src/HOL/Tools/inductive.ML
author haftmann
Wed Nov 25 09:13:46 2009 +0100 (2009-11-25)
changeset 33957 e9afca2118d4
parent 33955 fff6f11b1f09
child 33966 b863967f23ea
permissions -rw-r--r--
normalized uncurry take/drop
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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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    {preds: term list, elims: thm list, raw_induct: thm,
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     induct: thm, intrs: thm list}
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  val morph_result: morphism -> inductive_result -> inductive_result
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  type inductive_info = {names: string list, coind: bool} * inductive_result
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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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    {quiet_mode: bool, verbose: bool, alt_name: binding, coind: bool,
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      no_elim: bool, no_ind: bool, skip_mono: bool, fork_mono: bool}
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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: 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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    inductive_flags ->
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    term list -> (Attrib.binding * term) list -> thm list ->
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    term list -> (binding * mixfix) list ->
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    local_theory -> inductive_result * local_theory
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  val declare_rules: 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 = Generic_Data
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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)) : T =
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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 = 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
wenzelm@18463
   319
  #> hol_simplify inductive_rulify_fallback
wenzelm@30552
   320
  #> Simplifier.norm_hhf;
wenzelm@10729
   321
wenzelm@10729
   322
end;
wenzelm@10729
   323
berghofe@5094
   324
wenzelm@6424
   325
berghofe@21024
   326
(** proofs for (co)inductive predicates **)
wenzelm@6424
   327
berghofe@26534
   328
(* prove monotonicity *)
berghofe@5094
   329
wenzelm@29388
   330
fun prove_mono quiet_mode skip_mono fork_mono predT fp_fun monos ctxt =
wenzelm@29388
   331
 (message (quiet_mode orelse skip_mono andalso !quick_and_dirty orelse fork_mono)
berghofe@26534
   332
    "  Proving monotonicity ...";
wenzelm@32970
   333
  (if skip_mono then Skip_Proof.prove else if fork_mono then Goal.prove_future else Goal.prove) ctxt
wenzelm@29388
   334
    [] []
wenzelm@17985
   335
    (HOLogic.mk_Trueprop
wenzelm@24815
   336
      (Const (@{const_name Orderings.mono}, (predT --> predT) --> HOLogic.boolT) $ fp_fun))
wenzelm@25380
   337
    (fn _ => EVERY [rtac @{thm monoI} 1,
haftmann@32652
   338
      REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI'}] 1),
berghofe@21024
   339
      REPEAT (FIRST
berghofe@21024
   340
        [atac 1,
wenzelm@32952
   341
         resolve_tac (maps mk_mono monos @ get_monos ctxt) 1,
haftmann@32652
   342
         etac @{thm le_funE} 1, dtac @{thm le_boolD} 1])]));
berghofe@5094
   343
wenzelm@6424
   344
wenzelm@10735
   345
(* prove introduction rules *)
berghofe@5094
   346
wenzelm@26477
   347
fun prove_intrs quiet_mode coind mono fp_def k params intr_ts rec_preds_defs ctxt =
berghofe@5094
   348
  let
wenzelm@26477
   349
    val _ = clean_message quiet_mode "  Proving the introduction rules ...";
berghofe@5094
   350
berghofe@21024
   351
    val unfold = funpow k (fn th => th RS fun_cong)
berghofe@21024
   352
      (mono RS (fp_def RS
haftmann@32652
   353
        (if coind then @{thm def_gfp_unfold} else @{thm def_lfp_unfold})));
berghofe@5094
   354
berghofe@5094
   355
    fun select_disj 1 1 = []
berghofe@5094
   356
      | select_disj _ 1 = [rtac disjI1]
berghofe@5094
   357
      | select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
berghofe@5094
   358
berghofe@21024
   359
    val rules = [refl, TrueI, notFalseI, exI, conjI];
berghofe@21024
   360
berghofe@22605
   361
    val intrs = map_index (fn (i, intr) => rulify
wenzelm@32970
   362
      (Skip_Proof.prove ctxt (map (fst o dest_Free) params) [] intr (fn _ => EVERY
berghofe@21024
   363
       [rewrite_goals_tac rec_preds_defs,
berghofe@21024
   364
        rtac (unfold RS iffD2) 1,
berghofe@21024
   365
        EVERY1 (select_disj (length intr_ts) (i + 1)),
wenzelm@17985
   366
        (*Not ares_tac, since refl must be tried before any equality assumptions;
wenzelm@17985
   367
          backtracking may occur if the premises have extra variables!*)
berghofe@21024
   368
        DEPTH_SOLVE_1 (resolve_tac rules 1 APPEND assume_tac 1)]))) intr_ts
berghofe@5094
   369
berghofe@5094
   370
  in (intrs, unfold) end;
berghofe@5094
   371
wenzelm@6424
   372
wenzelm@10735
   373
(* prove elimination rules *)
berghofe@5094
   374
wenzelm@26477
   375
fun prove_elims quiet_mode cs params intr_ts intr_names unfold rec_preds_defs ctxt =
berghofe@5094
   376
