src/HOL/Tools/inductive.ML
author blanchet
Thu Nov 05 11:58:07 2009 +0100 (2009-11-05)
changeset 33577 ea36b70a6c1c
parent 33317 b4534348b8fd
child 33578 0c3ba1e010d2
permissions -rw-r--r--
added "nitpick_def" attribute to lfp/gfp definition generated by the inductive package;
this ensures that Nitpick can find the definition and determine whether its inductive
or coinductive
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(*  Title:      HOL/Tools/inductive.ML
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    Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
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    Author:     Stefan Berghofer and Markus Wenzel, TU Muenchen
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(Co)Inductive Definition module for HOL.
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Features:
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  * least or greatest fixedpoints
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  * mutually recursive definitions
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  * definitions involving arbitrary monotone operators
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  * automatically proves introduction and elimination rules
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  Introduction rules have the form
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  [| M Pj ti, ..., Q x, ... |] ==> Pk t
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  where M is some monotone operator (usually the identity)
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  Q x is any side condition on the free variables
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  ti, t are any terms
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  Pj, Pk are two of the predicates being defined in mutual recursion
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*)
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signature BASIC_INDUCTIVE =
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sig
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  type inductive_result
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  val morph_result: morphism -> inductive_result -> inductive_result
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  type inductive_info
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  val the_inductive: Proof.context -> string -> inductive_info
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  val print_inductives: Proof.context -> unit
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  val mono_add: attribute
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  val mono_del: attribute
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  val get_monos: Proof.context -> thm list
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  val mk_cases: Proof.context -> term -> thm
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  val inductive_forall_name: string
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  val inductive_forall_def: thm
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  val rulify: thm -> thm
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  val inductive_cases: (Attrib.binding * string list) list -> local_theory ->
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    thm list list * local_theory
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  val inductive_cases_i: (Attrib.binding * term list) list -> local_theory ->
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    thm list list * local_theory
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  type inductive_flags
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  val add_inductive_i:
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    inductive_flags -> ((binding * typ) * mixfix) list ->
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    (string * typ) list -> (Attrib.binding * term) list -> thm list -> local_theory ->
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    inductive_result * local_theory
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  val add_inductive: bool -> bool ->
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    (binding * string option * mixfix) list ->
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    (binding * string option * mixfix) list ->
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    (Attrib.binding * string) list ->
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    (Facts.ref * Attrib.src list) list ->
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    bool -> local_theory -> inductive_result * local_theory
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  val add_inductive_global: serial -> inductive_flags ->
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    ((binding * typ) * mixfix) list -> (string * typ) list -> (Attrib.binding * term) list ->
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    thm list -> theory -> inductive_result * theory
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  val arities_of: thm -> (string * int) list
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  val params_of: thm -> term list
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  val partition_rules: thm -> thm list -> (string * thm list) list
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  val partition_rules': thm -> (thm * 'a) list -> (string * (thm * 'a) list) list
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  val unpartition_rules: thm list -> (string * 'a list) list -> 'a list
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  val infer_intro_vars: thm -> int -> thm list -> term list list
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  val setup: theory -> theory
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end;
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signature INDUCTIVE =
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sig
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  include BASIC_INDUCTIVE
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  type add_ind_def
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  val declare_rules: string -> binding -> bool -> bool -> string list ->
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    thm list -> binding list -> Attrib.src list list -> (thm * string list) list ->
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    thm -> local_theory -> thm list * thm list * thm * local_theory
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  val add_ind_def: add_ind_def
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  val gen_add_inductive_i: add_ind_def -> inductive_flags ->
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    ((binding * typ) * mixfix) list -> (string * typ) list -> (Attrib.binding * term) list ->
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    thm list -> local_theory -> inductive_result * local_theory
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  val gen_add_inductive: add_ind_def -> bool -> bool ->
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    (binding * string option * mixfix) list ->
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    (binding * string option * mixfix) list ->
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    (Attrib.binding * string) list -> (Facts.ref * Attrib.src list) list ->
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    bool -> local_theory -> inductive_result * local_theory
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  val gen_ind_decl: add_ind_def -> bool ->
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    OuterParse.token list -> (bool -> local_theory -> local_theory) * OuterParse.token list
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end;
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structure Inductive: INDUCTIVE =
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struct
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(** theory context references **)
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val inductive_forall_name = "HOL.induct_forall";
