)) = (case assoc (cs, body) of
berghofe@14799
   478
          None => (body, [cname]) :: cs
berghofe@14799
   479
        | Some cnames => overwrite (cs, (body, cnames @ [cname])));
berghofe@14799
   480
    val cases' = sort (int_ord o Library.swap o pairself (length o snd))
berghofe@14799
   481
      (foldl count_cases ([], cases));
berghofe@14799
   482
    fun mk_case1 (cname, (vs, body), _) = Syntax.const "_case1" $
berghofe@14799
   483
      list_comb (Syntax.const cname, vs) $ body;
berghofe@14799
   484
  in
berghofe@14799
   485
    Syntax.const "_case_syntax" $ x $
berghofe@14799
   486
      foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) (map mk_case1
berghofe@14799
   487
        (case cases' of
berghofe@14799
   488
           [] => cases
berghofe@14799
   489
         | (default, cnames) :: _ =>
berghofe@14799
   490
           if length cnames = 1 then cases
berghofe@14799
   491
           else if length cnames = length constrs then
berghofe@14799
   492
             [hd cases, ("dummy_pattern", ([], default), false)]
berghofe@14799
   493
           else
berghofe@14799
   494
             filter_out (fn (cname, _, _) => cname mem cnames) cases @
berghofe@14799
   495
             [("dummy_pattern", ([], default), false)]))
berghofe@14799
   496
  end;
berghofe@14799
   497
berghofe@14799
   498
fun make_case_tr' case_names descr = flat (map
berghofe@14799
   499
  (fn ((_, (_, _, constrs)), case_name) => map (rpair (case_tr' constrs))
berghofe@14799
   500
    (NameSpace.accesses' case_name)) (descr ~~ case_names));
berghofe@14799
   501
berghofe@14799
   502
val trfun_setup =
berghofe@14799
   503
  [Theory.add_advanced_trfuns ([], [("_case_syntax", case_tr)], [], [])];
berghofe@14799
   504
berghofe@14799
   505
berghofe@5177
   506
(* prepare types *)
berghofe@5177
   507
berghofe@5177
   508
fun read_typ sign ((Ts, sorts), str) =
berghofe@5177
   509
  let
berghofe@5177
   510
    val T = Type.no_tvars (Sign.read_typ (sign, (curry assoc)
berghofe@5177
   511
      (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
berghofe@5177
   512
  in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
berghofe@5177
   513
berghofe@5177
   514
fun cert_typ sign ((Ts, sorts), raw_T) =
berghofe@5177
   515
  let
berghofe@5177
   516
    val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
berghofe@5177
   517
      TYPE (msg, _, _) => error msg;
berghofe@5177
   518
    val sorts' = add_typ_tfrees (T, sorts)
berghofe@5177
   519
  in (Ts @ [T],
berghofe@5177
   520
      case duplicates (map fst sorts') of
berghofe@5177
   521
         [] => sorts'
berghofe@5177
   522
       | dups => error ("Inconsistent sort constraints for " ^ commas dups))
berghofe@5177
   523
  end;
berghofe@5177
   524
berghofe@5177
   525
berghofe@5177
   526
(**** make datatype info ****)
berghofe@5177
   527
berghofe@5177
   528
fun make_dt_info descr induct reccomb_names rec_thms
wenzelm@10121
   529
    (((((((((i, (_, (tname, _, _))), case_name), case_thms),
wenzelm@10121
   530
      exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
wenzelm@10121
   531
  (tname,
wenzelm@10121
   532
   {index = i,
wenzelm@10121
   533
    descr = descr,
wenzelm@10121
   534
    rec_names = reccomb_names,
wenzelm@10121
   535
    rec_rewrites = rec_thms,
wenzelm@10121
   536
    case_name = case_name,
wenzelm@10121
   537
    case_rewrites = case_thms,
wenzelm@10121
   538
    induction = induct,
wenzelm@10121
   539
    exhaustion = exhaustion_thm,
wenzelm@10121
   540
    distinct = distinct_thm,
wenzelm@10121
   541
    inject = inject,
wenzelm@10121
   542
    nchotomy = nchotomy,
wenzelm@10121
   543
    case_cong = case_cong,
wenzelm@10121
   544
    weak_case_cong = weak_case_cong});
berghofe@5177
   545
berghofe@5177
   546
berghofe@5177
   547
(********************* axiomatic introduction of datatypes ********************)
berghofe@5177
   548
wenzelm@8437
   549
fun add_and_get_axioms_atts label tnames attss ts thy =
wenzelm@8437
   550
  foldr (fn (((tname, atts), t), (thy', axs)) =>
berghofe@5177
   551
    let
wenzelm@8437