  let
wenzelm@26477
   377
    val _ = clean_message quiet_mode "  Proving the elimination rules ...";
berghofe@5094
   378
berghofe@22605
   379
    val ([pname], ctxt') = ctxt |>
berghofe@22605
   380
      Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
berghofe@22605
   381
      Variable.variant_fixes ["P"];
berghofe@21024
   382
    val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
berghofe@21024
   383
berghofe@21024
   384
    fun dest_intr r =
berghofe@21024
   385
      (the (dest_predicate cs params (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))),
berghofe@21024
   386
       Logic.strip_assums_hyp r, Logic.strip_params r);
berghofe@21024
   387
berghofe@21024
   388
    val intrs = map dest_intr intr_ts ~~ intr_names;
berghofe@21024
   389
berghofe@21024
   390
    val rules1 = [disjE, exE, FalseE];
berghofe@21024
   391
    val rules2 = [conjE, FalseE, notTrueE];
berghofe@21024
   392
berghofe@21024
   393
    fun prove_elim c =
berghofe@21024
   394
      let
haftmann@33077
   395
        val Ts = arg_types_of (length params) c;
berghofe@21024
   396
        val (anames, ctxt'') = Variable.variant_fixes (mk_names "a" (length Ts)) ctxt';
berghofe@21024
   397
        val frees = map Free (anames ~~ Ts);
berghofe@21024
   398
berghofe@21024
   399
        fun mk_elim_prem ((_, _, us, _), ts, params') =
berghofe@21024
   400
          list_all (params',
berghofe@21024
   401
            Logic.list_implies (map (HOLogic.mk_Trueprop o HOLogic.mk_eq)
berghofe@21024
   402
              (frees ~~ us) @ ts, P));
wenzelm@33317
   403
        val c_intrs = filter (equal c o #1 o #1 o #1) intrs;
berghofe@21024
   404
        val prems = HOLogic.mk_Trueprop (list_comb (c, params @ frees)) ::
berghofe@21024
   405
           map mk_elim_prem (map #1 c_intrs)
berghofe@21024
   406
      in
wenzelm@32970
   407
        (Skip_Proof.prove ctxt'' [] prems P
berghofe@21024
   408
          (fn {prems, ...} => EVERY
berghofe@21024
   409
            [cut_facts_tac [hd prems] 1,
berghofe@21024
   410
             rewrite_goals_tac rec_preds_defs,
berghofe@21024
   411
             dtac (unfold RS iffD1) 1,
berghofe@21024
   412
             REPEAT (FIRSTGOAL (eresolve_tac rules1)),
berghofe@21024
   413
             REPEAT (FIRSTGOAL (eresolve_tac rules2)),
berghofe@21024
   414
             EVERY (map (fn prem =>
berghofe@21024
   415
               DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_preds_defs prem, conjI] 1)) (tl prems))])
berghofe@21024
   416
          |> rulify
berghofe@21048
   417
          |> singleton (ProofContext.export ctxt'' ctxt),
berghofe@21048
   418
         map #2 c_intrs)
berghofe@21024
   419
      end
berghofe@21024
   420
berghofe@21024
   421
   in map prove_elim cs end;
berghofe@5094
   422
wenzelm@6424
   423
wenzelm@10735
   424
(* derivation of simplified elimination rules *)
berghofe@5094
   425
wenzelm@11682
   426
local
wenzelm@11682
   427
wenzelm@11682
   428
(*delete needless equality assumptions*)
wenzelm@29064
   429
val refl_thin = Goal.prove_global @{theory HOL} [] [] @{prop "!!P. a = a ==> P ==> P"}
haftmann@22838
   430
  (fn _ => assume_tac 1);
berghofe@21024
   431
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
wenzelm@11682
   432
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
wenzelm@11682
   433
berghofe@23762
   434
fun simp_case_tac ss i =
berghofe@23762
   435
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i;
wenzelm@21367
   436
wenzelm@11682
   437
in
wenzelm@9598
   438
wenzelm@21367
   439
fun mk_cases ctxt prop =
wenzelm@7107
   440
  let
wenzelm@21367
   441
    val thy = ProofContext.theory_of ctxt;
wenzelm@32149
   442
    val ss = simpset_of ctxt;
wenzelm@21367
   443
wenzelm@21526
   444
    fun err msg =
wenzelm@21526
   445
      error (Pretty.string_of (Pretty.block
wenzelm@24920
   446
        [Pretty.str msg, Pretty.fbrk, Syntax.pretty_term ctxt prop]));
wenzelm@21526
   447
wenzelm@24861
   448
    val elims = Induct.find_casesP ctxt prop;
wenzelm@21367
   449
wenzelm@21367
   450
    val cprop = Thm.cterm_of thy prop;
berghofe@23762
   451
    val tac = ALLGOALS (simp_case_tac ss) THEN prune_params_tac;
wenzelm@21367
   452
    fun mk_elim rl =
wenzelm@21367
   453
      Thm.implies_intr cprop (Tactic.rule_by_tactic tac (Thm.assume cprop RS rl))
wenzelm@21367
   454
      |> singleton (Variable.export (Variable.auto_fixes prop ctxt) ctxt);
wenzelm@7107
   455
  in
wenzelm@7107
   456
    (case get_first (try mk_elim) elims of
skalberg@15531
   457
      SOME r => r
wenzelm@21526
   458
    | NONE => err "Proposition not an inductive predicate:")
wenzelm@7107
   459
  end;
wenzelm@7107
   460
wenzelm@11682
   461
end;
wenzelm@11682
   462
wenzelm@7107
   463
wenzelm@21367
   464
(* inductive_cases *)
wenzelm@7107
   465
wenzelm@21367
   466
fun gen_inductive_cases prep_att prep_prop args lthy =
wenzelm@9598
   467
  let
wenzelm@21367
   468
    val thy = ProofContext.theory_of lthy;
wenzelm@12876
   469
    val facts = args |> map (fn ((a, atts), props) =>
wenzelm@21367
   470
      ((a, map (prep_att thy) atts),
wenzelm@21367
   471
        map (Thm.no_attributes o single o mk_cases lthy o prep_prop lthy) props));
wenzelm@33671
   472
  in lthy |> Local_Theory.notes facts |>> map snd end;
berghofe@5094
   473
wenzelm@24509
