src/HOL/Tools/inductive_package.ML
author wenzelm
Thu Aug 02 21:45:07 2007 +0200 (2007-08-02)
changeset 24133 75063f96618f
parent 24039 273698405054
child 24509 23ee6b7788c2
permissions -rw-r--r--
added int type constraints to accomodate hacked SML/NJ;
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(*  Title:      HOL/Tools/inductive_package.ML
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    ID:         $Id$
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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_PACKAGE =
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sig
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  val quiet_mode: bool ref
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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: ((bstring * Attrib.src list) * string list) list ->
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    Proof.context -> thm list list * local_theory
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  val inductive_cases_i: ((bstring * Attrib.src list) * term list) list ->
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    Proof.context -> thm list list * local_theory
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  val add_inductive_i: bool -> bstring -> bool -> bool -> bool ->
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    (string * typ option * mixfix) list ->
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    (string * typ option) list -> ((bstring * Attrib.src list) * term) list -> thm list ->
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      local_theory -> inductive_result * local_theory
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  val add_inductive: bool -> bool -> (string * string option * mixfix) list ->
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    (string * string option * mixfix) list ->
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    ((bstring * Attrib.src list) * string) list -> (thmref * Attrib.src list) list ->
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    local_theory -> inductive_result * local_theory
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  val add_inductive_global: bool -> bstring -> bool -> bool -> bool ->
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    (string * typ option * mixfix) list -> (string * typ option) list ->
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    ((bstring * Attrib.src list) * term) list -> 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 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_PACKAGE =
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sig
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  include BASIC_INDUCTIVE_PACKAGE
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  type add_ind_def
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  val declare_rules: bstring -> bool -> bool -> string list ->
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    thm list -> bstring 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 ->
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    bool -> bstring -> bool -> bool -> bool ->
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    (string * typ option * mixfix) list ->
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    (string * typ option) list -> ((bstring * Attrib.src list) * term) list -> thm list ->
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      local_theory -> inductive_result * local_theory
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  val gen_add_inductive: add_ind_def ->
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    bool -> bool -> (string * string option * mixfix) list ->
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    (string * string option * mixfix) list ->
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    ((bstring * Attrib.src list) * string) list -> (thmref * Attrib.src list) list ->
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    local_theory -> inductive_result * local_theory
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  val gen_ind_decl: add_ind_def ->
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    bool -> OuterParse.token list ->
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    (Toplevel.transition -> Toplevel.transition) * OuterParse.token list
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end;
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structure InductivePackage: INDUCTIVE_PACKAGE =
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struct
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(** theory context references **)
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val mono_name = "Orderings.mono";
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val gfp_name = "FixedPoint.gfp";
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val lfp_name = "FixedPoint.lfp";
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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 (fn s => mk_meta_eq (the (find_first
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  (equal (Sign.read_prop HOL.thy s) o prop_of) simp_thms)))