   552
      val (thy'', [ax]) = thy' |>
berghofe@5661
   553
        Theory.add_path tname |>
wenzelm@8437
   554
        PureThy.add_axioms_i [((label, t), atts)];
berghofe@5661
   555
    in (Theory.parent_path thy'', ax::axs)
wenzelm@8437
   556
    end) (tnames ~~ attss ~~ ts, (thy, []));
wenzelm@8437
   557
wenzelm@8437
   558
fun add_and_get_axioms label tnames =
wenzelm@8437
   559
  add_and_get_axioms_atts label tnames (replicate (length tnames) []);
berghofe@5177
   560
berghofe@5177
   561
fun add_and_get_axiomss label tnames tss thy =
berghofe@5177
   562
  foldr (fn ((tname, ts), (thy', axss)) =>
berghofe@5177
   563
    let
wenzelm@8437
   564
      val (thy'', [axs]) = thy' |>
berghofe@5661
   565
        Theory.add_path tname |>
berghofe@5177
   566
        PureThy.add_axiomss_i [((label, ts), [])];
berghofe@5661
   567
    in (Theory.parent_path thy'', axs::axss)
berghofe@5177
   568
    end) (tnames ~~ tss, (thy, []));
berghofe@5177
   569
wenzelm@8437
   570
fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
wenzelm@8437
   571
    case_names_induct case_names_exhausts thy =
berghofe@5177
   572
  let
berghofe@5177
   573
    val descr' = flat descr;
berghofe@5177
   574
    val recTs = get_rec_types descr' sorts;
berghofe@5578
   575
    val used = foldr add_typ_tfree_names (recTs, []);
berghofe@5177
   576
    val newTs = take (length (hd descr), recTs);
berghofe@5177
   577
berghofe@7015
   578
    val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
berghofe@13641
   579
      (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
berghofe@13641
   580
        cargs) constrs) descr';
berghofe@7015
   581
berghofe@5177
   582
    (**** declare new types and constants ****)
berghofe@5177
   583
berghofe@5177
   584
    val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
berghofe@5177
   585
berghofe@5177
   586
    val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
berghofe@5177
   587
      map (fn ((_, cargs), (cname, mx)) =>
berghofe@5177
   588
        (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
berghofe@5177
   589
          (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
berghofe@5177
   590
berghofe@5578
   591
    val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
wenzelm@12338
   592
      replicate (length descr') HOLogic.typeS);
berghofe@5177
   593
berghofe@5177
   594
    val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
berghofe@5177
   595
      map (fn (_, cargs) =>
berghofe@5177
   596
        let
berghofe@7015
   597
          val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@7015
   598
          val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
berghofe@7015
   599
berghofe@13641
   600
          fun mk_argT (dt, T) =
berghofe@13641
   601
            binder_types T ---> nth_elem (body_index dt, rec_result_Ts);
berghofe@7015
   602
berghofe@7015
   603
          val argTs = Ts @ map mk_argT recs
berghofe@5177
   604
        in argTs ---> nth_elem (i, rec_result_Ts)
berghofe@5177
   605
        end) constrs) descr');
berghofe@5177
   606
berghofe@5177
   607
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
berghofe@5177
   608
    val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   609
      (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   610
        (1 upto (length descr')));
berghofe@5177
   611
berghofe@9739
   612
    val size_names = DatatypeProp.indexify_names
berghofe@9739
   613
      (map (fn T => name_of_typ T ^ "_size") (drop (length (hd descr), recTs)));
berghofe@5177
   614
wenzelm@12338
   615
    val freeT = TFree (variant used "'t", HOLogic.typeS);
berghofe@5177
   616
    val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
berghofe@5177
   617
      map (fn (_, cargs) =>
berghofe@5177
   618
        let val Ts = map (typ_of_dtyp descr' sorts) cargs
berghofe@5177
   619
        in Ts ---> freeT end) constrs) (hd descr);
berghofe@5177
   620
berghofe@5177
   621
    val case_names = map (fn s => (s ^ "_case")) new_type_names;
berghofe@5177
   622
berghofe@6305
   623
    val thy2' = thy |>