   474
val inductive_cases = gen_inductive_cases Attrib.intern_src Syntax.read_prop;
wenzelm@24509
   475
val inductive_cases_i = gen_inductive_cases (K I) Syntax.check_prop;
wenzelm@7107
   476
wenzelm@6424
   477
wenzelm@30722
   478
val ind_cases_setup =
wenzelm@30722
   479
  Method.setup @{binding ind_cases}
wenzelm@30722
   480
    (Scan.lift (Scan.repeat1 Args.name_source --
wenzelm@30722
   481
      Scan.optional (Args.$$$ "for" |-- Scan.repeat1 Args.name) []) >>
wenzelm@30722
   482
      (fn (raw_props, fixes) => fn ctxt =>
wenzelm@30722
   483
        let
wenzelm@30722
   484
          val (_, ctxt') = Variable.add_fixes fixes ctxt;
wenzelm@30722
   485
          val props = Syntax.read_props ctxt' raw_props;
wenzelm@30722
   486
          val ctxt'' = fold Variable.declare_term props ctxt';
wenzelm@30722
   487
          val rules = ProofContext.export ctxt'' ctxt (map (mk_cases ctxt'') props)
wenzelm@30722
   488
        in Method.erule 0 rules end))
wenzelm@30722
   489
    "dynamic case analysis on predicates";
wenzelm@9598
   490
wenzelm@9598
   491
wenzelm@10735
   492
(* prove induction rule *)
berghofe@5094
   493
wenzelm@26477
   494
fun prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono
berghofe@21024
   495
    fp_def rec_preds_defs ctxt =
berghofe@5094
   496
  let
wenzelm@26477
   497
    val _ = clean_message quiet_mode "  Proving the induction rule ...";
wenzelm@20047
   498
    val thy = ProofContext.theory_of ctxt;
berghofe@5094
   499
berghofe@21024
   500
    (* predicates for induction rule *)
berghofe@21024
   501
berghofe@22605
   502
    val (pnames, ctxt') = ctxt |>
berghofe@22605
   503
      Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
berghofe@22605
   504
      Variable.variant_fixes (mk_names "P" (length cs));
haftmann@33077
   505
    val preds = map2 (curry Free) pnames
haftmann@33077
   506
      (map (fn c => arg_types_of (length params) c ---> HOLogic.boolT) cs);
berghofe@21024
   507
berghofe@21024
   508
    (* transform an introduction rule into a premise for induction rule *)
berghofe@21024
   509
berghofe@21024
   510
    fun mk_ind_prem r =
berghofe@21024
   511
      let
wenzelm@33669
   512
        fun subst s =
wenzelm@33669
   513
          (case dest_predicate cs params s of
berghofe@21024
   514
            SOME (_, i, ys, (_, Ts)) =>
berghofe@21024
   515
              let
berghofe@21024
   516
                val k = length Ts;
berghofe@21024
   517
                val bs = map Bound (k - 1 downto 0);
berghofe@23762
   518
                val P = list_comb (List.nth (preds, i),
berghofe@23762
   519
                  map (incr_boundvars k) ys @ bs);
berghofe@21024
   520
                val Q = list_abs (mk_names "x" k ~~ Ts,
berghofe@23762
   521
                  HOLogic.mk_binop inductive_conj_name
berghofe@23762
   522
                    (list_comb (incr_boundvars k s, bs), P))
berghofe@21024
   523
              in (Q, case Ts of [] => SOME (s, P) | _ => NONE) end
wenzelm@33669
   524
          | NONE =>
wenzelm@33669
   525
              (case s of
wenzelm@33669
   526
                (t $ u) => (fst (subst t) $ fst (subst u), NONE)
wenzelm@33669
   527
              | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
wenzelm@33669
   528
              | _ => (s, NONE)));
berghofe@7293
   529
wenzelm@33338
   530
        fun mk_prem s prems =
wenzelm@33338
   531
          (case subst s of
wenzelm@33338
   532
            (_, SOME (t, u)) => t :: u :: prems
wenzelm@33338
   533
          | (t, _) => t :: prems);
berghofe@21024
   534
berghofe@21024
   535
        val SOME (_, i, ys, _) = dest_predicate cs params
berghofe@21024
   536
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))
berghofe@21024
   537
berghofe@21024
   538
      in list_all_free (Logic.strip_params r,
wenzelm@33338
   539
        Logic.list_implies (map HOLogic.mk_Trueprop (fold_rev mk_prem
wenzelm@33338
   540
          (map HOLogic.dest_Trueprop (Logic.strip_assums_hyp r)) []),
berghofe@21024
   541
            HOLogic.mk_Trueprop (list_comb (List.nth (preds, i), ys))))
berghofe@21024
   542
      end;
berghofe@21024
   543
berghofe@21024
   544
    val ind_prems = map mk_ind_prem intr_ts;
berghofe@21024
   545
wenzelm@21526
   546
berghofe@21024
   547
    (* make conclusions for induction rules *)
berghofe@21024
   548
berghofe@21024
   549
    val Tss = map (binder_types o fastype_of) preds;
berghofe@21024
   550
    val (xnames, ctxt'') =
berghofe@21024
   551
      Variable.variant_fixes (mk_names "x" (length (flat Tss))) ctxt';
berghofe@21024
   552
    val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
berghofe@21024
   553
        (map (fn (((xnames, Ts), c), P) =>
berghofe@21024
   554
           let val frees = map Free (xnames ~~ Ts)
berghofe@21024
   555
           in HOLogic.mk_imp
berghofe@21024
   556
             (list_comb (c, params @ frees), list_comb (P, frees))
berghofe@21024
   557
           end) (unflat Tss xnames ~~ Tss ~~ cs ~~ preds)));
berghofe@5094
   558
paulson@13626
   559
berghofe@5094
   560
    (* make predicate for instantiation of abstract induction rule *)
berghofe@5094
   561
berghofe@21024
   562
    val ind_pred = fold_rev lambda (bs @ xs) (foldr1 HOLogic.mk_conj
wenzelm@33338
   563
      (map_index (fn (i, P) => fold_rev (curry HOLogic.mk_imp)
