src/Tools/induct.ML
author wenzelm
Sun Nov 06 21:51:46 2011 +0100 (2011-11-06)
changeset 45375 7fe19930dfc9
parent 45328 e5b33eecbf6e
child 46961 5c6955f487e5
permissions -rw-r--r--
more explicit representation of rule_attribute vs. declaration_attribute vs. mixed_attribute;
misc tuning;
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(*  Title:      Tools/induct.ML
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    Author:     Markus Wenzel, TU Muenchen
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Proof by cases, induction, and coinduction.
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*)
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signature INDUCT_ARGS =
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sig
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  val cases_default: thm
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  val atomize: thm list
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  val rulify: thm list
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  val rulify_fallback: thm list
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  val equal_def: thm
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  val dest_def: term -> (term * term) option
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  val trivial_tac: int -> tactic
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end;
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signature INDUCT =
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sig
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  (*rule declarations*)
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  val vars_of: term -> term list
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  val dest_rules: Proof.context ->
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    {type_cases: (string * thm) list, pred_cases: (string * thm) list,
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      type_induct: (string * thm) list, pred_induct: (string * thm) list,
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      type_coinduct: (string * thm) list, pred_coinduct: (string * thm) list}
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  val print_rules: Proof.context -> unit
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  val lookup_casesT: Proof.context -> string -> thm option
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  val lookup_casesP: Proof.context -> string -> thm option
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  val lookup_inductT: Proof.context -> string -> thm option
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  val lookup_inductP: Proof.context -> string -> thm option
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  val lookup_coinductT: Proof.context -> string -> thm option
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  val lookup_coinductP: Proof.context -> string -> thm option
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  val find_casesT: Proof.context -> typ -> thm list
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  val find_casesP: Proof.context -> term -> thm list
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  val find_inductT: Proof.context -> typ -> thm list
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  val find_inductP: Proof.context -> term -> thm list
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  val find_coinductT: Proof.context -> typ -> thm list
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  val find_coinductP: Proof.context -> term -> thm list
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  val cases_type: string -> attribute
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  val cases_pred: string -> attribute
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  val cases_del: attribute
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  val induct_type: string -> attribute
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  val induct_pred: string -> attribute
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  val induct_del: attribute
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  val coinduct_type: string -> attribute
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  val coinduct_pred: string -> attribute
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  val coinduct_del: attribute
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  val map_simpset: (simpset -> simpset) -> Context.generic -> Context.generic
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  val induct_simp_add: attribute
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  val induct_simp_del: attribute
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  val no_simpN: string
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  val casesN: string
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  val inductN: string
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  val coinductN: string
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  val typeN: string
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  val predN: string
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  val setN: string
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  (*proof methods*)
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  val arbitrary_tac: Proof.context -> int -> (string * typ) list -> int -> tactic
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  val add_defs: (binding option * (term * bool)) option list -> Proof.context ->
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    (term option list * thm list) * Proof.context
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  val atomize_term: theory -> term -> term
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  val atomize_cterm: conv
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  val atomize_tac: int -> tactic
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  val inner_atomize_tac: int -> tactic
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  val rulified_term: thm -> theory * term
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  val rulify_tac: int -> tactic
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  val simplified_rule: Proof.context -> thm -> thm
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  val simplify_tac: Proof.context -> int -> tactic
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  val trivial_tac: int -> tactic
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  val rotate_tac: int -> int -> int -> tactic
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  val internalize: int -> thm -> thm
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  val guess_instance: Proof.context -> thm -> int -> thm -> thm Seq.seq
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  val cases_tac: Proof.context -> bool -> term option list list -> thm option ->
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    thm list -> int -> cases_tactic
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  val get_inductT: Proof.context -> term option list list -> thm list list
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  type case_data = (((string * string list) * string list) list * int) (* FIXME -> rule_cases.ML *)
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  val gen_induct_tac: (theory -> case_data * thm -> case_data * thm) ->
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    Proof.context -> bool -> (binding option * (term * bool)) option list list ->
