src/HOL/Tools/datatype_package.ML
author wenzelm
Sun Feb 27 15:31:40 2000 +0100 (2000-02-27)
changeset 8306 9855f1801d2b
parent 8279 3453f73fad71
child 8325 80855ae484ce
permissions -rw-r--r--
HOLogic.dest_conj;
add_cases_induct: induct_method setup;
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(*  Title:      HOL/Tools/datatype_package.ML
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    ID:         $Id$
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    Author:     Stefan Berghofer
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    Copyright   1998  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 exhaust_tac : string -> int -> tactic
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  val cases_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 -> 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 * theory attribute list) list list ->
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    (thm * theory attribute list) list list -> (thm * theory attribute 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 : 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 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 cases_of: Sign.sg -> string -> thm
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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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val exhaustion_of = #exhaustion oo datatype_info_sg_err
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fun cases_of sg name = if name = HOLogic.boolN then case_split_thm else exhaustion_of sg name;
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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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fun find_tname var Bi =
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  let val frees = map dest_Free (term_frees Bi)
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      val params = 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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fun induct_tac s i state =
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  let
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    val vars = Syntax.read_idents s;
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    val (_, _, Bi, _) = dest_state (state, i);
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    val {sign, ...} = rep_thm state;
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    val tn = find_tname (hd vars) Bi;
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    val {induction, ...} = datatype_info_sg_err sign tn;
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    val ind_vnames = map (fn (_ $ Var (ixn, _)) =>
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      implode (tl (explode (Syntax.string_of_vname ixn))))
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        (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induction)));
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    val insts = (ind_vnames ~~ vars) handle LIST _ =>
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      error ("Induction rule for type " ^ tn ^ " has different number of variables")
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  in
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    occs_in_prems (res_inst_tac insts induction) vars i state
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  end;
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(* generic exhaustion tactic for datatypes *)
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fun gen_exhaust_tac get_rule aterm i state =
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  let
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    val rule = get_rule (Thm.sign_of_thm state) (infer_tname state i aterm);
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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 res_inst_tac [(exh_vname, aterm)] rule i state end;
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val exhaust_tac = gen_exhaust_tac exhaustion_of;
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val cases_tac = gen_exhaust_tac cases_of;
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(* add_cases_induct *)
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fun add_cases_induct infos =
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  let
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    fun add (ths, (name, {induction, exhaustion, ...}: datatype_info)) =
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      (("", induction), [InductMethod.induct_type_global name]) ::
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       (("", exhaustion), [InductMethod.cases_type_global name]) :: ths;
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  in PureThy.add_thms (foldl add ([], infos)) end;
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(**** simplification procedure for showing distinctness of constructors ****)
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fun stripT (i, Type ("fun", [_, T])) = stripT (i + 1, T)
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  | stripT p = p;
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fun stripC (i, f $ x) = stripC (i + 1, f)