wenzelm@33338
   564
         (make_bool_args HOLogic.mk_not I bs i)
wenzelm@33338
   565
         (list_comb (P, make_args' argTs xs (binder_types (fastype_of P))))) preds));
berghofe@5094
   566
berghofe@5094
   567
    val ind_concl = HOLogic.mk_Trueprop
haftmann@23881
   568
      (HOLogic.mk_binrel "HOL.ord_class.less_eq" (rec_const, ind_pred));
berghofe@5094
   569
haftmann@32652
   570
    val raw_fp_induct = (mono RS (fp_def RS @{thm def_lfp_induct}));
paulson@13626
   571
wenzelm@32970
   572
    val induct = Skip_Proof.prove ctxt'' [] ind_prems ind_concl
wenzelm@20248
   573
      (fn {prems, ...} => EVERY
wenzelm@17985
   574
        [rewrite_goals_tac [inductive_conj_def],
berghofe@21024
   575
         DETERM (rtac raw_fp_induct 1),
haftmann@32652
   576
         REPEAT (resolve_tac [@{thm le_funI}, @{thm le_boolI}] 1),
haftmann@32610
   577
         rewrite_goals_tac simp_thms'',
berghofe@21024
   578
         (*This disjE separates out the introduction rules*)
berghofe@21024
   579
         REPEAT (FIRSTGOAL (eresolve_tac [disjE, exE, FalseE])),
berghofe@5094
   580
         (*Now break down the individual cases.  No disjE here in case
berghofe@5094
   581
           some premise involves disjunction.*)
paulson@13747
   582
         REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
berghofe@21024
   583
         REPEAT (FIRSTGOAL
berghofe@21024
   584
           (resolve_tac [conjI, impI] ORELSE' (etac notE THEN' atac))),
berghofe@21024
   585
         EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [rewrite_rule
haftmann@32610
   586
             (inductive_conj_def :: rec_preds_defs @ simp_thms'') prem,
berghofe@22980
   587
           conjI, refl] 1)) prems)]);
berghofe@5094
   588
wenzelm@32970
   589
    val lemma = Skip_Proof.prove ctxt'' [] []
wenzelm@17985
   590
      (Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
berghofe@21024
   591
        [rewrite_goals_tac rec_preds_defs,
berghofe@5094
   592
         REPEAT (EVERY
berghofe@5094
   593
           [REPEAT (resolve_tac [conjI, impI] 1),
haftmann@32652
   594
            REPEAT (eresolve_tac [@{thm le_funE}, @{thm le_boolE}] 1),
berghofe@21024
   595
            atac 1,
berghofe@21024
   596
            rewrite_goals_tac simp_thms',
berghofe@21024
   597
            atac 1])])
berghofe@5094
   598
berghofe@21024
   599
  in singleton (ProofContext.export ctxt'' ctxt) (induct RS lemma) end;
berghofe@5094
   600
wenzelm@6424
   601
wenzelm@6424
   602
berghofe@21024
   603
(** specification of (co)inductive predicates **)
wenzelm@10729
   604
wenzelm@33458
   605
fun mk_ind_def quiet_mode skip_mono fork_mono alt_name coind
wenzelm@33458
   606
    cs intr_ts monos params cnames_syn lthy =
wenzelm@33458
   607
  let
haftmann@24915
   608
    val fp_name = if coind then @{const_name Inductive.gfp} else @{const_name Inductive.lfp};
berghofe@5094
   609
haftmann@33077
   610
    val argTs = fold (combine (op =) o arg_types_of (length params)) cs [];
berghofe@21024
   611
    val k = log 2 1 (length cs);
berghofe@21024
   612
    val predT = replicate k HOLogic.boolT ---> argTs ---> HOLogic.boolT;
wenzelm@33458
   613
    val p :: xs = map Free (Variable.variant_frees lthy intr_ts
berghofe@21024
   614
      (("p", predT) :: (mk_names "x" (length argTs) ~~ argTs)));
wenzelm@33458
   615
    val bs = map Free (Variable.variant_frees lthy (p :: xs @ intr_ts)
berghofe@21024
   616
      (map (rpair HOLogic.boolT) (mk_names "b" k)));
berghofe@21024
   617
wenzelm@33458
   618
    fun subst t =
wenzelm@33458
   619
      (case dest_predicate cs params t of
berghofe@21024
   620
        SOME (_, i, ts, (Ts, Us)) =>
berghofe@23762
   621
          let
berghofe@23762
   622
            val l = length Us;
wenzelm@33669
   623
            val zs = map Bound (l - 1 downto 0);
berghofe@21024
   624
          in
berghofe@21024
   625
            list_abs (map (pair "z") Us, list_comb (p,
berghofe@23762
   626
              make_bool_args' bs i @ make_args argTs
berghofe@23762
   627
                ((map (incr_boundvars l) ts ~~ Ts) @ (zs ~~ Us))))
berghofe@21024
   628
          end
wenzelm@33669
   629
      | NONE =>
wenzelm@33669
   630
          (case t of
wenzelm@33669
   631
            t1 $ t2 => subst t1 $ subst t2
wenzelm@33669
   632
          | Abs (x, T, u) => Abs (x, T, subst u)
wenzelm@33669
   633
          | _ => t));
berghofe@5149
   634
berghofe@5094
   635
    (* transform an introduction rule into a conjunction  *)
berghofe@21024
   636
    (*   [| p_i t; ... |] ==> p_j u                       *)
berghofe@5094
   637
    (* is transformed into                                *)
berghofe@21024
   638
    (*   b_j & x_j = u & p b_j t & ...                    *)
berghofe@5094
   639
berghofe@5094
   640
    fun transform_rule r =
berghofe@5094
   641
      let
berghofe@21024
   642
        val SOME (_, i, ts, (Ts, _)) = dest_predicate cs params
berghofe@21048
   643
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r));
berghofe@21048
   644
        val ps = make_bool_args HOLogic.mk_not I bs i @
berghofe@21048
   645
          map HOLogic.mk_eq (make_args' argTs xs Ts ~~ ts) @
berghofe@21048
   646
          map (subst o HOLogic.dest_Trueprop)
berghofe@21048
   647
            (Logic.strip_assums_hyp r)
wenzelm@33338
   648
