boopscript.sml

源程序漏洞检查

(*
 * Copyright 2003 Georg Weissenbacher
 * Institute for Software Technology/Graz University of Technology
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 *)

open HolKernel Parse basicHol90Lib intLib numLib realLib;

val _ = new_theory "boop";

val _ = bossLib.Hol_datatype `loc = 
    IntLoc of int
  | RealLoc of real
  | NumLoc of num
`;

val BOOP_UNREPINT_THM = bossLib.Define `
    unrepInt (IntLoc i) = i
`;

val BOOP_UNREPREAL_THM = bossLib.Define `
    unrepReal (RealLoc r) = r
`;

val BOOP_UNREPNUM_THM = bossLib.Define `
    unrepNum (NumLoc i) = i
`;

val BOOP_SHIFTLEFT_THM = bossLib.Define `
   (BOOP_SHIFTLEFT (v:int) 0n = v ) /\
   (BOOP_SHIFTLEFT (v:int) (SUC n) = (BOOP_SHIFTLEFT (v+v) n))
`;

val BOOP_SHIFTRIGHT_THM = bossLib.Define `
   (BOOP_SHIFTRIGHT (v:int) 0n = v ) /\
   (BOOP_SHIFTRIGHT (v:int) (SUC n) = (BOOP_SHIFTRIGHT (v / 2) n))
`;

val BOOP_SHIFTMULDIV_THM = store_thm (
    "BOOP_SHIFTMULDIV_THM",
    ``!a n. BOOP_SHIFTLEFT (2 * a) n / 2 = BOOP_SHIFTLEFT a n``,
    Tactical.THENL (bossLib.Induct_on `n`,
        [
          Tactical.THEN (REWRITE_TAC [BOOP_SHIFTLEFT_THM],
            Tactical.THEN (ONCE_REWRITE_TAC [integerTheory.INT_MUL_SYM],
                           simpLib.FULL_SIMP_TAC intSimps.int_ss 
                             [integerTheory.INT_MUL_DIV, 
                              integerTheory.INT_MUL_RID]
                          )), 
	  Tactical.THEN (REWRITE_TAC [BOOP_SHIFTLEFT_THM, 
                                      integerTheory.INT_DOUBLE],
	                 ASM_REWRITE_TAC [])])
);

val BOOP_SHIFTLR_THM = store_thm (
    "BOOP_SHIFTLR_THM",
    ``!a n. BOOP_SHIFTRIGHT (BOOP_SHIFTLEFT a n) n = a``,
    Tactical.THENL (bossLib.Induct_on `n`,
        [
          REWRITE_TAC [BOOP_SHIFTLEFT_THM, BOOP_SHIFTRIGHT_THM],
          Tactical.THEN (REWRITE_TAC [BOOP_SHIFTLEFT_THM,
                                      BOOP_SHIFTRIGHT_THM],
	    Tactical.THEN (REWRITE_TAC [integerTheory.INT_DOUBLE],
              Tactical.THEN (REWRITE_TAC [BOOP_SHIFTMULDIV_THM],
                             ASM_REWRITE_TAC [])))])
);

val _ = save_thm ("BOOP_UNREPINT_THM",  BOOP_UNREPINT_THM);
val _ = save_thm ("BOOP_UNREPREAL_THM",  BOOP_UNREPREAL_THM);
val _ = save_thm ("BOOP_UNREPNUM_THM",  BOOP_UNREPNUM_THM);
val _ = save_thm ("BOOP_SHIFTLEFT_THM",  BOOP_SHIFTLEFT_THM);
val _ = save_thm ("BOOP_SHIFTRIGHT_THM",  BOOP_SHIFTRIGHT_THM);

val _ = export_theory ();