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    (string * typ) list list -> term option list -> thm list option ->
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    thm list -> int -> cases_tactic
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  val induct_tac: Proof.context -> bool -> (binding option * (term * bool)) option list list ->
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    (string * typ) list list -> term option list -> thm list option ->
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    thm list -> int -> cases_tactic
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  val coinduct_tac: Proof.context -> term option list -> term option list -> thm option ->
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    thm list -> int -> cases_tactic
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  val gen_induct_setup: binding ->
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   (Proof.context -> bool -> (binding option * (term * bool)) option list list ->
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    (string * typ) list list -> term option list -> thm list option ->
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    thm list -> int -> cases_tactic) ->
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   theory -> theory
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  val setup: theory -> theory
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end;
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functor Induct(Induct_Args: INDUCT_ARGS): INDUCT =
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struct
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(** variables -- ordered left-to-right, preferring right **)
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fun vars_of tm =
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  rev (distinct (op =) (Term.fold_aterms (fn t as Var _ => cons t | _ => I) tm []));
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local
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val mk_var = Net.encode_type o #2 o Term.dest_Var;
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fun concl_var which thm = mk_var (which (vars_of (Thm.concl_of thm))) handle Empty =>
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  raise THM ("No variables in conclusion of rule", 0, [thm]);
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in
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fun left_var_prem thm = mk_var (hd (vars_of (hd (Thm.prems_of thm)))) handle Empty =>
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  raise THM ("No variables in major premise of rule", 0, [thm]);
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val left_var_concl = concl_var hd;
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val right_var_concl = concl_var List.last;
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end;
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(** constraint simplification **)
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(* rearrange parameters and premises to allow application of one-point-rules *)
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fun swap_params_conv ctxt i j cv =
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  let
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    fun conv1 0 ctxt = Conv.forall_conv (cv o snd) ctxt
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      | conv1 k ctxt =
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          Conv.rewr_conv @{thm swap_params} then_conv
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          Conv.forall_conv (conv1 (k - 1) o snd) ctxt
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    fun conv2 0 ctxt = conv1 j ctxt
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      | conv2 k ctxt = Conv.forall_conv (conv2 (k - 1) o snd) ctxt
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  in conv2 i ctxt end;
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fun swap_prems_conv 0 = Conv.all_conv
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  | swap_prems_conv i =
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      Conv.implies_concl_conv (swap_prems_conv (i - 1)) then_conv
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      Conv.rewr_conv Drule.swap_prems_eq
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fun drop_judgment ctxt = Object_Logic.drop_judgment (Proof_Context.theory_of ctxt);
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fun find_eq ctxt t =
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  let
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    val l = length (Logic.strip_params t);
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    val Hs = Logic.strip_assums_hyp t;
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    fun find (i, t) =
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      (case Induct_Args.dest_def (drop_judgment ctxt t) of
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        SOME (Bound j, _) => SOME (i, j)
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      | SOME (_, Bound j) => SOME (i, j)
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      | _ => NONE);
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  in
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    (case get_first find (map_index I Hs) of
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      NONE => NONE
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    | SOME (0, 0) => NONE
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    | SOME (i, j) => SOME (i, l - j - 1, j))
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  end;
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fun mk_swap_rrule ctxt ct =
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  (case find_eq ctxt (term_of ct) of
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    NONE => NONE
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  | SOME (i, k, j) => SOME (swap_params_conv ctxt k j (K (swap_prems_conv i)) ct));
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val rearrange_eqs_simproc =
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  Simplifier.simproc_global
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    (Thm.theory_of_thm Drule.swap_prems_eq) "rearrange_eqs" ["all t"]
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    (fn thy => fn ss => fn t =>
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      mk_swap_rrule (Simplifier.the_context ss) (cterm_of thy t));
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(* rotate k premises to the left by j, skipping over first j premises *)
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fun rotate_conv 0 j 0 = Conv.all_conv
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  | rotate_conv 0 j k = swap_prems_conv j then_conv rotate_conv 1 j (k - 1)
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  | rotate_conv i j k = Conv.implies_concl_conv (rotate_conv (i - 1) j k);
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fun rotate_tac j 0 = K all_tac
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  | rotate_tac j k = SUBGOAL (fn (goal, i) =>
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      CONVERSION (rotate_conv
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        j (length (Logic.strip_assums_hyp goal) - j - k) k) i);
