src/Pure/Isar/rule_cases.ML
author wenzelm
Thu Oct 29 13:21:38 2009 +0100 (2009-10-29)
changeset 33303 1e1210f31207
parent 31794 71af1fd6a5e4
child 33368 b1cf34f1855c
permissions -rw-r--r--
separate "inner_rule" tag indicates parts of induction rules -- avoids unclear overlap with "internal" tag;
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(*  Title:      Pure/Isar/rule_cases.ML
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    Author:     Markus Wenzel, TU Muenchen
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Annotations and local contexts of rules.
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*)
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infix 1 THEN_ALL_NEW_CASES;
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signature BASIC_RULE_CASES =
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sig
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  type cases
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  type cases_tactic
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  val CASES: cases -> tactic -> cases_tactic
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  val NO_CASES: tactic -> cases_tactic
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  val SUBGOAL_CASES: ((term * int) -> cases_tactic) -> int -> cases_tactic
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  val THEN_ALL_NEW_CASES: (int -> cases_tactic) * (int -> tactic) -> int -> cases_tactic
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end
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signature RULE_CASES =
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sig
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  include BASIC_RULE_CASES
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  datatype T = Case of
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   {fixes: (string * typ) list,
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    assumes: (string * term list) list,
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    binds: (indexname * term option) list,
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    cases: (string * T) list}
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  val strip_params: term -> (string * typ) list
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  val make_common: bool -> theory * term -> (string * string list) list -> cases
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  val make_nested: bool -> term -> theory * term -> (string * string list) list -> cases
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  val apply: term list -> T -> T
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  val consume: thm list -> thm list -> ('a * int) * thm ->
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    (('a * (int * thm list)) * thm) Seq.seq
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  val add_consumes: int -> thm -> thm
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  val get_consumes: thm -> int
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  val consumes: int -> attribute
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  val consumes_default: int -> attribute
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  val name: string list -> thm -> thm
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  val case_names: string list -> attribute
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  val case_conclusion: string * string list -> attribute
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  val is_inner_rule: thm -> bool
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  val inner_rule: attribute
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  val save: thm -> thm -> thm
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  val get: thm -> (string * string list) list * int
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  val rename_params: string list list -> thm -> thm
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  val params: string list list -> attribute
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  val mutual_rule: Proof.context -> thm list -> (int list * thm) option
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  val strict_mutual_rule: Proof.context -> thm list -> int list * thm
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end;
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structure RuleCases: RULE_CASES =
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struct
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(** cases **)
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datatype T = Case of
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 {fixes: (string * typ) list,
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  assumes: (string * term list) list,
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  binds: (indexname * term option) list,
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  cases: (string * T) list};
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type cases = (string * T option) list;
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val case_conclN = "case";
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val case_hypsN = "hyps";
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val case_premsN = "prems";
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val strip_params = map (apfst (perhaps (try Name.dest_skolem))) o Logic.strip_params;
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local
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fun abs xs t = Term.list_abs (xs, t);
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fun app us t = Term.betapplys (t, us);
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fun dest_binops cs tm =
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  let
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    val n = length cs;
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    fun dest 0 _ = []
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      | dest 1 t = [t]
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      | dest k (_ $ t $ u) = t :: dest (k - 1) u
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      | dest _ _ = raise TERM ("Expected " ^ string_of_int n ^ " binop arguments", [tm]);
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  in cs ~~ dest n tm end;
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fun extract_fixes NONE prop = (strip_params prop, [])
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  | extract_fixes (SOME outline) prop =
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      chop (length (Logic.strip_params outline)) (strip_params prop);
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fun extract_assumes _ NONE prop = ([("", Logic.strip_assums_hyp prop)], [])
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  | extract_assumes qual (SOME outline) prop =
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      let val (hyps, prems) =
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        chop (length (Logic.strip_assums_hyp outline)) (Logic.strip_assums_hyp prop)
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      in ([(qual case_hypsN, hyps)], [(qual case_premsN, prems)]) end;
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fun extract_case is_open thy (case_outline, raw_prop) name concls =
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  let
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    val rename = if is_open then I else apfst (Name.internal o Name.clean);
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    val props = Logic.dest_conjunctions (Drule.norm_hhf thy raw_prop);
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    val len = length props;
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    val nested = is_some case_outline andalso len > 1;
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    fun extract prop =
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      let
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        val (fixes1, fixes2) = extract_fixes case_outline prop
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          |> apfst (map rename);
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        val abs_fixes = abs (fixes1 @ fixes2);
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        fun abs_fixes1 t =
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          if not nested then abs_fixes t
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          else abs fixes1 (app (map (Term.dummy_pattern o #2) fixes2) (abs fixes2 t));
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        val (assumes1, assumes2) = extract_assumes (Long_Name.qualify name) case_outline prop
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          |> pairself (map (apsnd (maps Logic.dest_conjunctions)));