      in
wenzelm@33338
   649
        fold_rev (fn (x, T) => fn P => HOLogic.exists_const T $ Abs (x, T, P))
wenzelm@33338
   650
          (Logic.strip_params r)
wenzelm@33338
   651
          (if null ps then HOLogic.true_const else foldr1 HOLogic.mk_conj ps)
berghofe@5094
   652
      end
berghofe@5094
   653
berghofe@5094
   654
    (* make a disjunction of all introduction rules *)
berghofe@5094
   655
berghofe@21024
   656
    val fp_fun = fold_rev lambda (p :: bs @ xs)
berghofe@21024
   657
      (if null intr_ts then HOLogic.false_const
berghofe@21024
   658
       else foldr1 HOLogic.mk_disj (map transform_rule intr_ts));
berghofe@5094
   659
berghofe@21024
   660
    (* add definiton of recursive predicates to theory *)
berghofe@5094
   661
wenzelm@28083
   662
    val rec_name =
haftmann@28965
   663
      if Binding.is_empty alt_name then
wenzelm@30223
   664
        Binding.name (space_implode "_" (map (Binding.name_of o fst) cnames_syn))
wenzelm@28083
   665
      else alt_name;
berghofe@5094
   666
wenzelm@33458
   667
    val ((rec_const, (_, fp_def)), lthy') = lthy
wenzelm@33671
   668
      |> Local_Theory.conceal
wenzelm@33766
   669
      |> Local_Theory.define
berghofe@21024
   670
        ((rec_name, case cnames_syn of [(_, syn)] => syn | _ => NoSyn),
blanchet@33577
   671
         ((Binding.empty, [Attrib.internal (K Nitpick_Defs.add)]),
blanchet@33577
   672
         fold_rev lambda params
wenzelm@33278
   673
           (Const (fp_name, (predT --> predT) --> predT) $ fp_fun)))
wenzelm@33671
   674
      ||> Local_Theory.restore_naming lthy;
berghofe@21024
   675
    val fp_def' = Simplifier.rewrite (HOL_basic_ss addsimps [fp_def])
wenzelm@33458
   676
      (cterm_of (ProofContext.theory_of lthy') (list_comb (rec_const, params)));
wenzelm@33278
   677
    val specs =
wenzelm@33278
   678
      if length cs < 2 then []
wenzelm@33278
   679
      else
wenzelm@33278
   680
        map_index (fn (i, (name_mx, c)) =>
wenzelm@33278
   681
          let
wenzelm@33278
   682
            val Ts = arg_types_of (length params) c;
wenzelm@33458
   683
            val xs = map Free (Variable.variant_frees lthy intr_ts
wenzelm@33278
   684
              (mk_names "x" (length Ts) ~~ Ts))
wenzelm@33278
   685
          in
wenzelm@33278
   686
            (name_mx, (Attrib.empty_binding, fold_rev lambda (params @ xs)
wenzelm@33278
   687
              (list_comb (rec_const, params @ make_bool_args' bs i @
wenzelm@33278
   688
                make_args argTs (xs ~~ Ts)))))
wenzelm@33278
   689
          end) (cnames_syn ~~ cs);
wenzelm@33458
   690
    val (consts_defs, lthy'') = lthy'
wenzelm@33671
   691
      |> Local_Theory.conceal
wenzelm@33766
   692
      |> fold_map Local_Theory.define specs
wenzelm@33671
   693
      ||> Local_Theory.restore_naming lthy';
berghofe@21024
   694
    val preds = (case cs of [_] => [rec_const] | _ => map #1 consts_defs);
berghofe@5094
   695
wenzelm@33458
   696
    val mono = prove_mono quiet_mode skip_mono fork_mono predT fp_fun monos lthy'';
wenzelm@33458
   697
    val ((_, [mono']), lthy''') =
wenzelm@33671
   698
      Local_Theory.note (apfst Binding.conceal Attrib.empty_binding, [mono]) lthy'';
berghofe@5094
   699
wenzelm@33458
   700
  in (lthy''', rec_name, mono', fp_def', map (#2 o #2) consts_defs,
berghofe@21024
   701
    list_comb (rec_const, params), preds, argTs, bs, xs)
berghofe@21024
   702
  end;
berghofe@5094
   703
wenzelm@33669
   704
fun declare_rules rec_binding coind no_ind cnames
wenzelm@33669
   705
    intrs intr_bindings intr_atts elims raw_induct lthy =
berghofe@23762
   706
  let
wenzelm@30223
   707
    val rec_name = Binding.name_of rec_binding;
haftmann@32773
   708
    fun rec_qualified qualified = Binding.qualify qualified rec_name;
wenzelm@30223
   709
    val intr_names = map Binding.name_of intr_bindings;
wenzelm@33368
   710
    val ind_case_names = Rule_Cases.case_names intr_names;
berghofe@23762
   711
    val induct =
berghofe@23762
   712
      if coind then
wenzelm@33368
   713
        (raw_induct, [Rule_Cases.case_names [rec_name],
wenzelm@33368
   714
          Rule_Cases.case_conclusion (rec_name, intr_names),
wenzelm@33368
   715
          Rule_Cases.consumes 1, Induct.coinduct_pred (hd cnames)])
berghofe@23762
   716
      else if no_ind orelse length cnames > 1 then
wenzelm@33368
   717
        (raw_induct, [ind_case_names, Rule_Cases.consumes 0])
wenzelm@33368
   718
      else (raw_induct RSN (2, rev_mp), [ind_case_names, Rule_Cases.consumes 1]);
berghofe@23762
   719
wenzelm@33458
   720
    val (intrs', lthy1) =
wenzelm@33458
   721
      lthy |>
wenzelm@33671
   722
      Local_Theory.notes
wenzelm@33278
   723
        (map (rec_qualified false) intr_bindings ~~ intr_atts ~~
wenzelm@33278
   724
          map (fn th => [([th],
wenzelm@33369
   725
           [Attrib.internal (K (Context_Rules.intro_query NONE)),
blanchet@33056
   726
            Attrib.internal (K Nitpick_Intros.add)])]) intrs) |>>
berghofe@24744
   727
      map (hd o snd);
wenzelm@33458
   728
    val (((_, elims'), (_, [induct'])), lthy2) =
wenzelm@33458
   729
      lthy1 |>
wenzelm@33671
   730
      Local_Theory.note ((rec_qualified true (Binding.name "intros"), []), intrs') ||>>
berghofe@23762
   731
      fold_map (fn (name, (elim, cases)) =>
wenzelm@33671
   732