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  ["(~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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(** 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 (NameSpace.extern_table (space, tab))),
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     Pretty.big_list "monotonicity rules:" (map (ProofContext.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 (apfst (fn tab =>
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  fold (fn name => Symtab.update_new (name, info)) names tab
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    handle Symtab.DUP d => error ("Duplicate definition of (co)inductive predicate " ^ quote d)));
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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 le_funD)
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      handle THM _ => thm RS 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 ("HOL.ord_class.less_eq", _) $ _ $ _) =>
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      [dest_less_concl (Seq.hd (REPEAT (FIRSTGOAL
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         (resolve_tac [le_funI, le_boolI'])) thm))]
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    | _ => [thm]
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  end handle THM _ => error ("Bad monotonicity theorem:\n" ^ string_of_thm 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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val quiet_mode = ref false;
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fun message s = if ! quiet_mode then () else writeln s;
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fun clean_message s = if ! quick_and_dirty then () else message s;
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val note_theorems = LocalTheory.notes Thm.theoremK;
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val note_theorem = LocalTheory.note Thm.theoremK;
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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 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 ("arbitrary", 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_eq 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)
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        (List.drop (binder_types (fastype_of c), k)))
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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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    ProofContext.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", ProofContext.string_of_term ctxt p,
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    "in introduction rule " ^ quote name, ProofContext.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 ((name, att), rule) =
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  let
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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 (ProofContext.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 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 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 name rule') t;
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            List.app check_prem (prems ~~ aprems))
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         else err_in_rule ctxt name rule' bad_concl
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     | _ => err_in_rule ctxt name rule' bad_concl);
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    ((name, att), arule)
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  end;
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val rulify =  (* FIXME norm_hhf *)
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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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  (*#> standard*);
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end;
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(** proofs for (co)inductive predicates **)
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(* prove monotonicity -- NOT subject to quick_and_dirty! *)
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berghofe@21024
   324
fun prove_mono predT fp_fun monos ctxt =
wenzelm@10735
   325
 (message "  Proving monotonicity ...";
berghofe@21024
   326
  Goal.prove ctxt [] []   (*NO quick_and_dirty here!*)
wenzelm@17985
   327
    (HOLogic.mk_Trueprop
berghofe@21024
   328
      (Const (mono_name, (predT --> predT) --> HOLogic.boolT) $ fp_fun))
wenzelm@17985
   329
    (fn _ => EVERY [rtac monoI 1,
berghofe@21024
   330
      REPEAT (resolve_tac [le_funI, le_boolI'] 1),
berghofe@21024
   331
      REPEAT (FIRST
berghofe@21024
   332
        [atac 1,
wenzelm@21367
   333
         resolve_tac (List.concat (map mk_mono monos) @ get_monos ctxt) 1,
berghofe@21024
   334
         etac le_funE 1, dtac le_boolD 1])]));
berghofe@5094
   335
wenzelm@6424
   336
wenzelm@10735
   337
(* prove introduction rules *)
berghofe@5094
   338
berghofe@22605
   339