berghofe@5177
   624
berghofe@5177
   625
      (** new types **)
berghofe@5177
   626
berghofe@5177
   627
      curry (foldr (fn (((name, mx), tvs), thy') => thy' |>
wenzelm@6385
   628
          TypedefPackage.add_typedecls [(name, tvs, mx)]))
wenzelm@6385
   629
        (types_syntax ~~ tyvars) |>
berghofe@5661
   630
      add_path flat_names (space_implode "_" new_type_names) |>
berghofe@5177
   631
berghofe@5177
   632
      (** primrec combinators **)
berghofe@5177
   633
berghofe@5177
   634
      Theory.add_consts_i (map (fn ((name, T), T') =>
berghofe@5177
   635
        (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
berghofe@5177
   636
          (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
berghofe@5177
   637
berghofe@5177
   638
      (** case combinators **)
berghofe@5177
   639
berghofe@5177
   640
      Theory.add_consts_i (map (fn ((name, T), Ts) =>
berghofe@5177
   641
        (name, Ts @ [T] ---> freeT, NoSyn))
berghofe@14799
   642
          (case_names ~~ newTs ~~ case_fn_Ts));
berghofe@6305
   643
wenzelm@6394
   644
    val reccomb_names' = map (Sign.intern_const (Theory.sign_of thy2')) reccomb_names;
wenzelm@6394
   645
    val case_names' = map (Sign.intern_const (Theory.sign_of thy2')) case_names;
berghofe@6305
   646
berghofe@6305
   647
    val thy2 = thy2' |>
berghofe@5177
   648
berghofe@5177
   649
      (** size functions **)
berghofe@5177
   650
berghofe@7015
   651
      (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
berghofe@5177
   652
        (Sign.base_name s, T --> HOLogic.natT, NoSyn))
berghofe@7015
   653
          (size_names ~~ drop (length (hd descr), recTs)))) |>
berghofe@5661
   654
berghofe@5661
   655
      (** constructors **)
berghofe@5661
   656
berghofe@5661
   657
      parent_path flat_names |>
berghofe@5661
   658
      curry (foldr (fn (((((_, (_, _, constrs)), T), tname),
berghofe@5661
   659
        constr_syntax'), thy') => thy' |>
berghofe@5661
   660
          add_path flat_names tname |>
berghofe@5661
   661
            Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
berghofe@5661
   662
              (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
berghofe@5661
   663
                (constrs ~~ constr_syntax')) |>
berghofe@5661
   664
          parent_path flat_names))
berghofe@5661
   665
            (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
berghofe@5177
   666
berghofe@5177
   667
    (**** introduction of axioms ****)
berghofe@5177
   668
berghofe@5661
   669
    val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
berghofe@9739
   670
    val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
berghofe@5661
   671
wenzelm@8437
   672
    val (thy3, (([induct], [rec_thms]), inject)) =
wenzelm@8437
   673
      thy2 |>
berghofe@5661
   674
      Theory.add_path (space_implode "_" new_type_names) |>
wenzelm@10911
   675
      PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts),
berghofe@13340
   676
        [case_names_induct])] |>>>
wenzelm@8437
   677
      PureThy.add_axiomss_i [(("recs", rec_axs), [])] |>>
wenzelm@8437
   678
      (if no_size then I else #1 o PureThy.add_axiomss_i [(("size", size_axs), [])]) |>>
wenzelm@8437
   679
      Theory.parent_path |>>>
berghofe@5177
   680
      add_and_get_axiomss "inject" new_type_names
berghofe@5177
   681
        (DatatypeProp.make_injs descr sorts);
berghofe@7015
   682
    val size_thms = if no_size then [] else get_thms thy3 "size";
berghofe@5177
   683
    val (thy4, distinct) = add_and_get_axiomss "distinct" new_type_names
berghofe@5177
   684
      (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
wenzelm@8437
   685
wenzelm@8437
   686
    val exhaust_ts = DatatypeProp.make_casedists descr sorts;
wenzelm@8437
   687
    val (thy5, exhaustion) = add_and_get_axioms_atts "exhaust" new_type_names
wenzelm@8437
   688
      (map Library.single case_names_exhausts) exhaust_ts thy4;
berghofe@5177
   689
    val (thy6, case_thms) = add_and_get_axiomss "cases" new_type_names
berghofe@5177
   690
      (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