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  | stripC p = p;
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val distinctN = "constr_distinct";
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exception ConstrDistinct of term;
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fun distinct_proc sg _ (t as Const ("op =", _) $ t1 $ t2) =
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  (case (stripC (0, t1), stripC (0, t2)) of
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     ((i, Const (cname1, T1)), (j, Const (cname2, T2))) =>
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         (case (stripT (0, T1), stripT (0, T2)) of
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            ((i', Type (tname1, _)), (j', Type (tname2, _))) =>
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                if tname1 = tname2 andalso not (cname1 = cname2) andalso i = i' andalso j = j' then
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                   (case (constrs_of_sg sg tname1) of
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                      Some constrs => let val cnames = map (fst o dest_Const) constrs
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                        in if cname1 mem cnames andalso cname2 mem cnames then
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                             let val eq_t = Logic.mk_equals (t, Const ("False", HOLogic.boolT));
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                                 val eq_ct = cterm_of sg eq_t;
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                                 val Datatype_thy = theory "Datatype";
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                                 val [In0_inject, In1_inject, In0_not_In1, In1_not_In0] =
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                                   map (get_thm Datatype_thy)
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                                     ["In0_inject", "In1_inject", "In0_not_In1", "In1_not_In0"]
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                             in (case (#distinct (datatype_info_sg_err sg tname1)) of
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                                 QuickAndDirty => Some (Thm.invoke_oracle
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                                   Datatype_thy distinctN (sg, ConstrDistinct eq_t))
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                               | FewConstrs thms => Some (prove_goalw_cterm [] eq_ct (K
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                                   [rtac eq_reflection 1, rtac iffI 1, rtac notE 1,
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                                    atac 2, resolve_tac thms 1, etac FalseE 1]))
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                               | ManyConstrs (thm, ss) => Some (prove_goalw_cterm [] eq_ct (K
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                                   [rtac eq_reflection 1, rtac iffI 1, dtac thm 1,
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                                    full_simp_tac ss 1,
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                                    REPEAT (dresolve_tac [In0_inject, In1_inject] 1),
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                                    eresolve_tac [In0_not_In1 RS notE, In1_not_In0 RS notE] 1,
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                                    etac FalseE 1])))
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                             end
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                           else None
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                        end
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                    | None => None)
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                else None
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          | _ => None)
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   | _ => None)
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  | distinct_proc sg _ _ = None;
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val distinct_pats = [Thm.read_cterm (Theory.sign_of HOL.thy) ("s = t", HOLogic.termT)];
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val distinct_simproc = mk_simproc distinctN distinct_pats distinct_proc;
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val dist_ss = HOL_ss addsimprocs [distinct_simproc];
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val simproc_setup =
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  [Theory.add_oracle (distinctN, fn (_, ConstrDistinct t) => t),
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   fn thy => (simpset_ref_of thy := simpset_of thy addsimprocs [distinct_simproc]; thy)];
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(* prepare types *)