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(* rulify operators around definition *)
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fun rulify_defs_conv ctxt ct =
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  if exists_subterm (is_some o Induct_Args.dest_def) (term_of ct) andalso
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    not (is_some (Induct_Args.dest_def (drop_judgment ctxt (term_of ct))))
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  then
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    (Conv.forall_conv (rulify_defs_conv o snd) ctxt else_conv
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     Conv.implies_conv (Conv.try_conv (rulify_defs_conv ctxt))
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       (Conv.try_conv (rulify_defs_conv ctxt)) else_conv
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     Conv.first_conv (map Conv.rewr_conv Induct_Args.rulify) then_conv
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       Conv.try_conv (rulify_defs_conv ctxt)) ct
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  else Conv.no_conv ct;
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(** induct data **)
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(* rules *)
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type rules = (string * thm) Item_Net.T;
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fun init_rules index : rules =
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  Item_Net.init
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    (fn ((s1, th1), (s2, th2)) => s1 = s2 andalso Thm.eq_thm_prop (th1, th2))
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    (single o index);
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fun filter_rules (rs: rules) th =
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  filter (fn (_, th') => Thm.eq_thm_prop (th, th')) (Item_Net.content rs);
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fun lookup_rule (rs: rules) = AList.lookup (op =) (Item_Net.content rs);
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fun pretty_rules ctxt kind rs =
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  let val thms = map snd (Item_Net.content rs)
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  in Pretty.big_list kind (map (Display.pretty_thm ctxt) thms) end;
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(* context data *)
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structure Data = Generic_Data
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(
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  type T = (rules * rules) * (rules * rules) * (rules * rules) * simpset;
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  val empty =
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    ((init_rules (left_var_prem o #2), init_rules (Thm.major_prem_of o #2)),
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     (init_rules (right_var_concl o #2), init_rules (Thm.major_prem_of o #2)),
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     (init_rules (left_var_concl o #2), init_rules (Thm.concl_of o #2)),
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     empty_ss addsimprocs [rearrange_eqs_simproc] addsimps [Drule.norm_hhf_eq]);
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  val extend = I;
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  fun merge (((casesT1, casesP1), (inductT1, inductP1), (coinductT1, coinductP1), simpset1),
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      ((casesT2, casesP2), (inductT2, inductP2), (coinductT2, coinductP2), simpset2)) =
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    ((Item_Net.merge (casesT1, casesT2), Item_Net.merge (casesP1, casesP2)),
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     (Item_Net.merge (inductT1, inductT2), Item_Net.merge (inductP1, inductP2)),
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     (Item_Net.merge (coinductT1, coinductT2), Item_Net.merge (coinductP1, coinductP2)),
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     merge_ss (simpset1, simpset2));
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);
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val get_local = Data.get o Context.Proof;
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fun dest_rules ctxt =
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  let val ((casesT, casesP), (inductT, inductP), (coinductT, coinductP), _) = get_local ctxt in
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    {type_cases = Item_Net.content casesT,
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     pred_cases = Item_Net.content casesP,
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     type_induct = Item_Net.content inductT,
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     pred_induct = Item_Net.content inductP,
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     type_coinduct = Item_Net.content coinductT,
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     pred_coinduct = Item_Net.content coinductP}
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  end;
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fun print_rules ctxt =
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  let val ((casesT, casesP), (inductT, inductP), (coinductT, coinductP), _) = get_local ctxt in
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   [pretty_rules ctxt "coinduct type:" coinductT,
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    pretty_rules ctxt "coinduct pred:" coinductP,
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    pretty_rules ctxt "induct type:" inductT,
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    pretty_rules ctxt "induct pred:" inductP,
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    pretty_rules ctxt "cases type:" casesT,
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    pretty_rules ctxt "cases pred:" casesP]
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    |> Pretty.chunks |> Pretty.writeln
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  end;
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val _ =
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  Outer_Syntax.improper_command "print_induct_rules" "print induction and cases rules"
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    Keyword.diag (Scan.succeed (Toplevel.no_timing o Toplevel.unknown_context o
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      Toplevel.keep (print_rules o Toplevel.context_of)));
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(* access rules *)
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val lookup_casesT = lookup_rule o #1 o #1 o get_local;
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val lookup_casesP = lookup_rule o #2 o #1 o get_local;
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val lookup_inductT = lookup_rule o #1 o #2 o get_local;
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val lookup_inductP = lookup_rule o #2 o #2 o get_local;
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val lookup_coinductT = lookup_rule o #1 o #3 o get_local;
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val lookup_coinductP = lookup_rule o #2 o #3 o get_local;
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fun find_rules which how ctxt x =
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  map snd (Item_Net.retrieve (which (get_local ctxt)) (how x));