fun prove_intrs coind mono fp_def k params intr_ts rec_preds_defs ctxt =
berghofe@5094
   340
  let
wenzelm@10735
   341
    val _ = clean_message "  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
berghofe@21024
   345
        (if coind then def_gfp_unfold else 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
berghofe@22605
   354
      (SkipProof.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
berghofe@21024
   367
fun prove_elims cs params intr_ts intr_names unfold rec_preds_defs ctxt =
berghofe@5094
   368
  let
wenzelm@10735
   369
    val _ = clean_message "  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
berghofe@21024
   387
        val Ts = List.drop (binder_types (fastype_of c), length params);
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));
berghofe@21024
   395
        val c_intrs = (List.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
berghofe@21048
   399
        (SkipProof.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*)
haftmann@22838
   421
val refl_thin = Goal.prove_global HOL.thy [] []
haftmann@22838
   422
  (Sign.read_prop HOL.thy "!!P. a = a ==> P ==> P")
haftmann@22838
   423
  (fn _ => assume_tac 1);
berghofe@21024
   424
val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
wenzelm@11682
   425
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
wenzelm@11682
   426
berghofe@23762
   427
fun simp_case_tac ss i =
berghofe@23762
   428
  EVERY' [elim_tac, asm_full_simp_tac ss, elim_tac, REPEAT o bound_hyp_subst_tac] i;
wenzelm@21367
   429
wenzelm@11682
   430
in
wenzelm@9598
   431
wenzelm@21367
   432
fun mk_cases ctxt prop =
wenzelm@7107
   433
  let
wenzelm@21367
   434
    val thy = ProofContext.theory_of ctxt;
wenzelm@21367
   435
    val ss = Simplifier.local_simpset_of ctxt;
wenzelm@21367
   436
wenzelm@21526
   437
    fun err msg =
wenzelm@21526
   438
      error (Pretty.string_of (Pretty.block
wenzelm@21526
   439
        [Pretty.str msg, Pretty.fbrk, ProofContext.pretty_term ctxt prop]));
wenzelm@21526
   440
berghofe@23762
   441
    val elims = InductAttrib.find_casesS ctxt prop;
wenzelm@21367
   442
wenzelm@21367
   443
    val cprop = Thm.cterm_of thy prop;
berghofe@23762
   444
    val tac = ALLGOALS (simp_case_tac ss) THEN prune_params_tac;
wenzelm@21367
   445
    fun mk_elim rl =
wenzelm@21367
   446
      Thm.implies_intr cprop (Tactic.rule_by_tactic tac (Thm.assume cprop RS rl))
wenzelm@21367
   447
      |> singleton (Variable.export (Variable.auto_fixes prop ctxt) ctxt);
wenzelm@7107
   448
  in
wenzelm@7107
   449
    (case get_first (try mk_elim) elims of
skalberg@15531
   450
      SOME r => r
wenzelm@21526
   451
    | NONE => err "Proposition not an inductive predicate:")
wenzelm@7107
   452
  end;
wenzelm@7107
   453
wenzelm@11682
   454
end;
wenzelm@11682
   455
wenzelm@7107
   456
wenzelm@21367
   457
(* inductive_cases *)
wenzelm@7107
   458
wenzelm@21367
   459
fun gen_inductive_cases prep_att prep_prop args lthy =
wenzelm@9598
   460
  let
wenzelm@21367
   461
    val thy = ProofContext.theory_of lthy;
wenzelm@12876
   462
    val facts = args |> map (fn ((a, atts), props) =>
wenzelm@21367
   463
      ((a, map (prep_att thy) atts),
wenzelm@21367
   464
        map (Thm.no_attributes o single o mk_cases lthy o prep_prop lthy) props));
wenzelm@21433
   465
  in lthy |> note_theorems facts |>> map snd end;
berghofe@5094
   466
wenzelm@21367
   467
val inductive_cases = gen_inductive_cases Attrib.intern_src ProofContext.read_prop;
wenzelm@12172
   468
val inductive_cases_i = gen_inductive_cases (K I) ProofContext.cert_prop;
wenzelm@7107
   469
wenzelm@6424
   470
berghofe@22275
   471
fun ind_cases src = Method.syntax (Scan.lift (Scan.repeat1 Args.name --
berghofe@22275
   472
    Scan.optional (Args.$$$ "for" |-- Scan.repeat1 Args.name) [])) src
berghofe@22275
   473
  #> (fn ((raw_props, fixes), ctxt) =>
berghofe@22275
   474
    let
berghofe@22275
   475
      val (_, ctxt') = Variable.add_fixes fixes ctxt;
berghofe@22275
   476
      val props = map (ProofContext.read_prop ctxt') raw_props;
berghofe@22275
   477
      val ctxt'' = fold Variable.declare_term props ctxt';
berghofe@22275
   478
      val rules = ProofContext.export ctxt'' ctxt (map (mk_cases ctxt'') props)
berghofe@22275
   479
    in Method.erule 0 rules end);
wenzelm@9598
   480
wenzelm@9598
   481
wenzelm@9598
   482
wenzelm@10735
   483
(* prove induction rule *)
berghofe@5094
   484
berghofe@21024
   485
fun prove_indrule cs argTs bs xs rec_const params intr_ts mono
berghofe@21024
   486
    fp_def rec_preds_defs ctxt =
berghofe@5094
   487
  let
wenzelm@10735
   488
    val _ = clean_message "  Proving the induction rule ...";
wenzelm@20047
   489
    val thy = ProofContext.theory_of ctxt;
berghofe@5094
   490
berghofe@21024
   491
    (* predicates for induction rule *)
berghofe@21024
   492
berghofe@22605
   493
    val (pnames, ctxt') = ctxt |>
berghofe@22605
   494
      Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
berghofe@22605
   495
      Variable.variant_fixes (mk_names "P" (length cs));
berghofe@21024
   496
    val preds = map Free (pnames ~~
berghofe@21024
   497