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val inductive_forall_def = @{thm induct_forall_def};
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val inductive_conj_name = "HOL.induct_conj";
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val inductive_conj_def = @{thm induct_conj_def};
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val inductive_conj = @{thms induct_conj};
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val inductive_atomize = @{thms induct_atomize};
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val inductive_rulify = @{thms induct_rulify};
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val inductive_rulify_fallback = @{thms induct_rulify_fallback};
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val notTrueE = TrueI RSN (2, notE);
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val notFalseI = Seq.hd (atac 1 notI);
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val simp_thms' = map mk_meta_eq
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  @{lemma "(~True) = False" "(~False) = True"
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      "(True --> P) = P" "(False --> P) = True"
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      "(P & True) = P" "(True & P) = P"
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    by (fact simp_thms)+};
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val simp_thms'' = map mk_meta_eq [@{thm inf_fun_eq}, @{thm inf_bool_eq}] @ simp_thms';
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val simp_thms''' = map mk_meta_eq
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  [@{thm le_fun_def}, @{thm le_bool_def}, @{thm sup_fun_eq}, @{thm sup_bool_eq}];
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(** context data **)
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type inductive_result =
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  {preds: term list, elims: thm list, raw_induct: thm,
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   induct: thm, intrs: thm list};
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fun morph_result phi {preds, elims, raw_induct: thm, induct, intrs} =
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  let
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    val term = Morphism.term phi;
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    val thm = Morphism.thm phi;
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    val fact = Morphism.fact phi;
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  in
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   {preds = map term preds, elims = fact elims, raw_induct = thm raw_induct,
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    induct = thm induct, intrs = fact intrs}
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  end;
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type inductive_info =
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  {names: string list, coind: bool} * inductive_result;
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structure InductiveData = GenericDataFun
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(
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  type T = inductive_info Symtab.table * thm list;
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  val empty = (Symtab.empty, []);
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  val extend = I;
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  fun merge _ ((tab1, monos1), (tab2, monos2)) =
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    (Symtab.merge (K true) (tab1, tab2), Thm.merge_thms (monos1, monos2));
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);
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val get_inductives = InductiveData.get o Context.Proof;
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fun print_inductives ctxt =
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  let
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    val (tab, monos) = get_inductives ctxt;
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    val space = Consts.space_of (ProofContext.consts_of ctxt);
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  in
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    [Pretty.strs ("(co)inductives:" :: map #1 (Name_Space.extern_table (space, tab))),
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     Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm ctxt) monos)]
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    |> Pretty.chunks |> Pretty.writeln
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  end;
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(* get and put data *)
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fun the_inductive ctxt name =
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  (case Symtab.lookup (#1 (get_inductives ctxt)) name of
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    NONE => error ("Unknown (co)inductive predicate " ^ quote name)
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  | SOME info => info);
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fun put_inductives names info = InductiveData.map
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  (apfst (fold (fn name => Symtab.update (name, info)) names));
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(** monotonicity rules **)
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val get_monos = #2 o get_inductives;
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val map_monos = InductiveData.map o apsnd;
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fun mk_mono thm =
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  let
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    val concl = concl_of thm;
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    fun eq2mono thm' = [thm' RS (thm' RS eq_to_mono)] @
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      (case concl of
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          (_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
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        | _ => [thm' RS (thm' RS eq_to_mono2)]);
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    fun dest_less_concl thm = dest_less_concl (thm RS @{thm le_funD})
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      handle THM _ => thm RS @{thm le_boolD}
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  in
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    case concl of
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      Const ("==", _) $ _ $ _ => eq2mono (thm RS meta_eq_to_obj_eq)
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    | _ $ (Const ("op =", _) $ _ $ _) => eq2mono thm
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    | _ $ (Const (@{const_name HOL.less_eq}, _) $ _ $ _) =>
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      [dest_less_concl (Seq.hd (REPEAT (FIRSTGOAL
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         (resolve_tac [@{thm le_funI}, @{thm le_boolI'}])) thm))]
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    | _ => [thm]
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  end handle THM _ =>
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    error ("Bad monotonicity theorem:\n" ^ Display.string_of_thm_without_context thm);
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val mono_add = Thm.declaration_attribute (map_monos o fold Thm.add_thm o mk_mono);
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val mono_del = Thm.declaration_attribute (map_monos o fold Thm.del_thm o mk_mono);
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(** misc utilities **)
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fun message quiet_mode s = if quiet_mode then () else writeln s;
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fun clean_message quiet_mode s = if ! quick_and_dirty then () else message quiet_mode s;
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fun coind_prefix true = "co"
