# Theory Iff_Oracle

theory Iff_Oracle
imports Main
```(*  Title:      HOL/ex/Iff_Oracle.thy
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
Author:     Makarius
*)

section ‹Example of Declaring an Oracle›

theory Iff_Oracle
imports Main
begin

subsection ‹Oracle declaration›

text ‹
This oracle makes tautologies of the form @{prop "P ⟷ P ⟷ P ⟷ P"}.
The length is specified by an integer, which is checked to be even
and positive.
›

oracle iff_oracle = ‹
let
fun mk_iff 1 = Var (("P", 0), @{typ bool})
| mk_iff n = HOLogic.mk_eq (Var (("P", 0), @{typ bool}), mk_iff (n - 1));
in
fn (thy, n) =>
if n > 0 andalso n mod 2 = 0
then Thm.global_cterm_of thy (HOLogic.mk_Trueprop (mk_iff n))
else raise Fail ("iff_oracle: " ^ string_of_int n)
end
›

subsection ‹Oracle as low-level rule›

ML ‹iff_oracle (@{theory}, 2)›
ML ‹iff_oracle (@{theory}, 10)›

ML ‹
Thm.peek_status (iff_oracle (@{theory}, 10));
@{assert} (#oracle it);
›

text ‹These oracle calls had better fail.›

ML ‹
(iff_oracle (@{theory}, 5); error "Bad oracle")
handle Fail _ => writeln "Oracle failed, as expected"
›

ML ‹
(iff_oracle (@{theory}, 1); error "Bad oracle")
handle Fail _ => writeln "Oracle failed, as expected"
›

subsection ‹Oracle as proof method›

method_setup iff =
‹Scan.lift Parse.nat >> (fn n => fn ctxt =>
SIMPLE_METHOD
(HEADGOAL (resolve_tac ctxt [iff_oracle (Proof_Context.theory_of ctxt, n)])
handle Fail _ => no_tac))›

lemma "A ⟷ A"
by (iff 2)

lemma "A ⟷ A ⟷ A ⟷ A ⟷ A ⟷ A ⟷ A ⟷ A ⟷ A ⟷ A"
by (iff 10)

lemma "A ⟷ A ⟷ A ⟷ A ⟷ A"
apply (iff 5)?
oops

lemma A
apply (iff 1)?
oops

end
```