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val find_casesT = find_rules (#1 o #1) Net.encode_type;
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val find_casesP = find_rules (#2 o #1) I;
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val find_inductT = find_rules (#1 o #2) Net.encode_type;
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val find_inductP = find_rules (#2 o #2) I;
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val find_coinductT = find_rules (#1 o #3) Net.encode_type;
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val find_coinductP = find_rules (#2 o #3) I;
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(** attributes **)
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local
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fun mk_att f g name =
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  Thm.mixed_attribute (fn (context, thm) =>
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    let
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      val thm' = g thm;
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      val context' = Data.map (f (name, thm')) context;
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    in (context', thm') end);
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fun del_att which =
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  Thm.declaration_attribute (fn th => Data.map (which (pairself (fn rs =>
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    fold Item_Net.remove (filter_rules rs th) rs))));
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fun map1 f (x, y, z, s) = (f x, y, z, s);
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fun map2 f (x, y, z, s) = (x, f y, z, s);
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fun map3 f (x, y, z, s) = (x, y, f z, s);
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fun map4 f (x, y, z, s) = (x, y, z, f s);
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fun add_casesT rule x = map1 (apfst (Item_Net.update rule)) x;
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fun add_casesP rule x = map1 (apsnd (Item_Net.update rule)) x;
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fun add_inductT rule x = map2 (apfst (Item_Net.update rule)) x;
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fun add_inductP rule x = map2 (apsnd (Item_Net.update rule)) x;
wenzelm@33373
   313
fun add_coinductT rule x = map3 (apfst (Item_Net.update rule)) x;
wenzelm@33373
   314
fun add_coinductP rule x = map3 (apsnd (Item_Net.update rule)) x;
wenzelm@24830
   315
wenzelm@45375
   316
val consumes0 = Rule_Cases.default_consumes 0;
wenzelm@45375
   317
val consumes1 = Rule_Cases.default_consumes 1;
wenzelm@24830
   318
wenzelm@24830
   319
in
wenzelm@24830
   320
wenzelm@24830
   321
val cases_type = mk_att add_casesT consumes0;
wenzelm@24861
   322
val cases_pred = mk_att add_casesP consumes1;
wenzelm@27140
   323
val cases_del = del_att map1;
wenzelm@27140
   324
wenzelm@24830
   325
val induct_type = mk_att add_inductT consumes0;
wenzelm@24861
   326
val induct_pred = mk_att add_inductP consumes1;
wenzelm@27140
   327
val induct_del = del_att map2;
wenzelm@27140
   328
wenzelm@24830
   329
val coinduct_type = mk_att add_coinductT consumes0;
wenzelm@24861
   330
val coinduct_pred = mk_att add_coinductP consumes1;
wenzelm@27140
   331
val coinduct_del = del_att map3;
wenzelm@24830
   332
wenzelm@37524
   333
fun map_simpset f = Data.map (map4 f);
wenzelm@36602
   334
wenzelm@36602
   335
fun induct_simp f =
wenzelm@36602
   336
  Thm.declaration_attribute (fn thm => fn context =>
wenzelm@37525
   337
      map_simpset
wenzelm@37525
   338
        (Simplifier.with_context (Context.proof_of context) (fn ss => f (ss, [thm]))) context);
wenzelm@36602
   339
wenzelm@36602
   340
val induct_simp_add = induct_simp (op addsimps);
wenzelm@36602
   341
val induct_simp_del = induct_simp (op delsimps);
berghofe@34907
   342
wenzelm@24830
   343
end;
wenzelm@24830
   344
wenzelm@24830
   345
wenzelm@24830
   346
wenzelm@24830
   347
(** attribute syntax **)
wenzelm@24830
   348
berghofe@34907
   349
val no_simpN = "no_simp";
wenzelm@24830
   350
val casesN = "cases";
wenzelm@24830
   351
val inductN = "induct";
wenzelm@24830
   352
val coinductN = "coinduct";
wenzelm@24830
   353
wenzelm@24830
   354
val typeN = "type";
wenzelm@24861
   355
val predN = "pred";
wenzelm@24830
   356
val setN = "set";
wenzelm@24830
   357
wenzelm@24830
   358
local
wenzelm@24830
   359
wenzelm@24830
   360
fun spec k arg =
wenzelm@24830
   361
  Scan.lift (Args.$$$ k -- Args.colon) |-- arg ||
wenzelm@24830
   362
  Scan.lift (Args.$$$ k) >> K "";
wenzelm@24830
   363
wenzelm@30528
   364
fun attrib add_type add_pred del =
wenzelm@35400
   365
  spec typeN (Args.type_name false) >> add_type ||
wenzelm@35400
   366
  spec predN (Args.const false) >> add_pred ||
wenzelm@35400
   367
  spec setN (Args.const false) >> add_pred ||
wenzelm@30528
   368
  Scan.lift Args.del >> K del;
wenzelm@24830
   369
wenzelm@24830
   370
in
wenzelm@24830
   371
wenzelm@30528
   372
val attrib_setup =
wenzelm@30722
   373
  Attrib.setup @{binding cases} (attrib cases_type cases_pred cases_del)
wenzelm@30722
   374
    "declaration of cases rule" #>
wenzelm@30722
   375
  Attrib.setup @{binding induct} (attrib induct_type induct_pred induct_del)
wenzelm@30722
   376
    "declaration of induction rule" #>
wenzelm@30722
   377
  Attrib.setup @{binding coinduct} (attrib coinduct_type coinduct_pred coinduct_del)
berghofe@34907
   378
    "declaration of coinduction rule" #>
wenzelm@36602
   379
  Attrib.setup @{binding induct_simp} (Attrib.add_del induct_simp_add induct_simp_del)
berghofe@34907
   380
    "declaration of rules for simplifying induction or cases rules";
wenzelm@24830
   381
wenzelm@24830
   382
end;
wenzelm@24830
   383
wenzelm@24830
   384
wenzelm@24830
   385
wenzelm@24830
   386
(** method utils **)
wenzelm@24830
   387
wenzelm@24830
   388
(* alignment *)
wenzelm@24830
   389
wenzelm@24830
   390
fun align_left msg xs ys =
wenzelm@24830
   391
  let val m = length xs and n = length ys
haftmann@33957
   392
  in if m < n then error msg else (take n xs ~~ ys) end;
wenzelm@24830
   393
wenzelm@24830
   394
fun align_right msg xs ys =
wenzelm@24830
   395
  let val m = length xs and n = length ys
haftmann@33957
   396
  in if m < n then error msg else (drop (m - n) xs ~~ ys) end;
wenzelm@24830
   397
wenzelm@24830
   398
wenzelm@24830
   399
(* prep_inst *)
wenzelm@24830
   400
wenzelm@32432
   401
fun prep_inst ctxt align tune (tm, ts) =
wenzelm@24830
   402
  let
wenzelm@42361
   403
    val cert = Thm.cterm_of (Proof_Context.theory_of ctxt);
wenzelm@24830
   404
    fun prep_var (x, SOME t) =
wenzelm@24830
   405
          let
wenzelm@24830
   406
            val cx = cert x;
wenzelm@26626
   407
            val xT = #T (Thm.rep_cterm cx);
wenzelm@24830
   408
            val ct = cert (tune t);
wenzelm@32432
   409
            val tT = #T (Thm.rep_cterm ct);
wenzelm@24830
   410
          in
wenzelm@32432
   411
            if Type.could_unify (tT, xT) then SOME (cx, ct)
wenzelm@24830
   412
            else error (Pretty.string_of (Pretty.block
wenzelm@24830
   413
             [Pretty.str "Ill-typed instantiation:", Pretty.fbrk,
wenzelm@32432
   414
              Syntax.pretty_term ctxt (Thm.term_of ct), Pretty.str " ::", Pretty.brk 1,
wenzelm@32432
   415
              Syntax.pretty_typ ctxt tT]))