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  | coind_prefix false = "";
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fun log (b:int) m n = if m >= n then 0 else 1 + log b (b * m) n;
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fun make_bool_args f g [] i = []
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  | make_bool_args f g (x :: xs) i =
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      (if i mod 2 = 0 then f x else g x) :: make_bool_args f g xs (i div 2);
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fun make_bool_args' xs =
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  make_bool_args (K HOLogic.false_const) (K HOLogic.true_const) xs;
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fun arg_types_of k c = Library.drop (k, binder_types (fastype_of c));
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fun find_arg T x [] = sys_error "find_arg"
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  | find_arg T x ((p as (_, (SOME _, _))) :: ps) =
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      apsnd (cons p) (find_arg T x ps)
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  | find_arg T x ((p as (U, (NONE, y))) :: ps) =
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      if (T: typ) = U then (y, (U, (SOME x, y)) :: ps)
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      else apsnd (cons p) (find_arg T x ps);
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fun make_args Ts xs =
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  map (fn (T, (NONE, ())) => Const (@{const_name undefined}, T) | (_, (SOME t, ())) => t)
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    (fold (fn (t, T) => snd o find_arg T t) xs (map (rpair (NONE, ())) Ts));
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fun make_args' Ts xs Us =
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  fst (fold_map (fn T => find_arg T ()) Us (Ts ~~ map (pair NONE) xs));
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fun dest_predicate cs params t =
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  let
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    val k = length params;
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    val (c, ts) = strip_comb t;
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    val (xs, ys) = chop k ts;
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    val i = find_index (fn c' => c' = c) cs;
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  in
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    if xs = params andalso i >= 0 then
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      SOME (c, i, ys, chop (length ys) (arg_types_of k c))
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    else NONE
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  end;
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fun mk_names a 0 = []
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  | mk_names a 1 = [a]
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  | mk_names a n = map (fn i => a ^ string_of_int i) (1 upto n);
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(** process rules **)
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local
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fun err_in_rule ctxt name t msg =
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  error (cat_lines ["Ill-formed introduction rule " ^ quote name,
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    Syntax.string_of_term ctxt t, msg]);
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fun err_in_prem ctxt name t p msg =
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  error (cat_lines ["Ill-formed premise", Syntax.string_of_term ctxt p,
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    "in introduction rule " ^ quote name, Syntax.string_of_term ctxt t, msg]);
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val bad_concl = "Conclusion of introduction rule must be an inductive predicate";
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val bad_ind_occ = "Inductive predicate occurs in argument of inductive predicate";
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val bad_app = "Inductive predicate must be applied to parameter(s) ";
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fun atomize_term thy = MetaSimplifier.rewrite_term thy inductive_atomize [];
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in
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fun check_rule ctxt cs params ((binding, att), rule) =
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  let
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    val err_name = Binding.str_of binding;
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    val params' = Term.variant_frees rule (Logic.strip_params rule);
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    val frees = rev (map Free params');
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    val concl = subst_bounds (frees, Logic.strip_assums_concl rule);
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    val prems = map (curry subst_bounds frees) (Logic.strip_assums_hyp rule);
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    val rule' = Logic.list_implies (prems, concl);
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    val aprems = map (atomize_term (ProofContext.theory_of ctxt)) prems;
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    val arule = list_all_free (params', Logic.list_implies (aprems, concl));
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    fun check_ind err t = case dest_predicate cs params t of
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        NONE => err (bad_app ^
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          commas (map (Syntax.string_of_term ctxt) params))
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      | SOME (_, _, ys, _) =>
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          if exists (fn c => exists (fn t => Logic.occs (c, t)) ys) cs
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          then err bad_ind_occ else ();
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    fun check_prem' prem t =
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      if head_of t mem cs then
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        check_ind (err_in_prem ctxt err_name rule prem) t
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      else (case t of
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          Abs (_, _, t) => check_prem' prem t
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        | t $ u => (check_prem' prem t; check_prem' prem u)
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        | _ => ());
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    fun check_prem (prem, aprem) =
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      if can HOLogic.dest_Trueprop aprem then check_prem' prem prem
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      else err_in_prem ctxt err_name rule prem "Non-atomic premise";
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  in
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    (case concl of
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       Const ("Trueprop", _) $ t =>
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         if head_of t mem cs then
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           (check_ind (err_in_rule ctxt err_name rule') t;
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            List.app check_prem (prems ~~ aprems))
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         else err_in_rule ctxt err_name rule' bad_concl
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     | _ => err_in_rule ctxt err_name rule' bad_concl);
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    ((binding, att), arule)
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  end;
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val rulify =
