src/HOL/Tools/datatype_package.ML
author haftmann
Sat Nov 18 00:20:28 2006 +0100 (2006-11-18)
changeset 21419 809e7520234a
parent 21350 6e58289b6685
child 21459 20c2ddee8bc5
permissions -rw-r--r--
added instance for class size
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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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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 ->
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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} * theory
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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 ->
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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} * theory
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  val rep_datatype_i : string list option -> (thm list * attribute list) list list ->
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    (thm list * attribute list) list list -> (thm list * attribute list) ->
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    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} * theory
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  val rep_datatype : string list option -> (thmref * Attrib.src list) list list ->
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    (thmref * Attrib.src list) list list -> thmref * Attrib.src list -> 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} * theory
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  val get_datatypes : theory -> DatatypeAux.datatype_info Symtab.table
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  val get_datatype : theory -> string -> DatatypeAux.datatype_info option
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  val the_datatype : theory -> string -> DatatypeAux.datatype_info
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  val get_datatype_spec : theory -> string -> ((string * sort) list * (string * typ list) list) option
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  val get_datatype_constrs : theory -> string -> (string * typ) list option
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  val print_datatypes : theory -> unit
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  val setup: theory -> theory
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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 DatatypesData = TheoryDataFun
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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 extend = I;
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  fun merge _ tabs : T = Symtab.merge (K true) tabs;
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  fun print sg tab =
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    Pretty.writeln (Pretty.strs ("datatypes:" ::
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      map #1 (NameSpace.extern_table (Sign.type_space sg, tab))));
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end);
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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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val get_datatype = Symtab.lookup o get_datatypes;
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fun the_datatype thy name = (case get_datatype 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 get_datatype_descr thy dtco =
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  get_datatype thy dtco
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  |> Option.map (fn info as { descr, index, ... } => 
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       (info, (((fn SOME (_, dtys, cos) => (dtys, cos)) o AList.lookup (op =) descr) index)));
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fun get_datatype_spec thy dtco =
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  let
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    fun mk_cons typ_of_dtyp (co, tys) =
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      (co, map typ_of_dtyp tys);
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    fun mk_dtyp ({ sorts = raw_sorts, descr, ... } : DatatypeAux.datatype_info, (dtys, cos)) =
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      let
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        val sorts = map ((fn v => (v, (the o AList.lookup (op =) raw_sorts) v))
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          o DatatypeAux.dest_DtTFree) dtys;
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        val typ_of_dtyp = DatatypeAux.typ_of_dtyp descr sorts;
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        val tys = map typ_of_dtyp dtys;
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      in (sorts, map (mk_cons typ_of_dtyp) cos) end;
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  in Option.map mk_dtyp (get_datatype_descr thy dtco) end;
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fun get_datatype_constrs thy dtco =
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  case get_datatype_spec thy dtco
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   of SOME (sorts, cos) =>
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        let
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          fun subst (v, sort) = TVar ((v, 0), sort);
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          fun subst_ty (TFree v) = subst v
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            | subst_ty ty = ty;
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          val dty = Type (dtco, map subst sorts);
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          fun mk_co (co, tys) = (co, map (Term.map_atyps subst_ty) tys ---> dty);
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        in SOME (map mk_co cos) end
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    | NONE => NONE;
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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 AList.lookup (op =) (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 AList.lookup (op =) 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 (a, _) => member (op =) vars a)
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                      (fold Term.add_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 (ixn, x)
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  | prep_var _ = NONE;
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fun prep_inst (concl, xs) = (*exception Library.UnequalLengths*)
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  let val vs = InductAttrib.vars_of concl
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  in map_filter 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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  SUBGOAL (fn (Bi,_) =>
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  let