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fun read_typ sign ((Ts, sorts), str) =
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  let
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    val T = Type.no_tvars (Sign.read_typ (sign, (curry assoc)
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      (map (apfst (rpair ~1)) sorts)) str) handle TYPE (msg, _, _) => error msg
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  in (Ts @ [T], add_typ_tfrees (T, sorts)) end;
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fun cert_typ sign ((Ts, sorts), raw_T) =
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  let
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    val T = Type.no_tvars (Sign.certify_typ sign raw_T) handle
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      TYPE (msg, _, _) => error msg;
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    val sorts' = add_typ_tfrees (T, sorts)
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  in (Ts @ [T],
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      case duplicates (map fst sorts') of
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         [] => sorts'
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       | dups => error ("Inconsistent sort constraints for " ^ commas dups))
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  end;
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(**** make datatype info ****)
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fun make_dt_info descr induct reccomb_names rec_thms
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  ((((((((i, (_, (tname, _, _))), case_name), case_thms),
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    exhaustion_thm), distinct_thm), inject), nchotomy), case_cong) = (tname,
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      {index = i,
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       descr = descr,
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       rec_names = reccomb_names,
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       rec_rewrites = rec_thms,
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       case_name = case_name,
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       case_rewrites = case_thms,
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       induction = induct,
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       exhaustion = exhaustion_thm,
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       distinct = distinct_thm,
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       inject = inject,
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       nchotomy = nchotomy,
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       case_cong = case_cong});
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fun store_clasimp thy (cla, simp) =
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  (claset_ref_of thy := cla; simpset_ref_of thy := simp);
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(********************* axiomatic introduction of datatypes ********************)
berghofe@5177
   319
berghofe@5177
   320
fun add_and_get_axioms label tnames ts thy =
berghofe@5177
   321
  foldr (fn ((tname, t), (thy', axs)) =>
berghofe@5177
   322
    let
berghofe@5177
   323
      val thy'' = thy' |>
berghofe@5661
   324
        Theory.add_path tname |>
berghofe@5177
   325
        PureThy.add_axioms_i [((label, t), [])];
wenzelm@7904
   326
      val ax = PureThy.get_thm thy'' label
berghofe@5661
   327
    in (Theory.parent_path thy'', ax::axs)
berghofe@5177
   328
    end) (tnames ~~ ts, (thy, []));
berghofe@5177
   329
berghofe@5177
   330
fun add_and_get_axiomss label tnames tss thy =
berghofe@5177
   331
  foldr (fn ((tname, ts), (thy', axss)) =>
berghofe@5177
   332
    let
berghofe@5177
   333
      val thy'' = thy' |>
berghofe@5661
   334
        Theory.add_path tname |>
berghofe@5177
   335
        PureThy.add_axiomss_i [((label, ts), [])];
berghofe@5177
   336
      val axs = PureThy.get_thms thy'' label
berghofe@5661
   337
    in (Theory.parent_path thy'', axs::axss)
berghofe@5177
   338
    end) (tnames ~~ tss, (thy, []));
berghofe@5177
   339
berghofe@5661
   340
fun add_datatype_axm flat_names new_type_names descr sorts types_syntax constr_syntax dt_info thy =
berghofe@5177
   341
  let
berghofe@5177
   342
    val descr' = flat descr;
berghofe@5177
   343
    val recTs = get_rec_types descr' sorts;
berghofe@5578
   344
    val used = foldr add_typ_tfree_names (recTs, []);
berghofe@5177
   345
    val newTs = take (length (hd descr), recTs);
berghofe@5177
   346
berghofe@7015
   347
    val no_size = exists (fn (_, (_, _, constrs)) => exists (fn (_, cargs) => exists
berghofe@7015
   348
      (fn (DtType ("fun", [_, DtRec _])) => true | _ => false) cargs) constrs) descr';
berghofe@7015
   349
berghofe@5177
   350
    (**** declare new types and constants ****)
berghofe@5177
   351
berghofe@5177
   352
    val tyvars = map (fn (_, (_, Ts, _)) => map dest_DtTFree Ts) (hd descr);
berghofe@5177
   353
berghofe@5177
   354
    val constr_decls = map (fn (((_, (_, _, constrs)), T), constr_syntax') =>
berghofe@5177
   355
      map (fn ((_, cargs), (cname, mx)) =>