        Local_Theory.note
wenzelm@33458
   733
          ((Binding.qualify true (Long_Name.base_name name) (Binding.name "cases"),
wenzelm@33458
   734
            [Attrib.internal (K (Rule_Cases.case_names cases)),
wenzelm@33458
   735
             Attrib.internal (K (Rule_Cases.consumes 1)),
wenzelm@33458
   736
             Attrib.internal (K (Induct.cases_pred name)),
wenzelm@33458
   737
             Attrib.internal (K (Context_Rules.elim_query NONE))]), [elim]) #>
berghofe@23762
   738
        apfst (hd o snd)) (if null elims then [] else cnames ~~ elims) ||>>
wenzelm@33671
   739
      Local_Theory.note
haftmann@32773
   740
        ((rec_qualified true (Binding.name (coind_prefix coind ^ "induct")),
wenzelm@28107
   741
          map (Attrib.internal o K) (#2 induct)), [rulify (#1 induct)]);
berghofe@23762
   742
wenzelm@33458
   743
    val lthy3 =
wenzelm@33458
   744
      if no_ind orelse coind then lthy2
wenzelm@33458
   745
      else
wenzelm@33458
   746
        let val inducts = cnames ~~ Project_Rule.projects lthy2 (1 upto length cnames) induct' in
wenzelm@33458
   747
          lthy2 |>
wenzelm@33671
   748
          Local_Theory.notes [((rec_qualified true (Binding.name "inducts"), []),
wenzelm@33458
   749
            inducts |> map (fn (name, th) => ([th],
wenzelm@33458
   750
              [Attrib.internal (K ind_case_names),
wenzelm@33458
   751
               Attrib.internal (K (Rule_Cases.consumes 1)),
wenzelm@33458
   752
               Attrib.internal (K (Induct.induct_pred name))])))] |> snd
wenzelm@33458
   753
        end;
wenzelm@33458
   754
  in (intrs', elims', induct', lthy3) end;
berghofe@23762
   755
berghofe@26534
   756
type inductive_flags =
wenzelm@33669
   757
  {quiet_mode: bool, verbose: bool, alt_name: binding, coind: bool,
wenzelm@33669
   758
    no_elim: bool, no_ind: bool, skip_mono: bool, fork_mono: bool};
berghofe@26534
   759
berghofe@26534
   760
type add_ind_def =
berghofe@26534
   761
  inductive_flags ->
wenzelm@28084
   762
  term list -> (Attrib.binding * term) list -> thm list ->
haftmann@29581
   763
  term list -> (binding * mixfix) list ->
wenzelm@33458
   764
  local_theory -> inductive_result * local_theory;
berghofe@23762
   765
wenzelm@33669
   766
fun add_ind_def {quiet_mode, verbose, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono}
wenzelm@33458
   767
    cs intros monos params cnames_syn lthy =
berghofe@9072
   768
  let
wenzelm@25288
   769
    val _ = null cnames_syn andalso error "No inductive predicates given";
wenzelm@30223
   770
    val names = map (Binding.name_of o fst) cnames_syn;
wenzelm@26477
   771
    val _ = message (quiet_mode andalso not verbose)
wenzelm@28083
   772
      ("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^ commas_quote names);
berghofe@9072
   773
wenzelm@33671
   774
    val cnames = map (Local_Theory.full_name lthy o #1) cnames_syn;  (* FIXME *)
berghofe@23762
   775
    val ((intr_names, intr_atts), intr_ts) =
wenzelm@33458
   776
      apfst split_list (split_list (map (check_rule lthy cs params) intros));
berghofe@21024
   777
wenzelm@33458
   778
    val (lthy1, rec_name, mono, fp_def, rec_preds_defs, rec_const, preds,
wenzelm@29388
   779
      argTs, bs, xs) = mk_ind_def quiet_mode skip_mono fork_mono alt_name coind cs intr_ts
wenzelm@33458
   780
        monos params cnames_syn lthy;
berghofe@9072
   781
wenzelm@26477
   782
    val (intrs, unfold) = prove_intrs quiet_mode coind mono fp_def (length bs + length xs)
wenzelm@33458
   783
      params intr_ts rec_preds_defs lthy1;
wenzelm@33459
   784
    val elims =
wenzelm@33459
   785
      if no_elim then []
wenzelm@33459
   786
      else
wenzelm@33459
   787
        prove_elims quiet_mode cs params intr_ts (map Binding.name_of intr_names)
wenzelm@33459
   788
          unfold rec_preds_defs lthy1;
berghofe@22605
   789
    val raw_induct = zero_var_indexes
wenzelm@33459
   790
      (if no_ind then Drule.asm_rl
wenzelm@33459
   791
       else if coind then
berghofe@23762
   792
         singleton (ProofContext.export
wenzelm@33458
   793
           (snd (Variable.add_fixes (map (fst o dest_Free) params) lthy1)) lthy1)
wenzelm@28839
   794
           (rotate_prems ~1 (ObjectLogic.rulify
wenzelm@28839
   795
             (fold_rule rec_preds_defs
haftmann@32652
   796
               (rewrite_rule simp_thms'''
haftmann@32652
   797
                (mono RS (fp_def RS @{thm def_coinduct}))))))
berghofe@21024
   798
       else
wenzelm@26477
   799
         prove_indrule quiet_mode cs argTs bs xs rec_const params intr_ts mono fp_def
wenzelm@33458
   800
           rec_preds_defs lthy1);
berghofe@5094
   801
wenzelm@33669
   802
    val (intrs', elims', induct, lthy2) = declare_rules rec_name coind no_ind
wenzelm@33458
   803
      cnames intrs intr_names intr_atts elims raw_induct lthy1;
berghofe@21048
   804
berghofe@21048
   805
    val result =
berghofe@21048
   806
      {preds = preds,
berghofe@21048
   807
       intrs = intrs',
berghofe@21048
   808
       elims = elims',
berghofe@21048
   809
       raw_induct = rulify raw_induct,
berghofe@23762
   810
       induct = induct};
wenzelm@21367
   811
wenzelm@33458
   812
    val lthy3 = lthy2
wenzelm@33671
   813
      |> Local_Theory.declaration false (fn phi =>
wenzelm@25380
   814
        let val result' = morph_result phi result;