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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 (map_filter I (flat varss))) Bi
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                val {sign, ...} = Thm.rep_thm state
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            in (#induction (the_datatype sign tn), "Induction rule for type " ^ tn) 
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            end
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    val concls = HOLogic.dest_concls (Thm.concl_of rule);
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    val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths =>
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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 end)
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  i state;
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fun induct_tac s =
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  gen_induct_tac Tactic.res_inst_tac'
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    (map (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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  in inst_tac [(ixn, 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", 0), t)] case_split_thm i state
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        else case_inst_tac inst_tac t
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               (#exhaustion (the_datatype (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.thm);
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val varss =
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  Args.and_list (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name))));
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val inst_tac = RuleInsts.bires_inst_tac false;
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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)) = maps 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 (AList.lookup (op =) descr i)));
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    val bnames = map the_bname (distinct (op =) (maps 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 (maps (dt_cases descr) (map #2 descr));
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fun exhaust_cases descr i = dt_cases descr (the (AList.lookup (op =) 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, _, _))) => member (op =) new name) descr);
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end;
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(*Name management for ATP linkup. The suffix here must agree with the one given
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  for notE in Clasimp.addIff*)
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fun name_notE th =
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    Thm.name_thm (Thm.name_of_thm th ^ "_iff1", th RS notE);
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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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  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]),
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    (("", size_thms @ rec_thms), [RecfunCodegen.add NONE]),
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    (("", flat inject), [iff_add]),
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    (("", map name_notE (flat distinct)), [Classical.safe_elim NONE]),
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    (("", weak_case_congs), [cong_att])]
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  #> snd;
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(* add_cases_induct *)
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fun add_cases_induct infos induction thy =
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  let
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    val inducts = ProjectRule.projections (ProofContext.init thy) induction;
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    fun named_rules (name, {index, exhaustion, ...}: datatype_info) =
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      [(("", nth inducts index), [InductAttrib.induct_type name]),
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       (("", exhaustion), [InductAttrib.cases_type name])];
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    fun unnamed_rule i =
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      (("", nth inducts i), [PureThy.kind_internal, InductAttrib.induct_type ""]);
wenzelm@18462
   329
  in
wenzelm@19874
   330
    thy |> PureThy.add_thms
haftmann@21045
   331
      (maps named_rules infos @
wenzelm@19874
   332
        map unnamed_rule (length infos upto length inducts - 1)) |> snd
wenzelm@19874
   333
    |> PureThy.add_thmss [(("inducts", inducts), [])] |> snd
wenzelm@18462
   334
  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
wenzelm@19539
   350
fun distinct_proc thy ss (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
wenzelm@19539
   356
                   (case (get_datatype_descr thy) tname1 of
haftmann@19346
   357
                      SOME (_, (_, constrs)) => let val cnames = map fst 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));
wenzelm@19539
   360
                                 val eq_ct = cterm_of thy eq_t;
wenzelm@19539
   361
                                 val Datatype_thy = ThyInfo.the_theory "Datatype" thy;
berghofe@7015
   362
                                 val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
wenzelm@16486
   363
                                   map (get_thm Datatype_thy o Name)
berghofe@7015
   364
                                     ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
wenzelm@19539
   365
                             in (case (#distinct (the_datatype thy tname1)) of
skalberg@15531
   366
                                 QuickAndDirty => SOME (Thm.invoke_oracle
wenzelm@19539
   367
                                   Datatype_thy distinctN (thy, ConstrDistinct eq_t))
wenzelm@20054
   368
                               | FewConstrs thms =>
wenzelm@20054
   369
                                   SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
wenzelm@20054
   370
                                     (EVERY [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
wenzelm@20054
   371
                                       atac 2, resolve_tac thms 1, etac FalseE 1])))
wenzelm@20054
   372
                               | ManyConstrs (thm, simpset) =>
wenzelm@20054
   373
                                   SOME (Goal.prove (Simplifier.the_context ss) [] [] eq_t (K
wenzelm@20054
   374
                                     (EVERY [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
wenzelm@20054
   375
                                      full_simp_tac (Simplifier.inherit_context ss simpset) 1,
wenzelm@20054
   376
                                      REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