berghofe@5177
   691
    val (split_ts, split_asm_ts) = ListPair.unzip
berghofe@5177
   692
      (DatatypeProp.make_splits new_type_names descr sorts thy6);
berghofe@5177
   693
    val (thy7, split) = add_and_get_axioms "split" new_type_names split_ts thy6;
berghofe@5177
   694
    val (thy8, split_asm) = add_and_get_axioms "split_asm" new_type_names
berghofe@5177
   695
      split_asm_ts thy7;
berghofe@5177
   696
    val (thy9, nchotomys) = add_and_get_axioms "nchotomy" new_type_names
berghofe@5177
   697
      (DatatypeProp.make_nchotomys descr sorts) thy8;
berghofe@5177
   698
    val (thy10, case_congs) = add_and_get_axioms "case_cong" new_type_names
berghofe@5177
   699
      (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
nipkow@8601
   700
    val (thy11, weak_case_congs) = add_and_get_axioms "weak_case_cong" new_type_names
nipkow@8601
   701
      (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
wenzelm@8405
   702
berghofe@6305
   703
    val dt_infos = map (make_dt_info descr' induct reccomb_names' rec_thms)
berghofe@6305
   704
      ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
berghofe@7015
   705
        exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
wenzelm@10121
   706
          nchotomys ~~ case_congs ~~ weak_case_congs);
berghofe@5177
   707
berghofe@5177
   708
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
wenzelm@9386
   709
    val split_thms = split ~~ split_asm;
berghofe@5177
   710
nipkow@8601
   711
    val thy12 = thy11 |>
berghofe@14799
   712
      Theory.add_advanced_trfuns ([], [], make_case_tr' case_names' (hd descr), []) |>
berghofe@5661
   713
      Theory.add_path (space_implode "_" new_type_names) |>
oheimb@11345
   714
      add_rules simps case_thms size_thms rec_thms inject distinct
oheimb@11345
   715
                weak_case_congs Simplifier.cong_add_global |> 
berghofe@5177
   716
      put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
wenzelm@11805
   717
      add_cases_induct dt_infos induct |>
wenzelm@9386
   718
      Theory.parent_path |>
berghofe@13466
   719
      (#1 o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
berghofe@13466
   720
      DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
berghofe@5177
   721
  in
nipkow@8601
   722
    (thy12,
berghofe@5177
   723
     {distinct = distinct,
berghofe@5177
   724
      inject = inject,
berghofe@5177
   725
      exhaustion = exhaustion,
berghofe@5177
   726
      rec_thms = rec_thms,
berghofe@5177
   727
      case_thms = case_thms,
wenzelm@9386
   728
      split_thms = split_thms,
berghofe@5177
   729
      induction = induct,
berghofe@5177
   730
      size = size_thms,
berghofe@5177
   731
      simps = simps})
berghofe@5177
   732
  end;
berghofe@5177
   733
berghofe@5177
   734
berghofe@5177
   735
(******************* definitional introduction of datatypes *******************)
berghofe@5177
   736
wenzelm@8437
   737
fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
wenzelm@8437
   738
    case_names_induct case_names_exhausts thy =
berghofe@5177
   739
  let
wenzelm@6360
   740
    val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
berghofe@5177
   741
berghofe@7015
   742
    val (thy2, inject, distinct, dist_rewrites, simproc_dists, induct) = thy |>
berghofe@5661
   743
      DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
wenzelm@8437
   744
        types_syntax constr_syntax case_names_induct;
berghofe@5177
   745
wenzelm@8437
   746
    val (thy3, casedist_thms) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
wenzelm@8437
   747
      sorts induct case_names_exhausts thy2;
berghofe@8478
   748
    val (thy4, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
berghofe@7015
   749
      flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
wenzelm@8437
   750
    val (thy6, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms
berghofe@5661
   751
      flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
berghofe@5177
   752
    val (thy7, split_thms) = DatatypeAbsProofs.prove_split_thms new_type_names
