src/Tools/induct_tacs.ML
author haftmann
Mon, 22 Sep 2008 08:00:24 +0200
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child 30161 c26e515f1c29
permissions -rw-r--r--
fixed headers
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(*  Title:      Tools/induct_tacs.ML
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    ID:         $Id$
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    Author:     Makarius
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Unstructured induction and cases analysis.
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*)
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signature INDUCT_TACS =
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sig
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  val case_tac: Proof.context -> string -> int -> tactic
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  val case_rule_tac: Proof.context -> string -> thm -> int -> tactic
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  val induct_tac: Proof.context -> string option list list -> int -> tactic
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  val induct_rules_tac: Proof.context -> string option list list -> thm list -> int -> tactic
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  val setup: theory -> theory
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end
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structure InductTacs: INDUCT_TACS =
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struct
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(* case analysis *)
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fun check_type ctxt t =
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  let
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    val u = singleton (Variable.polymorphic ctxt) t;
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    val U = Term.fastype_of u;
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    val _ = Term.is_TVar U andalso
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      error ("Cannot determine type of " ^ Syntax.string_of_term ctxt u);
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  in (u, U) end;
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fun gen_case_tac ctxt0 (s, opt_rule) i st =
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  let
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    val ((_, goal), ctxt) = Variable.focus_subgoal i st ctxt0;
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    val rule =
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      (case opt_rule of
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        SOME rule => rule
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      | NONE =>
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          (case Induct.find_casesT ctxt
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              (#2 (check_type ctxt (ProofContext.read_term_schematic ctxt s))) of
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            rule :: _ => rule
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          | [] => @{thm case_split}));
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    val _ = Method.trace ctxt [rule];
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    val xi =
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      (case Induct.vars_of (Thm.term_of (Thm.cprem_of rule 1)) of
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        Var (xi, _) :: _ => xi
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      | _ => raise THM ("Malformed cases rule", 0, [rule]));
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  in res_inst_tac ctxt [(xi, s)] rule i st end
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  handle THM _ => Seq.empty;
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fun case_tac ctxt s = gen_case_tac ctxt (s, NONE);
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fun case_rule_tac ctxt s rule = gen_case_tac ctxt (s, SOME rule);
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(* induction *)
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local
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fun prep_var (Var (ixn, _), SOME x) = SOME (ixn, x)
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  | prep_var _ = NONE;
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fun prep_inst (concl, xs) =
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  let val vs = Induct.vars_of concl
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  in map_filter prep_var (Library.drop (length vs - length xs, vs) ~~ xs) end;
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in
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fun gen_induct_tac ctxt0 (varss, opt_rules) i st =
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  let
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    val ((_, goal), ctxt) = Variable.focus_subgoal i st ctxt0;
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    val (prems, concl) = Logic.strip_horn (Thm.term_of goal);
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    fun induct_var name =
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      let
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        val t = Syntax.read_term ctxt name;
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        val (x, _) = Term.dest_Free t handle TERM _ =>
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          error ("Induction argument not a variable: " ^ Syntax.string_of_term ctxt t);
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        val eq_x = fn Free (y, _) => x = y | _ => false;
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        val _ =
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          if Term.exists_subterm eq_x concl then ()
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          else error ("No such variable in subgoal: " ^ Syntax.string_of_term ctxt t);
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        val _ =
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          if (exists o Term.exists_subterm) eq_x prems then
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            warning ("Induction variable occurs also among premises: " ^ Syntax.string_of_term ctxt t)
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          else ();
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      in #1 (check_type ctxt t) end;
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    val argss = map (map (Option.map induct_var)) varss;
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    val rule =
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      (case opt_rules of
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        SOME rules => #2 (RuleCases.strict_mutual_rule ctxt rules)
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      | NONE =>
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          (case map_filter (RuleCases.mutual_rule ctxt) (Induct.get_inductT ctxt argss) of
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            (_, rule) :: _ => rule
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          | [] => raise THM ("No induction rules", 0, [])));
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    val rule' = rule |> Conv.fconv_rule (Conv.concl_conv ~1 ObjectLogic.atomize);
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    val _ = Method.trace ctxt [rule'];
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    val concls = Logic.dest_conjunctions (Thm.concl_of rule);
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    val insts = maps prep_inst (concls ~~ varss) handle Library.UnequalLengths =>
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      error "Induction rule has different numbers of variables";
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  in res_inst_tac ctxt insts rule' i st end
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  handle THM _ => Seq.empty;
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end;
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fun induct_tac ctxt args = gen_induct_tac ctxt (args, NONE);
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fun induct_rules_tac ctxt args rules = gen_induct_tac ctxt (args, SOME rules);
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(* method syntax *)
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local
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val rule_spec = Scan.lift (Args.$$$ "rule" -- Args.$$$ ":");
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val opt_rule = Scan.option (rule_spec |-- Attrib.thm);
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val opt_rules = Scan.option (rule_spec |-- Attrib.thms);
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val varss =
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  OuterParse.and_list'
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    (Scan.repeat (Scan.unless rule_spec (Scan.lift (Args.maybe Args.name_source))));
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in
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val setup =
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  Method.add_methods
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eaa9fef9f4c1 Args.name_source(_position) for proper position information;
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   [("case_tac", Method.goal_args_ctxt' (Scan.lift Args.name_source -- opt_rule) gen_case_tac,
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      "unstructured case analysis on types"),
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    ("induct_tac", Method.goal_args_ctxt' (varss -- opt_rules) gen_induct_tac,
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      "unstructured induction on types")];
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end;
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end;
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