wenzelm@24830
   416
          end
wenzelm@24830
   417
      | prep_var (_, NONE) = NONE;
wenzelm@24830
   418
    val xs = vars_of tm;
wenzelm@24830
   419
  in
wenzelm@24830
   420
    align "Rule has fewer variables than instantiations given" xs ts
wenzelm@24830
   421
    |> map_filter prep_var
wenzelm@24830
   422
  end;
wenzelm@24830
   423
wenzelm@24830
   424
wenzelm@24830
   425
(* trace_rules *)
wenzelm@24830
   426
wenzelm@24830
   427
fun trace_rules _ kind [] = error ("Unable to figure out " ^ kind ^ " rule")
wenzelm@24830
   428
  | trace_rules ctxt _ rules = Method.trace ctxt rules;
wenzelm@24830
   429
wenzelm@24830
   430
berghofe@34987
   431
(* mark equality constraints in cases rule *)
berghofe@34987
   432
wenzelm@37524
   433
val equal_def' = Thm.symmetric Induct_Args.equal_def;
berghofe@34987
   434
berghofe@34987
   435
fun mark_constraints n ctxt = Conv.fconv_rule
wenzelm@45130
   436
  (Conv.prems_conv ~1 (Conv.params_conv ~1 (K (Conv.prems_conv n
wenzelm@41228
   437
     (Raw_Simplifier.rewrite false [equal_def']))) ctxt));
berghofe@34987
   438
berghofe@34987
   439
val unmark_constraints = Conv.fconv_rule
wenzelm@41228
   440
  (Raw_Simplifier.rewrite true [Induct_Args.equal_def]);
berghofe@34987
   441
wenzelm@37525
   442
berghofe@34987
   443
(* simplify *)
berghofe@34987
   444
berghofe@34987
   445
fun simplify_conv' ctxt =
berghofe@34987
   446
  Simplifier.full_rewrite (Simplifier.context ctxt (#4 (get_local ctxt)));
berghofe@34987
   447
berghofe@34987
   448
fun simplify_conv ctxt ct =
wenzelm@37524
   449
  if exists_subterm (is_some o Induct_Args.dest_def) (term_of ct) then
berghofe@34987
   450
    (Conv.try_conv (rulify_defs_conv ctxt) then_conv simplify_conv' ctxt) ct
berghofe@34987
   451
  else Conv.all_conv ct;
berghofe@34987
   452
berghofe@34987
   453
fun gen_simplified_rule cv ctxt =
berghofe@34987
   454
  Conv.fconv_rule (Conv.prems_conv ~1 (cv ctxt));
berghofe@34987
   455
berghofe@34987
   456
val simplified_rule' = gen_simplified_rule simplify_conv';
berghofe@34987
   457
val simplified_rule = gen_simplified_rule simplify_conv;
berghofe@34987
   458
berghofe@34987
   459
fun simplify_tac ctxt = CONVERSION (simplify_conv ctxt);
berghofe@34987
   460
wenzelm@37524
   461
val trivial_tac = Induct_Args.trivial_tac;
berghofe@34987
   462
berghofe@34987
   463
wenzelm@24830
   464
wenzelm@24830
   465
(** cases method **)
wenzelm@24830
   466
wenzelm@24830
   467
(*
wenzelm@24830
   468
  rule selection scheme:
wenzelm@24830
   469
          cases         - default case split
wenzelm@24861
   470
    `A t` cases ...     - predicate/set cases
wenzelm@24830
   471
          cases t       - type cases
wenzelm@24830
   472
    ...   cases ... r   - explicit rule
wenzelm@24830
   473
*)
wenzelm@24830
   474
wenzelm@24830
   475
local
wenzelm@24830
   476
wenzelm@24830
   477
fun get_casesT ctxt ((SOME t :: _) :: _) = find_casesT ctxt (Term.fastype_of t)
wenzelm@24830
   478
  | get_casesT _ _ = [];
wenzelm@24830
   479
wenzelm@24861
   480
fun get_casesP ctxt (fact :: _) = find_casesP ctxt (Thm.concl_of fact)
wenzelm@24861
   481
  | get_casesP _ _ = [];
wenzelm@24830
   482
wenzelm@24830
   483
in
wenzelm@24830
   484
berghofe@34987
   485
fun cases_tac ctxt simp insts opt_rule facts =
wenzelm@24830
   486
  let
wenzelm@42361
   487
    val thy = Proof_Context.theory_of ctxt;
wenzelm@24830
   488
wenzelm@24830
   489
    fun inst_rule r =
berghofe@34987
   490
      (if null insts then r
wenzelm@45131
   491
       else
wenzelm@45131
   492
         (align_left "Rule has fewer premises than arguments given" (Thm.prems_of r) insts
wenzelm@45131
   493
           |> maps (prep_inst ctxt align_left I)
wenzelm@45131
   494
           |> Drule.cterm_instantiate) r)
wenzelm@45131
   495
      |> simp ? mark_constraints (Rule_Cases.get_constraints r) ctxt
wenzelm@45131
   496
      |> pair (Rule_Cases.get r);
wenzelm@24830
   497
wenzelm@24830
   498
    val ruleq =
wenzelm@24830
   499
      (case opt_rule of
wenzelm@24830
   500
        SOME r => Seq.single (inst_rule r)
wenzelm@24830
   501
      | NONE =>
wenzelm@37524
   502
          (get_casesP ctxt facts @ get_casesT ctxt insts @ [Induct_Args.cases_default])
wenzelm@24830
   503
          |> tap (trace_rules ctxt casesN)
wenzelm@24830
   504
          |> Seq.of_list |> Seq.maps (Seq.try inst_rule));
wenzelm@24830
   505
  in
wenzelm@24830
   506
    fn i => fn st =>
wenzelm@24830
   507
      ruleq
wenzelm@33368
   508
      |> Seq.maps (Rule_Cases.consume [] facts)
wenzelm@24830
   509
      |> Seq.maps (fn ((cases, (_, more_facts)), rule) =>
wenzelm@45131
   510
        let
wenzelm@45131
   511
          val rule' = rule
wenzelm@45131
   512
            |> simp ? (simplified_rule' ctxt #> unmark_constraints);
berghofe@34987
   513
        in
berghofe@34987
   514
          CASES (Rule_Cases.make_common (thy,
berghofe@34987
   515
              Thm.prop_of (Rule_Cases.internalize_params rule')) cases)
wenzelm@45130
   516
            ((Method.insert_tac more_facts THEN' rtac rule' THEN_ALL_NEW
berghofe@34987
   517
                (if simp then TRY o trivial_tac else K all_tac)) i) st
berghofe@34987
   518
        end)
wenzelm@24830
   519
  end;
wenzelm@24830
   520
wenzelm@24830
   521
end;
wenzelm@24830
   522
wenzelm@24830
   523
wenzelm@24830
   524
wenzelm@24830
   525
(** induct method **)
wenzelm@24830
   526
wenzelm@24830
   527
val conjunction_congs = [@{thm Pure.all_conjunction}, @{thm imp_conjunction}];
wenzelm@24830
   528
wenzelm@24830
   529
wenzelm@24830
   530
(* atomize *)
wenzelm@24830
   531
wenzelm@24830
   532
fun atomize_term thy =
wenzelm@41228
   533
  Raw_Simplifier.rewrite_term thy Induct_Args.atomize []
wenzelm@35625
   534
  #> Object_Logic.drop_judgment thy;
wenzelm@24830
   535
wenzelm@41228
   536
val atomize_cterm = Raw_Simplifier.rewrite true Induct_Args.atomize;
wenzelm@24830
   537
wenzelm@37524
   538
val atomize_tac = Simplifier.rewrite_goal_tac Induct_Args.atomize;
wenzelm@24830
   539
wenzelm@24830
   540
val inner_atomize_tac =
wenzelm@24830
   541
  Simplifier.rewrite_goal_tac (map Thm.symmetric conjunction_congs) THEN' atomize_tac;
wenzelm@24830
   542
wenzelm@24830
   543
wenzelm@24830
   544
(* rulify *)
wenzelm@24830
   545
wenzelm@24830
   546
fun rulify_term thy =
wenzelm@41228
   547
  Raw_Simplifier.rewrite_term thy (Induct_Args.rulify @ conjunction_congs) [] #>
wenzelm@41228
   548
  Raw_Simplifier.rewrite_term thy Induct_Args.rulify_fallback [];
wenzelm@24830
   549
wenzelm@24830
   550
fun rulified_term thm =
wenzelm@24830
   551
  let
wenzelm@24830
   552
    val thy = Thm.theory_of_thm thm;
wenzelm@24830
   553
    val rulify = rulify_term thy;
wenzelm@24830
   554
    val (As, B) = Logic.strip_horn (Thm.prop_of thm);
wenzelm@24830
   555
  in (thy, Logic.list_implies (map rulify As, rulify B)) end;
wenzelm@24830
   556
wenzelm@24830
   557
val rulify_tac =
wenzelm@37524
   558
  Simplifier.rewrite_goal_tac (Induct_Args.rulify @ conjunction_congs) THEN'
wenzelm@37524
   559
  Simplifier.rewrite_goal_tac Induct_Args.rulify_fallback THEN'
wenzelm@24830
   560
  Goal.conjunction_tac THEN_ALL_NEW
wenzelm@24830
   561
  (Simplifier.rewrite_goal_tac [@{thm Pure.conjunction_imp}] THEN' Goal.norm_hhf_tac);
wenzelm@24830
   562
wenzelm@24830
   563
wenzelm@24830
   564
(* prepare rule *)
wenzelm@24830
   565
wenzelm@32432
   566
fun rule_instance ctxt inst rule =
wenzelm@32432
   567