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  hol_simplify inductive_conj
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  #> hol_simplify inductive_rulify
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  #> hol_simplify inductive_rulify_fallback
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  #> Simplifier.norm_hhf;
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end;
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(** proofs for (co)inductive predicates **)
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(* prove monotonicity *)
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fun prove_mono quiet_mode skip_mono fork_mono predT fp_fun monos ctxt =
wenzelm@29388
   323
 (message (quiet_mode orelse skip_mono andalso !quick_and_dirty orelse fork_mono)
berghofe@26534
   324
    "  Proving monotonicity ...";
wenzelm@32970
   325
  (if skip_mono then Skip_Proof.prove else if fork_mono then Goal.prove_future else Goal.prove) ctxt
wenzelm@29388
   326
    [] []
wenzelm@17985
   327
    (HOLogic.mk_Trueprop
wenzelm@24815
   328
      (Const (@{const_name Orderings.mono}, (predT --> predT) --> HOLogic.boolT) $ fp_fun))
wenzelm@25380
   329
    (fn _ => EVERY [rtac @{thm monoI} 1,
haftmann@32652
   330
      REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI'}] 1),
berghofe@21024
   331
      REPEAT (FIRST
berghofe@21024
   332
        [atac 1,
wenzelm@32952
   333
         resolve_tac (maps mk_mono monos @ get_monos ctxt) 1,
haftmann@32652
   334
         etac @{thm le_funE} 1, dtac @{thm le_boolD} 1])]));
berghofe@5094
   335
wenzelm@6424
   336
wenzelm@10735
   337
(* prove introduction rules *)
berghofe@5094
   338
wenzelm@26477
   339
fun prove_intrs quiet_mode coind mono fp_def k params intr_ts rec_preds_defs ctxt =
berghofe@5094
   340
  let
wenzelm@26477
   341
    val _ = clean_message quiet_mode "  Proving the introduction rules ...";
berghofe@5094
   342
berghofe@21024
   343
    val unfold = funpow k (fn th => th RS fun_cong)
berghofe@21024
   344
      (mono RS (fp_def RS
haftmann@32652
   345
        (if coind then @{thm def_gfp_unfold} else @{thm def_lfp_unfold})));
berghofe@5094
   346
berghofe@5094
   347
    fun select_disj 1 1 = []
berghofe@5094
   348
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   349
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   350
berghofe@21024
   351
    val rules = [refl, TrueI, notFalseI, exI, conjI];
berghofe@21024
   352
berghofe@22605
   353
    val intrs = map_index (fn (i, intr) => rulify
wenzelm@32970
   354
      (Skip_Proof.prove ctxt (map (fst o dest_Free) params) [] intr (fn _ => EVERY
berghofe@21024
   355
       [rewrite_goals_tac rec_preds_defs,
berghofe@21024
   356
        rtac (unfold RS iffD2) 1,
berghofe@21024
   357
        EVERY1 (select_disj (length intr_ts) (i + 1)),
wenzelm@17985
   358
        (*Not ares_tac, since refl must be tried before any equality assumptions;
wenzelm@17985
   359
          backtracking may occur if the premises have extra variables!*)
berghofe@21024
   360
        DEPTH_SOLVE_1 (resolve_tac rules 1 APPEND assume_tac 1)]))) intr_ts
berghofe@5094
   361
berghofe@5094
   362
  in (intrs, unfold) end;
berghofe@5094
   363
wenzelm@6424
   364
wenzelm@10735
   365
(* prove elimination rules *)
berghofe@5094
   366
wenzelm@26477
   367
fun prove_elims quiet_mode cs params intr_ts intr_names unfold rec_preds_defs ctxt =
berghofe@5094
   368
  let
wenzelm@26477
   369
    val _ = clean_message quiet_mode "  Proving the elimination rules ...";
berghofe@5094
   370
berghofe@22605
   371
    val ([pname], ctxt') = ctxt |>
berghofe@22605
   372
      Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
berghofe@22605
   373
      Variable.variant_fixes ["P"];
berghofe@21024
   374
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@21024
   375
berghofe@21024
   376
    fun dest_intr r =
berghofe@21024
   377
      (the (dest_predicate cs params (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))),
berghofe@21024
   378
       Logic.strip_assums_hyp r, Logic.strip_params r);
berghofe@21024
   379
berghofe@21024
   380
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@21024
   381
berghofe@21024
   382
    val rules1 = [disjE, exE, FalseE];
berghofe@21024
   383
    val rules2 = [conjE, FalseE, notTrueE];
berghofe@21024
   384
berghofe@21024
   385
    fun prove_elim c =
berghofe@21024
   386
      let
haftmann@33077
   387
        val Ts = arg_types_of (length params) c;
berghofe@21024
   388
        val (anames, ctxt'') = Variable.variant_fixes (mk_names "a" (length Ts)) ctxt';
berghofe@21024
   389
        val frees = map Free (anames ~~ Ts);
berghofe@21024
   390
berghofe@21024
   391
        fun mk_elim_prem ((_, _, us, _), ts, params') =
berghofe@21024
   392
          list_all (params',
berghofe@21024
   393
            Logic.list_implies (map (HOLogic.mk_Trueprop o HOLogic.mk_eq)
berghofe@21024
   394
              (frees ~~ us) @ ts, P));
wenzelm@33317
   395
        val c_intrs = filter (equal c o #1 o #1 o #1) intrs;
berghofe@21024
   396
        val prems = HOLogic.mk_Trueprop (list_comb (c, params @ frees)) ::
berghofe@21024
   397
           map mk_elim_prem (map #1 c_intrs)
berghofe@21024
   398
      in
wenzelm@32970
   399
        (Skip_Proof.prove ctxt'' [] prems P
berghofe@21024
   400
          (fn {prems, ...} => EVERY
berghofe@21024
   401
            [cut_facts_tac [hd prems] 1,
berghofe@21024
   402
             rewrite_goals_tac rec_preds_defs,
berghofe@21024
   403
             dtac (unfold RS iffD1) 1,
berghofe@21024
   404
             REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@21024
   405
             REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@21024
   406
             EVERY (map (fn prem =>
berghofe@21024
   407
               DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_preds_defs prem, conjI] 1)) (tl prems))])
berghofe@21024
   408
          |> rulify
berghofe@21048
   409
          |> singleton (ProofContext.export ctxt'' ctxt),
berghofe@21048
   410
         map #2 c_intrs)
berghofe@21024
   411
      end
berghofe@21024
   412
berghofe@21024
   413
   in map prove_elim cs end;
berghofe@5094
   414
wenzelm@6424
   415
wenzelm@10735
   416
(* derivation of simplified elimination rules *)
berghofe@5094
   417
wenzelm@11682
   418
local
wenzelm@11682
   419
wenzelm@11682
   420
(*delete needless equality assumptions*)
wenzelm@29064
   421
val refl_thin = Goal.prove_global @{theory HOL} [] [] @{prop "!!P. a = a ==> P ==> P"}
haftmann@22838
   422
  (fn _ => assume_tac 1);
berghofe@21024
   423
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
wenzelm@11682
   424
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
wenzelm@11682
   425
berghofe@23762
   426
fun simp_case_tac ss i =
berghofe@23762
   427
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i;
wenzelm@21367
   428
wenzelm@11682
   429
in
wenzelm@9598
   430
wenzelm@21367
   431
fun mk_cases ctxt prop =
wenzelm@7107
   432
  let
wenzelm@21367
   433
    val thy = ProofContext.theory_of ctxt;
wenzelm@32149
   434
    val ss = simpset_of ctxt;
wenzelm@21367
   435
wenzelm@21526
   436
    fun err msg =
wenzelm@21526
   437
      error (Pretty.string_of (Pretty.block
wenzelm@24920
   438
        [Pretty.str msg, Pretty.fbrk, Syntax.pretty_term ctxt prop]));
wenzelm@21526
   439
wenzelm@24861
   440
    val elims = Induct.find_casesP ctxt prop;
wenzelm@21367
   441
wenzelm@21367
   442
    val cprop = Thm.cterm_of thy prop;
berghofe@23762
   443
    val tac = ALLGOALS (simp_case_tac ss) THEN prune_params_tac;
wenzelm@21367
   444
    fun mk_elim rl =
wenzelm@21367
   445
      Thm.implies_intr cprop (Tactic.rule_by_tactic tac (Thm.assume cprop RS rl))
wenzelm@21367
   446
      |> singleton (Variable.export (Variable.auto_fixes prop ctxt) ctxt);
wenzelm@7107
   447
  in
wenzelm@7107
   448
    (case get_first (try mk_elim) elims of
skalberg@15531
   449
      SOME r => r
wenzelm@21526
   450
    | NONE => err "Proposition not an inductive predicate:")
wenzelm@7107
   451
  end;
