(* Title: Tools/induction.ML Author: Tobias Nipkow, TU Muenchen
Alternative proof method "induction" that gives induction hypotheses the name "IH".
*)
signature INDUCTION = sig val induction_context_tactic: bool -> (binding option * (term * bool)) optionlistlist ->
(string * typ) listlist -> term optionlist -> thm listoption ->
thm list -> int -> context_tactic val induction_tac: Proof.context -> bool -> (binding option * (term * bool)) optionlistlist ->
(string * typ) listlist -> term optionlist -> thm listoption ->
thm list -> int -> tactic end
structure Induction: INDUCTION = struct
val ind_hypsN = "IH";
fun preds_of t =
(case strip_comb t of
(p as Var _, _) => [p]
| (p as Free _, _) => [p]
| (_, ts) => maps preds_of ts);
val induction_context_tactic =
Induct.gen_induct_context_tactic (fn arg as ((cases, consumes), th) => ifnot (forall (null o #2 o #1) cases) then arg else let val (prems, concl) = Logic.strip_horn (Thm.prop_of th); val prems' = drop consumes prems; val ps = preds_of concl;
fun hname_of t = if exists_subterm (member (op aconv) ps) t then ind_hypsN else Rule_Cases.case_hypsN;
val hnamess = map (map hname_of o Logic.strip_assums_hyp) prems'; val n = Int.min (length hnamess, length cases); val cases' = map (fn (((cn, _), concls), hns) => ((cn, hns), concls))
(take n cases ~~ take n hnamess); in ((cases', consumes), th) end);
fun induction_tac ctxt simp def_insts arbitrary taking opt_rule facts i =
induction_context_tactic simp def_insts arbitrary taking opt_rule facts i
|> NO_CONTEXT_TACTIC ctxt;
val _ =
Theory.local_setup (Induct.gen_induct_setup \<^binding>\<open>induction\<close> induction_context_tactic);
end
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