src/Tools/induct_tacs.ML

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