  Drule.cterm_instantiate (prep_inst ctxt align_left I (Thm.prop_of rule, inst)) rule;
wenzelm@24830
   568
wenzelm@24830
   569
fun internalize k th =
wenzelm@24830
   570
  th |> Thm.permute_prems 0 k
wenzelm@24830
   571
  |> Conv.fconv_rule (Conv.concl_conv (Thm.nprems_of th - k) atomize_cterm);
wenzelm@24830
   572
wenzelm@24830
   573
wenzelm@24830
   574
(* guess rule instantiation -- cannot handle pending goal parameters *)
wenzelm@24830
   575
wenzelm@24830
   576
local
wenzelm@24830
   577
wenzelm@32032
   578
fun dest_env thy env =
wenzelm@24830
   579
  let
wenzelm@24830
   580
    val cert = Thm.cterm_of thy;
wenzelm@24830
   581
    val certT = Thm.ctyp_of thy;
wenzelm@32032
   582
    val pairs = Vartab.dest (Envir.term_env env);
wenzelm@32032
   583
    val types = Vartab.dest (Envir.type_env env);
wenzelm@24830
   584
    val ts = map (cert o Envir.norm_term env o #2 o #2) pairs;
wenzelm@24830
   585
    val xs = map2 (curry (cert o Var)) (map #1 pairs) (map (#T o Thm.rep_cterm) ts);
wenzelm@32032
   586
  in (map (fn (xi, (S, T)) => (certT (TVar (xi, S)), certT T)) types, xs ~~ ts) end;
wenzelm@24830
   587
wenzelm@24830
   588
in
wenzelm@24830
   589
wenzelm@26940
   590
fun guess_instance ctxt rule i st =
wenzelm@24830
   591
  let
wenzelm@42361
   592
    val thy = Proof_Context.theory_of ctxt;
wenzelm@26626
   593
    val maxidx = Thm.maxidx_of st;
wenzelm@24830
   594
    val goal = Thm.term_of (Thm.cprem_of st i);  (*exception Subscript*)
wenzelm@29276
   595
    val params = rev (Term.rename_wrt_term goal (Logic.strip_params goal));
wenzelm@24830
   596
  in
wenzelm@24830
   597
    if not (null params) then
wenzelm@24830
   598
      (warning ("Cannot determine rule instantiation due to pending parameter(s): " ^
wenzelm@42284
   599
        commas_quote (map (Syntax.string_of_term ctxt o Syntax_Trans.mark_boundT) params));
wenzelm@24830
   600
      Seq.single rule)
wenzelm@24830
   601
    else
wenzelm@24830
   602
      let
wenzelm@24830
   603
        val rule' = Thm.incr_indexes (maxidx + 1) rule;
wenzelm@24830
   604
        val concl = Logic.strip_assums_concl goal;
wenzelm@24830
   605
      in
wenzelm@32032
   606
        Unify.smash_unifiers thy [(Thm.concl_of rule', concl)] (Envir.empty (Thm.maxidx_of rule'))
wenzelm@43333
   607
        |> Seq.map (fn env => Drule.instantiate_normalize (dest_env thy env) rule')
wenzelm@24830
   608
      end
wenzelm@43333
   609
  end
wenzelm@43333
   610
  handle General.Subscript => Seq.empty;
wenzelm@24830
   611
wenzelm@24830
   612
end;
wenzelm@24830
   613
wenzelm@24830
   614
wenzelm@24830
   615
(* special renaming of rule parameters *)
wenzelm@24830
   616
wenzelm@24830
   617
fun special_rename_params ctxt [[SOME (Free (z, Type (T, _)))]] [thm] =
wenzelm@24830
   618
      let
wenzelm@42488
   619
        val x = Name.clean (Variable.revert_fixed ctxt z);
wenzelm@24830
   620
        fun index i [] = []
wenzelm@24830
   621
          | index i (y :: ys) =
wenzelm@24830
   622
              if x = y then x ^ string_of_int i :: index (i + 1) ys
wenzelm@24830
   623
              else y :: index i ys;
wenzelm@24830
   624
        fun rename_params [] = []
wenzelm@24830
   625
          | rename_params ((y, Type (U, _)) :: ys) =
wenzelm@24830
   626
              (if U = T then x else y) :: rename_params ys
wenzelm@24830
   627
          | rename_params ((y, _) :: ys) = y :: rename_params ys;
wenzelm@24830
   628
        fun rename_asm A =
wenzelm@24830
   629
          let
wenzelm@24830
   630
            val xs = rename_params (Logic.strip_params A);
wenzelm@24830
   631
            val xs' =
wenzelm@28375
   632
              (case filter (fn x' => x' = x) xs of
wenzelm@24830
   633
                [] => xs | [_] => xs | _ => index 1 xs);
wenzelm@45328
   634
          in Logic.list_rename_params xs' A end;
wenzelm@24830
   635
        fun rename_prop p =
wenzelm@24830
   636
          let val (As, C) = Logic.strip_horn p
wenzelm@24830
   637
          in Logic.list_implies (map rename_asm As, C) end;
wenzelm@24830
   638
        val cp' = cterm_fun rename_prop (Thm.cprop_of thm);
wenzelm@24830
   639
        val thm' = Thm.equal_elim (Thm.reflexive cp') thm;
wenzelm@33368
   640
      in [Rule_Cases.save thm thm'] end
wenzelm@24830
   641
  | special_rename_params _ _ ths = ths;
wenzelm@24830
   642
wenzelm@24830
   643
wenzelm@45132
   644
(* arbitrary_tac *)
wenzelm@24830
   645
wenzelm@24830
   646
local
wenzelm@24830
   647
wenzelm@24830
   648
fun goal_prefix k ((c as Const ("all", _)) $ Abs (a, T, B)) = c $ Abs (a, T, goal_prefix k B)
wenzelm@45156
   649
  | goal_prefix 0 _ = Term.dummy_prop
wenzelm@24830
   650
  | goal_prefix k ((c as Const ("==>", _)) $ A $ B) = c $ A $ goal_prefix (k - 1) B
wenzelm@45156
   651
  | goal_prefix _ _ = Term.dummy_prop;
wenzelm@24830
   652
wenzelm@24830
   653
fun goal_params k (Const ("all", _) $ Abs (_, _, B)) = goal_params k B + 1
wenzelm@24830
   654
  | goal_params 0 _ = 0
wenzelm@24830
   655
  | goal_params k (Const ("==>", _) $ _ $ B) = goal_params (k - 1) B
wenzelm@24830
   656
  | goal_params _ _ = 0;
wenzelm@24830
   657
wenzelm@24830
   658
fun meta_spec_tac ctxt n (x, T) = SUBGOAL (fn (goal, i) =>
wenzelm@24830
   659
  let
wenzelm@42361
   660
    val thy = Proof_Context.theory_of ctxt;
wenzelm@24830
   661
    val cert = Thm.cterm_of thy;
wenzelm@24830
   662
wenzelm@24830
   663
    val v = Free (x, T);
wenzelm@24830
   664
    fun spec_rule prfx (xs, body) =
wenzelm@24830
   665
      @{thm Pure.meta_spec}
wenzelm@42488
   666
      |> Thm.rename_params_rule ([Name.clean (Variable.revert_fixed ctxt x)], 1)
wenzelm@24830
   667
      |> Thm.lift_rule (cert prfx)
wenzelm@24830
   668
      |> `(Thm.prop_of #> Logic.strip_assums_concl)
wenzelm@24830
   669
      |-> (fn pred $ arg =>
wenzelm@24830
   670
        Drule.cterm_instantiate
wenzelm@24830
   671
          [(cert (Term.head_of pred), cert (Logic.rlist_abs (xs, body))),
wenzelm@24830
   672
           (cert (Term.head_of arg), cert (Logic.rlist_abs (xs, v)))]);
wenzelm@24830
   673
wenzelm@24830
   674
    fun goal_concl k xs (Const ("all", _) $ Abs (a, T, B)) = goal_concl k ((a, T) :: xs) B
wenzelm@24830
   675
      | goal_concl 0 xs B =
wenzelm@24830
   676
          if not (Term.exists_subterm (fn t => t aconv v) B) then NONE
wenzelm@44241
   677
          else SOME (xs, absfree (x, T) (Term.incr_boundvars 1 B))
wenzelm@24830
   678
      | goal_concl k xs (Const ("==>", _) $ _ $ B) = goal_concl (k - 1) xs B
wenzelm@24830
   679
      | goal_concl _ _ _ = NONE;
wenzelm@24830
   680
  in
wenzelm@24830
   681
    (case goal_concl n [] goal of
wenzelm@24830
   682
      SOME concl =>
wenzelm@24830
   683
        (compose_tac (false, spec_rule (goal_prefix n goal) concl, 1) THEN' rtac asm_rl) i
wenzelm@24830
   684
    | NONE => all_tac)
wenzelm@24830
   685
  end);
wenzelm@24830
   686
wenzelm@24832
   687
fun miniscope_tac p = CONVERSION o
wenzelm@41228
   688
  Conv.params_conv p (K (Raw_Simplifier.rewrite true [Thm.symmetric Drule.norm_hhf_eq]));
wenzelm@24830
   689
wenzelm@24830
   690
in
wenzelm@24830
   691
wenzelm@45132
   692
fun arbitrary_tac _ _ [] = K all_tac
wenzelm@45132
   693
  | arbitrary_tac ctxt n xs = SUBGOAL (fn (goal, i) =>
wenzelm@24830
   694
     (EVERY' (map (meta_spec_tac ctxt n) xs) THEN'
wenzelm@24832
   695
      (miniscope_tac (goal_params n goal) ctxt)) i);
wenzelm@24830
   696
wenzelm@24830
   697
end;
wenzelm@24830
   698
wenzelm@24830
   699
