/*
 * Reduce Boolean.rules
 *
 * Created on 06 April 2006, 00:00
 */

/**
 * bit-wise boolean expressions
 */
~~$a => $a;
$a & $a => $a :: sideEffectFree($a);
$a | $a => $a :: sideEffectFree($a);

$a ^ $a => 0 :: sideEffectFree($a);

$a & ~$a => 0 :: sideEffectFree($a);
~$a & $a => 0 :: sideEffectFree($a);

$a | ~$a => -1 :: sideEffectFree($a);
~$a | $a => -1 :: sideEffectFree($a);

$a ^ ~$a => -1 :: sideEffectFree($a);
~$a ^ $a => -1 :: sideEffectFree($a);

~$a & ~$b => ~($a | $b);
~$a | ~$b => ~($a & $b);
~$a ^ ~$b => $a ^ $b;

($a & $b) | ($a & $c) => $a & ($b | $c) :: sideEffectFree($a);
($b & $a) | ($c & $a) => ($b | $c) & $a :: sideEffectFree($a) && sideEffectFree($c);
($a | $b) & ($a | $c) => $a | ($b & $c) :: sideEffectFree($a);

/**
 * arithmetic boolean expressions
 */
!($a < $b) => $a >= $b;
!($a > $b) => $a <= $b;
!($a <= $b) => $a > $b;
!($a >= $b) => $a < $b;

/**
 * logical boolean expressions
 */
!!$a => $a;
$a == $a => true :: sideEffectFree($a);
$a != $a => false :: sideEffectFree($a);
$a == !$a => false :: sideEffectFree($a);
!$a == $a => false :: sideEffectFree($a);
$a != !$a => true :: sideEffectFree($a);
!$a != $a => true :: sideEffectFree($a);

true && $a => $a;
$a && true => $a;
true || $a => true;
$a || true => true :: sideEffectFree($a);
$a == true => $a;
true == $a => $a;
$a != true => !$a;
true != $a => !$a;

false && $a => false;
$a && false => false :: sideEffectFree($a);
false || $a => $a;
$a || false => $a;
$a == false => !$a;
false == $a => !$a;
$a != false => $a;
false != $a => $a;

!($a == $b) => $a != $b;
!($a != $b) => $a == $b;
!$a && !$b => !($a || $b);
!$a || !$b => !($a && $b);
($a && $b) || ($a && $c) => $a && ($b || $c) :: sideEffectFree($a);
($a || $b) && ($a || $c) => $a || ($b && $c) :: sideEffectFree($a);

/**
 * object comparison identities
 */

this == null => false;
null == this => false;
this != null => true;
null != this => true;

/**
 * conditional statements
 */
true ? $a : $b => $a;
false ? $a : $b => $b;
$a ? true : false => $a;
$a ? false : true => !$a;
!$a ? $b : $c => $a ? $c : $b;
$a ? $b : $b => $b :: sideEffectFree($a);
$a ? $a : $b => $a || $b :: sideEffectFree($a);
$a ? $b : $a => $a && $b :: sideEffectFree($a);