wenzelm@7107
   452
wenzelm@11682
   453
end;
wenzelm@11682
   454
wenzelm@7107
   455
wenzelm@21367
   456
(* inductive_cases *)
wenzelm@7107
   457
wenzelm@21367
   458
fun gen_inductive_cases prep_att prep_prop args lthy =
wenzelm@9598
   459
  let
wenzelm@21367
   460
    val thy = ProofContext.theory_of lthy;
wenzelm@12876
   461
    val facts = args |> map (fn ((a, atts), props) =>
wenzelm@21367
   462
      ((a, map (prep_att thy) atts),
wenzelm@21367
   463
        map (Thm.no_attributes o single o mk_cases lthy o prep_prop lthy) props));
haftmann@31177
   464
  in lthy |> LocalTheory.notes Thm.generatedK facts |>> map snd end;
berghofe@5094
   465
wenzelm@24509
   466
val inductive_cases = gen_inductive_cases Attrib.intern_src Syntax.read_prop;
wenzelm@24509
   467
val inductive_cases_i = gen_inductive_cases (K I) Syntax.check_prop;
wenzelm@7107
   468
wenzelm@6424
   469
wenzelm@30722
   470
val ind_cases_setup =
wenzelm@30722
   471
  Method.setup @{binding ind_cases}
wenzelm@30722
   472
    (Scan.lift (Scan.repeat1 Args.name_source --
wenzelm@30722
   473
      Scan.optional (Args.$$$ "for" |-- Scan.repeat1 Args.name) []) >>
wenzelm@30722
   474
      (fn (raw_props, fixes) => fn ctxt =>
wenzelm@30722
   475
        let
wenzelm@30722
   476
          val (_, ctxt') = Variable.add_fixes fixes ctxt;
wenzelm@30722
   477
          val props = Syntax.read_props ctxt' raw_props;
wenzelm@30722
   478
          val ctxt'' = fold Variable.declare_term props ctxt';
wenzelm@30722
   479
          val rules = ProofContext.export ctxt'' ctxt (map (mk_cases ctxt'') props)
wenzelm@30722
   480
        in Method.erule 0 rules end))
wenzelm@30722
   481
    "dynamic case analysis on predicates";
wenzelm@9598
   482
wenzelm@9598
   483
wenzelm@10735
   484
(* prove induction rule *)
berghofe@5094
   485
wenzelm@26477
   486
fun prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono
berghofe@21024
   487
    fp_def rec_preds_defs ctxt =
berghofe@5094
   488
  let
wenzelm@26477
   489
    val _ = clean_message quiet_mode "  Proving the induction rule ...";
wenzelm@20047
   490
    val thy = ProofContext.theory_of ctxt;
berghofe@5094
   491
berghofe@21024
   492
    (* predicates for induction rule *)
berghofe@21024
   493
berghofe@22605
   494
    val (pnames, ctxt') = ctxt |>
berghofe@22605
   495
      Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
berghofe@22605
   496
      Variable.variant_fixes (mk_names "P" (length cs));
haftmann@33077
   497
    val preds = map2 (curry Free) pnames
haftmann@33077
   498
      (map (fn c => arg_types_of (length params) c ---> HOLogic.boolT) cs);
berghofe@21024
   499
berghofe@21024
   500
    (* transform an introduction rule into a premise for induction rule *)
berghofe@21024
   501
berghofe@21024
   502
    fun mk_ind_prem r =
berghofe@21024
   503
      let
berghofe@21024
   504
        fun subst s = (case dest_predicate cs params s of
berghofe@21024
   505
            SOME (_, i, ys, (_, Ts)) =>
berghofe@21024
   506
              let
berghofe@21024
   507
                val k = length Ts;
berghofe@21024
   508
                val bs = map Bound (k - 1 downto 0);
berghofe@23762
   509
                val P = list_comb (List.nth (preds, i),
berghofe@23762
   510
                  map (incr_boundvars k) ys @ bs);
berghofe@21024
   511
                val Q = list_abs (mk_names "x" k ~~ Ts,
berghofe@23762
   512
                  HOLogic.mk_binop inductive_conj_name
berghofe@23762
   513
                    (list_comb (incr_boundvars k s, bs), P))
berghofe@21024
   514
              in (Q, case Ts of [] => SOME (s, P) | _ => NONE) end
berghofe@21024
   515
          | NONE => (case s of
berghofe@21024
   516
              (t $ u) => (fst (subst t) $ fst (subst u), NONE)
berghofe@21024
   517
            | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
berghofe@21024
   518
            | _ => (s, NONE)));
berghofe@7293
   519
berghofe@21024
   520
        fun mk_prem (s, prems) = (case subst s of
berghofe@21024
   521
              (_, SOME (t, u)) => t :: u :: prems
berghofe@21024
   522
            | (t, _) => t :: prems);
berghofe@21024
   523
berghofe@21024
   524
        val SOME (_, i, ys, _) = dest_predicate cs params
berghofe@21024
   525
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))
berghofe@21024
   526
berghofe@21024
   527
      in list_all_free (Logic.strip_params r,
wenzelm@30190
   528
        Logic.list_implies (map HOLogic.mk_Trueprop (List.foldr mk_prem
berghofe@21024
   529
          [] (map HOLogic.dest_Trueprop (Logic.strip_assums_hyp r))),
berghofe@21024
   530
            HOLogic.mk_Trueprop (list_comb (List.nth (preds, i), ys))))
berghofe@21024
   531
      end;
berghofe@21024
   532
berghofe@21024
   533
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@21024
   534
wenzelm@21526
   535
berghofe@21024
   536
    (* make conclusions for induction rules *)
berghofe@21024
   537
berghofe@21024
   538
    val Tss = map (binder_types o fastype_of) preds;
berghofe@21024
   539
    val (xnames, ctxt'') =
berghofe@21024
   540
      Variable.variant_fixes (mk_names "x" (length (flat Tss))) ctxt';
berghofe@21024
   541
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@21024
   542
        (map (fn (((xnames, Ts), c), P) =>
berghofe@21024
   543
           let val frees = map Free (xnames ~~ Ts)
berghofe@21024
   544
           in HOLogic.mk_imp
berghofe@21024
   545
             (list_comb (c, params @ frees), list_comb (P, frees))
berghofe@21024
   546
           end) (unflat Tss xnames ~~ Tss ~~ cs ~~ preds)));
berghofe@5094
   547
paulson@13626
   548
berghofe@5094
   549
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   550
berghofe@21024
   551
    val ind_pred = fold_rev lambda (bs @ xs) (foldr1 HOLogic.mk_conj
wenzelm@30190
   552
      (map_index (fn (i, P) => List.foldr HOLogic.mk_imp
berghofe@21024
   553
         (list_comb (P, make_args' argTs xs (binder_types (fastype_of P))))
berghofe@21024
   554
         (make_bool_args HOLogic.mk_not I bs i)) preds));
berghofe@5094
   555
berghofe@5094
   556
    val ind_concl = HOLogic.mk_Trueprop
haftmann@23881
   557
      (HOLogic.mk_binrel "HOL.ord_class.less_eq" (rec_const, ind_pred));
berghofe@5094
   558
haftmann@32652
   559
    val raw_fp_induct = (mono RS (fp_def RS @{thm def_lfp_induct}));
paulson@13626
   560
wenzelm@32970
   561
    val induct = Skip_Proof.prove ctxt'' [] ind_prems ind_concl
wenzelm@20248
   562
      (fn {prems, ...} => EVERY
wenzelm@17985
   563
        [rewrite_goals_tac [inductive_conj_def],
berghofe@21024
   564
         DETERM (rtac raw_fp_induct 1),
haftmann@32652
   565
         REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI}] 1),
haftmann@32610
   566
         rewrite_goals_tac simp_thms'',
berghofe@21024
   567
         (*This disjE separates out the introduction rules*)
berghofe@21024
   568
         REPEAT (FIRSTGOAL (eresolve_tac [disjE, exE, FalseE])),
berghofe@5094
   569
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   570
           some premise involves disjunction.*)
paulson@13747
   571
         REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
berghofe@21024
   572
         REPEAT (FIRSTGOAL
berghofe@21024
   573
           (resolve_tac [conjI, impI] ORELSE' (etac notE THEN' atac))),
berghofe@21024
   574
         EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [rewrite_rule
haftmann@32610
   575
             (inductive_conj_def :: rec_preds_defs @ simp_thms'') prem,
berghofe@22980
   576
           conjI, refl] 1)) prems)]);
berghofe@5094
   577
wenzelm@32970
   578
    val lemma = Skip_Proof.prove ctxt'' [] []
wenzelm@17985
   579
      (Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
berghofe@21024
   580
        [rewrite_goals_tac rec_preds_defs,
berghofe@5094
   581
         REPEAT (EVERY
berghofe@5094
   582
           [REPEAT (resolve_tac [conjI, impI] 1),
haftmann@32652
   583
            REPEAT (eresolve_tac [@{thm le_funE}, @{thm le_boolE}] 1),
berghofe@21024
   584
            atac 1,
berghofe@21024
   585
            rewrite_goals_tac simp_thms',