wenzelm@20054
   377
                                      eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
wenzelm@20054
   378
                                      etac FalseE 1]))))
berghofe@7015
   379
                             end
skalberg@15531
   380
                           else NONE
berghofe@7015
   381
                        end
skalberg@15531
   382
                    | NONE => NONE)
skalberg@15531
   383
                else NONE
skalberg@15531
   384
          | _ => NONE)
skalberg@15531
   385
   | _ => NONE)
wenzelm@20054
   386
  | distinct_proc _ _ _ = NONE;
berghofe@7015
   387
wenzelm@13462
   388
val distinct_simproc =
wenzelm@16430
   389
  Simplifier.simproc HOL.thy distinctN ["s = t"] distinct_proc;
berghofe@7015
   390
berghofe@7015
   391
val dist_ss = HOL_ss addsimprocs [distinct_simproc];
berghofe@7015
   392
berghofe@7015
   393
val simproc_setup =
wenzelm@18708
   394
  Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t) #>
wenzelm@18708
   395
  (fn thy => ((change_simpset_of thy) (fn ss => ss addsimprocs [distinct_simproc]); thy));
berghofe@7015
   396
berghofe@7015
   397
berghofe@14799
   398
(**** translation rules for case ****)
berghofe@14799
   399
wenzelm@18857
   400
fun case_tr context [t, u] =
berghofe@14799
   401
    let
wenzelm@18857
   402
      val thy = Context.theory_of context;
berghofe@14799
   403
      fun case_error s name ts = raise TERM ("Error in case expression" ^
skalberg@15570
   404
        getOpt (Option.map (curry op ^ " for datatype ") name, "") ^ ":\n" ^ s, ts);
wenzelm@21187
   405
      fun dest_case1 (Const ("_case1", _) $ t $ u) =
wenzelm@21187
   406
          (case strip_comb t of
wenzelm@21187
   407
            (Const (s, _), ts) =>
wenzelm@21187
   408
              (case try (unprefix Syntax.constN) s of
wenzelm@21187
   409
                SOME c => (c, ts)
wenzelm@21187
   410
              | NONE => (Sign.intern_const thy s, ts))
wenzelm@21253
   411
          | (Free (s, _), ts) => (Sign.intern_const thy s, ts)
skalberg@15531
   412
          | _ => case_error "Head is not a constructor" NONE [t, u], u)
berghofe@14799
   413
        | dest_case1 t = raise TERM ("dest_case1", [t]);
berghofe@14799
   414
      fun dest_case2 (Const ("_case2", _) $ t $ u) = t :: dest_case2 u
berghofe@14799
   415
        | dest_case2 t = [t];
berghofe@14799
   416
      val cases as ((cname, _), _) :: _ = map dest_case1 (dest_case2 u);
wenzelm@18857
   417
      val tab = Symtab.dest (get_datatypes thy);
berghofe@14799
   418
      val (cases', default) = (case split_last cases of
skalberg@15531
   419
          (cases', (("dummy_pattern", []), t)) => (cases', SOME t)
skalberg@15531
   420
        | _ => (cases, NONE))
haftmann@21045
   421
      fun abstr (Free (x, T)) body = Term.absfree (x, T, body)
haftmann@21045
   422
        | abstr (Const ("_constrain", _) $ Free (x, T) $ tT) body =
berghofe@14799
   423
            Syntax.const Syntax.constrainAbsC $ Term.absfree (x, T, body) $ tT
haftmann@21045
   424
        | abstr (Const ("Pair", _) $ x $ y) body =
haftmann@21045
   425
            Syntax.const "split" $ (abstr x o abstr y) body
haftmann@21045
   426
        | abstr t _ = case_error "Illegal pattern" NONE [t];
berghofe@14799
   427
    in case find_first (fn (_, {descr, index, ...}) =>
haftmann@21045
   428
      exists (equal cname o fst) (#3 (snd (nth descr index)))) tab of
skalberg@15531
   429
        NONE => case_error ("Not a datatype constructor: " ^ cname) NONE [u]
berghofe@18319
   430
      | SOME (tname, {descr, sorts, case_name, index, ...}) =>
berghofe@14799
   431
        let
berghofe@14799
   432
          val _ = if exists (equal "dummy_pattern" o fst o fst) cases' then
skalberg@15531
   433
            case_error "Illegal occurrence of '_' dummy pattern" (SOME tname) [u] else ();
haftmann@21045
   434
          val (_, (_, dts, constrs)) = nth descr index;
haftmann@21045
   435
          fun find_case (s, dt) cases =
berghofe@14799
   436
            (case find_first (equal s o fst o fst) cases' of
haftmann@21045
   437
               NONE => (list_abs (map (rpair dummyT)
berghofe@20173
   438
                 (DatatypeProp.make_tnames (map (typ_of_dtyp descr sorts) dt)),
berghofe@20173
   439
                 case default of
berghofe@20173
   440
                   NONE => (warning ("No clause for constructor " ^ s ^
berghofe@20173
   441
                     " in case expression"); Const ("undefined", dummyT))
haftmann@21045
   442
                 | SOME t => t), cases)
skalberg@15531
   443
             | SOME (c as ((_, vs), t)) =>
berghofe@14799
   444
                 if length dt <> length vs then
berghofe@14799
   445
                    case_error ("Wrong number of arguments for constructor " ^ s)
skalberg@15531
   446
                      (SOME tname) vs
haftmann@21045
   447
                 else (fold_rev abstr vs t, remove (op =) c cases))
haftmann@21045
   448
          val (fs, cases'') = fold_map find_case constrs cases'
berghofe@14799
   449
        in case (cases'', length constrs = length cases', default) of
skalberg@15531
   450
            ([], true, SOME _) =>
skalberg@15531
   451
              case_error "Extra '_' dummy pattern" (SOME tname) [u]
berghofe@14799
   452
          | (_ :: _, _, _) =>
wenzelm@19046
   453
              let val extra = distinct (op =) (map (fst o fst) cases'')
berghofe@14799
   454
              in case extra \\ map fst constrs of
berghofe@14799
   455
                  [] => case_error ("More than one clause for constructor(s) " ^
skalberg@15531
   456
                    commas extra) (SOME tname) [u]
berghofe@14799
   457
                | extra' => case_error ("Illegal constructor(s): " ^ commas extra')
skalberg@15531
   458
                    (SOME tname) [u]
berghofe@14799
   459
              end
berghofe@14799
   460
          | _ => list_comb (Syntax.const case_name, fs) $ t
berghofe@14799
   461
        end
berghofe@14799
   462
    end
wenzelm@18857
   463
  | case_tr _ ts = raise TERM ("case_tr", ts);
berghofe@14799
   464
wenzelm@18857
   465
fun case_tr' constrs context ts =
berghofe@14799
   466
  if length ts <> length constrs + 1 then raise Match else
berghofe@14799
   467
  let
wenzelm@21253
   468
    val consts = Context.cases Sign.consts_of ProofContext.consts_of context;
wenzelm@21253
   469
berghofe@14799
   470
    val (fs, x) = split_last ts;
berghofe@14799
   471
    fun strip_abs 0 t = ([], t)
berghofe@14799
   472
      | strip_abs i (Abs p) =
berghofe@14799
   473
        let val (x, u) = Syntax.atomic_abs_tr' p
berghofe@14799
   474
        in apfst (cons x) (strip_abs (i-1) u) end
berghofe@14799
   475
      | strip_abs i (Const ("split", _) $ t) = (case strip_abs (i+1) t of
berghofe@14799
   476
          (v :: v' :: vs, u) => (Syntax.const "Pair" $ v $ v' :: vs, u));
berghofe@14799
   477
    fun is_dependent i t =
berghofe@14799