berghofe@5177
   356
        (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
berghofe@5177
   357
          (constrs ~~ constr_syntax')) ((hd descr) ~~ newTs ~~ constr_syntax);
berghofe@5177
   358
berghofe@5578
   359
    val rec_result_Ts = map TFree (variantlist (replicate (length descr') "'t", used) ~~
berghofe@5578
   360
      replicate (length descr') HOLogic.termS);
berghofe@5177
   361
berghofe@5177
   362
    val reccomb_fn_Ts = flat (map (fn (i, (_, _, constrs)) =>
berghofe@5177
   363
      map (fn (_, cargs) =>
berghofe@5177
   364
        let
berghofe@7015
   365
          val Ts = map (typ_of_dtyp descr' sorts) cargs;
berghofe@7015
   366
          val recs = filter (is_rec_type o fst) (cargs ~~ Ts);
berghofe@7015
   367
berghofe@7015
   368
          fun mk_argT (DtRec k, _) = nth_elem (k, rec_result_Ts)
berghofe@7015
   369
            | mk_argT (DtType ("fun", [_, DtRec k]), Type ("fun", [T, _])) =
berghofe@7015
   370
               T --> nth_elem (k, rec_result_Ts);
berghofe@7015
   371
berghofe@7015
   372
          val argTs = Ts @ map mk_argT recs
berghofe@5177
   373
        in argTs ---> nth_elem (i, rec_result_Ts)
berghofe@5177
   374
        end) constrs) descr');
berghofe@5177
   375
berghofe@5177
   376
    val big_reccomb_name = (space_implode "_" new_type_names) ^ "_rec";
berghofe@5177
   377
    val reccomb_names = if length descr' = 1 then [big_reccomb_name] else
berghofe@5177
   378
      (map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int)
berghofe@5177
   379
        (1 upto (length descr')));
berghofe@5177
   380
berghofe@5177
   381
    val big_size_name = space_implode "_" new_type_names ^ "_size";
berghofe@5177
   382
    val size_names = if length (flat (tl descr)) = 1 then [big_size_name] else
berghofe@5177
   383
      map (fn i => big_size_name ^ "_" ^ string_of_int i)
berghofe@5177
   384
        (1 upto length (flat (tl descr)));
berghofe@5177
   385
berghofe@5578
   386
    val freeT = TFree (variant used "'t", HOLogic.termS);
berghofe@5177
   387
    val case_fn_Ts = map (fn (i, (_, _, constrs)) =>
berghofe@5177
   388
      map (fn (_, cargs) =>
berghofe@5177
   389
        let val Ts = map (typ_of_dtyp descr' sorts) cargs
berghofe@5177
   390
        in Ts ---> freeT end) constrs) (hd descr);
berghofe@5177
   391
berghofe@5177
   392
    val case_names = map (fn s => (s ^ "_case")) new_type_names;
berghofe@5177
   393
berghofe@6305
   394
    val thy2' = thy |>
berghofe@5177
   395
berghofe@5177
   396
      (** new types **)
berghofe@5177
   397
berghofe@5177
   398
      curry (foldr (fn (((name, mx), tvs), thy') => thy' |>
wenzelm@6385
   399
          TypedefPackage.add_typedecls [(name, tvs, mx)]))
wenzelm@6385
   400
        (types_syntax ~~ tyvars) |>
berghofe@5661
   401
      add_path flat_names (space_implode "_" new_type_names) |>
berghofe@5177
   402
berghofe@5177
   403
      (** primrec combinators **)
berghofe@5177
   404
berghofe@5177
   405
      Theory.add_consts_i (map (fn ((name, T), T') =>
berghofe@5177
   406
        (name, reccomb_fn_Ts @ [T] ---> T', NoSyn))
berghofe@5177
   407
          (reccomb_names ~~ recTs ~~ rec_result_Ts)) |>
berghofe@5177
   408
berghofe@5177
   409
      (** case combinators **)
berghofe@5177
   410
berghofe@5177
   411
      Theory.add_consts_i (map (fn ((name, T), Ts) =>
berghofe@5177
   412
        (name, Ts @ [T] ---> freeT, NoSyn))
berghofe@5177
   413
          (case_names ~~ newTs ~~ case_fn_Ts)) |>
berghofe@6305
   414
      Theory.add_trrules_i (DatatypeProp.make_case_trrules new_type_names descr);
berghofe@6305
   415
wenzelm@6394
   416
    val reccomb_names' = map (Sign.intern_const (Theory.sign_of thy2')) reccomb_names;
wenzelm@6394
   417
    val case_names' = map (Sign.intern_const (Theory.sign_of thy2')) case_names;
berghofe@6305
   418
berghofe@6305
   419
    val thy2 = thy2' |>
berghofe@5177
   420
berghofe@5177
   421
      (** size functions **)
berghofe@5177
   422
berghofe@7015
   423
      (if no_size then I else Theory.add_consts_i (map (fn (s, T) =>
berghofe@5177
   424
        (Sign.base_name s, T --> HOLogic.natT, NoSyn))
berghofe@7015
   425
          (size_names ~~ drop (length (hd descr), recTs)))) |>
berghofe@5661
   426
berghofe@5661
   427
      (** constructors **)
berghofe@5661
   428
berghofe@5661
   429
      parent_path flat_names |>
berghofe@5661
   430
      curry (foldr (fn (((((_, (_, _, constrs)), T), tname),
berghofe@5661
   431
        constr_syntax'), thy') => thy' |>
berghofe@5661
   432
          add_path flat_names tname |>
berghofe@5661
   433
            Theory.add_consts_i (map (fn ((_, cargs), (cname, mx)) =>
berghofe@5661
   434
              (cname, map (typ_of_dtyp descr' sorts) cargs ---> T, mx))
berghofe@5661
   435
                (constrs ~~ constr_syntax')) |>
berghofe@5661
   436
          parent_path flat_names))
berghofe@5661
   437
            (hd descr ~~ newTs ~~ new_type_names ~~ constr_syntax);
berghofe@5177
   438
berghofe@5177
   439
    (**** introduction of axioms ****)
berghofe@5177
   440
berghofe@5661
   441
    val rec_axs = DatatypeProp.make_primrecs new_type_names descr sorts thy2;
berghofe@7015
   442
