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(* Title: HOL/Examples/Iff_Oracle.thy
Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Author: Makarius
*)
section \<open>Example of Declaring an Oracle\<close>
theory Iff_Oracle
imports Main
begin
subsection \<open>Oracle declaration\<close>
text \<open>
This oracle makes tautologies of the form \<^prop>\<open>P \<longleftrightarrow> P \<longleftrightarrow> P \<longleftrightarrow> P\<close>.
The length is specified by an integer, which is checked to be even
and positive.
\<close>
oracle iff_oracle = \<open>
let
fun mk_iff 1 = Var (("P", 0), \<^typ>\<open>bool\<close>)
| mk_iff n = HOLogic.mk_eq (Var (("P", 0), \<^typ>\<open>bool\<close>), 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
\<close>
subsection \<open>Oracle as low-level rule\<close>
ML \<open>iff_oracle (\<^theory>, 2)\<close>
ML \<open>iff_oracle (\<^theory>, 10)\<close>
ML \<open>
\<^assert> (map (#1 o #1) (Thm_Deps.all_oracles [iff_oracle (\<^theory>, 10)]) = [\<^oracle_name>\<open>iff_oracle\<close>]);
\<close>
text \<open>These oracle calls had better fail.\<close>
ML \<open>
(iff_oracle (\<^theory>, 5); error "Bad oracle")
handle Fail _ => writeln "Oracle failed, as expected"
\<close>
ML \<open>
(iff_oracle (\<^theory>, 1); error "Bad oracle")
handle Fail _ => writeln "Oracle failed, as expected"
\<close>
subsection \<open>Oracle as proof method\<close>
method_setup iff =
\<open>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))\<close>
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
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