      map (fn c => List.drop (binder_types (fastype_of c), length params) --->
berghofe@21024
   498
        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,
berghofe@21024
   528
        Logic.list_implies (map HOLogic.mk_Trueprop (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
berghofe@21024
   552
      (map_index (fn (i, P) => 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
paulson@13626
   559
    val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
paulson@13626
   560
berghofe@21024
   561
    val induct = SkipProof.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),
berghofe@21024
   565
         REPEAT (resolve_tac [le_funI, le_boolI] 1),
haftmann@22460
   566
         rewrite_goals_tac (inf_fun_eq :: inf_bool_eq :: 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
berghofe@22980
   575
             (inductive_conj_def :: rec_preds_defs @ simp_thms') prem,
berghofe@22980
   576
           conjI, refl] 1)) prems)]);
berghofe@5094
   577
berghofe@21024
   578
    val lemma = SkipProof.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),
berghofe@21024
   583
            REPEAT (eresolve_tac [le_funE, 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
berghofe@21024
   594
fun mk_ind_def alt_name coind cs intr_ts monos
berghofe@21024
   595
      params cnames_syn ctxt =
berghofe@5094
   596
  let
wenzelm@10735
   597
    val fp_name = if coind then gfp_name else lfp_name;
berghofe@5094
   598
berghofe@21024
   599
    val argTs = fold (fn c => fn Ts => Ts @
berghofe@21024
   600
      (List.drop (binder_types (fastype_of c), length params) \\ Ts)) cs [];
berghofe@21024
   601
    val k = log 2 1 (length cs);
berghofe@21024
   602
    val predT = replicate k HOLogic.boolT ---> argTs ---> HOLogic.boolT;
berghofe@21024
   603
    val p :: xs = map Free (Variable.variant_frees ctxt intr_ts
berghofe@21024
   604
      (("p", predT) :: (mk_names "x" (length argTs) ~~ argTs)));
berghofe@21024
   605
    val bs = map Free (Variable.variant_frees ctxt (p :: xs @ intr_ts)
berghofe@21024
   606
      (map (rpair HOLogic.boolT) (mk_names "b" k)));
berghofe@21024
   607
berghofe@21024
   608
    fun subst t = (case dest_predicate cs params t of
berghofe@21024
   609
        SOME (_, i, ts, (Ts, Us)) =>
berghofe@23762
   610
          let
berghofe@23762
   611
            val l = length Us;
berghofe@23762
   612
            val zs = map Bound (l - 1 downto 0)
berghofe@21024
   613
          in
berghofe@21024
   614
            list_abs (map (pair "z") Us, list_comb (p,
berghofe@23762
   615
              make_bool_args' bs i @ make_args argTs
berghofe@23762
   616
                ((map (incr_boundvars l) ts ~~ Ts) @ (zs ~~ Us))))
berghofe@21024
   617
          end
berghofe@21024
   618
      | NONE => (case t of
berghofe@21024
   619
          t1 $ t2 => subst t1 $ subst t2
berghofe@21024
   620
        | Abs (x, T, u) => Abs (x, T, subst u)
berghofe@21024
   621
        | _ => t));
berghofe@5149
   622
berghofe@5094
   623
    (* transform an introduction rule into a conjunction  *)
berghofe@21024
   624
    (*   [| p_i t; ... |] ==> p_j u                       *)
berghofe@5094
   625
    (* is transformed into                                *)
berghofe@21024
   626
    (*   b_j & x_j = u & p b_j t & ...                    *)
berghofe@5094
   627
berghofe@5094
   628
    fun transform_rule r =
berghofe@5094
   629
      let
berghofe@21024
   630
        val SOME (_, i, ts, (Ts, _)) = dest_predicate cs params
berghofe@21048
   631
          (HOLogic.dest_Trueprop (Logic.strip_assums_concl r));
berghofe@21048
   632
        val ps = make_bool_args HOLogic.mk_not I bs i @
berghofe@21048
   633
          map HOLogic.mk_eq (make_args' argTs xs Ts ~~ ts) @
berghofe@21048
   634
          map (subst o HOLogic.dest_Trueprop)
berghofe@21048
   635
            (Logic.strip_assums_hyp r)
berghofe@21024
   636
      in foldr (fn ((x, T), P) => HOLogic.exists_const T $ (Abs (x, T, P)))
berghofe@21048
   637
        (if null ps then HOLogic.true_const else foldr1 HOLogic.mk_conj ps)
berghofe@21048
   638
        (Logic.strip_params r)
berghofe@5094
   639
      end
berghofe@5094
   640
berghofe@5094
   641
    (* make a disjunction of all introduction rules *)
berghofe@5094
   642
berghofe@21024
   643
    val fp_fun = fold_rev lambda (p :: bs @ xs)
berghofe@21024
   644
      (if null intr_ts then HOLogic.false_const
berghofe@21024
   645
       else foldr1 HOLogic.mk_disj (map transform_rule intr_ts));
berghofe@5094
   646
berghofe@21024
   647
    (* add definiton of recursive predicates to theory *)
berghofe@5094
   648
berghofe@14235
   649
    val rec_name = if alt_name = "" then
berghofe@21024
   650
      space_implode "_" (map fst cnames_syn) else alt_name;
berghofe@5094
   651
berghofe@21024
   652
    val ((rec_const, (_, fp_def)), ctxt') = ctxt |>
wenzelm@21433
   653
      LocalTheory.def Thm.internalK
berghofe@21024
   654
        ((rec_name, case cnames_syn of [(_, syn)] => syn | _ => NoSyn),
berghofe@21024
   655
         (("", []), fold_rev lambda params
berghofe@21024
   656
           (Const (fp_name, (predT --> predT) --> predT) $ fp_fun)));