    val size_axs = if no_size then [] else DatatypeProp.make_size new_type_names descr sorts thy2;
berghofe@5661
   443
berghofe@5177
   444
    val (thy3, inject) = thy2 |>
berghofe@5661
   445
      Theory.add_path (space_implode "_" new_type_names) |>
berghofe@5177
   446
      PureThy.add_axioms_i [(("induct", DatatypeProp.make_ind descr sorts), [])] |>
berghofe@5661
   447
      PureThy.add_axiomss_i [(("recs", rec_axs), [])] |>
berghofe@7015
   448
      (if no_size then I else PureThy.add_axiomss_i [(("size", size_axs), [])]) |>
berghofe@5661
   449
      Theory.parent_path |>
berghofe@5177
   450
      add_and_get_axiomss "inject" new_type_names
berghofe@5177
   451
        (DatatypeProp.make_injs descr sorts);
wenzelm@7904
   452
    val induct = get_thm thy3 "induct";
berghofe@5661
   453
    val rec_thms = get_thms thy3 "recs";
berghofe@7015
   454
    val size_thms = if no_size then [] else get_thms thy3 "size";
berghofe@5177
   455
    val (thy4, distinct) = add_and_get_axiomss "distinct" new_type_names
berghofe@5177
   456
      (DatatypeProp.make_distincts new_type_names descr sorts thy3) thy3;
berghofe@5177
   457
    val (thy5, exhaustion) = add_and_get_axioms "exhaust" new_type_names
berghofe@5661
   458
      (DatatypeProp.make_casedists descr sorts) thy4;
berghofe@5177
   459
    val (thy6, case_thms) = add_and_get_axiomss "cases" new_type_names
berghofe@5177
   460
      (DatatypeProp.make_cases new_type_names descr sorts thy5) thy5;
berghofe@5177
   461
    val (split_ts, split_asm_ts) = ListPair.unzip
berghofe@5177
   462
      (DatatypeProp.make_splits new_type_names descr sorts thy6);
berghofe@5177
   463
    val (thy7, split) = add_and_get_axioms "split" new_type_names split_ts thy6;
berghofe@5177
   464
    val (thy8, split_asm) = add_and_get_axioms "split_asm" new_type_names
berghofe@5177
   465
      split_asm_ts thy7;
berghofe@5177
   466
    val (thy9, nchotomys) = add_and_get_axioms "nchotomy" new_type_names
berghofe@5177
   467
      (DatatypeProp.make_nchotomys descr sorts) thy8;
berghofe@5177
   468
    val (thy10, case_congs) = add_and_get_axioms "case_cong" new_type_names
berghofe@5177
   469
      (DatatypeProp.make_case_congs new_type_names descr sorts thy9) thy9;
berghofe@5177
   470
    
berghofe@6305
   471
    val dt_infos = map (make_dt_info descr' induct reccomb_names' rec_thms)
berghofe@6305
   472
      ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names' ~~ case_thms ~~
berghofe@7015
   473
        exhaustion ~~ replicate (length (hd descr)) QuickAndDirty ~~ inject ~~
berghofe@7015
   474
          nchotomys ~~ case_congs);
berghofe@5177
   475
berghofe@5177
   476
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   477
berghofe@5661
   478
    val thy11 = thy10 |>
berghofe@5661
   479
      Theory.add_path (space_implode "_" new_type_names) |>
wenzelm@6092
   480
      PureThy.add_thmss [(("simps", simps), [])] |>
berghofe@5177
   481
      put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
wenzelm@8306
   482
      add_cases_induct dt_infos |>
berghofe@5177
   483
      Theory.parent_path;
berghofe@5177
   484
berghofe@5661
   485
    val _ = store_clasimp thy11 ((claset_of thy11, simpset_of thy11)
berghofe@5177
   486
      addsimps2 flat case_thms addsimps2 size_thms addsimps2 rec_thms
berghofe@7015
   487
      addIffs flat (inject @ distinct));
berghofe@5177
   488
berghofe@5177
   489
  in
berghofe@5661
   490
    (thy11,
berghofe@5177
   491
     {distinct = distinct,
berghofe@5177
   492
      inject = inject,
berghofe@5177
   493
      exhaustion = exhaustion,
berghofe@5177
   494
      rec_thms = rec_thms,
berghofe@5177
   495
      case_thms = case_thms,
berghofe@5177
   496
      split_thms = split ~~ split_asm,
berghofe@5177
   497
      induction = induct,
berghofe@5177
   498
      size = size_thms,
berghofe@5177
   499
      simps = simps})
berghofe@5177
   500
  end;
berghofe@5177
   501
berghofe@5177
   502
berghofe@5177
   503
(******************* definitional introduction of datatypes *******************)
berghofe@5177
   504
berghofe@5661
   505
fun add_datatype_def flat_names new_type_names descr sorts types_syntax constr_syntax dt_info thy =
berghofe@5177
   506
  let
wenzelm@6360
   507
    val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
berghofe@5177
   508
berghofe@7015
   509
    val (thy2, inject, distinct, dist_rewrites, simproc_dists, induct) = thy |>
berghofe@5661
   510
      DatatypeRepProofs.representation_proofs flat_names dt_info new_type_names descr sorts
berghofe@5177
   511
        types_syntax constr_syntax;
berghofe@5177
   512
berghofe@5177
   513
    val (thy3, casedist_thms) =
berghofe@5177
   514
      DatatypeAbsProofs.prove_casedist_thms new_type_names descr sorts induct thy2;
berghofe@5177
   515
    val (thy4, reccomb_names, rec_thms) = DatatypeAbsProofs.prove_primrec_thms
berghofe@7015
   516
      flat_names new_type_names descr sorts dt_info inject dist_rewrites dist_ss induct thy3;
berghofe@7015
   517
    val (thy6, case_names, case_thms) = DatatypeAbsProofs.prove_case_thms
berghofe@5661
   518
      flat_names new_type_names descr sorts reccomb_names rec_thms thy4;
berghofe@5177
   519
    val (thy7, split_thms) = DatatypeAbsProofs.prove_split_thms new_type_names
