header {* 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.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)) *}
text {* These oracle calls had better fail. *}
ML {*
(iff_oracle (@{theory}, 5); error "Bad oracle")
handle Fail _ => warning "Oracle failed, as expected"
*}
ML {*
(iff_oracle (@{theory}, 1); error "Bad oracle")
handle Fail _ => warning "Oracle failed, as expected"
*}
subsection {* Oracle as proof method *}
method_setup iff = {*
Scan.lift Parse.nat >> (fn n => fn ctxt =>
SIMPLE_METHOD
(HEADGOAL (rtac (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