berghofe@21024
   657
    val fp_def' = Simplifier.rewrite (HOL_basic_ss addsimps [fp_def])
berghofe@21024
   658
      (cterm_of (ProofContext.theory_of ctxt') (list_comb (rec_const, params)));
berghofe@21024
   659
    val specs = if length cs < 2 then [] else
berghofe@21024
   660
      map_index (fn (i, (name_mx, c)) =>
berghofe@21024
   661
        let
berghofe@21024
   662
          val Ts = List.drop (binder_types (fastype_of c), length params);
berghofe@21024
   663
          val xs = map Free (Variable.variant_frees ctxt intr_ts
berghofe@21024
   664
            (mk_names "x" (length Ts) ~~ Ts))
berghofe@21024
   665
        in
berghofe@21024
   666
          (name_mx, (("", []), fold_rev lambda (params @ xs)
berghofe@21024
   667
            (list_comb (rec_const, params @ make_bool_args' bs i @
berghofe@21024
   668
              make_args argTs (xs ~~ Ts)))))
berghofe@21024
   669
        end) (cnames_syn ~~ cs);
berghofe@23762
   670
    val (consts_defs, ctxt'') = LocalTheory.defs Thm.internalK specs ctxt';
berghofe@21024
   671
    val preds = (case cs of [_] => [rec_const] | _ => map #1 consts_defs);
berghofe@5094
   672
berghofe@21024
   673
    val mono = prove_mono predT fp_fun monos ctxt''
berghofe@5094
   674
berghofe@21024
   675
  in (ctxt'', rec_name, mono, fp_def', map (#2 o #2) consts_defs,
berghofe@21024
   676
    list_comb (rec_const, params), preds, argTs, bs, xs)
berghofe@21024
   677
  end;
berghofe@5094
   678
berghofe@23762
   679
fun declare_rules rec_name coind no_ind cnames intrs intr_names intr_atts
berghofe@23762
   680
      elims raw_induct ctxt =
berghofe@23762
   681
  let
berghofe@23762
   682
    val ind_case_names = RuleCases.case_names intr_names;
berghofe@23762
   683
    val induct =
berghofe@23762
   684
      if coind then
berghofe@23762
   685
        (raw_induct, [RuleCases.case_names [rec_name],
berghofe@23762
   686
          RuleCases.case_conclusion (rec_name, intr_names),
berghofe@23762
   687
          RuleCases.consumes 1, InductAttrib.coinduct_set (hd cnames)])
berghofe@23762
   688
      else if no_ind orelse length cnames > 1 then
berghofe@23762
   689
        (raw_induct, [ind_case_names, RuleCases.consumes 0])
berghofe@23762
   690
      else (raw_induct RSN (2, rev_mp), [ind_case_names, RuleCases.consumes 1]);
berghofe@23762
   691
berghofe@23762
   692
    val (intrs', ctxt1) =
berghofe@23762
   693
      ctxt |>
berghofe@23762
   694
      note_theorems
berghofe@23762
   695
        (map (NameSpace.qualified rec_name) intr_names ~~
berghofe@23762
   696
         intr_atts ~~ map (fn th => [([th],
berghofe@23762
   697
           [Attrib.internal (K (ContextRules.intro_query NONE))])]) intrs) |>>
berghofe@23762
   698
      map (hd o snd); (* FIXME? *)
berghofe@23762
   699
    val (((_, elims'), (_, [induct'])), ctxt2) =
berghofe@23762
   700
      ctxt1 |>
berghofe@23762
   701
      note_theorem ((NameSpace.qualified rec_name "intros", []), intrs') ||>>
berghofe@23762
   702
      fold_map (fn (name, (elim, cases)) =>
berghofe@23762
   703
        note_theorem ((NameSpace.qualified (Sign.base_name name) "cases",
berghofe@23762
   704
          [Attrib.internal (K (RuleCases.case_names cases)),
berghofe@23762
   705
           Attrib.internal (K (RuleCases.consumes 1)),
berghofe@23762
   706
           Attrib.internal (K (InductAttrib.cases_set name)),
berghofe@23762
   707
           Attrib.internal (K (ContextRules.elim_query NONE))]), [elim]) #>
berghofe@23762
   708
        apfst (hd o snd)) (if null elims then [] else cnames ~~ elims) ||>>
berghofe@23762
   709
      note_theorem ((NameSpace.qualified rec_name (coind_prefix coind ^ "induct"),
berghofe@23762
   710
        map (Attrib.internal o K) (#2 induct)), [rulify (#1 induct)]);
berghofe@23762
   711
berghofe@23762
   712
    val ctxt3 = if no_ind orelse coind then ctxt2 else
berghofe@23762
   713
      let val inducts = cnames ~~ ProjectRule.projects ctxt2 (1 upto length cnames) induct'
berghofe@23762
   714
      in
berghofe@23762
   715
        ctxt2 |>
berghofe@23762
   716
        note_theorems [((NameSpace.qualified rec_name "inducts", []),
berghofe@23762
   717
          inducts |> map (fn (name, th) => ([th],
berghofe@23762
   718
            [Attrib.internal (K ind_case_names),
berghofe@23762
   719
             Attrib.internal (K (RuleCases.consumes 1)),
berghofe@23762
   720
             Attrib.internal (K (InductAttrib.induct_set name))])))] |> snd
berghofe@23762
   721
      end
berghofe@23762
   722
  in (intrs', elims', induct', ctxt3) end;
berghofe@23762
   723
berghofe@23762
   724
type add_ind_def = bool -> bstring -> bool -> bool -> bool ->
berghofe@23762
   725
  term list -> ((string * Attrib.src list) * term) list -> thm list ->
berghofe@23762
   726
  term list -> (string * mixfix) list ->
berghofe@23762
   727
  local_theory -> inductive_result * local_theory
berghofe@23762
   728
berghofe@21024
   729
fun add_ind_def verbose alt_name coind no_elim no_ind cs
berghofe@21048
   730
    intros monos params cnames_syn ctxt =
berghofe@9072
   731
  let
wenzelm@10735
   732
    val _ =
