src/FOLP/simpdata.ML
 author skalberg Thu, 03 Mar 2005 12:43:01 +0100 changeset 15570 8d8c70b41bab parent 15531 08c8dad8e399 child 17325 d9d50222808e permissions -rw-r--r--
Move towards standard functions.

(*  Title:      FOLP/simpdata.ML
ID:         \$Id\$
Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright   1991  University of Cambridge

Simplification data for FOLP
*)

(*** Rewrite rules ***)

fun int_prove_fun_raw s =
(writeln s;  prove_goal IFOLP.thy s
(fn prems => [ (cut_facts_tac prems 1), (IntPr.fast_tac 1) ]));

fun int_prove_fun s = int_prove_fun_raw ("?p : "^s);

val conj_rews = map int_prove_fun
["P & True <-> P",     "True & P <-> P",
"P & False <-> False", "False & P <-> False",
"P & P <-> P",
"P & ~P <-> False",   "~P & P <-> False",
"(P & Q) & R <-> P & (Q & R)"];

val disj_rews = map int_prove_fun
["P | True <-> True",  "True | P <-> True",
"P | False <-> P",    "False | P <-> P",
"P | P <-> P",
"(P | Q) | R <-> P | (Q | R)"];

val not_rews = map int_prove_fun
["~ False <-> True",   "~ True <-> False"];

val imp_rews = map int_prove_fun
["(P --> False) <-> ~P",       "(P --> True) <-> True",
"(False --> P) <-> True",     "(True --> P) <-> P",
"(P --> P) <-> True",         "(P --> ~P) <-> ~P"];

val iff_rews = map int_prove_fun
["(True <-> P) <-> P",         "(P <-> True) <-> P",
"(P <-> P) <-> True",
"(False <-> P) <-> ~P",       "(P <-> False) <-> ~P"];

val quant_rews = map int_prove_fun
["(ALL x. P) <-> P",    "(EX x. P) <-> P"];

(*These are NOT supplied by default!*)
val distrib_rews  = map int_prove_fun
["~(P|Q) <-> ~P & ~Q",
"P & (Q | R) <-> P&Q | P&R", "(Q | R) & P <-> Q&P | R&P",
"(P | Q --> R) <-> (P --> R) & (Q --> R)",
"~(EX x. NORM(P(x))) <-> (ALL x. ~NORM(P(x)))",
"((EX x. NORM(P(x))) --> Q) <-> (ALL x. NORM(P(x)) --> Q)",
"(EX x. NORM(P(x))) & NORM(Q) <-> (EX x. NORM(P(x)) & NORM(Q))",
"NORM(Q) & (EX x. NORM(P(x))) <-> (EX x. NORM(Q) & NORM(P(x)))"];

val P_Imp_P_iff_T = int_prove_fun_raw "p:P ==> ?p:(P <-> True)";

fun make_iff_T th = th RS P_Imp_P_iff_T;

val refl_iff_T = make_iff_T refl;

val norm_thms = [(norm_eq RS sym, norm_eq),
(NORM_iff RS iff_sym, NORM_iff)];

(* Conversion into rewrite rules *)

val not_P_imp_P_iff_F = int_prove_fun_raw "p:~P ==> ?p:(P <-> False)";

fun mk_eq th = case concl_of th of
_ \$ (Const("op <->",_)\$_\$_) \$ _ => th
| _ \$ (Const("op =",_)\$_\$_) \$ _ => th
| _ \$ (Const("Not",_)\$_) \$ _ => th RS not_P_imp_P_iff_F
| _ => make_iff_T th;

val mksimps_pairs =
[("op -->", [mp]), ("op &", [conjunct1,conjunct2]),
("All", [spec]), ("True", []), ("False", [])];

fun mk_atomize pairs =
let fun atoms th =
(case concl_of th of
Const("Trueprop",_) \$ p =>
(case head_of p of
Const(a,_) =>
(case assoc(pairs,a) of
SOME(rls) => List.concat (map atoms ([th] RL rls))
| NONE => [th])
| _ => [th])
| _ => [th])
in atoms end;

fun mk_rew_rules th = map mk_eq (mk_atomize mksimps_pairs th);

(*destruct function for analysing equations*)
fun dest_red(_ \$ (red \$ lhs \$ rhs) \$ _) = (red,lhs,rhs)
| dest_red t = raise TERM("FOL/dest_red", [t]);

structure FOLP_SimpData : SIMP_DATA =
struct
val refl_thms         = [refl, iff_refl]
val trans_thms        = [trans, iff_trans]
val red1              = iffD1
val red2              = iffD2
val mk_rew_rules      = mk_rew_rules
val case_splits       = []         (*NO IF'S!*)
val norm_thms         = norm_thms
val subst_thms        = [subst];
val dest_red          = dest_red
end;

structure FOLP_Simp = SimpFun(FOLP_SimpData);

(*not a component of SIMP_DATA, but an argument of SIMP_TAC *)
val FOLP_congs =
[all_cong,ex_cong,eq_cong,
conj_cong,disj_cong,imp_cong,iff_cong,not_cong] @ pred_congs;

val IFOLP_rews =
[refl_iff_T] @ conj_rews @ disj_rews @ not_rews @
imp_rews @ iff_rews @ quant_rews;

open FOLP_Simp;

val auto_ss = empty_ss setauto ares_tac [TrueI];

val IFOLP_ss = auto_ss addcongs FOLP_congs addrews IFOLP_rews;

(*Classical version...*)
fun prove_fun s =
(writeln s;  prove_goal FOLP.thy s
(fn prems => [ (cut_facts_tac prems 1), (Cla.fast_tac FOLP_cs 1) ]));

val cla_rews = map prove_fun
["?p:P | ~P",          "?p:~P | P",
"?p:~ ~ P <-> P",     "?p:(~P --> P) <-> P"];

val FOLP_rews = IFOLP_rews@cla_rews;

val FOLP_ss = auto_ss addcongs FOLP_congs addrews FOLP_rews;