berghofe@5177
   753
      descr sorts inject dist_rewrites casedist_thms case_thms thy6;
berghofe@5177
   754
    val (thy8, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
berghofe@5177
   755
      descr sorts casedist_thms thy7;
berghofe@5177
   756
    val (thy9, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
berghofe@5177
   757
      descr sorts nchotomys case_thms thy8;
nipkow@8601
   758
    val (thy10, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
nipkow@8601
   759
      descr sorts thy9;
nipkow@8601
   760
    val (thy11, size_thms) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
nipkow@8601
   761
      descr sorts reccomb_names rec_thms thy10;
berghofe@5177
   762
berghofe@5177
   763
    val dt_infos = map (make_dt_info (flat descr) induct reccomb_names rec_thms)
berghofe@5177
   764
      ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
wenzelm@10121
   765
        casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
berghofe@5177
   766
berghofe@5177
   767
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   768
nipkow@8601
   769
    val thy12 = thy11 |>
berghofe@14799
   770
      Theory.add_advanced_trfuns ([], [], make_case_tr' case_names (hd descr), []) |>
berghofe@5661
   771
      Theory.add_path (space_implode "_" new_type_names) |>
oheimb@11345
   772
      add_rules simps case_thms size_thms rec_thms inject distinct
oheimb@11345
   773
                weak_case_congs (Simplifier.change_global_ss (op addcongs)) |> 
berghofe@5177
   774
      put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
wenzelm@11805
   775
      add_cases_induct dt_infos induct |>
wenzelm@9386
   776
      Theory.parent_path |>
berghofe@13466
   777
      (#1 o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
berghofe@13466
   778
      DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
berghofe@5177
   779
  in
nipkow@8601
   780
    (thy12,
berghofe@5177
   781
     {distinct = distinct,
berghofe@5177
   782
      inject = inject,
berghofe@5177
   783
      exhaustion = casedist_thms,
berghofe@5177
   784
      rec_thms = rec_thms,
berghofe@5177
   785
      case_thms = case_thms,
berghofe@5177
   786
      split_thms = split_thms,
berghofe@5177
   787
      induction = induct,
berghofe@5177
   788
      size = size_thms,
berghofe@5177
   789
      simps = simps})
berghofe@5177
   790
  end;
berghofe@5177
   791
berghofe@5177
   792
wenzelm@6385
   793
(*********************** declare existing type as datatype *********************)
berghofe@5177
   794
wenzelm@6385
   795
fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
berghofe@5177
   796
  let
wenzelm@12922
   797
    val _ = Theory.requires thy0 "Inductive" "datatype representations";
wenzelm@12922
   798
wenzelm@6385
   799
    fun app_thmss srcs thy = foldl_map (fn (thy, x) => apply_theorems x thy) (thy, srcs);
wenzelm@6385
   800
    fun app_thm src thy = apsnd Library.hd (apply_theorems [src] thy);
wenzelm@6385
   801
wenzelm@6385
   802
    val (((thy1, induction), inject), distinct) = thy0
wenzelm@6385
   803
      |> app_thmss raw_distinct
wenzelm@6385
   804
      |> apfst (app_thmss raw_inject)
wenzelm@6385
   805
      |> apfst (apfst (app_thm raw_induction));
wenzelm@6394
   806
    val sign = Theory.sign_of thy1;
berghofe@5177
   807
berghofe@5177
   808
    val induction' = freezeT induction;
berghofe@5177
   809
berghofe@5177
   810
    fun err t = error ("Ill-formed predicate in induction rule: " ^
berghofe@5177
   811
      Sign.string_of_term sign t);
berghofe@5177
   812
berghofe@5177
   813
    fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
berghofe@7015
   814
          ((tname, map dest_TFree Ts) handle TERM _ => err t)
berghofe@5177
   815
      | get_typ t = err t;
berghofe@5177
   816
wenzelm@8437
   817
    val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
berghofe@5177
   818
    val new_type_names = if_none alt_names (map fst dtnames);
berghofe@5177
   819
berghofe@5177
   820
    fun get_constr t = (case Logic.strip_assums_concl t of
berghofe@5177
   821
        _ $ (_ $ t') => (case head_of t' of