berghofe@21024
   733
      if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^
berghofe@21024
   734
        commas_quote (map fst cnames_syn)) else ();
berghofe@9072
   735
wenzelm@21526
   736
    val cnames = map (Sign.full_name (ProofContext.theory_of ctxt) o #1) cnames_syn;  (* FIXME *)
berghofe@23762
   737
    val ((intr_names, intr_atts), intr_ts) =
berghofe@23762
   738
      apfst split_list (split_list (map (check_rule ctxt cs params) intros));
berghofe@21024
   739
berghofe@21024
   740
    val (ctxt1, rec_name, mono, fp_def, rec_preds_defs, rec_const, preds,
berghofe@21024
   741
      argTs, bs, xs) = mk_ind_def alt_name coind cs intr_ts
berghofe@21024
   742
        monos params cnames_syn ctxt;
berghofe@9072
   743
berghofe@21024
   744
    val (intrs, unfold) = prove_intrs coind mono fp_def (length bs + length xs)
berghofe@22605
   745
      params intr_ts rec_preds_defs ctxt1;
berghofe@21048
   746
    val elims = if no_elim then [] else
berghofe@23762
   747
      prove_elims cs params intr_ts intr_names unfold rec_preds_defs ctxt1;
berghofe@22605
   748
    val raw_induct = zero_var_indexes
berghofe@21024
   749
      (if no_ind then Drule.asm_rl else
berghofe@23762
   750
       if coind then
berghofe@23762
   751
         singleton (ProofContext.export
berghofe@23762
   752
           (snd (Variable.add_fixes (map (fst o dest_Free) params) ctxt1)) ctxt1)
berghofe@23762
   753
           (rotate_prems ~1 (ObjectLogic.rulify (rule_by_tactic
berghofe@23762
   754
             (rewrite_tac [le_fun_def, le_bool_def, sup_fun_eq, sup_bool_eq] THEN
berghofe@23762
   755
               fold_tac rec_preds_defs) (mono RS (fp_def RS def_coinduct)))))
berghofe@21024
   756
       else
berghofe@21024
   757
         prove_indrule cs argTs bs xs rec_const params intr_ts mono fp_def
berghofe@22605
   758
           rec_preds_defs ctxt1);
berghofe@5094
   759
berghofe@23762
   760
    val (intrs', elims', induct, ctxt2) = declare_rules rec_name coind no_ind
berghofe@23762
   761
      cnames intrs intr_names intr_atts elims raw_induct ctxt1;
berghofe@21048
   762
wenzelm@21526
   763
    val names = map #1 cnames_syn;
berghofe@21048
   764
    val result =
berghofe@21048
   765
      {preds = preds,
berghofe@21048
   766
       intrs = intrs',
berghofe@21048
   767
       elims = elims',
berghofe@21048
   768
       raw_induct = rulify raw_induct,
berghofe@23762
   769
       induct = induct};
wenzelm@21367
   770
berghofe@23762
   771
    val ctxt3 = ctxt2
wenzelm@21526
   772
      |> Context.proof_map (put_inductives names ({names = names, coind = coind}, result))
wenzelm@21526
   773
      |> LocalTheory.declaration (fn phi =>
wenzelm@21526
   774
        let
berghofe@23762
   775
          val names' = map (LocalTheory.target_name ctxt2 o Morphism.name phi) names;
wenzelm@22667
   776
          val result' = morph_result phi result;
wenzelm@21526
   777
        in put_inductives names' ({names = names', coind = coind}, result') end);
berghofe@23762
   778
  in (result, ctxt3) end;
berghofe@5094
   779
wenzelm@6424
   780
wenzelm@10735
   781
(* external interfaces *)
berghofe@5094
   782
berghofe@23762
   783
fun gen_add_inductive_i mk_def verbose alt_name coind no_elim no_ind
berghofe@23762
   784
    cnames_syn pnames pre_intros monos ctxt =
berghofe@5094
   785
  let
berghofe@21024
   786
    val thy = ProofContext.theory_of ctxt;
wenzelm@6424
   787
    val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
berghofe@5094
   788
berghofe@21024
   789
    val frees = fold (Term.add_frees o snd) pre_intros [];
berghofe@21024
   790
    fun type_of s = (case AList.lookup op = frees s of
berghofe@21024
   791
      NONE => error ("No such variable: " ^ s) | SOME T => T);
berghofe@5094
   792
berghofe@21766
   793
    fun is_abbrev ((name, atts), t) =
berghofe@21766
   794
      can (Logic.strip_assums_concl #> Logic.dest_equals) t andalso
berghofe@21766
   795
      (name = "" andalso null atts orelse
berghofe@21766
   796
       error "Abbreviations may not have names or attributes");
berghofe@21766
   797
berghofe@21766
   798
    fun expand_atom tab (t as Free xT) =
berghofe@21766
   799
          the_default t (AList.lookup op = tab xT)
berghofe@21766
   800
      | expand_atom tab t = t;
berghofe@21766
   801
    fun expand [] r = r
berghofe@21766
   802
      | expand tab r = Envir.beta_norm (Term.map_aterms (expand_atom tab) r);
berghofe@21766
   803
berghofe@21766
   804
    val (_, ctxt') = Variable.add_fixes (map #1 cnames_syn) ctxt;
berghofe@21766
   805
berghofe@21766
   806
    fun prep_abbrevs [] abbrevs' abbrevs'' = (rev abbrevs', rev abbrevs'')
berghofe@21766
   807
      | prep_abbrevs ((_, abbrev) :: abbrevs) abbrevs' abbrevs'' =
berghofe@21766
   808
          let val ((s, T), t) =
berghofe@21766
   809
            LocalDefs.abs_def (snd (LocalDefs.cert_def ctxt' abbrev))
berghofe@21766
   810
          in case find_first (equal s o #1) cnames_syn of
berghofe@21766
   811
              NONE => error ("Head of abbreviation " ^ quote s ^ " undeclared")
berghofe@21766
   812
            | SOME (_, _, mx) => prep_abbrevs abbrevs