   478
      let val k = length (strip_abs_vars t) - i
berghofe@14799
   479
      in k < 0 orelse exists (fn j => j >= k)
berghofe@14799
   480
        (loose_bnos (strip_abs_body t))
berghofe@14799
   481
      end;
berghofe@14799
   482
    val cases = map (fn ((cname, dts), t) =>
wenzelm@21253
   483
      (Consts.extern_early consts cname,
berghofe@14799
   484
       strip_abs (length dts) t, is_dependent (length dts) t))
berghofe@14799
   485
      (constrs ~~ fs);
haftmann@21045
   486
    fun count_cases (_, _, true) = I
haftmann@21045
   487
      | count_cases (cname, (_, body), false) =
haftmann@21045
   488
          AList.map_default (op = : term * term -> bool)
haftmann@21045
   489
            (body, []) (cons cname)
haftmann@21045
   490
    val cases' = sort (int_ord o swap o pairself (length o snd))
haftmann@21045
   491
      (fold_rev count_cases cases []);
berghofe@14799
   492
    fun mk_case1 (cname, (vs, body), _) = Syntax.const "_case1" $
berghofe@14799
   493
      list_comb (Syntax.const cname, vs) $ body;
berghofe@20173
   494
    fun is_undefined (Const ("undefined", _)) = true
berghofe@20173
   495
      | is_undefined _ = false;
berghofe@14799
   496
  in
berghofe@14799
   497
    Syntax.const "_case_syntax" $ x $
berghofe@14799
   498
      foldr1 (fn (t, u) => Syntax.const "_case2" $ t $ u) (map mk_case1
berghofe@20173
   499
        (case find_first (is_undefined o fst) cases' of
berghofe@20173
   500
           SOME (_, cnames) =>
berghofe@20173
   501
           if length cnames = length constrs then [hd cases]
berghofe@20173
   502
           else filter_out (fn (_, (_, body), _) => is_undefined body) cases
berghofe@20173
   503
         | NONE => case cases' of
berghofe@14799
   504
           [] => cases
berghofe@14799
   505
         | (default, cnames) :: _ =>
berghofe@14799
   506
           if length cnames = 1 then cases
berghofe@14799
   507
           else if length cnames = length constrs then
berghofe@14799
   508
             [hd cases, ("dummy_pattern", ([], default), false)]
berghofe@14799
   509
           else
haftmann@21045
   510
             filter_out (fn (cname, _, _) => member (op =) cnames cname) cases @
berghofe@14799
   511
             [("dummy_pattern", ([], default), false)]))
berghofe@14799
   512
  end;
berghofe@14799
   513
haftmann@21045
   514
fun make_case_tr' case_names descr = maps
haftmann@21045
   515
  (fn ((_, (_, _, constrs)), case_name) =>
haftmann@21045
   516
    map (rpair (case_tr' constrs)) (NameSpace.accesses' case_name))
haftmann@21045
   517
      (descr ~~ case_names);
berghofe@14799
   518
berghofe@14799
   519
val trfun_setup =
wenzelm@18708
   520
  Theory.add_advanced_trfuns ([], [("_case_syntax", case_tr)], [], []);
berghofe@14799
   521
berghofe@14799
   522
berghofe@5177
   523
(* prepare types *)
berghofe@5177
   524
berghofe@5177
   525
fun read_typ sign ((Ts, sorts), str) =
berghofe@5177
   526
  let
haftmann@17521
   527
    val T = Type.no_tvars (Sign.read_typ (sign, AList.lookup (op =)
berghofe@5177
   528
      (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
berghofe@5177
   529
  in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
berghofe@5177
   530
berghofe@5177
   531
fun cert_typ sign ((Ts, sorts), raw_T) =
berghofe@5177
   532
  let
berghofe@5177
   533
    val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
berghofe@5177
   534
      TYPE (msg, _, _) => error msg;
berghofe@5177
   535
    val sorts' = add_typ_tfrees (T, sorts)
berghofe@5177
   536
  in (Ts @ [T],
wenzelm@18964
   537
      case duplicates (op =) (map fst sorts') of
berghofe@5177
   538
         [] => sorts'
berghofe@5177
   539
       | dups => error ("Inconsistent sort constraints for " ^ commas dups))
berghofe@5177
   540
  end;
berghofe@5177
   541
berghofe@5177
   542
berghofe@5177
   543
(**** make datatype info ****)
berghofe@5177
   544
berghofe@18319
   545
fun make_dt_info descr sorts induct reccomb_names rec_thms
wenzelm@10121
   546
    (((((((((i, (_, (tname, _, _))), case_name), case_thms),
wenzelm@10121
   547
      exhaustion_thm), distinct_thm), inject), nchotomy), case_cong), weak_case_cong) =
wenzelm@10121
   548
  (tname,
wenzelm@10121
   549
   {index = i,
wenzelm@10121
   550
    descr = descr,
berghofe@18319
   551
    sorts = sorts,
wenzelm@10121
   552
    rec_names = reccomb_names,
wenzelm@10121
   553
    rec_rewrites = rec_thms,
wenzelm@10121
   554
    case_name = case_name,
wenzelm@10121
   555
    case_rewrites = case_thms,
wenzelm@10121
   556
    induction = induct,
wenzelm@10121
   557
    exhaustion = exhaustion_thm,
wenzelm@10121
   558
    distinct = distinct_thm,
wenzelm@10121
   559
    inject = inject,
wenzelm@10121
   560
    nchotomy = nchotomy,
wenzelm@10121
   561
    case_cong = case_cong,
wenzelm@10121
   562
    weak_case_cong = weak_case_cong});
berghofe@5177
   563
berghofe@5177
   564
berghofe@5177
   565
(********************* axiomatic introduction of datatypes ********************)
berghofe@5177
   566
haftmann@20597
   567
fun add_axiom label t atts thy =
haftmann@20597
   568
  thy
haftmann@20597
   569
  |> PureThy.add_axioms_i [((label, t), atts)];
haftmann@20597
   570
haftmann@20597
   571
fun add_axioms label ts atts thy =
haftmann@20597
   572
  thy
haftmann@20597
   573
  |> PureThy.add_axiomss_i [((label, ts), atts)];
wenzelm@8437
   574
haftmann@20597
   575
fun add_and_get_axioms_atts label tnames ts attss =
haftmann@20597
   576
  fold_map (fn (tname, (atts, t)) => fn thy =>
haftmann@20597
   577
    thy
haftmann@20597
   578
    |> Theory.add_path tname
haftmann@20597
   579
    |> add_axiom label t atts
haftmann@20597
   580
    ||> Theory.parent_path
haftmann@20597
   581
    |-> (fn [ax] => pair ax)) (tnames ~~ (attss ~~ ts));
berghofe@5177
   582
haftmann@20597
   583
fun add_and_get_axioms label tnames ts =
haftmann@20597
   584
  add_and_get_axioms_atts label tnames ts (replicate (length tnames) []);
haftmann@20597
   585
haftmann@20597
   586
fun add_and_get_axiomss label tnames tss =
haftmann@20597
   587
  fold_map (fn (tname, ts) => fn thy =>
haftmann@20597
   588
    thy
haftmann@20597
   589
    |> Theory.add_path tname
haftmann@20597
   590
    |> add_axioms label ts []
haftmann@20597
   591
    ||> Theory.parent_path
haftmann@20597
   592
    |-> (fn [ax] => pair ax)) (tnames ~~ tss);
berghofe@5177
   593
wenzelm@19716
   594
fun specify_consts args thy =
haftmann@20597
   595
  let
haftmann@20597
   596
    val specs = map (fn (c, T, mx) =>
haftmann@20597
   597
      Const (Sign.full_name thy (Syntax.const_name c mx), T)) args;
haftmann@20597
   598
  in
haftmann@20597
   599
    thy
haftmann@20597
   600
    |> Sign.add_consts_i args
haftmann@20597
   601
    |> Theory.add_finals_i false specs
haftmann@20597
   602
  end;
wenzelm@19716
   603
wenzelm@8437
   604
fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
wenzelm@8437
   605
    case_names_induct case_names_exhausts thy =