berghofe@5177
   822
            Const (cname, cT) => (case strip_type cT of
berghofe@5177
   823
                (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
berghofe@5177
   824
              | _ => err t)
berghofe@5177
   825
          | _ => err t)
berghofe@5177
   826
      | _ => err t);
berghofe@5177
   827
berghofe@5177
   828
    fun make_dt_spec [] _ _ = []
berghofe@5177
   829
      | make_dt_spec ((tname, tvs)::dtnames') i constrs =
berghofe@5177
   830
          let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
berghofe@5177
   831
          in (i, (tname, map DtTFree tvs, map snd constrs'))::
berghofe@5177
   832
            (make_dt_spec dtnames' (i + 1) constrs'')
berghofe@5177
   833
          end;
berghofe@5177
   834
berghofe@5177
   835
    val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
berghofe@5177
   836
    val sorts = add_term_tfrees (concl_of induction', []);
wenzelm@6385
   837
    val dt_info = get_datatypes thy1;
berghofe@5177
   838
wenzelm@8437
   839
    val case_names_induct = mk_case_names_induct descr;
wenzelm@8437
   840
    val case_names_exhausts = mk_case_names_exhausts descr (map #1 dtnames);
wenzelm@8437
   841
    
wenzelm@8437
   842
wenzelm@6427
   843
    val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
berghofe@5177
   844
wenzelm@6385
   845
    val (thy2, casedist_thms) = thy1 |>
wenzelm@8437
   846
      DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
wenzelm@8437
   847
        case_names_exhausts;
berghofe@8478
   848
    val (thy3, (reccomb_names, rec_thms)) = DatatypeAbsProofs.prove_primrec_thms
berghofe@7015
   849
      false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
wenzelm@8437
   850
    val (thy4, (case_thms, case_names)) = DatatypeAbsProofs.prove_case_thms false
berghofe@5177
   851
      new_type_names [descr] sorts reccomb_names rec_thms thy3;
berghofe@5177
   852
    val (thy5, split_thms) = DatatypeAbsProofs.prove_split_thms
berghofe@5177
   853
      new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
berghofe@5177
   854
    val (thy6, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
berghofe@5177
   855
      [descr] sorts casedist_thms thy5;
berghofe@5177
   856
    val (thy7, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
berghofe@5177
   857
      [descr] sorts nchotomys case_thms thy6;
nipkow@8601
   858
    val (thy8, weak_case_congs) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
nipkow@8601
   859
      [descr] sorts thy7;
nipkow@8601
   860
    val (thy9, size_thms) =
wenzelm@10930
   861
      if Sign.exists_stamp "NatArith" (Theory.sign_of thy8) then
berghofe@5661
   862
        DatatypeAbsProofs.prove_size_thms false new_type_names
nipkow@8601
   863
          [descr] sorts reccomb_names rec_thms thy8
nipkow@8601
   864
      else (thy8, []);
berghofe@5177
   865
wenzelm@9149
   866
    val (thy10, [induction']) = thy9 |>
wenzelm@9149
   867
      (#1 o store_thmss "inject" new_type_names inject) |>
wenzelm@9149
   868
      (#1 o store_thmss "distinct" new_type_names distinct) |>
wenzelm@9149
   869
      Theory.add_path (space_implode "_" new_type_names) |>
wenzelm@9149
   870
      PureThy.add_thms [(("induct", induction), [case_names_induct])];
wenzelm@9149
   871
wenzelm@9149
   872
    val dt_infos = map (make_dt_info descr induction' reccomb_names rec_thms)
wenzelm@10121
   873
      ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
wenzelm@10121
   874
        map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
berghofe@5177
   875
berghofe@5177
   876
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   877
wenzelm@9149
   878
    val thy11 = thy10 |>
berghofe@14799
   879
      Theory.add_advanced_trfuns ([], [], make_case_tr' case_names descr, []) |>
oheimb@11345
   880
      add_rules simps case_thms size_thms rec_thms inject distinct
oheimb@11345
   881
                weak_case_congs (Simplifier.change_global_ss (op addcongs)) |> 
wenzelm@9149
   882
      put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
wenzelm@11805
   883
