Quelle  Iff_Oracle.thy  Sprache: unbekannt

(*  Title:      HOL/Examples/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 (🚫, 2)›
ML ‹iff_oracle (🚫, 10)›

ML ‹
 🚫 (map (#1 o #1) (Thm_Deps.all_oracles [iff_oracle (🚫, 10)]) = [🚫‹iff_oracle›]);
 ›

text ‹These oracle calls had better fail.›

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

ML ‹
 (iff_oracle (🚫, 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