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        val concl = ObjectLogic.drop_judgment thy (Logic.strip_assums_concl prop);
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        val binds =
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          (case_conclN, concl) :: dest_binops concls concl
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          |> map (fn (x, t) => ((x, 0), SOME (abs_fixes t)));
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      in
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       ((fixes1, map (apsnd (map abs_fixes1)) assumes1),
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        ((fixes2, map (apsnd (map abs_fixes)) assumes2), binds))
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      end;
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    val cases = map extract props;
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    fun common_case ((fixes1, assumes1), ((fixes2, assumes2), binds)) =
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      Case {fixes = fixes1 @ fixes2, assumes = assumes1 @ assumes2, binds = binds, cases = []};
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    fun inner_case (_, ((fixes2, assumes2), binds)) =
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      Case {fixes = fixes2, assumes = assumes2, binds = binds, cases = []};
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    fun nested_case ((fixes1, assumes1), _) =
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      Case {fixes = fixes1, assumes = assumes1, binds = [],
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        cases = map string_of_int (1 upto len) ~~ map inner_case cases};
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  in
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    if len = 0 then NONE
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    else if len = 1 then SOME (common_case (hd cases))
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    else if is_none case_outline orelse length (distinct (op =) (map fst cases)) > 1 then NONE
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    else SOME (nested_case (hd cases))
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  end;
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fun make is_open rule_struct (thy, prop) cases =
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  let
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    val n = length cases;
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    val nprems = Logic.count_prems prop;
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    fun add_case (name, concls) (cs, i) =
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      ((case try (fn () =>
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          (Option.map (curry Logic.nth_prem i) rule_struct, Logic.nth_prem (i, prop))) () of
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        NONE => (name, NONE)
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      | SOME p => (name, extract_case is_open thy p name concls)) :: cs, i - 1);
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  in fold_rev add_case (Library.drop (n - nprems, cases)) ([], n) |> #1 end;
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in
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fun make_common is_open = make is_open NONE;
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fun make_nested is_open rule_struct = make is_open (SOME rule_struct);
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fun apply args =
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  let
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    fun appl (Case {fixes, assumes, binds, cases}) =
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      let
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        val assumes' = map (apsnd (map (app args))) assumes;
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        val binds' = map (apsnd (Option.map (app args))) binds;
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        val cases' = map (apsnd appl) cases;
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      in Case {fixes = fixes, assumes = assumes', binds = binds', cases = cases'} end;
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  in appl end;
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end;
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(** tactics with cases **)
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type cases_tactic = thm -> (cases * thm) Seq.seq;
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fun CASES cases tac st = Seq.map (pair cases) (tac st);
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fun NO_CASES tac = CASES [] tac;
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fun SUBGOAL_CASES tac i st =
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  (case try Logic.nth_prem (i, Thm.prop_of st) of
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    SOME goal => tac (goal, i) st
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  | NONE => Seq.empty);
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fun (tac1 THEN_ALL_NEW_CASES tac2) i st =
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  st |> tac1 i |> Seq.maps (fn (cases, st') =>
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    CASES cases (Seq.INTERVAL tac2 i (i + nprems_of st' - nprems_of st)) st');
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(** consume facts **)
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local
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fun unfold_prems n defs th =
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  if null defs then th
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  else Conv.fconv_rule (Conv.prems_conv n (MetaSimplifier.rewrite true defs)) th;
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fun unfold_prems_concls defs th =
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  if null defs orelse not (can Logic.dest_conjunction (Thm.concl_of th)) then th
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  else
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    Conv.fconv_rule
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      (Conv.concl_conv ~1 (Conjunction.convs
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        (Conv.prems_conv ~1 (MetaSimplifier.rewrite true defs)))) th;
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in
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fun consume defs facts ((xx, n), th) =
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  let val m = Int.min (length facts, n) in
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    th
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    |> unfold_prems n defs
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    |> unfold_prems_concls defs
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    |> Drule.multi_resolve (Library.take (m, facts))
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    |> Seq.map (pair (xx, (n - m, Library.drop (m, facts))))
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  end;
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end;
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val consumes_tagN = "consumes";
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fun lookup_consumes th =
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  (case AList.lookup (op =) (Thm.get_tags th) consumes_tagN of
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    NONE => NONE
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  | SOME s =>
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      (case Lexicon.read_nat s of SOME n => SOME n
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      | _ => raise THM ("Malformed 'consumes' tag of theorem", 0, [th])));
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fun get_consumes th = the_default 0 (lookup_consumes th);
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fun put_consumes NONE th = th
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  | put_consumes (SOME n) th = th
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      |> Thm.untag_rule consumes_tagN
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      |> Thm.tag_rule (consumes_tagN, string_of_int (if n < 0 then Thm.nprems_of th + n else n));
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fun add_consumes k th = put_consumes (SOME (k + get_consumes th)) th;
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val save_consumes = put_consumes o lookup_consumes;
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fun consumes n = Thm.rule_attribute (K (put_consumes (SOME n)));
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fun consumes_default n x =
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  if is_some (lookup_consumes (#2 x)) then x else consumes n x;