      add_cases_induct dt_infos induction' |>
wenzelm@9386
   884
      Theory.parent_path |>
berghofe@13466
   885
      (#1 o store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)) |>
berghofe@13466
   886
      DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos);
berghofe@5177
   887
  in
wenzelm@9149
   888
    (thy11,
berghofe@5177
   889
     {distinct = distinct,
berghofe@5177
   890
      inject = inject,
berghofe@5177
   891
      exhaustion = casedist_thms,
berghofe@5177
   892
      rec_thms = rec_thms,
berghofe@5177
   893
      case_thms = case_thms,
berghofe@5177
   894
      split_thms = split_thms,
wenzelm@8437
   895
      induction = induction',
berghofe@5177
   896
      size = size_thms,
berghofe@5177
   897
      simps = simps})
berghofe@5177
   898
  end;
berghofe@5177
   899
wenzelm@6385
   900
val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
wenzelm@6385
   901
val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
wenzelm@6385
   902
berghofe@5177
   903
wenzelm@11958
   904
berghofe@5177
   905
(******************************** add datatype ********************************)
berghofe@5177
   906
berghofe@14887
   907
fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
berghofe@5177
   908
  let
wenzelm@12922
   909
    val _ = Theory.requires thy "Datatype_Universe" "datatype definitions";
berghofe@5177
   910
berghofe@5177
   911
    (* this theory is used just for parsing *)
berghofe@5177
   912
berghofe@5177
   913
    val tmp_thy = thy |>
wenzelm@5892
   914
      Theory.copy |>
berghofe@5177
   915
      Theory.add_types (map (fn (tvs, tname, mx, _) =>
berghofe@5177
   916
        (tname, length tvs, mx)) dts);
berghofe@5177
   917
wenzelm@6394
   918
    val sign = Theory.sign_of tmp_thy;
berghofe@5177
   919
berghofe@5661
   920
    val (tyvars, _, _, _)::_ = dts;
berghofe@5177
   921
    val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
berghofe@5177
   922
      let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
berghofe@5177
   923
      in (case duplicates tvs of
berghofe@5661
   924
            [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
berghofe@5661
   925
                  else error ("Mutually recursive datatypes must have same type parameters")
berghofe@5177
   926
          | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
berghofe@5177
   927
              " : " ^ commas dups))
berghofe@5177
   928
      end) dts);
berghofe@5177
   929
berghofe@5177
   930
    val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
berghofe@5177
   931
      [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
berghofe@5177
   932
berghofe@5177
   933
    fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
berghofe@5177
   934
      let
berghofe@5661
   935
        fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
berghofe@5279
   936
          let
berghofe@5279
   937
            val (cargs', sorts'') = foldl (prep_typ sign) (([], sorts'), cargs);
berghofe@5279
   938
            val _ = (case foldr add_typ_tfree_names (cargs', []) \\ tvs of
berghofe@5279
   939
                [] => ()
berghofe@5279
   940
              | vs => error ("Extra type variables on rhs: " ^ commas vs))
berghofe@5661
   941
          in (constrs @ [((if flat_names then Sign.full_name sign else
berghofe@5661
   942
                Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
berghofe@5177
   943
                   map (dtyp_of_typ new_dts) cargs')],
berghofe@5177
   944
              constr_syntax' @ [(cname, mx')], sorts'')
berghofe@5177
   945
          end handle ERROR =>
berghofe@5177
   946
            error ("The error above occured in constructor " ^ cname ^
berghofe@5177
   947
              " of datatype " ^ tname);
berghofe@5177
   948
berghofe@5177
   949
        val (constrs', constr_syntax', sorts') =
berghofe@5177
   950
          foldl prep_constr (([], [], sorts), constrs)
berghofe@5177
   951
wenzelm@8405
   952
      in
berghofe@5177
   953
        case duplicates (map fst constrs') of
berghofe@5177
   954
           [] =>
berghofe@5177