berghofe@21024
   586
            atac 1])])
berghofe@5094
   587
berghofe@21024
   588
  in singleton (ProofContext.export ctxt'' ctxt) (induct RS lemma) end;
berghofe@5094
   589
wenzelm@6424
   590
wenzelm@6424
   591
berghofe@21024
   592
(** specification of (co)inductive predicates **)
wenzelm@10729
   593
wenzelm@29388
   594
fun mk_ind_def quiet_mode skip_mono fork_mono alt_name coind cs intr_ts monos params cnames_syn ctxt =
wenzelm@33278
   595
  let  (* FIXME proper naming convention: lthy *)
haftmann@24915
   596
    val fp_name = if coind then @{const_name Inductive.gfp} else @{const_name Inductive.lfp};
berghofe@5094
   597
haftmann@33077
   598
    val argTs = fold (combine (op =) o arg_types_of (length params)) cs [];
berghofe@21024
   599
    val k = log 2 1 (length cs);
berghofe@21024
   600
    val predT = replicate k HOLogic.boolT ---> argTs ---> HOLogic.boolT;
berghofe@21024
   601
    val p :: xs = map Free (Variable.variant_frees ctxt intr_ts
berghofe@21024
   602
      (("p", predT) :: (mk_names "x" (length argTs) ~~ argTs)));
berghofe@21024
   603
    val bs = map Free (Variable.variant_frees ctxt (p :: xs @ intr_ts)
berghofe@21024
   604
      (map (rpair HOLogic.boolT) (mk_names "b" k)));
berghofe@21024
   605
berghofe@21024
   606
    fun subst t = (case dest_predicate cs params t of
berghofe@21024
   607
        SOME (_, i, ts, (Ts, Us)) =>
berghofe@23762
   608
          let
berghofe@23762
   609
            val l = length Us;
berghofe@23762
   610
            val zs = map Bound (l - 1 downto 0)
berghofe@21024
   611
          in
berghofe@21024
   612
            list_abs (map (pair "z") Us, list_comb (p,
berghofe@23762
   613
              make_bool_args' bs i @ make_args argTs
berghofe@23762
   614
                ((map (incr_boundvars l) ts ~~ Ts) @ (zs ~~ Us))))
berghofe@21024
   615
          end
berghofe@21024
   616
      | NONE => (case t of
berghofe@21024
   617
          t1 $ t2 => subst t1 $ subst t2
berghofe@21024
   618
        | Abs (x, T, u) => Abs (x, T, subst u)
berghofe@21024
   619
        | _ => t));
berghofe@5149
   620
berghofe@5094
   621
    (* transform an introduction rule into a conjunction  *)
berghofe@21024
   622
    (*   [| p_i t; ... |] ==> p_j u                       *)
berghofe@5094
   623
    (* is transformed into                                *)
berghofe@21024
   624
    (*   b_j & x_j = u & p b_j t & ...                    *)
berghofe@5094
   625
berghofe@5094
   626
    fun transform_rule r =
berghofe@5094
   627
      let
berghofe@21024
   628
        val SOME (_, i, ts, (Ts, _)) = dest_predicate cs params
berghofe@21048
   629
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r));
berghofe@21048
   630
        val ps = make_bool_args HOLogic.mk_not I bs i @
berghofe@21048
   631
          map HOLogic.mk_eq (make_args' argTs xs Ts ~~ ts) @
berghofe@21048
   632
          map (subst o HOLogic.dest_Trueprop)
berghofe@21048
   633
            (Logic.strip_assums_hyp r)
wenzelm@30190
   634
      in List.foldr (fn ((x, T), P) => HOLogic.exists_const T $ (Abs (x, T, P)))
berghofe@21048
   635
        (if null ps then HOLogic.true_const else foldr1 HOLogic.mk_conj ps)
berghofe@21048
   636
        (Logic.strip_params r)
berghofe@5094
   637
      end
berghofe@5094
   638
berghofe@5094
   639
    (* make a disjunction of all introduction rules *)
berghofe@5094
   640
berghofe@21024
   641
    val fp_fun = fold_rev lambda (p :: bs @ xs)
berghofe@21024
   642
      (if null intr_ts then HOLogic.false_const
berghofe@21024
   643
       else foldr1 HOLogic.mk_disj (map transform_rule intr_ts));
berghofe@5094
   644
berghofe@21024
   645
    (* add definiton of recursive predicates to theory *)
berghofe@5094
   646
wenzelm@28083
   647
    val rec_name =
haftmann@28965
   648
      if Binding.is_empty alt_name then
wenzelm@30223
   649
        Binding.name (space_implode "_" (map (Binding.name_of o fst) cnames_syn))
wenzelm@28083
   650
      else alt_name;
berghofe@5094
   651
wenzelm@33278
   652
    val ((rec_const, (_, fp_def)), ctxt') = ctxt
wenzelm@33278
   653
      |> LocalTheory.conceal
wenzelm@33278
   654
      |> LocalTheory.define Thm.internalK
berghofe@21024
   655
        ((rec_name, case cnames_syn of [(_, syn)] => syn | _ => NoSyn),
blanchet@33577
   656
         ((Binding.empty, [Attrib.internal (K Nitpick_Defs.add)]),
blanchet@33577
   657
         fold_rev lambda params
wenzelm@33278
   658
           (Const (fp_name, (predT --> predT) --> predT) $ fp_fun)))
wenzelm@33278
   659
      ||> LocalTheory.restore_naming ctxt;
berghofe@21024
   660
    val fp_def' = Simplifier.rewrite (HOL_basic_ss addsimps [fp_def])
berghofe@21024
   661
      (cterm_of (ProofContext.theory_of ctxt') (list_comb (rec_const, params)));
wenzelm@33278
   662
    val specs =
wenzelm@33278
   663
      if length cs < 2 then []
wenzelm@33278
   664
      else
wenzelm@33278
   665
        map_index (fn (i, (name_mx, c)) =>
wenzelm@33278
   666
          let
wenzelm@33278
   667
            val Ts = arg_types_of (length params) c;
wenzelm@33278
   668
            val xs = map Free (Variable.variant_frees ctxt intr_ts
wenzelm@33278
   669
              (mk_names "x" (length Ts) ~~ Ts))
wenzelm@33278
   670
          in
wenzelm@33278
   671
            (name_mx, (Attrib.empty_binding, fold_rev lambda (params @ xs)
wenzelm@33278
   672
              (list_comb (rec_const, params @ make_bool_args' bs i @
wenzelm@33278
   673
                make_args argTs (xs ~~ Ts)))))
wenzelm@33278
   674
          end) (cnames_syn ~~ cs);
wenzelm@33278
   675
    val (consts_defs, ctxt'') = ctxt'
wenzelm@33278
   676
      |> LocalTheory.conceal
wenzelm@33278
   677
      |> fold_map (LocalTheory.define Thm.internalK) specs
wenzelm@33278
   678
      ||> LocalTheory.restore_naming ctxt';
berghofe@21024
   679
    val preds = (case cs of [_] => [rec_const] | _ => map #1 consts_defs);
berghofe@5094
   680
wenzelm@29388
   681
    val mono = prove_mono quiet_mode skip_mono fork_mono predT fp_fun monos ctxt'';
wenzelm@29388
   682
    val ((_, [mono']), ctxt''') =
wenzelm@33278
   683
      LocalTheory.note Thm.internalK (apfst Binding.conceal Attrib.empty_binding, [mono]) ctxt'';
berghofe@5094
   684
wenzelm@29388
   685
  in (ctxt''', rec_name, mono', fp_def', map (#2 o #2) consts_defs,
berghofe@21024
   686
    list_comb (rec_const, params), preds, argTs, bs, xs)
berghofe@21024
   687
  end;
berghofe@5094
   688
wenzelm@28083
   689
fun declare_rules kind rec_binding coind no_ind cnames intrs intr_bindings intr_atts
berghofe@23762
   690
      elims raw_induct ctxt =
berghofe@23762
   691
  let
wenzelm@30223
   692
    val rec_name = Binding.name_of rec_binding;
haftmann@32773
   693
    fun rec_qualified qualified = Binding.qualify qualified rec_name;
wenzelm@30223
   694
    val intr_names = map Binding.name_of intr_bindings;
berghofe@23762
   695
    val ind_case_names = RuleCases.case_names intr_names;
berghofe@23762
   696
    val induct =
berghofe@23762
   697
      if coind then
berghofe@23762
   698
        (raw_induct, [RuleCases.case_names [rec_name],
berghofe@23762
   699
          RuleCases.case_conclusion (rec_name, intr_names),
wenzelm@24861
   700
          RuleCases.consumes 1, Induct.coinduct_pred (hd cnames)])
berghofe@23762
   701
      else if no_ind orelse length cnames > 1 then
berghofe@23762
   702
        (raw_induct, [ind_case_names, RuleCases.consumes 0])
berghofe@23762
   703
      else (raw_induct RSN (2, rev_mp), [ind_case_names, RuleCases.consumes 1]);
berghofe@23762
   704
berghofe@23762
   705
    val (intrs', ctxt1) =
berghofe@23762
   706
      ctxt |>
wenzelm@26128
   707
      LocalTheory.notes kind
wenzelm@33278
   708
        (map (rec_qualified false) intr_bindings ~~ intr_atts ~~
wenzelm@33278
   709
          map (fn th => [([th],
blanchet@29868
   710
           [Attrib.internal (K (ContextRules.intro_query NONE)),
blanchet@33056
   711
            Attrib.internal (K Nitpick_Intros.add)])]) intrs) |>>
berghofe@24744
   712
      map (hd o snd);
berghofe@23762
   713
