# File ‹simpdata.ML›

```(*  Title:      ZF/simpdata.ML
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright   1991  University of Cambridge

Rewriting for ZF set theory: specialized extraction of rewrites from theorems.
*)

(*** New version of mk_rew_rules ***)

(*Should False yield False<->True, or should it solve goals some other way?*)

(*Analyse a theorem to atomic rewrite rules*)
fun atomize (conn_pairs, mem_pairs) th =
let fun tryrules pairs t =
case head_of t of
Const(a,_) =>
(case AList.lookup (op =) pairs a of
SOME rls => maps (atomize (conn_pairs, mem_pairs)) ([th] RL rls)
| NONE => [th])
| _ => [th]
in case Thm.concl_of th of
\<^Const_>‹Trueprop for P› =>
(case P of
\<^Const_>‹mem for a b› => tryrules mem_pairs b
| \<^Const_>‹True› => []
| \<^Const_>‹False› => []
| A => tryrules conn_pairs A)
| _                       => [th]
end;

(*Analyse a rigid formula*)
val ZF_conn_pairs =
[(\<^const_name>‹Ball›, [@{thm bspec}]),
(\<^const_name>‹All›, [@{thm spec}]),
(\<^const_name>‹imp›, [@{thm mp}]),
(\<^const_name>‹conj›, [@{thm conjunct1}, @{thm conjunct2}])];

(*Analyse a:b, where b is rigid*)
val ZF_mem_pairs =
[(\<^const_name>‹Collect›, [@{thm CollectD1}, @{thm CollectD2}]),
(\<^const_name>‹Diff›, [@{thm DiffD1}, @{thm DiffD2}]),
(\<^const_name>‹Int›, [@{thm IntD1}, @{thm IntD2}])];

val ZF_atomize = atomize (ZF_conn_pairs, ZF_mem_pairs);

```