berghofe@21766
   813
                (((s, T), expand abbrevs' t) :: abbrevs')
berghofe@21766
   814
                (((s, mx), expand abbrevs' t) :: abbrevs'') (* FIXME: do not expand *)
berghofe@21766
   815
          end;
berghofe@21766
   816
berghofe@21766
   817
    val (abbrevs, pre_intros') = List.partition is_abbrev pre_intros;
berghofe@21766
   818
    val (abbrevs', abbrevs'') = prep_abbrevs abbrevs [] [];
berghofe@21766
   819
    val _ = (case gen_inter (op = o apsnd fst)
berghofe@21766
   820
      (fold (Term.add_frees o snd) abbrevs' [], abbrevs') of
berghofe@21766
   821
        [] => ()
berghofe@21766
   822
      | xs => error ("Bad abbreviation(s): " ^ commas (map fst xs)));
berghofe@21766
   823
berghofe@21024
   824
    val params = map
berghofe@21024
   825
      (fn (s, SOME T) => Free (s, T) | (s, NONE) => Free (s, type_of s)) pnames;
berghofe@21766
   826
    val cnames_syn' = filter_out (fn (s, _, _) =>
berghofe@21766
   827
      exists (equal s o fst o fst) abbrevs') cnames_syn;
berghofe@21024
   828
    val cs = map
berghofe@21766
   829
      (fn (s, SOME T, _) => Free (s, T) | (s, NONE, _) => Free (s, type_of s)) cnames_syn';
berghofe@21766
   830
    val cnames_syn'' = map (fn (s, _, mx) => (s, mx)) cnames_syn';
berghofe@5094
   831
berghofe@21024
   832
    fun close_rule (x, r) = (x, list_all_free (rev (fold_aterms
berghofe@21024
   833
      (fn t as Free (v as (s, _)) =>
berghofe@21024
   834
            if Variable.is_fixed ctxt s orelse member op = cs t orelse
berghofe@21024
   835
              member op = params t then I else insert op = v
berghofe@21024
   836
        | _ => I) r []), r));
berghofe@5094
   837
berghofe@23762
   838
    val intros = map (apsnd (expand abbrevs') #> close_rule) pre_intros';
berghofe@21048
   839
  in
berghofe@21766
   840
    ctxt |>
berghofe@23762
   841
    mk_def verbose alt_name coind no_elim no_ind cs intros monos
berghofe@21766
   842
      params cnames_syn'' ||>
wenzelm@21793
   843
    fold (snd oo LocalTheory.abbrev Syntax.default_mode) abbrevs''
berghofe@21048
   844
  end;
berghofe@5094
   845
berghofe@23762
   846
fun gen_add_inductive mk_def verbose coind cnames_syn pnames_syn intro_srcs raw_monos ctxt =
berghofe@5094
   847
  let
berghofe@21024
   848
    val (_, ctxt') = Specification.read_specification (cnames_syn @ pnames_syn) [] ctxt;
berghofe@21766
   849
    val intrs = map (fn ((name, att), s) => apsnd hd (hd (snd (fst
berghofe@21766
   850
      (Specification.read_specification [] [((name, att), [s])] ctxt'))))
berghofe@21766
   851
      handle ERROR msg =>
berghofe@21766
   852
        cat_error msg ("The error(s) above occurred for\n" ^
berghofe@21766
   853
          (if name = "" then "" else name ^ ": ") ^ s)) intro_srcs;
berghofe@21024
   854
    val pnames = map (fn (s, _, _) =>
berghofe@21024
   855
      (s, SOME (ProofContext.infer_type ctxt' s))) pnames_syn;
berghofe@21024
   856
    val cnames_syn' = map (fn (s, _, mx) =>
berghofe@21024
   857
      (s, SOME (ProofContext.infer_type ctxt' s), mx)) cnames_syn;
wenzelm@21350
   858
    val (monos, ctxt'') = LocalTheory.theory_result (IsarCmd.apply_theorems raw_monos) ctxt;
wenzelm@6424
   859
  in
berghofe@23762
   860
    gen_add_inductive_i mk_def verbose "" coind false false cnames_syn' pnames intrs monos ctxt''
berghofe@5094
   861
  end;
berghofe@5094
   862
berghofe@23762
   863
val add_inductive_i = gen_add_inductive_i add_ind_def;
berghofe@23762
   864
val add_inductive = gen_add_inductive add_ind_def;
berghofe@23762
   865
wenzelm@21526
   866
fun add_inductive_global verbose alt_name coind no_elim no_ind cnames_syn pnames pre_intros monos =
wenzelm@21526
   867
  TheoryTarget.init NONE #>
wenzelm@21526
   868
  add_inductive_i verbose alt_name coind no_elim no_ind cnames_syn pnames pre_intros monos #>
wenzelm@21526
   869
  (fn (_, lthy) =>
wenzelm@21526
   870
    (#2 (the_inductive (LocalTheory.target_of lthy)
wenzelm@21526
   871
      (LocalTheory.target_name lthy (#1 (hd cnames_syn)))),
wenzelm@21526
   872
    ProofContext.theory_of (LocalTheory.exit lthy)));
wenzelm@6424
   873
wenzelm@6424
   874
berghofe@22789
   875
(* read off arities of inductive predicates from raw induction rule *)
berghofe@22789
   876
fun arities_of induct =
berghofe@22789
   877
  map (fn (_ $ t $ u) =>
berghofe@22789
   878
      (fst (dest_Const (head_of t)), length (snd (strip_comb u))))
berghofe@22789
   879
    (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct)));
berghofe@22789
   880
berghofe@22789
   881
(* read off parameters of inductive predicate from raw induction rule *)
berghofe@22789
   882
fun params_of induct =
berghofe@22789
   883
  let
berghofe@22789
   884
    val (_ $ t $ u :: _) =
berghofe@22789
   885
      HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of induct));
berghofe@22789
   886
    val (_, ts) = strip_comb t;
berghofe@22789
   887
    val (_, us) = strip_comb u
berghofe@22789
   888
  in
berghofe@22789
   889
    List.take (ts, length ts - length us)
berghofe@22789
   890
  end;
berghofe@22789
   891
berghofe@22789
   892
val pname_of_intr =