berghofe@5177
   606
  let
haftmann@21045
   607
    val descr' = flat descr;
berghofe@5177
   608
    val recTs = get_rec_types descr' sorts;
haftmann@21045
   609
    val used = map fst (fold Term.add_tfreesT recTs []);
skalberg@15570
   610
    val newTs = Library.take (length (hd descr), recTs);
berghofe@5177
   611
berghofe@7015
   612
    val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
berghofe@13641
   613
      (fn dt => is_rec_type dt andalso not (null (fst (strip_dtyp dt))))
berghofe@13641
   614
        cargs) constrs) descr';
berghofe@7015
   615
berghofe@5177
   616
    (**** declare new types and constants ****)
berghofe@5177
   617
berghofe@5177
   618
    val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
berghofe@5177
   619
berghofe@5177
   620
    val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
berghofe@5177
   621
      map (fn ((_, cargs), (cname, mx)) =>
berghofe@5177
   622
        (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
berghofe@5177
   623
          (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
berghofe@5177
   624
berghofe@15457
   625
    val (rec_result_Ts, reccomb_fn_Ts) = DatatypeProp.make_primrec_Ts descr sorts used;
berghofe@5177
   626
berghofe@5177
   627
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
berghofe@5177
   628
    val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   629
      (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   630
        (1 upto (length descr')));
berghofe@5177
   631
berghofe@9739
   632
    val size_names = DatatypeProp.indexify_names
skalberg@15570
   633
      (map (fn T => name_of_typ T ^ "_size") (Library.drop (length (hd descr), recTs)));
berghofe@5177
   634
wenzelm@20071
   635
    val freeT = TFree (Name.variant used "'t", HOLogic.typeS);
berghofe@5177
   636
    val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
berghofe@5177
   637
      map (fn (_, cargs) =>
berghofe@5177
   638
        let val Ts = map (typ_of_dtyp descr' sorts) cargs
berghofe@5177
   639
        in Ts ---> freeT end) constrs) (hd descr);
berghofe@5177
   640
berghofe@5177
   641
    val case_names = map (fn s => (s ^ "_case")) new_type_names;
berghofe@5177
   642
haftmann@21419
   643
    fun instance_size_class tyco thy =
haftmann@21419
   644
      let
haftmann@21419
   645
        val size_sort = ["Nat.size"];
haftmann@21419
   646
        val n = Sign.arity_number thy tyco;
haftmann@21419
   647
      in
haftmann@21419
   648
        thy
haftmann@21419
   649
        |> AxClass.prove_arity (tyco, replicate n HOLogic.typeS, size_sort)
haftmann@21419
   650
             (ClassPackage.intro_classes_tac [])
haftmann@21419
   651
      end
haftmann@21419
   652
haftmann@21045
   653
    val thy2' = thy
berghofe@5177
   654
berghofe@5177
   655
      (** new types **)
haftmann@21419
   656
      |> fold2 (fn (name, mx) => fn tvs => TypedefPackage.add_typedecls [(name, tvs, mx)])
haftmann@21419
   657
           types_syntax tyvars
haftmann@21419
   658
      |> fold (fn (_, (name, _, _)) => instance_size_class name) descr'
haftmann@21045
   659
      |> add_path flat_names (space_implode "_" new_type_names)
berghofe@5177
   660
berghofe@5177
   661
      (** primrec combinators **)
berghofe@5177
   662
haftmann@21045
   663
      |> specify_consts (map (fn ((name, T), T') =>
haftmann@21045
   664
           (name, reccomb_fn_Ts @ [T] ---> T', NoSyn)) (reccomb_names ~~ recTs ~~ rec_result_Ts))
berghofe@5177
   665
berghofe@5177
   666
      (** case combinators **)
berghofe@5177
   667
haftmann@21045
   668
      |> specify_consts (map (fn ((name, T), Ts) =>
haftmann@21045
   669
           (name, Ts @ [T] ---> freeT, NoSyn)) (case_names ~~ newTs ~~ case_fn_Ts));
berghofe@6305
   670
wenzelm@19716
   671
    val reccomb_names' = map (Sign.full_name thy2') reccomb_names;
wenzelm@19716
   672
    val case_names' = map (Sign.full_name thy2') case_names;
berghofe@6305
   673
haftmann@21045
   674
    val thy2 = thy2'
berghofe@5177
   675
berghofe@5177
   676
      (** size functions **)
berghofe@5177
   677
haftmann@21045
   678
      |> (if no_size then I else specify_consts (map (fn (s, T) =>
berghofe@5177
   679
        (Sign.base_name s, T --> HOLogic.natT, NoSyn))
haftmann@21045
   680
          (size_names ~~ Library.drop (length (hd descr), recTs))))
berghofe@5661
   681
berghofe@5661
   682
      (** constructors **)
berghofe@5661
   683
haftmann@21045
   684
      |> parent_path flat_names
haftmann@21045
   685
      |> fold (fn ((((_, (_, _, constrs)), T), tname),
haftmann@21045
   686
        constr_syntax') =>
haftmann@21045
   687
          add_path flat_names tname #>
wenzelm@19716
   688
            specify_consts (map (fn ((_, cargs), (cname, mx)) =>
berghofe@5661
   689
              (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
haftmann@21045
   690
                (constrs ~~ constr_syntax')) #>
haftmann@21045
   691
          parent_path flat_names)
berghofe@5661
   692
            (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
berghofe@5177
   693
berghofe@5177
   694
    (**** introduction of axioms ****)
berghofe@5177
   695
berghofe@5661
   696
    val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
berghofe@9739
   697
    val size_axs = if no_size then [] else DatatypeProp.make_size descr sorts thy2;
berghofe@5661
   698
haftmann@18377
   699
    val ((([induct], [rec_thms]), inject), thy3) =
haftmann@18377
   700
      thy2
haftmann@18377
   701
      |> Theory.add_path (space_implode "_" new_type_names)
haftmann@20597
   702
      |> add_axiom "induct" (DatatypeProp.make_ind descr sorts) [case_names_induct]
haftmann@20597
   703
      ||>> add_axioms "recs" rec_axs []
haftmann@20597
   704
      ||> (if no_size then I else add_axioms "size" size_axs [] #> snd)
haftmann@18377
   705
      ||> Theory.parent_path
haftmann@18377
   706
      ||>> add_and_get_axiomss "inject" new_type_names
haftmann@18377
   707
            (DatatypeProp.make_injs descr sorts);
wenzelm@16486
   708
    val size_thms = if no_size then [] else get_thms thy3 (Name "size");
haftmann@18377
   709
    val (distinct, thy4) = add_and_get_axiomss "distinct" new_type_names
berghofe@5177
   710
      (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
wenzelm@8437
   711
wenzelm@8437
   712
    val exhaust_ts = DatatypeProp.make_casedists descr sorts;
haftmann@18377
   713
    val (exhaustion, thy5) = add_and_get_axioms_atts "exhaust" new_type_names
haftmann@20597
   714
      exhaust_ts (map single case_names_exhausts) thy4;
haftmann@18377
   715
    val (case_thms, thy6) = add_and_get_axiomss "cases" new_type_names
berghofe@5177
   716
      (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
berghofe@5177
   717
    val (split_ts, split_asm_ts) = ListPair.unzip
berghofe@5177
   718
      (DatatypeProp.make_splits new_type_names descr sorts thy6);
haftmann@18377
   719
    val (split, thy7) = add_and_get_axioms "split" new_type_names split_ts thy6;