wenzelm@25380
   815
        in put_inductives cnames (*global names!?*) ({names = cnames, coind = coind}, result') end);
wenzelm@33458
   816
  in (result, lthy3) end;
berghofe@5094
   817
wenzelm@6424
   818
wenzelm@10735
   819
(* external interfaces *)
berghofe@5094
   820
wenzelm@26477
   821
fun gen_add_inductive_i mk_def
wenzelm@33669
   822
    (flags as {quiet_mode, verbose, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono})
wenzelm@25029
   823
    cnames_syn pnames spec monos lthy =
berghofe@5094
   824
  let
wenzelm@25029
   825
    val thy = ProofContext.theory_of lthy;
wenzelm@6424
   826
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
berghofe@5094
   827
berghofe@21766
   828
wenzelm@25029
   829
    (* abbrevs *)
wenzelm@25029
   830
wenzelm@30223
   831
    val (_, ctxt1) = Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn) lthy;
berghofe@21766
   832
wenzelm@25029
   833
    fun get_abbrev ((name, atts), t) =
wenzelm@25029
   834
      if can (Logic.strip_assums_concl #> Logic.dest_equals) t then
wenzelm@25029
   835
        let
haftmann@29006
   836
          val _ = Binding.is_empty name andalso null atts orelse
wenzelm@25029
   837
            error "Abbreviations may not have names or attributes";
wenzelm@25029
   838
          val ((x, T), rhs) = LocalDefs.abs_def (snd (LocalDefs.cert_def ctxt1 t));
wenzelm@28083
   839
          val var =
wenzelm@30223
   840
            (case find_first (fn ((c, _), _) => Binding.name_of c = x) cnames_syn of
wenzelm@25029
   841
              NONE => error ("Undeclared head of abbreviation " ^ quote x)
wenzelm@28083
   842
            | SOME ((b, T'), mx) =>
wenzelm@25029
   843
                if T <> T' then error ("Bad type specification for abbreviation " ^ quote x)
wenzelm@28083
   844
                else (b, mx));
wenzelm@28083
   845
        in SOME (var, rhs) end
wenzelm@25029
   846
      else NONE;
berghofe@21766
   847
wenzelm@25029
   848
    val abbrevs = map_filter get_abbrev spec;
wenzelm@30223
   849
    val bs = map (Binding.name_of o fst o fst) abbrevs;
wenzelm@25029
   850
berghofe@21766
   851
wenzelm@25029
   852
    (* predicates *)
berghofe@21766
   853
wenzelm@25029
   854
    val pre_intros = filter_out (is_some o get_abbrev) spec;
wenzelm@30223
   855
    val cnames_syn' = filter_out (member (op =) bs o Binding.name_of o fst o fst) cnames_syn;
wenzelm@30223
   856
    val cs = map (Free o apfst Binding.name_of o fst) cnames_syn';
wenzelm@25029
   857
    val ps = map Free pnames;
berghofe@5094
   858
wenzelm@30223
   859
    val (_, ctxt2) = lthy |> Variable.add_fixes (map (Binding.name_of o fst o fst) cnames_syn');
wenzelm@25143
   860
    val _ = map (fn abbr => LocalDefs.fixed_abbrev abbr ctxt2) abbrevs;
wenzelm@25143
   861
    val ctxt3 = ctxt2 |> fold (snd oo LocalDefs.fixed_abbrev) abbrevs;
wenzelm@25143
   862
    val expand = Assumption.export_term ctxt3 lthy #> ProofContext.cert_term lthy;
wenzelm@25029
   863
wenzelm@25029
   864
    fun close_rule r = list_all_free (rev (fold_aterms
berghofe@21024
   865
      (fn t as Free (v as (s, _)) =>
wenzelm@25029
   866
          if Variable.is_fixed ctxt1 s orelse
wenzelm@25029
   867
            member (op =) ps t then I else insert (op =) v
wenzelm@25029
   868
        | _ => I) r []), r);
berghofe@5094
   869
haftmann@26736
   870
    val intros = map (apsnd (Syntax.check_term lthy #> close_rule #> expand)) pre_intros;
wenzelm@25029
   871
    val preds = map (fn ((c, _), mx) => (c, mx)) cnames_syn';
berghofe@21048
   872
  in
wenzelm@25029
   873
    lthy
wenzelm@25029
   874
    |> mk_def flags cs intros monos ps preds
wenzelm@33671
   875
    ||> fold (snd oo Local_Theory.abbrev Syntax.mode_default) abbrevs
berghofe@21048
   876
  end;
berghofe@5094
   877
wenzelm@29388
   878
fun gen_add_inductive mk_def verbose coind cnames_syn pnames_syn intro_srcs raw_monos int lthy =
berghofe@5094
   879
  let
wenzelm@30486
   880
    val ((vars, intrs), _) = lthy
wenzelm@30486
   881
      |> ProofContext.set_mode ProofContext.mode_abbrev
wenzelm@30486
   882
      |> Specification.read_spec (cnames_syn @ pnames_syn) intro_srcs;
wenzelm@24721
   883
    val (cs, ps) = chop (length cnames_syn) vars;
wenzelm@24721
   884
    val monos = Attrib.eval_thms lthy raw_monos;
wenzelm@33669
   885
    val flags = {quiet_mode = false, verbose = verbose, alt_name = Binding.empty,
wenzelm@33669
   886
      coind = coind, no_elim = false, no_ind = false, skip_mono = false, fork_mono = not int};
wenzelm@26128
   887
  in
wenzelm@26128
   888
    lthy
wenzelm@30223
   889
    |> gen_add_inductive_i mk_def flags cs (map (apfst Binding.name_of o fst) ps) intrs monos
wenzelm@26128
   890
  end;
berghofe@5094
   891
berghofe@23762
   892
val add_inductive_i = gen_add_inductive_i add_ind_def;
berghofe@23762
   893
val add_inductive = gen_add_inductive add_ind_def;
berghofe@23762
   894
wenzelm@33726
   895
fun add_inductive_global flags cnames_syn pnames pre_intros monos thy =
wenzelm@25380
   896
  let
haftmann@29006
   897
    val name = Sign.full_name thy (fst (fst (hd cnames_syn)));
wenzelm@25380
   898
    val ctxt' = thy
wenzelm@33553
   899
      |> Theory_Target.init NONE
wenzelm@25380
   900
      |> add_inductive_i flags cnames_syn pnames pre_intros monos |> snd
wenzelm@33671