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(** case names **)
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val implode_args = space_implode ";";
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val explode_args = space_explode ";";
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val case_names_tagN = "case_names";
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fun add_case_names NONE = I
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  | add_case_names (SOME names) =
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      Thm.untag_rule case_names_tagN
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      #> Thm.tag_rule (case_names_tagN, implode_args names);
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fun lookup_case_names th =
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  AList.lookup (op =) (Thm.get_tags th) case_names_tagN
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  |> Option.map explode_args;
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val save_case_names = add_case_names o lookup_case_names;
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val name = add_case_names o SOME;
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fun case_names ss = Thm.rule_attribute (K (name ss));
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(** case conclusions **)
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val case_concl_tagN = "case_conclusion";
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fun get_case_concl name (a, b) =
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  if a = case_concl_tagN then
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    (case explode_args b of c :: cs => if c = name then SOME cs else NONE)
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  else NONE;
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fun add_case_concl (name, cs) = Thm.map_tags (fn tags =>
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  filter_out (is_some o get_case_concl name) tags @
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    [(case_concl_tagN, implode_args (name :: cs))]);
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fun get_case_concls th name =
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  these (get_first (get_case_concl name) (Thm.get_tags th));
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fun save_case_concls th =
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  let val concls = Thm.get_tags th |> map_filter
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    (fn (a, b) =>
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      if a = case_concl_tagN then (case explode_args b of c :: cs => SOME (c, cs) | _ => NONE)
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      else NONE)
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  in fold add_case_concl concls end;
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fun case_conclusion concl = Thm.rule_attribute (K (add_case_concl concl));
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(** inner rule **)
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val inner_rule_tagN = "inner_rule";
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fun is_inner_rule th =
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  AList.defined (op =) (Thm.get_tags th) inner_rule_tagN;
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fun put_inner_rule inner =
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  Thm.untag_rule inner_rule_tagN
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  #> inner ? Thm.tag_rule (inner_rule_tagN, "");
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val save_inner_rule = put_inner_rule o is_inner_rule;
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val inner_rule = Thm.rule_attribute (K (put_inner_rule true));
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(** case declarations **)
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(* access hints *)
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fun save th =
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  save_consumes th #>
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  save_case_names th #>
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  save_case_concls th #>
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  save_inner_rule th;
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fun get th =
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  let
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    val n = get_consumes th;
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    val cases =
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      (case lookup_case_names th of
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        NONE => map (rpair [] o Library.string_of_int) (1 upto (Thm.nprems_of th - n))
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      | SOME names => map (fn name => (name, get_case_concls th name)) names);
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  in (cases, n) end;
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(* params *)
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fun rename_params xss th =
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  th
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  |> fold_index (fn (i, xs) => Thm.rename_params_rule (xs, i + 1)) xss
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  |> save th;
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fun params xss = Thm.rule_attribute (K (rename_params xss));
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(** mutual_rule **)
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local
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fun equal_cterms ts us =
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  is_equal (list_ord (TermOrd.fast_term_ord o pairself Thm.term_of) (ts, us));
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fun prep_rule n th =
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  let
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    val th' = Thm.permute_prems 0 n th;
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    val prems = Library.take (Thm.nprems_of th' - n, Drule.cprems_of th');
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    val th'' = Drule.implies_elim_list th' (map Thm.assume prems);
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  in (prems, (n, th'')) end;
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in
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fun mutual_rule _ [] = NONE
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  | mutual_rule _ [th] = SOME ([0], th)
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  | mutual_rule ctxt (ths as th :: _) =
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      let
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        val ((_, ths'), ctxt') = Variable.import true ths ctxt;
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        val rules as (prems, _) :: _ = map (prep_rule (get_consumes th)) ths';
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        val (ns, rls) = split_list (map #2 rules);
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      in
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        if not (forall (equal_cterms prems o #1) rules) then NONE
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        else
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          SOME (ns,
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            rls
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            |> Conjunction.intr_balanced
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            |> Drule.implies_intr_list prems
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            |> singleton (Variable.export ctxt' ctxt)
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            |> save th
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            |> put_consumes (SOME 0))
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      end;
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wenzelm@18477
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end;
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fun strict_mutual_rule ctxt ths =
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  (case mutual_rule ctxt ths of
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    NONE => error "Failed to join given rules into one mutual rule"
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  | SOME res => res);
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end;
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structure Basic_Rule_Cases: BASIC_RULE_CASES = RuleCases;
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open Basic_Rule_Cases;