berghofe@5177
   520
      descr sorts inject dist_rewrites casedist_thms case_thms thy6;
berghofe@5177
   521
    val (thy8, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
berghofe@5177
   522
      descr sorts casedist_thms thy7;
berghofe@5177
   523
    val (thy9, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
berghofe@5177
   524
      descr sorts nchotomys case_thms thy8;
berghofe@5661
   525
    val (thy10, size_thms) = DatatypeAbsProofs.prove_size_thms flat_names new_type_names
berghofe@5177
   526
      descr sorts reccomb_names rec_thms thy9;
berghofe@5177
   527
berghofe@5177
   528
    val dt_infos = map (make_dt_info (flat descr) induct reccomb_names rec_thms)
berghofe@5177
   529
      ((0 upto length (hd descr) - 1) ~~ (hd descr) ~~ case_names ~~ case_thms ~~
berghofe@7015
   530
        casedist_thms ~~ simproc_dists ~~ inject ~~ nchotomys ~~ case_congs);
berghofe@5177
   531
berghofe@5177
   532
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   533
berghofe@5177
   534
    val thy11 = thy10 |>
berghofe@5661
   535
      Theory.add_path (space_implode "_" new_type_names) |>
wenzelm@6092
   536
      PureThy.add_thmss [(("simps", simps), [])] |>
berghofe@5177
   537
      put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
wenzelm@8306
   538
      add_cases_induct dt_infos |>
berghofe@5663
   539
      Theory.parent_path;
berghofe@5177
   540
berghofe@5177
   541
    val _ = store_clasimp thy11 ((claset_of thy11, simpset_of thy11)
berghofe@5177
   542
      addsimps2 flat case_thms addsimps2 size_thms addsimps2 rec_thms
berghofe@7015
   543
      addIffs flat (inject @ distinct));
berghofe@5177
   544
berghofe@5177
   545
  in
berghofe@5177
   546
    (thy11,
berghofe@5177
   547
     {distinct = distinct,
berghofe@5177
   548
      inject = inject,
berghofe@5177
   549
      exhaustion = casedist_thms,
berghofe@5177
   550
      rec_thms = rec_thms,
berghofe@5177
   551
      case_thms = case_thms,
berghofe@5177
   552
      split_thms = split_thms,
berghofe@5177
   553
      induction = induct,
berghofe@5177
   554
      size = size_thms,
berghofe@5177
   555
      simps = simps})
berghofe@5177
   556
  end;
berghofe@5177
   557
berghofe@5177
   558
wenzelm@6385
   559
(*********************** declare existing type as datatype *********************)
berghofe@5177
   560
wenzelm@6385
   561
fun gen_rep_datatype apply_theorems alt_names raw_distinct raw_inject raw_induction thy0 =
berghofe@5177
   562
  let
wenzelm@6385
   563
    fun app_thmss srcs thy = foldl_map (fn (thy, x) => apply_theorems x thy) (thy, srcs);
wenzelm@6385
   564
    fun app_thm src thy = apsnd Library.hd (apply_theorems [src] thy);
wenzelm@6385
   565
wenzelm@6385
   566
    val (((thy1, induction), inject), distinct) = thy0
wenzelm@6385
   567
      |> app_thmss raw_distinct
wenzelm@6385
   568
      |> apfst (app_thmss raw_inject)
wenzelm@6385
   569
      |> apfst (apfst (app_thm raw_induction));
wenzelm@6394
   570
    val sign = Theory.sign_of thy1;
berghofe@5177
   571
berghofe@5177
   572
    val induction' = freezeT induction;
berghofe@5177
   573
berghofe@5177
   574
    fun err t = error ("Ill-formed predicate in induction rule: " ^
berghofe@5177
   575
      Sign.string_of_term sign t);
berghofe@5177
   576
berghofe@5177
   577
    fun get_typ (t as _ $ Var (_, Type (tname, Ts))) =
berghofe@7015
   578
          ((tname, map dest_TFree Ts) handle TERM _ => err t)
berghofe@5177
   579
      | get_typ t = err t;
berghofe@5177
   580
wenzelm@8306
   581
    val dtnames = map get_typ (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induction')));
berghofe@5177
   582
    val new_type_names = if_none alt_names (map fst dtnames);
berghofe@5177
   583
berghofe@5177
   584
    fun get_constr t = (case Logic.strip_assums_concl t of
berghofe@5177
   585
        _ $ (_ $ t') => (case head_of t' of
berghofe@5177
   586
            Const (cname, cT) => (case strip_type cT of
berghofe@5177
   587
                (Ts, Type (tname, _)) => (tname, (cname, map (dtyp_of_typ dtnames) Ts))
berghofe@5177
   588
              | _ => err t)
berghofe@5177
   589
          | _ => err t)
berghofe@5177
   590
      | _ => err t);
berghofe@5177
   591
berghofe@5177
   592
    fun make_dt_spec [] _ _ = []
berghofe@5177
   593
      | make_dt_spec ((tname, tvs)::dtnames') i constrs =
berghofe@5177
   594
          let val (constrs', constrs'') = take_prefix (equal tname o fst) constrs
berghofe@5177
   595
          in (i, (tname, map DtTFree tvs, map snd constrs'))::
berghofe@5177
   596
            (make_dt_spec dtnames' (i + 1) constrs'')
berghofe@5177
   597
          end;
berghofe@5177
   598
berghofe@5177
   599
    val descr = make_dt_spec dtnames 0 (map get_constr (prems_of induction'));
berghofe@5177
   600
    val sorts = add_term_tfrees (concl_of induction', []);
wenzelm@6385
   601
    val dt_info = get_datatypes thy1;
berghofe@5177
   602
wenzelm@6427
   603
    val _ = message ("Proofs for datatype(s) " ^ commas_quote new_type_names);
berghofe@5177
   604
wenzelm@6385
   605
    val (thy2, casedist_thms) = thy1 |>
berghofe@5177
   606
      DatatypeAbsProofs.prove_casedist_thms new_type_names [descr] sorts induction;