haftmann@18377
   720
    val (split_asm, thy8) = add_and_get_axioms "split_asm" new_type_names
berghofe@5177
   721
      split_asm_ts thy7;
haftmann@18377
   722
    val (nchotomys, thy9) = add_and_get_axioms "nchotomy" new_type_names
berghofe@5177
   723
      (DatatypeProp.make_nchotomys descr sorts) thy8;
haftmann@18377
   724
    val (case_congs, thy10) = add_and_get_axioms "case_cong" new_type_names
berghofe@5177
   725
      (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
haftmann@18377
   726
    val (weak_case_congs, thy11) = add_and_get_axioms "weak_case_cong" new_type_names
nipkow@8601
   727
      (DatatypeProp.make_weak_case_congs new_type_names descr sorts thy10) thy10;
wenzelm@8405
   728
berghofe@18319
   729
    val dt_infos = map (make_dt_info descr' sorts induct reccomb_names' rec_thms)
berghofe@6305
   730
      ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
berghofe@7015
   731
        exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
wenzelm@10121
   732
          nchotomys ~~ case_congs ~~ weak_case_congs);
berghofe@5177
   733
haftmann@21045
   734
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
wenzelm@9386
   735
    val split_thms = split ~~ split_asm;
berghofe@5177
   736
haftmann@18518
   737
    val thy12 =
haftmann@18518
   738
      thy11
haftmann@18518
   739
      |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names' (hd descr), [])
haftmann@18518
   740
      |> Theory.add_path (space_implode "_" new_type_names)
haftmann@18518
   741
      |> add_rules simps case_thms size_thms rec_thms inject distinct
wenzelm@18728
   742
          weak_case_congs Simplifier.cong_add
haftmann@18518
   743
      |> put_datatypes (fold Symtab.update dt_infos dt_info)
haftmann@18518
   744
      |> add_cases_induct dt_infos induct
haftmann@18518
   745
      |> Theory.parent_path
haftmann@19599
   746
      |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
haftmann@19599
   747
      |> snd
haftmann@18518
   748
      |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
haftmann@21251
   749
      |> DatatypeHooks.all (map fst dt_infos);
berghofe@5177
   750
  in
haftmann@18008
   751
    ({distinct = distinct,
berghofe@5177
   752
      inject = inject,
berghofe@5177
   753
      exhaustion = exhaustion,
berghofe@5177
   754
      rec_thms = rec_thms,
berghofe@5177
   755
      case_thms = case_thms,
wenzelm@9386
   756
      split_thms = split_thms,
berghofe@5177
   757
      induction = induct,
berghofe@5177
   758
      size = size_thms,
haftmann@18008
   759
      simps = simps}, thy12)
berghofe@5177
   760
  end;
berghofe@5177
   761
berghofe@5177
   762
berghofe@5177
   763
(******************* definitional introduction of datatypes *******************)
berghofe@5177
   764
wenzelm@8437
   765
fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
wenzelm@8437
   766
    case_names_induct case_names_exhausts thy =
berghofe@5177
   767
  let
wenzelm@6360
   768
    val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
berghofe@5177
   769
haftmann@18314
   770
    val ((inject, distinct, dist_rewrites, simproc_dists, induct), thy2) = thy |>
berghofe@5661
   771
      DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
wenzelm@8437
   772
        types_syntax constr_syntax case_names_induct;
berghofe@5177
   773
haftmann@18314
   774
    val (casedist_thms, thy3) = DatatypeAbsProofs.prove_casedist_thms new_type_names descr
wenzelm@8437
   775
      sorts induct case_names_exhausts thy2;
haftmann@18314
   776
    val ((reccomb_names, rec_thms), thy4) = DatatypeAbsProofs.prove_primrec_thms
wenzelm@20054
   777
      flat_names new_type_names descr sorts dt_info inject dist_rewrites
wenzelm@20054
   778
      (Simplifier.theory_context thy3 dist_ss) induct thy3;
haftmann@18314
   779
    val ((case_thms, case_names), thy6) = DatatypeAbsProofs.prove_case_thms
berghofe@5661
   780
      flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
haftmann@18314
   781
    val (split_thms, thy7) = DatatypeAbsProofs.prove_split_thms new_type_names
berghofe@5177
   782
      descr sorts inject dist_rewrites casedist_thms case_thms thy6;
haftmann@18314
   783
    val (nchotomys, thy8) = DatatypeAbsProofs.prove_nchotomys new_type_names
berghofe@5177
   784
      descr sorts casedist_thms thy7;
haftmann@18314
   785
    val (case_congs, thy9) = DatatypeAbsProofs.prove_case_congs new_type_names
berghofe@5177
   786
      descr sorts nchotomys case_thms thy8;
haftmann@18314
   787
    val (weak_case_congs, thy10) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
nipkow@8601
   788
      descr sorts thy9;
haftmann@18314
   789
    val (size_thms, thy11) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
nipkow@8601
   790
      descr sorts reccomb_names rec_thms thy10;
berghofe@5177
   791
haftmann@21045
   792
    val dt_infos = map (make_dt_info (flat descr) sorts induct reccomb_names rec_thms)
berghofe@5177
   793
      ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
wenzelm@10121
   794
        casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
berghofe@5177
   795
haftmann@21045
   796
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   797
haftmann@18518
   798
    val thy12 =
haftmann@18518
   799
      thy11
haftmann@18518
   800
      |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names (hd descr), [])
haftmann@18518
   801
      |> Theory.add_path (space_implode "_" new_type_names)
haftmann@18518
   802
      |> add_rules simps case_thms size_thms rec_thms inject distinct
wenzelm@18728
   803
          weak_case_congs (Simplifier.attrib (op addcongs))
haftmann@18518
   804
      |> put_datatypes (fold Symtab.update dt_infos dt_info)
haftmann@18518
   805
      |> add_cases_induct dt_infos induct
haftmann@18518
   806
      |> Theory.parent_path
haftmann@18518
   807
      |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms) |> snd
haftmann@18518
   808
      |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
haftmann@21251
   809
      |> DatatypeHooks.all (map fst dt_infos);
berghofe@5177
   810
  in
haftmann@18008
   811
    ({distinct = distinct,
berghofe@5177
   812
      inject = inject,
berghofe@5177
   813
      exhaustion = casedist_thms,
berghofe@5177
   814
      rec_thms = rec_thms,
berghofe@5177
   815
      case_thms = case_thms,
berghofe@5177
   816
      split_thms = split_thms,
berghofe@5177
   817
      induction = induct,
berghofe@5177
   818
      size = size_thms,
haftmann@18008
   819
      simps = simps}, thy12)
berghofe@5177
   820
  end;
berghofe@5177
   821
berghofe@5177
   822
wenzelm@6385
   823
(*********************** declare existing type as datatype *********************)
berghofe@5177
   824
wenzelm@6385
   825
fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
berghofe@5177
   826
  let
haftmann@18418
   827
    val (((distinct, inject), [induction]), thy1) =
haftmann@18418
   828