wenzelm@24830
   700
(* add_defs *)
wenzelm@24830
   701
wenzelm@24830
   702
fun add_defs def_insts =
wenzelm@24830
   703
  let
berghofe@34907
   704
    fun add (SOME (_, (t, true))) ctxt = ((SOME t, []), ctxt)
berghofe@34907
   705
      | add (SOME (SOME x, (t, _))) ctxt =
wenzelm@28083
   706
          let val ([(lhs, (_, th))], ctxt') =
wenzelm@35624
   707
            Local_Defs.add_defs [((x, NoSyn), (Thm.empty_binding, t))] ctxt
wenzelm@24830
   708
          in ((SOME lhs, [th]), ctxt') end
berghofe@34907
   709
      | add (SOME (NONE, (t as Free _, _))) ctxt = ((SOME t, []), ctxt)
berghofe@34907
   710
      | add (SOME (NONE, (t, _))) ctxt =
berghofe@34907
   711
          let
wenzelm@43326
   712
            val (s, _) = Name.variant "x" (Variable.names_of ctxt);
berghofe@34907
   713
            val ([(lhs, (_, th))], ctxt') =
wenzelm@35624
   714
              Local_Defs.add_defs [((Binding.name s, NoSyn),
berghofe@34907
   715
                (Thm.empty_binding, t))] ctxt
berghofe@34907
   716
          in ((SOME lhs, [th]), ctxt') end
wenzelm@24830
   717
      | add NONE ctxt = ((NONE, []), ctxt);
wenzelm@24830
   718
  in fold_map add def_insts #> apfst (split_list #> apsnd flat) end;
wenzelm@24830
   719
wenzelm@24830
   720
wenzelm@24830
   721
(* induct_tac *)
wenzelm@24830
   722
wenzelm@24830
   723
(*
wenzelm@24830
   724
  rule selection scheme:
wenzelm@24861
   725
    `A x` induct ...     - predicate/set induction
wenzelm@24830
   726
          induct x       - type induction
wenzelm@24830
   727
    ...   induct ... r   - explicit rule
wenzelm@24830
   728
*)
wenzelm@24830
   729
wenzelm@24830
   730
fun get_inductT ctxt insts =
wenzelm@32188
   731
  fold_rev (map_product cons) (insts |> map
wenzelm@27323
   732
      ((fn [] => NONE | ts => List.last ts) #>
wenzelm@27323
   733
        (fn NONE => TVar (("'a", 0), []) | SOME t => Term.fastype_of t) #>
wenzelm@27323
   734
        find_inductT ctxt)) [[]]
wenzelm@33368
   735
  |> filter_out (forall Rule_Cases.is_inner_rule);
wenzelm@24830
   736
wenzelm@24861
   737
fun get_inductP ctxt (fact :: _) = map single (find_inductP ctxt (Thm.concl_of fact))
wenzelm@24861
   738
  | get_inductP _ _ = [];
wenzelm@24830
   739
wenzelm@45130
   740
type case_data = (((string * string list) * string list) list * int);
nipkow@45014
   741
nipkow@45014
   742
fun gen_induct_tac mod_cases ctxt simp def_insts arbitrary taking opt_rule facts =
wenzelm@24830
   743
  let
wenzelm@42361
   744
    val thy = Proof_Context.theory_of ctxt;
wenzelm@24830
   745
wenzelm@24830
   746
    val ((insts, defs), defs_ctxt) = fold_map add_defs def_insts ctxt |>> split_list;
berghofe@34907
   747
    val atomized_defs = map (map (Conv.fconv_rule atomize_cterm)) defs;
wenzelm@24830
   748
wenzelm@24830
   749
    fun inst_rule (concls, r) =
wenzelm@33368
   750
      (if null insts then `Rule_Cases.get r
wenzelm@24830
   751
       else (align_left "Rule has fewer conclusions than arguments given"
wenzelm@24830
   752
          (map Logic.strip_imp_concl (Logic.dest_conjunctions (Thm.concl_of r))) insts
wenzelm@32432
   753
        |> maps (prep_inst ctxt align_right (atomize_term thy))
wenzelm@33368
   754
        |> Drule.cterm_instantiate) r |> pair (Rule_Cases.get r))
nipkow@45014
   755
      |> mod_cases thy
wenzelm@24830
   756
      |> (fn ((cases, consumes), th) => (((cases, concls), consumes), th));
wenzelm@24830
   757
wenzelm@24830
   758
    val ruleq =
wenzelm@24830
   759
      (case opt_rule of
wenzelm@33368
   760
        SOME rs => Seq.single (inst_rule (Rule_Cases.strict_mutual_rule ctxt rs))
wenzelm@24830
   761
      | NONE =>
wenzelm@24861
   762
          (get_inductP ctxt facts @
wenzelm@24830
   763
            map (special_rename_params defs_ctxt insts) (get_inductT ctxt insts))
wenzelm@33368
   764
          |> map_filter (Rule_Cases.mutual_rule ctxt)
wenzelm@24830
   765
          |> tap (trace_rules ctxt inductN o map #2)
wenzelm@24830
   766
          |> Seq.of_list |> Seq.maps (Seq.try inst_rule));
wenzelm@24830
   767
nipkow@44942
   768
    fun rule_cases ctxt rule cases =
nipkow@44942
   769
      let
nipkow@44942
   770
        val rule' = Rule_Cases.internalize_params rule;
wenzelm@45131
   771
        val rule'' = rule' |> simp ? simplified_rule ctxt;
wenzelm@45130
   772
        val nonames = map (fn ((cn, _), cls) => ((cn, []), cls));
wenzelm@45130
   773
        val cases' = if Thm.eq_thm_prop (rule', rule'') then cases else nonames cases;
wenzelm@45130
   774
      in Rule_Cases.make_nested (Thm.prop_of rule'') (rulified_term rule'') cases' end;
wenzelm@24830
   775
  in
wenzelm@24830
   776
    (fn i => fn st =>
wenzelm@24830
   777
      ruleq
wenzelm@33368
   778
      |> Seq.maps (Rule_Cases.consume (flat defs) facts)
wenzelm@24830
   779
      |> Seq.maps (fn (((cases, concls), (more_consumes, more_facts)), rule) =>
wenzelm@24830
   780
        (PRECISE_CONJUNCTS (length concls) (ALLGOALS (fn j =>
wenzelm@24830
   781
          (CONJUNCTS (ALLGOALS
berghofe@34907
   782
            let
berghofe@34907
   783
              val adefs = nth_list atomized_defs (j - 1);
wenzelm@45130
   784
              val frees = fold (Term.add_frees o Thm.prop_of) adefs [];
berghofe@34907
   785
              val xs = nth_list arbitrary (j - 1);
berghofe@34907
   786
              val k = nth concls (j - 1) + more_consumes
berghofe@34907
   787
            in
berghofe@34907
   788
              Method.insert_tac (more_facts @ adefs) THEN'
berghofe@34907
   789
                (if simp then
berghofe@34907
   790
                   rotate_tac k (length adefs) THEN'
wenzelm@45132
   791
                   arbitrary_tac defs_ctxt k (List.partition (member op = frees) xs |> op @)
berghofe@34907
   792
                 else
wenzelm@45132
   793
                   arbitrary_tac defs_ctxt k xs)
berghofe@34907
   794
             end)
wenzelm@24830
   795
          THEN' inner_atomize_tac) j))
wenzelm@24830
   796
        THEN' atomize_tac) i st |> Seq.maps (fn st' =>
wenzelm@26940
   797
            guess_instance ctxt (internalize more_consumes rule) i st'
wenzelm@32432
   798
            |> Seq.map (rule_instance ctxt (burrow_options (Variable.polymorphic ctxt) taking))
wenzelm@24830
   799
            |> Seq.maps (fn rule' =>
berghofe@34907
   800
              CASES (rule_cases ctxt rule' cases)
wenzelm@45130
   801
                (rtac rule' i THEN
wenzelm@42361
   802
                  PRIMITIVE (singleton (Proof_Context.export defs_ctxt ctxt))) st'))))
berghofe@34907
   803
    THEN_ALL_NEW_CASES
berghofe@34907
   804
      ((if simp then simplify_tac ctxt THEN' (TRY o trivial_tac)
berghofe@34907
   805
        else K all_tac)
berghofe@34907
   806
       THEN_ALL_NEW rulify_tac)
wenzelm@24830
   807
  end;
wenzelm@24830
   808
nipkow@45014
   809
val induct_tac = gen_induct_tac (K I);
wenzelm@24830
   810
wenzelm@45130
   811
wenzelm@45130
   812
wenzelm@24830
   813
(** coinduct method **)
wenzelm@24830
   814
wenzelm@24830
   815
(*
wenzelm@24830
   816
  rule selection scheme:
wenzelm@24861
   817
    goal "A x" coinduct ...   - predicate/set coinduction
wenzelm@24830
   818
               coinduct x     - type coinduction
wenzelm@24830
   819
               coinduct ... r - explicit rule
wenzelm@24830
   820
*)
wenzelm@24830
   821
wenzelm@24830
   822
local
wenzelm@24830
   823
wenzelm@24830
   824
fun get_coinductT ctxt (SOME t :: _) = find_coinductT ctxt (Term.fastype_of t)