berghofe@5177
   607
    val (thy3, reccomb_names, rec_thms) = DatatypeAbsProofs.prove_primrec_thms
berghofe@7015
   608
      false new_type_names [descr] sorts dt_info inject distinct dist_ss induction thy2;
berghofe@5661
   609
    val (thy4, case_names, case_thms) = DatatypeAbsProofs.prove_case_thms false
berghofe@5177
   610
      new_type_names [descr] sorts reccomb_names rec_thms thy3;
berghofe@5177
   611
    val (thy5, split_thms) = DatatypeAbsProofs.prove_split_thms
berghofe@5177
   612
      new_type_names [descr] sorts inject distinct casedist_thms case_thms thy4;
berghofe@5177
   613
    val (thy6, nchotomys) = DatatypeAbsProofs.prove_nchotomys new_type_names
berghofe@5177
   614
      [descr] sorts casedist_thms thy5;
berghofe@5177
   615
    val (thy7, case_congs) = DatatypeAbsProofs.prove_case_congs new_type_names
berghofe@5177
   616
      [descr] sorts nchotomys case_thms thy6;
berghofe@5177
   617
    val (thy8, size_thms) =
wenzelm@6394
   618
      if exists (equal "Arith") (Sign.stamp_names_of (Theory.sign_of thy7)) then
berghofe@5661
   619
        DatatypeAbsProofs.prove_size_thms false new_type_names
berghofe@5177
   620
          [descr] sorts reccomb_names rec_thms thy7
berghofe@5177
   621
      else (thy7, []);
berghofe@5177
   622
berghofe@5177
   623
    val dt_infos = map (make_dt_info descr induction reccomb_names rec_thms)
berghofe@5177
   624
      ((0 upto length descr - 1) ~~ descr ~~ case_names ~~ case_thms ~~
berghofe@7015
   625
        casedist_thms ~~ map FewConstrs distinct ~~ inject ~~ nchotomys ~~ case_congs);
berghofe@5177
   626
berghofe@5177
   627
    val simps = flat (distinct @ inject @ case_thms) @ size_thms @ rec_thms;
berghofe@5177
   628
berghofe@5177
   629
    val thy9 = thy8 |>
berghofe@7743
   630
      store_thmss "inject" new_type_names inject |>
berghofe@7743
   631
      store_thmss "distinct" new_type_names distinct |>
berghofe@5661
   632
      Theory.add_path (space_implode "_" new_type_names) |>
berghofe@7743
   633
      PureThy.add_thms [(("induct", induction), [])] |>
wenzelm@6092
   634
      PureThy.add_thmss [(("simps", simps), [])] |>
berghofe@5177
   635
      put_datatypes (foldr Symtab.update (dt_infos, dt_info)) |>
wenzelm@8306
   636
      add_cases_induct dt_infos |>
berghofe@5177
   637
      Theory.parent_path;
berghofe@5177
   638
berghofe@5177
   639
    val _ = store_clasimp thy9 ((claset_of thy9, simpset_of thy9)
berghofe@5177
   640
      addsimps2 flat case_thms addsimps2 size_thms addsimps2 rec_thms
berghofe@7015
   641
      addIffs flat (inject @ distinct));
berghofe@5177
   642
berghofe@5177
   643
  in
berghofe@5177
   644
    (thy9,
berghofe@5177
   645
     {distinct = distinct,
berghofe@5177
   646
      inject = inject,
berghofe@5177
   647
      exhaustion = casedist_thms,
berghofe@5177
   648
      rec_thms = rec_thms,
berghofe@5177
   649
      case_thms = case_thms,
berghofe@5177
   650
      split_thms = split_thms,
berghofe@5177
   651
      induction = induction,
berghofe@5177
   652
      size = size_thms,
berghofe@5177
   653
      simps = simps})
berghofe@5177
   654
  end;
berghofe@5177
   655
wenzelm@6385
   656
val rep_datatype = gen_rep_datatype IsarThy.apply_theorems;
wenzelm@6385
   657
val rep_datatype_i = gen_rep_datatype IsarThy.apply_theorems_i;
wenzelm@6385
   658
berghofe@5177
   659
berghofe@5177
   660
(******************************** add datatype ********************************)
berghofe@5177
   661
berghofe@5661
   662
fun gen_add_datatype prep_typ flat_names new_type_names dts thy =
berghofe@5177
   663
  let
berghofe@5177
   664
    val _ = Theory.requires thy "Datatype" "datatype definitions";
berghofe@5177
   665
berghofe@5177
   666
    (* this theory is used just for parsing *)
berghofe@5177
   667
berghofe@5177
   668
    val tmp_thy = thy |>
wenzelm@5892
   669
      Theory.copy |>
berghofe@5177
   670
      Theory.add_types (map (fn (tvs, tname, mx, _) =>
berghofe@5177
   671
        (tname, length tvs, mx)) dts);
berghofe@5177
   672
wenzelm@6394
   673
    val sign = Theory.sign_of tmp_thy;
berghofe@5177
   674
berghofe@5661
   675
    val (tyvars, _, _, _)::_ = dts;
berghofe@5177
   676
    val (new_dts, types_syntax) = ListPair.unzip (map (fn (tvs, tname, mx, _) =>
berghofe@5177
   677
      let val full_tname = Sign.full_name sign (Syntax.type_name tname mx)
berghofe@5177
   678
      in (case duplicates tvs of
berghofe@5661
   679
            [] => if eq_set (tyvars, tvs) then ((full_tname, tvs), (tname, mx))
berghofe@5661
   680
                  else error ("Mutually recursive datatypes must have same type parameters")
berghofe@5177
   681
          | dups => error ("Duplicate parameter(s) for datatype " ^ full_tname ^
berghofe@5177
   682
              " : " ^ commas dups))
berghofe@5177
   683
      end) dts);
berghofe@5177
   684
berghofe@5177
   685
    val _ = (case duplicates (map fst new_dts) @ duplicates new_type_names of
berghofe@5177
   686
      [] => () | dups => error ("Duplicate datatypes: " ^ commas dups));
berghofe@5177
   687
berghofe@5177
   688
    fun prep_dt_spec ((dts', constr_syntax, sorts, i), (tvs, tname, mx, constrs)) =
berghofe@5177
   689
      let
berghofe@5661
   690