berghofe@22789
   893
  concl_of #> HOLogic.dest_Trueprop #> head_of #> dest_Const #> fst;
berghofe@22789
   894
berghofe@22789
   895
(* partition introduction rules according to predicate name *)
berghofe@22789
   896
fun partition_rules induct intros =
berghofe@22789
   897
  fold_rev (fn r => AList.map_entry op = (pname_of_intr r) (cons r)) intros
berghofe@22789
   898
    (map (rpair [] o fst) (arities_of induct));
berghofe@22789
   899
berghofe@22789
   900
fun unpartition_rules intros xs =
berghofe@22789
   901
  fold_map (fn r => AList.map_entry_yield op = (pname_of_intr r)
berghofe@22789
   902
    (fn x :: xs => (x, xs)) #>> the) intros xs |> fst;
berghofe@22789
   903
berghofe@22789
   904
(* infer order of variables in intro rules from order of quantifiers in elim rule *)
berghofe@22789
   905
fun infer_intro_vars elim arity intros =
berghofe@22789
   906
  let
berghofe@22789
   907
    val thy = theory_of_thm elim;
berghofe@22789
   908
    val _ :: cases = prems_of elim;
berghofe@22789
   909
    val used = map (fst o fst) (Term.add_vars (prop_of elim) []);
berghofe@22789
   910
    fun mtch (t, u) =
berghofe@22789
   911
      let
berghofe@22789
   912
        val params = Logic.strip_params t;
berghofe@22789
   913
        val vars = map (Var o apfst (rpair 0))
berghofe@22789
   914
          (Name.variant_list used (map fst params) ~~ map snd params);
berghofe@22789
   915
        val ts = map (curry subst_bounds (rev vars))
berghofe@22789
   916
          (List.drop (Logic.strip_assums_hyp t, arity));
berghofe@22789
   917
        val us = Logic.strip_imp_prems u;
berghofe@22789
   918
        val tab = fold (Pattern.first_order_match thy) (ts ~~ us)
berghofe@22789
   919
          (Vartab.empty, Vartab.empty);
berghofe@22789
   920
      in
berghofe@22789
   921
        map (Envir.subst_vars tab) vars
berghofe@22789
   922
      end
berghofe@22789
   923
  in
berghofe@22789
   924
    map (mtch o apsnd prop_of) (cases ~~ intros)
berghofe@22789
   925
  end;
berghofe@22789
   926
berghofe@22789
   927
wenzelm@6437
   928
(** package setup **)
wenzelm@6437
   929
wenzelm@6437
   930
(* setup theory *)
wenzelm@6437
   931
wenzelm@8634
   932
val setup =
berghofe@23762
   933
  Method.add_methods [("ind_cases", ind_cases,
berghofe@21024
   934
    "dynamic case analysis on predicates")] #>
berghofe@23762
   935
  Attrib.add_attributes [("mono", Attrib.add_del_args mono_add mono_del,
wenzelm@18728
   936
    "declaration of monotonicity rule")];
wenzelm@6437
   937
wenzelm@6437
   938
wenzelm@6437
   939
(* outer syntax *)
wenzelm@6424
   940
wenzelm@17057
   941
local structure P = OuterParse and K = OuterKeyword in
wenzelm@6424
   942
wenzelm@21367
   943
(* FIXME tmp *)
wenzelm@21367
   944
fun flatten_specification specs = specs |> maps
wenzelm@21367
   945
  (fn (a, (concl, [])) => concl |> map
wenzelm@21367
   946
        (fn ((b, atts), [B]) =>
wenzelm@21367
   947
              if a = "" then ((b, atts), B)
wenzelm@21367
   948
              else if b = "" then ((a, atts), B)
wenzelm@21367
   949
              else error ("Illegal nested case names " ^ quote (NameSpace.append a b))
wenzelm@21367
   950
          | ((b, _), _) => error ("Illegal simultaneous specification " ^ quote b))
wenzelm@21367
   951
    | (a, _) => error ("Illegal local specification parameters for " ^ quote a));
wenzelm@6424
   952
berghofe@23762
   953
fun gen_ind_decl mk_def coind =
wenzelm@22102
   954
  P.opt_target --
wenzelm@21367
   955
  P.fixes -- P.for_fixes --
wenzelm@22102
   956
  Scan.optional (P.$$$ "where" |-- P.!!! SpecParse.specification) [] --
wenzelm@22102
   957
  Scan.optional (P.$$$ "monos" |-- P.!!! SpecParse.xthms1) []
wenzelm@21367
   958
  >> (fn ((((loc, preds), params), specs), monos) =>
wenzelm@21367
   959
    Toplevel.local_theory loc
berghofe@23762
   960
      (fn lthy => lthy |> gen_add_inductive mk_def true coind preds params
berghofe@23762
   961
         (flatten_specification specs) monos |> snd));
berghofe@23762
   962
berghofe@23762
   963
val ind_decl = gen_ind_decl add_ind_def;
wenzelm@6424
   964
wenzelm@6723
   965
val inductiveP =
berghofe@23762
   966
  OuterSyntax.command "inductive" "define inductive predicates" K.thy_decl (ind_decl false);
wenzelm@6723
   967
wenzelm@6723
   968
val coinductiveP =
berghofe@23762
   969
  OuterSyntax.command "coinductive" "define coinductive predicates" K.thy_decl (ind_decl true);
wenzelm@6424
   970
wenzelm@7107
   971
wenzelm@7107
   972
val inductive_casesP =
berghofe@23762
   973
  OuterSyntax.command "inductive_cases"
wenzelm@21367
   974
    "create simplified instances of elimination rules (improper)" K.thy_script
wenzelm@22102
   975
    (P.opt_target -- P.and_list1 SpecParse.spec
wenzelm@21367
   976
      >> (fn (loc, specs) => Toplevel.local_theory loc (snd o inductive_cases specs)));
wenzelm@7107
   977
wenzelm@21367
   978
val _ = OuterSyntax.add_keywords ["monos"];
wenzelm@7107
   979
val _ = OuterSyntax.add_parsers [inductiveP, coinductiveP, inductive_casesP];
wenzelm@6424
   980
berghofe@5094
   981
end;
wenzelm@6424
   982
wenzelm@6424
   983
end;