      thy0
haftmann@18418
   829
      |> fold_map apply_theorems raw_distinct
haftmann@18418
   830
      ||>> fold_map apply_theorems raw_inject
haftmann@18418
   831
      ||>> apply_theorems [raw_induction];
berghofe@5177
   832
wenzelm@20218
   833
    val ((_, [induction']), _) = Variable.importT [induction] (Variable.thm_context induction);
berghofe@5177
   834
berghofe@5177
   835
    fun err t = error ("Ill-formed predicate in induction rule: " ^
haftmann@20715
   836
      Sign.string_of_term thy1 t);
berghofe@5177
   837
berghofe@5177
   838
    fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
berghofe@7015
   839
          ((tname, map dest_TFree Ts) handle TERM _ => err t)
berghofe@5177
   840
      | get_typ t = err t;
berghofe@5177
   841
wenzelm@8437
   842
    val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of induction')));
skalberg@15570
   843
    val new_type_names = getOpt (alt_names, map fst dtnames);
berghofe@5177
   844
berghofe@5177
   845
    fun get_constr t = (case Logic.strip_assums_concl t of
berghofe@5177
   846
        _ $ (_ $ t') => (case head_of t' of
berghofe@5177
   847
            Const (cname, cT) => (case strip_type cT of
berghofe@5177
   848
                (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
berghofe@5177
   849
              | _ => err t)
berghofe@5177
   850
          | _ => err t)
berghofe@5177
   851
      | _ => err t);
berghofe@5177
   852
berghofe@5177
   853
    fun make_dt_spec [] _ _ = []
berghofe@5177
   854
      | make_dt_spec ((tname, tvs)::dtnames') i constrs =
berghofe@5177
   855
          let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
berghofe@5177
   856
          in (i, (tname, map DtTFree tvs, map snd constrs'))::
berghofe@5177
   857
            (make_dt_spec dtnames' (i + 1) constrs'')
berghofe@5177
   858
          end;
berghofe@5177
   859
berghofe@5177
   860
    val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
berghofe@5177
   861
    val sorts = add_term_tfrees (concl_of induction', []);
wenzelm@6385
   862
    val dt_info = get_datatypes thy1;
berghofe@5177
   863
haftmann@21419
   864
    val (case_names_induct, case_names_exhausts) =
haftmann@21419
   865
      (mk_case_names_induct descr, mk_case_names_exhausts descr (map #1 dtnames));
wenzelm@8437
   866
wenzelm@6427
   867
    val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
berghofe@5177
   868
haftmann@18314
   869
    val (casedist_thms, thy2) = thy1 |>
wenzelm@8437
   870
      DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction
wenzelm@8437
   871
        case_names_exhausts;
haftmann@18314
   872
    val ((reccomb_names, rec_thms), thy3) = DatatypeAbsProofs.prove_primrec_thms
wenzelm@20054
   873
      false new_type_names [descr] sorts dt_info inject distinct
wenzelm@20054
   874
      (Simplifier.theory_context thy2 dist_ss) induction thy2;
haftmann@18314
   875
    val ((case_thms, case_names), thy4) = DatatypeAbsProofs.prove_case_thms false
berghofe@5177
   876
      new_type_names [descr] sorts reccomb_names rec_thms thy3;
haftmann@18314
   877
    val (split_thms, thy5) = DatatypeAbsProofs.prove_split_thms
berghofe@5177
   878
      new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
haftmann@18314
   879
    val (nchotomys, thy6) = DatatypeAbsProofs.prove_nchotomys new_type_names
berghofe@5177
   880
      [descr] sorts casedist_thms thy5;
haftmann@18314
   881
    val (case_congs, thy7) = DatatypeAbsProofs.prove_case_congs new_type_names
berghofe@5177
   882
      [descr] sorts nchotomys case_thms thy6;
haftmann@18314
   883
    val (weak_case_congs, thy8) = DatatypeAbsProofs.prove_weak_case_congs new_type_names
nipkow@8601
   884
      [descr] sorts thy7;
haftmann@18314
   885
    val (size_thms, thy9) =
wenzelm@21243
   886
      if Context.exists_name "Nat" thy8 then
berghofe@5661
   887
        DatatypeAbsProofs.prove_size_thms false new_type_names
nipkow@8601
   888
          [descr] sorts reccomb_names rec_thms thy8
haftmann@18314
   889
      else ([], thy8);
berghofe@5177
   890
haftmann@18377
   891
    val ((_, [induction']), thy10) =
haftmann@18377
   892
      thy9
haftmann@18377
   893
      |> store_thmss "inject" new_type_names inject
haftmann@18377
   894
      ||>> store_thmss "distinct" new_type_names distinct
haftmann@18377
   895
      ||> Theory.add_path (space_implode "_" new_type_names)
haftmann@18377
   896
      ||>> PureThy.add_thms [(("induct", induction), [case_names_induct])];
wenzelm@9149
   897
berghofe@18319
   898
    val dt_infos = map (make_dt_info descr sorts induction' reccomb_names rec_thms)
wenzelm@10121
   899
      ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~ casedist_thms ~~
wenzelm@10121
   900
        map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs ~~ weak_case_congs);
berghofe@5177
   901
haftmann@21045
   902
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   903
haftmann@19599
   904
    val thy11 =
haftmann@19599
   905
      thy10
haftmann@19599
   906
      |> Theory.add_advanced_trfuns ([], [], make_case_tr' case_names descr, [])
haftmann@19599
   907
      |> add_rules simps case_thms size_thms rec_thms inject distinct
haftmann@19599
   908
           weak_case_congs (Simplifier.attrib (op addcongs))
haftmann@19599
   909
      |> put_datatypes (fold Symtab.update dt_infos dt_info)
haftmann@19599
   910
      |> add_cases_induct dt_infos induction'
haftmann@19599
   911
      |> Theory.parent_path
haftmann@19599
   912
      |> store_thmss "splits" new_type_names (map (fn (x, y) => [x, y]) split_thms)
haftmann@19599
   913
      |> snd
haftmann@19599
   914
      |> DatatypeRealizer.add_dt_realizers sorts (map snd dt_infos)
haftmann@21251
   915
      |> DatatypeHooks.all (map fst dt_infos);
berghofe@5177
   916
  in
haftmann@18008
   917
    ({distinct = distinct,
berghofe@5177
   918
      inject = inject,
berghofe@5177
   919
      exhaustion = casedist_thms,
berghofe@5177
   920
      rec_thms = rec_thms,
berghofe@5177
   921
      case_thms = case_thms,
berghofe@5177
   922
      split_thms = split_thms,
wenzelm@8437
   923
      induction = induction',
berghofe@5177
   924
      size = size_thms,
haftmann@18008
   925
      simps = simps}, thy11)
berghofe@5177
   926
  end;
berghofe@5177
   927
wenzelm@21350
   928
val rep_datatype = gen_rep_datatype IsarCmd.apply_theorems;
wenzelm@21350
   929
val rep_datatype_i = gen_rep_datatype IsarCmd.apply_theorems_i;
wenzelm@6385
   930
berghofe@5177
   931
wenzelm@11958
   932
berghofe@5177
   933
(******************************** add datatype ********************************)
berghofe@5177
   934
berghofe@14887
   935
fun gen_add_datatype prep_typ err flat_names new_type_names dts thy =
berghofe@5177
   936
  let
wenzelm@20820
   937
    val _ = Theory.requires thy "Datatype" "datatype definitions";
berghofe@5177
   938
berghofe@5177
   939
    (* this theory is used just for parsing *)
berghofe@5177
   940
berghofe@5177
