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(* ========================================================================= *)
(* Explicit computations of group operations from extensible clauses. *)
(* ========================================================================= *)
needs "Library/grouptheory.ml";;
needs "Library/ringtheory.ml";;
let curve_clauses = ref ([]:thm list)
and curvezero_clauses = ref ([]:thm list)
and curveneg_clauses = ref ([]:thm list)
and curveadd_clauses = ref ([]:thm list)
and ecgroup_carriers = ref ([]:thm list)
and ecgroup_ids = ref ([]:thm list)
and ecgroup_invs = ref ([]:thm list)
and ecgroup_muls = ref ([]:thm list);;
(* ------------------------------------------------------------------------- *)
(* Augment store of clauses, both curve types and actual specific curves. *)
(* ------------------------------------------------------------------------- *)
let add_curve th = (curve_clauses := insert th (!curve_clauses));;
let add_curvezero th = (curvezero_clauses := insert th (!curvezero_clauses));;
let add_curveneg th = (curveneg_clauses := insert th (!curveneg_clauses));;
let add_curveadd th = (curveadd_clauses := insert th (!curveadd_clauses));;
let add_ecgroup defs th =
let [cth;ith;nth;ath] = CONJUNCTS(PURE_REWRITE_RULE defs th) in
(ecgroup_carriers := insert cth (!ecgroup_carriers);
ecgroup_ids := insert ith (!ecgroup_ids);
ecgroup_invs := insert nth (!ecgroup_invs);
ecgroup_muls := insert ath (!ecgroup_muls));;
(* ------------------------------------------------------------------------- *)
(* The actual conversions. *)
(* ------------------------------------------------------------------------- *)
let ECGROUP_CARRIER_CONV tm =
(GEN_REWRITE_CONV RAND_CONV (!ecgroup_carriers) THENC
GEN_REWRITE_CONV I [IN] THENC
GEN_REWRITE_CONV I (!curve_clauses) THENC
REWRITE_CONV[IN_INTEGER_MOD_RING_CARRIER] THENC
DEPTH_CONV(INTEGER_MOD_RING_RED_CONV ORELSEC INT_RED_CONV)) tm;;
let ECGROUP_ID_CONV tm =
(GEN_REWRITE_CONV I (!ecgroup_ids) THENC
TRY_CONV(GEN_REWRITE_CONV I (!curvezero_clauses) THENC
DEPTH_CONV INTEGER_MOD_RING_RED_CONV)) tm;;
let ECGROUP_INV_CONV tm =
(GEN_REWRITE_CONV RATOR_CONV (!ecgroup_invs) THENC
GEN_REWRITE_CONV I (!curveneg_clauses) THENC
DEPTH_CONV INTEGER_MOD_RING_RED_CONV) tm;;
let ECGROUP_MUL_CONV tm =
(GEN_REWRITE_CONV (RATOR_CONV o RATOR_CONV) (!ecgroup_muls) THENC
GEN_REWRITE_CONV I (!curveadd_clauses) THENC
DEPTH_CONV(INTEGER_MOD_RING_RED_CONV ORELSEC INT_RED_CONV) THENC
REPEATC(let_CONV THENC DEPTH_CONV INTEGER_MOD_RING_RED_CONV)) tm;;
let ECGROUP_POW_CONV =
let pth = prove
(`!G x m n.
x IN group_carrier G
==> group_pow G x (2 * n) = group_pow G (group_mul G x x) n`,
SIMP_TAC[GSYM GROUP_POW_2; GROUP_POW_POW])
and dth = prove
(`NUMERAL(BIT0 n) = 2 * NUMERAL n`,
REWRITE_TAC[MULT_2] THEN REWRITE_TAC[BIT0] THEN
REWRITE_TAC[NUMERAL]) in
let num_half_CONV = GEN_REWRITE_CONV I [dth] in
let conv_0 tm =
(GEN_REWRITE_CONV I [CONJUNCT1 group_pow] THENC
ECGROUP_ID_CONV) tm
and conv_1 = GEN_REWRITE_CONV I [CONJUNCT2 group_pow]
and conv_2 = PART_MATCH (lhand o rand) pth in
let rec conv tm =
match tm with
Comb(Comb(Comb(Const("group_pow",_),g),x),ntm) ->
let n = dest_numeral ntm in
if n =/ num_0 then conv_0 tm
else if mod_num n num_2 =/ num_1 then
(RAND_CONV num_CONV THENC conv_1 THENC
RAND_CONV conv THENC ECGROUP_MUL_CONV) tm
else
let th1 = RAND_CONV num_half_CONV tm in
let th2 = conv_2 (rand(concl th1)) in
let th3 = MP th2
(EQT_ELIM((ECGROUP_CARRIER_CONV(lhand(concl th2))))) in
let th4 = TRANS th1 th3 in
CONV_RULE(RAND_CONV(LAND_CONV ECGROUP_MUL_CONV THENC conv)) th4
| _ -> failwith "ECGROUP_POW_CONV" in
conv;;
|