    val (((_, elims'), (_, [induct'])), ctxt2) =
berghofe@23762
   714
      ctxt1 |>
haftmann@32773
   715
      LocalTheory.note kind ((rec_qualified true (Binding.name "intros"), []), intrs') ||>>
berghofe@23762
   716
      fold_map (fn (name, (elim, cases)) =>
haftmann@32773
   717
        LocalTheory.note kind ((Binding.qualify true (Long_Name.base_name name) (Binding.name "cases"),
berghofe@23762
   718
          [Attrib.internal (K (RuleCases.case_names cases)),
berghofe@23762
   719
           Attrib.internal (K (RuleCases.consumes 1)),
wenzelm@24861
   720
           Attrib.internal (K (Induct.cases_pred name)),
berghofe@23762
   721
           Attrib.internal (K (ContextRules.elim_query NONE))]), [elim]) #>
berghofe@23762
   722
        apfst (hd o snd)) (if null elims then [] else cnames ~~ elims) ||>>
wenzelm@28107
   723
      LocalTheory.note kind
haftmann@32773
   724
        ((rec_qualified true (Binding.name (coind_prefix coind ^ "induct")),
wenzelm@28107
   725
          map (Attrib.internal o K) (#2 induct)), [rulify (#1 induct)]);
berghofe@23762
   726
berghofe@23762
   727
    val ctxt3 = if no_ind orelse coind then ctxt2 else
wenzelm@32172
   728
      let val inducts = cnames ~~ Project_Rule.projects ctxt2 (1 upto length cnames) induct'
berghofe@23762
   729
      in
berghofe@23762
   730
        ctxt2 |>
haftmann@32773
   731
        LocalTheory.notes kind [((rec_qualified true (Binding.name "inducts"), []),
berghofe@23762
   732
          inducts |> map (fn (name, th) => ([th],
berghofe@23762
   733
            [Attrib.internal (K ind_case_names),
berghofe@23762
   734
             Attrib.internal (K (RuleCases.consumes 1)),
wenzelm@24861
   735
             Attrib.internal (K (Induct.induct_pred name))])))] |> snd
berghofe@23762
   736
      end
berghofe@23762
   737
  in (intrs', elims', induct', ctxt3) end;
berghofe@23762
   738
berghofe@26534
   739
type inductive_flags =
haftmann@29581
   740
  {quiet_mode: bool, verbose: bool, kind: string, alt_name: binding,
wenzelm@29388
   741
   coind: bool, no_elim: bool, no_ind: bool, skip_mono: bool, fork_mono: bool}
berghofe@26534
   742
berghofe@26534
   743
type add_ind_def =
berghofe@26534
   744
  inductive_flags ->
wenzelm@28084
   745
  term list -> (Attrib.binding * term) list -> thm list ->
haftmann@29581
   746
  term list -> (binding * mixfix) list ->
berghofe@23762
   747
  local_theory -> inductive_result * local_theory
berghofe@23762
   748
wenzelm@29388
   749
fun add_ind_def {quiet_mode, verbose, kind, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono}
wenzelm@24815
   750
    cs intros monos params cnames_syn ctxt =
berghofe@9072
   751
  let
wenzelm@25288
   752
    val _ = null cnames_syn andalso error "No inductive predicates given";
wenzelm@30223
   753
    val names = map (Binding.name_of o fst) cnames_syn;
wenzelm@26477
   754
    val _ = message (quiet_mode andalso not verbose)
wenzelm@28083
   755
      ("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^ commas_quote names);
berghofe@9072
   756
berghofe@30089
   757
    val cnames = map (LocalTheory.full_name ctxt o #1) cnames_syn;  (* FIXME *)
berghofe@23762
   758
    val ((intr_names, intr_atts), intr_ts) =
berghofe@23762
   759
      apfst split_list (split_list (map (check_rule ctxt cs params) intros));
berghofe@21024
   760
berghofe@21024
   761
    val (ctxt1, rec_name, mono, fp_def, rec_preds_defs, rec_const, preds,
wenzelm@29388
   762
      argTs, bs, xs) = mk_ind_def quiet_mode skip_mono fork_mono alt_name coind cs intr_ts
berghofe@26534
   763
        monos params cnames_syn ctxt;
berghofe@9072
   764
wenzelm@26477
   765
    val (intrs, unfold) = prove_intrs quiet_mode coind mono fp_def (length bs + length xs)
berghofe@22605
   766
      params intr_ts rec_preds_defs ctxt1;
berghofe@21048
   767
    val elims = if no_elim then [] else
wenzelm@30223
   768
      prove_elims quiet_mode cs params intr_ts (map Binding.name_of intr_names)
wenzelm@28083
   769
        unfold rec_preds_defs ctxt1;
berghofe@22605
   770
    val raw_induct = zero_var_indexes
berghofe@21024
   771
      (if no_ind then Drule.asm_rl else
berghofe@23762
   772
       if coind then
berghofe@23762
   773
         singleton (ProofContext.export
berghofe@23762
   774
           (snd (Variable.add_fixes (map (fst o dest_Free) params) ctxt1)) ctxt1)
wenzelm@28839
   775
           (rotate_prems ~1 (ObjectLogic.rulify
wenzelm@28839
   776
             (fold_rule rec_preds_defs
haftmann@32652
   777
               (rewrite_rule simp_thms'''
haftmann@32652
   778
                (mono RS (fp_def RS @{thm def_coinduct}))))))
berghofe@21024
   779
       else
wenzelm@26477
   780
         prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono fp_def
berghofe@22605
   781
           rec_preds_defs ctxt1);
berghofe@5094
   782
wenzelm@26128
   783
    val (intrs', elims', induct, ctxt2) = declare_rules kind rec_name coind no_ind
berghofe@23762
   784
      cnames intrs intr_names intr_atts elims raw_induct ctxt1;
berghofe@21048
   785
berghofe@21048
   786
    val result =
berghofe@21048
   787
      {preds = preds,
berghofe@21048
   788
       intrs = intrs',
berghofe@21048
   789
       elims = elims',
berghofe@21048
   790
       raw_induct = rulify raw_induct,
berghofe@23762
   791
       induct = induct};
wenzelm@21367
   792
berghofe@23762
   793
    val ctxt3 = ctxt2
wenzelm@21526
   794
      |> LocalTheory.declaration (fn phi =>
wenzelm@25380
   795
        let val result' = morph_result phi result;
wenzelm@25380
   796
        in put_inductives cnames (*global names!?*) ({names = cnames, coind = coind}, result') end);
berghofe@23762
   797
  in (result, ctxt3) end;
berghofe@5094
   798
wenzelm@6424
   799
wenzelm@10735
   800
(* external interfaces *)
berghofe@5094
   801
wenzelm@26477
   802
fun gen_add_inductive_i mk_def
wenzelm@29388
   803
    (flags as {quiet_mode, verbose, kind, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono})
wenzelm@25029
   804
    cnames_syn pnames spec monos lthy =
berghofe@5094
   805
  let
wenzelm@25029
   806
    val thy = ProofContext.theory_of lthy;
wenzelm@6424
   807
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
berghofe@5094
   808
berghofe@21766
   809
wenzelm@25029
   810
    (* abbrevs *)
wenzelm@25029
   811
wenzelm@30223
   812
    val (_, ctxt1) = Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn) lthy;
berghofe@21766
   813
wenzelm@25029
   814
    fun get_abbrev ((name, atts), t) =
wenzelm@25029
   815
      if can (Logic.strip_assums_concl #> Logic.dest_equals) t then
wenzelm@25029
   816
        let
haftmann@29006
   817
          val _ = Binding.is_empty name andalso null atts orelse
wenzelm@25029
   818
            error "Abbreviations may not have names or attributes";
wenzelm@25029
   819
          val ((x, T), rhs) = LocalDefs.abs_def (snd (LocalDefs.cert_def ctxt1 t));
wenzelm@28083
   820
          val var =
wenzelm@30223
   821
            (case find_first (fn ((c, _), _) => Binding.name_of c = x) cnames_syn of
wenzelm@25029
   822
              NONE => error ("Undeclared head of abbreviation " ^ quote x)
wenzelm@28083
   823
            | SOME ((b, T'), mx) =>
wenzelm@25029
   824
                if T <> T' then error ("Bad type specification for abbreviation " ^ quote x)
wenzelm@28083
   825
                else (b, mx));
wenzelm@28083
   826
        in SOME (var, rhs) end
wenzelm@25029
   827
      else NONE;
berghofe@21766
   828
wenzelm@25029
   829
    val abbrevs = map_filter get_abbrev spec;
wenzelm@30223
   830
    val bs = map (Binding.name_of o fst o fst) abbrevs;
wenzelm@25029
   831
berghofe@21766
   832
wenzelm@25029
   833
    (* predicates *)
berghofe@21766
   834
wenzelm@25029
   835
    val pre_intros = filter_out (is_some o get_abbrev) spec;
wenzelm@30223
   836
    val cnames_syn' = filter_out (member (op =) bs o Binding.name_of o fst o fst) cnames_syn;
wenzelm@30223
   837
    val cs = map (Free o apfst Binding.name_of o fst) cnames_syn';
wenzelm@25029
   838
    val ps = map Free pnames;
berghofe@5094
   839
wenzelm@30223
   840