   901
      |> Local_Theory.exit;
wenzelm@25380
   902
    val info = #2 (the_inductive ctxt' name);
wenzelm@25380
   903
  in (info, ProofContext.theory_of ctxt') end;
wenzelm@6424
   904
wenzelm@6424
   905
berghofe@22789
   906
(* read off arities of inductive predicates from raw induction rule *)
berghofe@22789
   907
fun arities_of induct =
berghofe@22789
   908
  map (fn (_ $ t $ u) =>
berghofe@22789
   909
      (fst (dest_Const (head_of t)), length (snd (strip_comb u))))
berghofe@22789
   910
    (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@22789
   911
berghofe@22789
   912
(* read off parameters of inductive predicate from raw induction rule *)
berghofe@22789
   913
fun params_of induct =
berghofe@22789
   914
  let
berghofe@22789
   915
    val (_ $ t $ u :: _) =
berghofe@22789
   916
      HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct));
berghofe@22789
   917
    val (_, ts) = strip_comb t;
berghofe@22789
   918
    val (_, us) = strip_comb u
berghofe@22789
   919
  in
berghofe@22789
   920
    List.take (ts, length ts - length us)
berghofe@22789
   921
  end;
berghofe@22789
   922
berghofe@22789
   923
val pname_of_intr =
berghofe@22789
   924
  concl_of #> HOLogic.dest_Trueprop #> head_of #> dest_Const #> fst;
berghofe@22789
   925
berghofe@22789
   926
(* partition introduction rules according to predicate name *)
berghofe@25822
   927
fun gen_partition_rules f induct intros =
berghofe@25822
   928
  fold_rev (fn r => AList.map_entry op = (pname_of_intr (f r)) (cons r)) intros
berghofe@22789
   929
    (map (rpair [] o fst) (arities_of induct));
berghofe@22789
   930
berghofe@25822
   931
val partition_rules = gen_partition_rules I;
berghofe@25822
   932
fun partition_rules' induct = gen_partition_rules fst induct;
berghofe@25822
   933
berghofe@22789
   934
fun unpartition_rules intros xs =
berghofe@22789
   935
  fold_map (fn r => AList.map_entry_yield op = (pname_of_intr r)
berghofe@22789
   936
    (fn x :: xs => (x, xs)) #>> the) intros xs |> fst;
berghofe@22789
   937
berghofe@22789
   938
(* infer order of variables in intro rules from order of quantifiers in elim rule *)
berghofe@22789
   939
fun infer_intro_vars elim arity intros =
berghofe@22789
   940
  let
berghofe@22789
   941
    val thy = theory_of_thm elim;
berghofe@22789
   942
    val _ :: cases = prems_of elim;
berghofe@22789
   943
    val used = map (fst o fst) (Term.add_vars (prop_of elim) []);
berghofe@22789
   944
    fun mtch (t, u) =
berghofe@22789
   945
      let
berghofe@22789
   946
        val params = Logic.strip_params t;
berghofe@22789
   947
        val vars = map (Var o apfst (rpair 0))
berghofe@22789
   948
          (Name.variant_list used (map fst params) ~~ map snd params);
berghofe@22789
   949
        val ts = map (curry subst_bounds (rev vars))
berghofe@22789
   950
          (List.drop (Logic.strip_assums_hyp t, arity));
berghofe@22789
   951
        val us = Logic.strip_imp_prems u;
berghofe@22789
   952
        val tab = fold (Pattern.first_order_match thy) (ts ~~ us)
berghofe@22789
   953
          (Vartab.empty, Vartab.empty);
berghofe@22789
   954
      in
wenzelm@32035
   955
        map (Envir.subst_term tab) vars
berghofe@22789
   956
      end
berghofe@22789
   957
  in
berghofe@22789
   958
    map (mtch o apsnd prop_of) (cases ~~ intros)
berghofe@22789
   959
  end;
berghofe@22789
   960
berghofe@22789
   961
wenzelm@25978
   962
wenzelm@6437
   963
(** package setup **)
wenzelm@6437
   964
wenzelm@6437
   965
(* setup theory *)
wenzelm@6437
   966
wenzelm@8634
   967
val setup =
wenzelm@30722
   968
  ind_cases_setup #>
wenzelm@30528
   969
  Attrib.setup @{binding mono} (Attrib.add_del mono_add mono_del)
wenzelm@30528
   970
    "declaration of monotonicity rule";
wenzelm@6437
   971
wenzelm@6437
   972
wenzelm@6437
   973
(* outer syntax *)
wenzelm@6424
   974
wenzelm@17057
   975
local structure P = OuterParse and K = OuterKeyword in
wenzelm@6424
   976
wenzelm@27353
   977
val _ = OuterKeyword.keyword "monos";
wenzelm@24867
   978
berghofe@23762
   979
fun gen_ind_decl mk_def coind =
wenzelm@21367
   980
  P.fixes -- P.for_fixes --
wenzelm@30486
   981
  Scan.optional SpecParse.where_alt_specs [] --
wenzelm@22102
   982
  Scan.optional (P.$$$ "monos" |-- P.!!! SpecParse.xthms1) []
wenzelm@26988
   983
  >> (fn (((preds, params), specs), monos) =>
wenzelm@30486
   984
      (snd oo gen_add_inductive mk_def true coind preds params specs monos));
berghofe@23762
   985
berghofe@23762
   986
val ind_decl = gen_ind_decl add_ind_def;
wenzelm@6424
   987
wenzelm@33458
   988
val _ =
wenzelm@33458
   989
  OuterSyntax.local_theory' "inductive" "define inductive predicates" K.thy_decl
wenzelm@33458
   990
    (ind_decl false);
wenzelm@33458
   991
wenzelm@33458
   992
val _ =
wenzelm@33458
   993
  OuterSyntax.local_theory' "coinductive" "define coinductive predicates" K.thy_decl
wenzelm@33458
   994
    (ind_decl true);
wenzelm@6723
   995
wenzelm@24867
   996
val _ =
wenzelm@26988
   997
  OuterSyntax.local_theory "inductive_cases"
wenzelm@21367
   998
    "create simplified instances of elimination rules (improper)" K.thy_script
wenzelm@30486
   999
    (P.and_list1 SpecParse.specs >> (snd oo inductive_cases));
wenzelm@7107
  1000
berghofe@5094
  1001
end;
wenzelm@6424
  1002
wenzelm@6424
  1003
end;