(* Title: Tools/cong_tac.ML
Author: Stefan Berghofer, TU Muenchen
Congruence tactic based on explicit instantiation.
*)
signature CONG_TAC =
sig
val cong_tac: Proof.context -> thm -> int -> tactic
end;
structure Cong_Tac: CONG_TAC =
struct
fun cong_tac ctxt cong = CSUBGOAL (fn (cgoal, i) =>
let
val goal = Thm.term_of cgoal;
in
(case Logic.strip_assums_concl goal of
_ $ (_ $ (f $ x) $ (g $ y)) =>
let
val cong' = Thm.lift_rule cgoal cong;
val _ $ (_ $ (f' $ x') $ (g' $ y')) = Logic.strip_assums_concl (Thm.prop_of cong');
val ps = Logic.strip_params (Thm.concl_of cong');
val insts =
[(f', f), (g', g), (x', x), (y', y)]
|> map (fn (t, u) => apply2 (Thm.cterm_of ctxt) (Term.head_of t, fold_rev Term.abs ps u));
in
fn st =>
compose_tac ctxt (false, Drule.cterm_instantiate insts cong', 2) i st
handle THM _ => no_tac st
end
| _ => no_tac)
end);
end;