        fun prep_constr ((constrs, constr_syntax', sorts'), (cname, cargs, mx')) =
berghofe@5279
   691
          let
berghofe@5279
   692
            val (cargs', sorts'') = foldl (prep_typ sign) (([], sorts'), cargs);
berghofe@5279
   693
            val _ = (case foldr add_typ_tfree_names (cargs', []) \\ tvs of
berghofe@5279
   694
                [] => ()
berghofe@5279
   695
              | vs => error ("Extra type variables on rhs: " ^ commas vs))
berghofe@5661
   696
          in (constrs @ [((if flat_names then Sign.full_name sign else
berghofe@5661
   697
                Sign.full_name_path sign tname) (Syntax.const_name cname mx'),
berghofe@5177
   698
                   map (dtyp_of_typ new_dts) cargs')],
berghofe@5177
   699
              constr_syntax' @ [(cname, mx')], sorts'')
berghofe@5177
   700
          end handle ERROR =>
berghofe@5177
   701
            error ("The error above occured in constructor " ^ cname ^
berghofe@5177
   702
              " of datatype " ^ tname);
berghofe@5177
   703
berghofe@5177
   704
        val (constrs', constr_syntax', sorts') =
berghofe@5177
   705
          foldl prep_constr (([], [], sorts), constrs)
berghofe@5177
   706
berghofe@5177
   707
      in 
berghofe@5177
   708
        case duplicates (map fst constrs') of
berghofe@5177
   709
           [] =>
berghofe@5177
   710
             (dts' @ [(i, (Sign.full_name sign (Syntax.type_name tname mx),
berghofe@5177
   711
                map DtTFree tvs, constrs'))],
berghofe@5177
   712
              constr_syntax @ [constr_syntax'], sorts', i + 1)
berghofe@5177
   713
         | dups => error ("Duplicate constructors " ^ commas dups ^
berghofe@5177
   714
             " in datatype " ^ tname)
berghofe@5177
   715
      end;
berghofe@5177
   716
berghofe@5661
   717
    val (dts', constr_syntax, sorts', i) = foldl prep_dt_spec (([], [], [], 0), dts);
berghofe@7015
   718
    val sorts = sorts' @ (map (rpair (Sign.defaultS sign)) (tyvars \\ map fst sorts'));
berghofe@5177
   719
    val dt_info = get_datatypes thy;
berghofe@7015
   720
    val (descr, _) = unfold_datatypes sign dts' sorts dt_info dts' i;
berghofe@5177
   721
    val _ = check_nonempty descr;
berghofe@5177
   722
berghofe@5177
   723
  in
berghofe@5177
   724
    (if (!quick_and_dirty) then add_datatype_axm else add_datatype_def)
berghofe@5661
   725
      flat_names new_type_names descr sorts types_syntax constr_syntax dt_info thy
berghofe@5177
   726
  end;
berghofe@5177
   727
berghofe@5177
   728
val add_datatype_i = gen_add_datatype cert_typ;
berghofe@5177
   729
val add_datatype = gen_add_datatype read_typ;
berghofe@5177
   730
wenzelm@6360
   731
wenzelm@6360
   732
(** package setup **)
wenzelm@6360
   733
wenzelm@6360
   734
(* setup theory *)
wenzelm@6360
   735
berghofe@7015
   736
val setup = [DatatypesData.init] @ simproc_setup;
wenzelm@6360
   737
wenzelm@6360
   738
wenzelm@6360
   739
(* outer syntax *)
wenzelm@6360
   740
wenzelm@6723
   741
local structure P = OuterParse and K = OuterSyntax.Keyword in
wenzelm@6360
   742
wenzelm@6360
   743
val datatype_decl =
wenzelm@6723
   744
  Scan.option (P.$$$ "(" |-- P.name --| P.$$$ ")") -- P.type_args -- P.name -- P.opt_infix --
wenzelm@6729
   745
    (P.$$$ "=" |-- P.enum1 "|" (P.name -- Scan.repeat P.typ -- P.opt_mixfix --| P.marg_comment));
wenzelm@6360
   746
wenzelm@6360
   747
fun mk_datatype args =
wenzelm@6360
   748
  let
wenzelm@6360
   749
    val names = map (fn ((((None, _), t), _), _) => t | ((((Some t, _), _), _), _) => t) args;
wenzelm@6360
   750
    val specs = map (fn ((((_, vs), t), mx), cons) => (vs, t, mx, map (fn ((x, y), z) => (x, y, z)) cons)) args;
wenzelm@6360
   751
  in #1 o add_datatype false names specs end;
wenzelm@6360
   752
wenzelm@6360
   753
val datatypeP =
wenzelm@6723
   754
  OuterSyntax.command "datatype" "define inductive datatypes" K.thy_decl
wenzelm@6723
   755
    (P.and_list1 datatype_decl >> (Toplevel.theory o mk_datatype));
wenzelm@6360
   756
wenzelm@6385
   757
wenzelm@6385
   758
val rep_datatype_decl =
wenzelm@6723
   759
  Scan.option (Scan.repeat1 P.name) --
wenzelm@6723
   760
    Scan.optional (P.$$$ "distinct" |-- P.!!! (P.and_list1 P.xthms1)) [] --
wenzelm@6723
   761
    Scan.optional (P.$$$ "inject" |-- P.!!! (P.and_list1 P.xthms1)) [] --
wenzelm@6723
   762
    (P.$$$ "induction" |-- P.!!! P.xthm);
wenzelm@6385
   763
wenzelm@6385
   764
fun mk_rep_datatype (((opt_ts, dss), iss), ind) = #1 o rep_datatype opt_ts dss iss ind;
wenzelm@6385
   765
wenzelm@6385
   766
val rep_datatypeP =
wenzelm@6723
   767
  OuterSyntax.command "rep_datatype" "represent existing types inductively" K.thy_decl
wenzelm@6385
   768
    (rep_datatype_decl >> (Toplevel.theory o mk_rep_datatype));
wenzelm@6385
   769
wenzelm@6385
   770
wenzelm@6479
   771
val _ = OuterSyntax.add_keywords ["distinct", "inject", "induction"];
wenzelm@6385
   772
val _ = OuterSyntax.add_parsers [datatypeP, rep_datatypeP];
wenzelm@6385
   773
wenzelm@6385
   774
end;
wenzelm@6385
   775
wenzelm@6360
   776
berghofe@5177
   777
end;
berghofe@5177
   778
wenzelm@6360
   779
structure BasicDatatypePackage: BASIC_DATATYPE_PACKAGE = DatatypePackage;
wenzelm@6360
   780
open BasicDatatypePackage;