   941
    val tmp_thy = thy |>
wenzelm@5892
   942
      Theory.copy |>
berghofe@5177
   943
      Theory.add_types (map (fn (tvs, tname, mx, _) =>
berghofe@5177
   944
        (tname, length tvs, mx)) dts);
berghofe@5177
   945
berghofe@5661
   946
    val (tyvars, _, _, _)::_ = dts;
berghofe@5177
   947
    val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
haftmann@20597
   948
      let val full_tname = Sign.full_name tmp_thy (Syntax.type_name tname mx)
wenzelm@18964
   949
      in (case duplicates (op =) tvs of
berghofe@5661
   950
            [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
berghofe@5661
   951
                  else error ("Mutually recursive datatypes must have same type parameters")
berghofe@5177
   952
          | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
berghofe@5177
   953
              " : " ^ commas dups))
berghofe@5177
   954
      end) dts);
berghofe@5177
   955
wenzelm@18964
   956
    val _ = (case duplicates (op =) (map fst new_dts) @ duplicates (op =) new_type_names of
berghofe@5177
   957
      [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
berghofe@5177
   958
haftmann@21045
   959
    fun prep_dt_spec (tvs, tname, mx, constrs) (dts', constr_syntax, sorts, i) =
berghofe@5177
   960
      let
haftmann@21045
   961
        fun prep_constr (cname, cargs, mx') (constrs, constr_syntax', sorts') =
berghofe@5279
   962
          let
haftmann@20597
   963
            val (cargs', sorts'') = Library.foldl (prep_typ tmp_thy) (([], sorts'), cargs);
haftmann@21045
   964
            val _ = (case fold (curry add_typ_tfree_names) cargs' [] \\ tvs of
berghofe@5279
   965
                [] => ()
berghofe@5279
   966
              | vs => error ("Extra type variables on rhs: " ^ commas vs))
haftmann@20597
   967
          in (constrs @ [((if flat_names then Sign.full_name tmp_thy else
haftmann@20597
   968
                Sign.full_name_path tmp_thy tname) (Syntax.const_name cname mx'),
berghofe@5177
   969
                   map (dtyp_of_typ new_dts) cargs')],
berghofe@5177
   970
              constr_syntax' @ [(cname, mx')], sorts'')
wenzelm@18678
   971
          end handle ERROR msg =>
wenzelm@18678
   972
            cat_error msg ("The error above occured in constructor " ^ cname ^
berghofe@5177
   973
              " of datatype " ^ tname);
berghofe@5177
   974
berghofe@5177
   975
        val (constrs', constr_syntax', sorts') =
haftmann@21045
   976
          fold prep_constr constrs ([], [], sorts)
berghofe@5177
   977
wenzelm@8405
   978
      in
wenzelm@18964
   979
        case duplicates (op =) (map fst constrs') of
berghofe@5177
   980
           [] =>
haftmann@20597
   981
             (dts' @ [(i, (Sign.full_name tmp_thy (Syntax.type_name tname mx),
berghofe@5177
   982
                map DtTFree tvs, constrs'))],
berghofe@5177
   983
              constr_syntax @ [constr_syntax'], sorts', i + 1)
berghofe@5177
   984
         | dups => error ("Duplicate constructors " ^ commas dups ^
berghofe@5177
   985
             " in datatype " ^ tname)
berghofe@5177
   986
      end;
berghofe@5177
   987
haftmann@21045
   988
    val (dts', constr_syntax, sorts', i) = fold prep_dt_spec dts ([], [], [], 0);
haftmann@20597
   989
    val sorts = sorts' @ (map (rpair (Sign.defaultS tmp_thy)) (tyvars \\ map fst sorts'));
berghofe@5177
   990
    val dt_info = get_datatypes thy;
haftmann@20597
   991
    val (descr, _) = unfold_datatypes tmp_thy dts' sorts dt_info dts' i;
berghofe@14887
   992
    val _ = check_nonempty descr handle (exn as Datatype_Empty s) =>
wenzelm@15661
   993
      if err then error ("Nonemptiness check failed for datatype " ^ s)
berghofe@14887
   994
      else raise exn;
berghofe@5177
   995
haftmann@21045
   996
    val descr' = flat descr;
wenzelm@8437
   997
    val case_names_induct = mk_case_names_induct descr';
wenzelm@8437
   998
    val case_names_exhausts = mk_case_names_exhausts descr' (map #1 new_dts);
berghofe@5177
   999
  in
berghofe@5177
  1000
    (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
wenzelm@8437
  1001
      flat_names new_type_names descr sorts types_syntax constr_syntax dt_info
wenzelm@8437
  1002
      case_names_induct case_names_exhausts thy
berghofe@5177
  1003
  end;
berghofe@5177
  1004
berghofe@5177
  1005
val add_datatype_i = gen_add_datatype cert_typ;
berghofe@14887
  1006
val add_datatype = gen_add_datatype read_typ true;
berghofe@5177
  1007
wenzelm@6360
  1008
haftmann@18451
  1009
wenzelm@6360
  1010
(** package setup **)
wenzelm@6360
  1011
wenzelm@6360
  1012
(* setup theory *)
wenzelm@6360
  1013
wenzelm@18708
  1014
val setup =
wenzelm@18708
  1015
  DatatypesData.init #> Method.add_methods tactic_emulations #> simproc_setup #> trfun_setup;
wenzelm@6360
  1016
wenzelm@6360
  1017
wenzelm@6360
  1018
(* outer syntax *)
wenzelm@6360
  1019
wenzelm@17057
  1020
local structure P = OuterParse and K = OuterKeyword in
wenzelm@6360
  1021
wenzelm@6360
  1022
val datatype_decl =
wenzelm@6723
  1023
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
wenzelm@12876
  1024
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix));
wenzelm@6360
  1025
wenzelm@6360
  1026
fun mk_datatype args =
wenzelm@6360
  1027
  let
skalberg@15531
  1028
    val names = map (fn ((((NONE, _), t), _), _) => t | ((((SOME t, _), _), _), _) => t) args;
wenzelm@12876
  1029
    val specs = map (fn ((((_, vs), t), mx), cons) =>
wenzelm@12876
  1030
      (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
haftmann@18008
  1031
  in snd o add_datatype false names specs end;
wenzelm@6360
  1032
wenzelm@6360
  1033
val datatypeP =
wenzelm@6723
  1034
  OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
wenzelm@6723
  1035
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
wenzelm@6360
  1036
wenzelm@6385
  1037
wenzelm@6385
  1038
val rep_datatype_decl =
wenzelm@6723
  1039
  Scan.option (Scan.repeat1 P.name) --
wenzelm@11958
  1040
    Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
wenzelm@11958
  1041
    Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [[]] --
wenzelm@6723
  1042
    (P.$$$ "induction" |-- P.!!! P.xthm);
wenzelm@6385
  1043
haftmann@18008
  1044
fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #2 o rep_datatype opt_ts dss iss ind;
wenzelm@6385
  1045
wenzelm@6385
  1046
val rep_datatypeP =
wenzelm@6723
  1047
  OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
wenzelm@6385
  1048
    (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
wenzelm@6385
  1049
wenzelm@6385
  1050
wenzelm@6479
  1051
val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
wenzelm@6385
  1052
val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
wenzelm@6385
  1053
wenzelm@6385
  1054
end;
wenzelm@6385
  1055
wenzelm@6360
  1056
berghofe@5177
  1057
end;
berghofe@5177
  1058
wenzelm@6360
  1059
structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
wenzelm@6360
  1060
open BasicDatatypePackage;
wenzelm@15704
  1061