wenzelm@24830
   825
  | get_coinductT _ _ = [];
wenzelm@24830
   826
wenzelm@24861
   827
fun get_coinductP ctxt goal = find_coinductP ctxt (Logic.strip_assums_concl goal);
wenzelm@24861
   828
wenzelm@24861
   829
fun main_prop_of th =
wenzelm@33368
   830
  if Rule_Cases.get_consumes th > 0 then Thm.major_prem_of th else Thm.concl_of th;
wenzelm@24830
   831
wenzelm@24830
   832
in
wenzelm@24830
   833
wenzelm@26924
   834
fun coinduct_tac ctxt inst taking opt_rule facts =
wenzelm@24830
   835
  let
wenzelm@42361
   836
    val thy = Proof_Context.theory_of ctxt;
wenzelm@24830
   837
wenzelm@24830
   838
    fun inst_rule r =
wenzelm@33368
   839
      if null inst then `Rule_Cases.get r
wenzelm@32432
   840
      else Drule.cterm_instantiate (prep_inst ctxt align_right I (main_prop_of r, inst)) r
wenzelm@33368
   841
        |> pair (Rule_Cases.get r);
wenzelm@24830
   842
wenzelm@24830
   843
    fun ruleq goal =
wenzelm@24830
   844
      (case opt_rule of
wenzelm@24830
   845
        SOME r => Seq.single (inst_rule r)
wenzelm@24830
   846
      | NONE =>
wenzelm@24861
   847
          (get_coinductP ctxt goal @ get_coinductT ctxt inst)
wenzelm@24830
   848
          |> tap (trace_rules ctxt coinductN)
wenzelm@24830
   849
          |> Seq.of_list |> Seq.maps (Seq.try inst_rule));
wenzelm@24830
   850
  in
wenzelm@24830
   851
    SUBGOAL_CASES (fn (goal, i) => fn st =>
wenzelm@24830
   852
      ruleq goal
wenzelm@33368
   853
      |> Seq.maps (Rule_Cases.consume [] facts)
wenzelm@24830
   854
      |> Seq.maps (fn ((cases, (_, more_facts)), rule) =>
wenzelm@26940
   855
        guess_instance ctxt rule i st
wenzelm@32432
   856
        |> Seq.map (rule_instance ctxt (burrow_options (Variable.polymorphic ctxt) taking))
wenzelm@24830
   857
        |> Seq.maps (fn rule' =>
berghofe@34907
   858
          CASES (Rule_Cases.make_common (thy,
berghofe@34907
   859
              Thm.prop_of (Rule_Cases.internalize_params rule')) cases)
wenzelm@45130
   860
            (Method.insert_tac more_facts i THEN rtac rule' i) st)))
wenzelm@24830
   861
  end;
wenzelm@24830
   862
wenzelm@24830
   863
end;
wenzelm@24830
   864
wenzelm@24830
   865
wenzelm@24830
   866
wenzelm@24830
   867
(** concrete syntax **)
wenzelm@24830
   868
wenzelm@24830
   869
val arbitraryN = "arbitrary";
wenzelm@24830
   870
val takingN = "taking";
wenzelm@24830
   871
val ruleN = "rule";
wenzelm@24830
   872
wenzelm@24830
   873
local
wenzelm@24830
   874
wenzelm@24830
   875
fun single_rule [rule] = rule
wenzelm@24830
   876
  | single_rule _ = error "Single rule expected";
wenzelm@24830
   877
wenzelm@24830
   878
fun named_rule k arg get =
wenzelm@24830
   879
  Scan.lift (Args.$$$ k -- Args.colon) |-- Scan.repeat arg :|--
wenzelm@24830
   880
    (fn names => Scan.peek (fn context => Scan.succeed (names |> map (fn name =>
wenzelm@24830
   881
      (case get (Context.proof_of context) name of SOME x => x
wenzelm@24830
   882
      | NONE => error ("No rule for " ^ k ^ " " ^ quote name))))));
wenzelm@24830
   883
wenzelm@24861
   884
fun rule get_type get_pred =
wenzelm@35400
   885
  named_rule typeN (Args.type_name false) get_type ||
wenzelm@35400
   886
  named_rule predN (Args.const false) get_pred ||
wenzelm@35400
   887
  named_rule setN (Args.const false) get_pred ||
wenzelm@24830
   888
  Scan.lift (Args.$$$ ruleN -- Args.colon) |-- Attrib.thms;
wenzelm@24830
   889
wenzelm@24861
   890
val cases_rule = rule lookup_casesT lookup_casesP >> single_rule;
wenzelm@24861
   891
val induct_rule = rule lookup_inductT lookup_inductP;
wenzelm@24861
   892
val coinduct_rule = rule lookup_coinductT lookup_coinductP >> single_rule;
wenzelm@24830
   893
wenzelm@24830
   894
val inst = Scan.lift (Args.$$$ "_") >> K NONE || Args.term >> SOME;
wenzelm@24830
   895
berghofe@34907
   896
val inst' = Scan.lift (Args.$$$ "_") >> K NONE ||
berghofe@34907
   897
  Args.term >> (SOME o rpair false) ||
berghofe@34907
   898
  Scan.lift (Args.$$$ "(") |-- (Args.term >> (SOME o rpair true)) --|
berghofe@34907
   899
    Scan.lift (Args.$$$ ")");
berghofe@34907
   900
wenzelm@24830
   901
val def_inst =
wenzelm@28083
   902
  ((Scan.lift (Args.binding --| (Args.$$$ "\<equiv>" || Args.$$$ "==")) >> SOME)
berghofe@34907
   903
      -- (Args.term >> rpair false)) >> SOME ||
berghofe@34907
   904
    inst' >> Option.map (pair NONE);
wenzelm@24830
   905
wenzelm@27370
   906
val free = Args.context -- Args.term >> (fn (_, Free v) => v | (ctxt, t) =>
wenzelm@27370
   907
  error ("Bad free variable: " ^ Syntax.string_of_term ctxt t));
wenzelm@24830
   908
wenzelm@24830
   909
fun unless_more_args scan = Scan.unless (Scan.lift
wenzelm@24830
   910
  ((Args.$$$ arbitraryN || Args.$$$ takingN || Args.$$$ typeN ||
wenzelm@24861
   911
    Args.$$$ predN || Args.$$$ setN || Args.$$$ ruleN) -- Args.colon)) scan;
wenzelm@24830
   912
wenzelm@24830
   913
val arbitrary = Scan.optional (Scan.lift (Args.$$$ arbitraryN -- Args.colon) |--
wenzelm@36960
   914
  Parse.and_list1' (Scan.repeat (unless_more_args free))) [];
wenzelm@24830
   915
wenzelm@24830
   916
val taking = Scan.optional (Scan.lift (Args.$$$ takingN -- Args.colon) |--
wenzelm@24830
   917
  Scan.repeat1 (unless_more_args inst)) [];
wenzelm@24830
   918
wenzelm@24830
   919
in
wenzelm@24830
   920
wenzelm@30722
   921
val cases_setup =
wenzelm@30722
   922
  Method.setup @{binding cases}
berghofe@34987
   923
    (Args.mode no_simpN --
wenzelm@36960
   924
      (Parse.and_list' (Scan.repeat (unless_more_args inst)) -- Scan.option cases_rule) >>
berghofe@34987
   925
      (fn (no_simp, (insts, opt_rule)) => fn ctxt =>
berghofe@34987
   926
        METHOD_CASES (fn facts => Seq.DETERM (HEADGOAL
berghofe@34987
   927
          (cases_tac ctxt (not no_simp) insts opt_rule facts)))))
wenzelm@30722
   928
    "case analysis on types or predicates/sets";
wenzelm@24830
   929
nipkow@45014
   930
fun gen_induct_setup binding itac =
nipkow@45014
   931
  Method.setup binding
wenzelm@36960
   932
    (Args.mode no_simpN -- (Parse.and_list' (Scan.repeat (unless_more_args def_inst)) --
berghofe@34907
   933
      (arbitrary -- taking -- Scan.option induct_rule)) >>
berghofe@34907
   934
      (fn (no_simp, (insts, ((arbitrary, taking), opt_rule))) => fn ctxt =>
wenzelm@30722
   935
        RAW_METHOD_CASES (fn facts =>
wenzelm@36960
   936
          Seq.DETERM
nipkow@45014
   937
            (HEADGOAL (itac ctxt (not no_simp) insts arbitrary taking opt_rule facts)))))
wenzelm@30722
   938
    "induction on types or predicates/sets";
wenzelm@24830
   939
nipkow@45014
   940
val induct_setup = gen_induct_setup @{binding induct} induct_tac;
nipkow@45014
   941
wenzelm@30722
   942
val coinduct_setup =
wenzelm@30722
   943
  Method.setup @{binding coinduct}
wenzelm@30722
   944
    (Scan.repeat (unless_more_args inst) -- taking -- Scan.option coinduct_rule >>
wenzelm@30722
   945
      (fn ((insts, taking), opt_rule) => fn ctxt =>
wenzelm@30722
   946
        RAW_METHOD_CASES (fn facts =>
wenzelm@30722
   947
          Seq.DETERM (HEADGOAL (coinduct_tac ctxt insts taking opt_rule facts)))))
wenzelm@30722
   948
    "coinduction on types or predicates/sets";
wenzelm@24830
   949
wenzelm@24830
   950
end;
wenzelm@24830
   951
wenzelm@24830
   952
wenzelm@24830
   953
wenzelm@24830
   954
(** theory setup **)
wenzelm@24830
   955
wenzelm@30722
   956
val setup = attrib_setup #> cases_setup  #> induct_setup #> coinduct_setup;
wenzelm@24830
   957
wenzelm@24830
   958
end;