    val (_, ctxt2) = lthy |> Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn');
wenzelm@25143
   841
    val _ = map (fn abbr => LocalDefs.fixed_abbrev abbr ctxt2) abbrevs;
wenzelm@25143
   842
    val ctxt3 = ctxt2 |> fold (snd oo LocalDefs.fixed_abbrev) abbrevs;
wenzelm@25143
   843
    val expand = Assumption.export_term ctxt3 lthy #> ProofContext.cert_term lthy;
wenzelm@25029
   844
wenzelm@25029
   845
    fun close_rule r = list_all_free (rev (fold_aterms
berghofe@21024
   846
      (fn t as Free (v as (s, _)) =>
wenzelm@25029
   847
          if Variable.is_fixed ctxt1 s orelse
wenzelm@25029
   848
            member (op =) ps t then I else insert (op =) v
wenzelm@25029
   849
        | _ => I) r []), r);
berghofe@5094
   850
haftmann@26736
   851
    val intros = map (apsnd (Syntax.check_term lthy #> close_rule #> expand)) pre_intros;
wenzelm@25029
   852
    val preds = map (fn ((c, _), mx) => (c, mx)) cnames_syn';
berghofe@21048
   853
  in
wenzelm@25029
   854
    lthy
wenzelm@25029
   855
    |> mk_def flags cs intros monos ps preds
wenzelm@25029
   856
    ||> fold (snd oo LocalTheory.abbrev Syntax.mode_default) abbrevs
berghofe@21048
   857
  end;
berghofe@5094
   858
wenzelm@29388
   859
fun gen_add_inductive mk_def verbose coind cnames_syn pnames_syn intro_srcs raw_monos int lthy =
berghofe@5094
   860
  let
wenzelm@30486
   861
    val ((vars, intrs), _) = lthy
wenzelm@30486
   862
      |> ProofContext.set_mode ProofContext.mode_abbrev
wenzelm@30486
   863
      |> Specification.read_spec (cnames_syn @ pnames_syn) intro_srcs;
wenzelm@24721
   864
    val (cs, ps) = chop (length cnames_syn) vars;
wenzelm@24721
   865
    val monos = Attrib.eval_thms lthy raw_monos;
haftmann@31177
   866
    val flags = {quiet_mode = false, verbose = verbose, kind = Thm.generatedK,
wenzelm@29388
   867
      alt_name = Binding.empty, coind = coind, no_elim = false, no_ind = false,
wenzelm@29388
   868
      skip_mono = false, fork_mono = not int};
wenzelm@26128
   869
  in
wenzelm@26128
   870
    lthy
wenzelm@33171
   871
    |> LocalTheory.set_group (serial ())
wenzelm@30223
   872
    |> gen_add_inductive_i mk_def flags cs (map (apfst Binding.name_of o fst) ps) intrs monos
wenzelm@26128
   873
  end;
berghofe@5094
   874
berghofe@23762
   875
val add_inductive_i = gen_add_inductive_i add_ind_def;
berghofe@23762
   876
val add_inductive = gen_add_inductive add_ind_def;
berghofe@23762
   877
wenzelm@26128
   878
fun add_inductive_global group flags cnames_syn pnames pre_intros monos thy =
wenzelm@25380
   879
  let
haftmann@29006
   880
    val name = Sign.full_name thy (fst (fst (hd cnames_syn)));
wenzelm@25380
   881
    val ctxt' = thy
wenzelm@25380
   882
      |> TheoryTarget.init NONE
wenzelm@26128
   883
      |> LocalTheory.set_group group
wenzelm@25380
   884
      |> add_inductive_i flags cnames_syn pnames pre_intros monos |> snd
wenzelm@25380
   885
      |> LocalTheory.exit;
wenzelm@25380
   886
    val info = #2 (the_inductive ctxt' name);
wenzelm@25380
   887
  in (info, ProofContext.theory_of ctxt') end;
wenzelm@6424
   888
wenzelm@6424
   889
berghofe@22789
   890
(* read off arities of inductive predicates from raw induction rule *)
berghofe@22789
   891
fun arities_of induct =
berghofe@22789
   892
  map (fn (_ $ t $ u) =>
berghofe@22789
   893
      (fst (dest_Const (head_of t)), length (snd (strip_comb u))))
berghofe@22789
   894
    (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@22789
   895
berghofe@22789
   896
(* read off parameters of inductive predicate from raw induction rule *)
berghofe@22789
   897
fun params_of induct =
berghofe@22789
   898
  let
berghofe@22789
   899
    val (_ $ t $ u :: _) =
berghofe@22789
   900
      HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct));
berghofe@22789
   901
    val (_, ts) = strip_comb t;
berghofe@22789
   902
    val (_, us) = strip_comb u
berghofe@22789
   903
  in
berghofe@22789
   904
    List.take (ts, length ts - length us)
berghofe@22789
   905
  end;
berghofe@22789
   906
berghofe@22789
   907
val pname_of_intr =
berghofe@22789
   908
  concl_of #> HOLogic.dest_Trueprop #> head_of #> dest_Const #> fst;
berghofe@22789
   909
berghofe@22789
   910
(* partition introduction rules according to predicate name *)
berghofe@25822
   911
fun gen_partition_rules f induct intros =
berghofe@25822
   912
  fold_rev (fn r => AList.map_entry op = (pname_of_intr (f r)) (cons r)) intros
berghofe@22789
   913
    (map (rpair [] o fst) (arities_of induct));
berghofe@22789
   914
berghofe@25822
   915
val partition_rules = gen_partition_rules I;
berghofe@25822
   916
fun partition_rules' induct = gen_partition_rules fst induct;
berghofe@25822
   917
berghofe@22789
   918
fun unpartition_rules intros xs =
berghofe@22789
   919
  fold_map (fn r => AList.map_entry_yield op = (pname_of_intr r)
berghofe@22789
   920
    (fn x :: xs => (x, xs)) #>> the) intros xs |> fst;
berghofe@22789
   921
berghofe@22789
   922
(* infer order of variables in intro rules from order of quantifiers in elim rule *)
berghofe@22789
   923
fun infer_intro_vars elim arity intros =
berghofe@22789
   924
  let
berghofe@22789
   925
    val thy = theory_of_thm elim;
berghofe@22789
   926
    val _ :: cases = prems_of elim;
berghofe@22789
   927
    val used = map (fst o fst) (Term.add_vars (prop_of elim) []);
berghofe@22789
   928
    fun mtch (t, u) =
berghofe@22789
   929
      let
berghofe@22789
   930
        val params = Logic.strip_params t;
berghofe@22789
   931
        val vars = map (Var o apfst (rpair 0))
berghofe@22789
   932
          (Name.variant_list used (map fst params) ~~ map snd params);
berghofe@22789
   933
        val ts = map (curry subst_bounds (rev vars))
berghofe@22789
   934
          (List.drop (Logic.strip_assums_hyp t, arity));
berghofe@22789
   935
        val us = Logic.strip_imp_prems u;
berghofe@22789
   936
        val tab = fold (Pattern.first_order_match thy) (ts ~~ us)
berghofe@22789
   937
          (Vartab.empty, Vartab.empty);
berghofe@22789
   938
      in
wenzelm@32035
   939
        map (Envir.subst_term tab) vars
berghofe@22789
   940
      end
berghofe@22789
   941
  in
berghofe@22789
   942
    map (mtch o apsnd prop_of) (cases ~~ intros)
berghofe@22789
   943
  end;
berghofe@22789
   944
berghofe@22789
   945
wenzelm@25978
   946
wenzelm@6437
   947
(** package setup **)
wenzelm@6437
   948
wenzelm@6437
   949
(* setup theory *)
wenzelm@6437
   950
wenzelm@8634
   951
val setup =
wenzelm@30722
   952
  ind_cases_setup #>
wenzelm@30528
   953
  Attrib.setup @{binding mono} (Attrib.add_del mono_add mono_del)
wenzelm@30528
   954
    "declaration of monotonicity rule";
wenzelm@6437
   955
wenzelm@6437
   956
wenzelm@6437
   957
(* outer syntax *)
wenzelm@6424
   958
wenzelm@17057
   959
local structure P = OuterParse and K = OuterKeyword in
wenzelm@6424
   960
wenzelm@27353
   961
val _ = OuterKeyword.keyword "monos";
wenzelm@24867
   962
berghofe@23762
   963
fun gen_ind_decl mk_def coind =
wenzelm@21367
   964
  P.fixes -- P.for_fixes --
wenzelm@30486
   965
  Scan.optional SpecParse.where_alt_specs [] --
wenzelm@22102
   966
  Scan.optional (P.$$$ "monos" |-- P.!!! SpecParse.xthms1) []
wenzelm@26988
   967
  >> (fn (((preds, params), specs), monos) =>
wenzelm@30486
   968
      (snd oo gen_add_inductive mk_def true coind preds params specs monos));
berghofe@23762
   969
berghofe@23762
   970
val ind_decl = gen_ind_decl add_ind_def;
wenzelm@6424
   971
wenzelm@29388
   972
val _ = OuterSyntax.local_theory' "inductive" "define inductive predicates" K.thy_decl (ind_decl false);
wenzelm@29388
   973
val _ = OuterSyntax.local_theory' "coinductive" "define coinductive predicates" K.thy_decl (ind_decl true);
wenzelm@6723
   974
wenzelm@24867
   975
val _ =
wenzelm@26988
   976
  OuterSyntax.local_theory "inductive_cases"
wenzelm@21367
   977
    "create simplified instances of elimination rules (improper)" K.thy_script
wenzelm@30486
   978
    (P.and_list1 SpecParse.specs >> (snd oo inductive_cases));
wenzelm@7107
   979
berghofe@5094
   980
end;
wenzelm@6424
   981
wenzelm@6424
   982
end;