   955
             (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
berghofe@5177
   956
                map DtTFree tvs, constrs'))],
berghofe@5177
   957
              constr_syntax @ [constr_syntax'], sorts', i + 1)
berghofe@5177
   958
         | dups => error ("Duplicate constructors " ^ commas dups ^
berghofe@5177
   959
             " in datatype " ^ tname)
berghofe@5177
   960
      end;
berghofe@5177
   961
berghofe@5661
   962
    val (dts', constr_syntax, sorts', i) = foldl prep_dt_spec (([], [], [], 0), dts);
berghofe@7015
   963
    val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
berghofe@5177
   964
    val dt_info = get_datatypes thy;
berghofe@7015
   965
    val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
berghofe@14887
   966
    val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
berghofe@14887
   967
      if err then error ("Nonemptiness check failed for datatype " ^ s)
berghofe@14887
   968
      else raise exn;
berghofe@5177
   969
wenzelm@8437
   970
    val descr' = flat descr;
wenzelm@8437
   971
    val case_names_induct = mk_case_names_induct descr';
wenzelm@8437
   972
    val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
berghofe@5177
   973
  in
berghofe@5177
   974
    (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
wenzelm@8437
   975
      flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
wenzelm@8437
   976
      case_names_induct case_names_exhausts thy
berghofe@5177
   977
  end;
berghofe@5177
   978
berghofe@5177
   979
val add_datatype_i = gen_add_datatype cert_typ;
berghofe@14887
   980
val add_datatype = gen_add_datatype read_typ true;
berghofe@5177
   981
wenzelm@6360
   982
wenzelm@6360
   983
(** package setup **)
wenzelm@6360
   984
wenzelm@6360
   985
(* setup theory *)
wenzelm@6360
   986
berghofe@14799
   987
val setup = [DatatypesData.init, Method.add_methods tactic_emulations] @ simproc_setup @ trfun_setup;
wenzelm@6360
   988
wenzelm@6360
   989
wenzelm@6360
   990
(* outer syntax *)
wenzelm@6360
   991
wenzelm@6723
   992
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6360
   993
wenzelm@6360
   994
val datatype_decl =
wenzelm@6723
   995
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
wenzelm@12876
   996
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
wenzelm@6360
   997
wenzelm@6360
   998
fun mk_datatype args =
wenzelm@6360
   999
  let
wenzelm@6360
  1000
    val names = map (fn ((((None, _), t), _), _) => t | ((((Some t, _), _), _), _) => t) args;
wenzelm@12876
  1001
    val specs = map (fn ((((_, vs), t), mx), cons) =>
wenzelm@12876
  1002
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
wenzelm@6360
  1003
  in #1 o add_datatype false names specs end;
wenzelm@6360
  1004
wenzelm@6360
  1005
val datatypeP =
wenzelm@6723
  1006
  OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
wenzelm@6723
  1007
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
wenzelm@6360
  1008
wenzelm@6385
  1009
wenzelm@6385
  1010
val rep_datatype_decl =
wenzelm@6723
  1011
  Scan.option (Scan.repeat1 P.name) --
wenzelm@11958
  1012
    Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
wenzelm@11958
  1013
    Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
wenzelm@6723
  1014
    (P.$$$ "induction" |-- P.!!! P.xthm);
wenzelm@6385
  1015
wenzelm@6385
  1016
fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #1 o rep_datatype opt_ts dss iss ind;
wenzelm@6385
  1017
wenzelm@6385
  1018
val rep_datatypeP =
wenzelm@6723
  1019
  OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
wenzelm@6385
  1020
    (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
wenzelm@6385
  1021
wenzelm@6385
  1022
wenzelm@6479
  1023
val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
wenzelm@6385
  1024
val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
wenzelm@6385
  1025
wenzelm@6385
  1026
end;
wenzelm@6385
  1027
wenzelm@6360
  1028
berghofe@5177
  1029
end;
berghofe@5177
  1030
wenzelm@6360
  1031
structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
wenzelm@6360
  1032
open BasicDatatypePackage;