and,or,not,xor

Usage

$\sim$ a
a $\wedge$ b
a $\vee$ b
xor(a, b)

Signatures

$\sim$:	% $\to$ %
$\wedge,\vee$,xor:	(%,%) $\to$ %

Parameter	Type	Description
a, b	%	elements of the type

Returns

$\sim a$ returns $not(a)$, while $a \vee b$ returns $(a~or~b)$, $a \wedge b$ returns $(a~and~b)$, and $\mbox{xor}(a, b)$ returns

$$(a \wedge \sim b) \vee (~\sim a \wedge b)\,.$$

The semantics of $not$, $or$ and $and$ can be logical or bitwise, depending on the actual type.

Remarks

For the type Boolean, the difference between $a \vee b$ and a or b is that $a \vee b$ guarantees that both expressions $a$ and $b$ are evaluated while a or b may evaluate only $a$ and return true if $a$ evaluates to true. There is a similar difference between $a \wedge b$ and a and b.

Example

If a and b are the MachineInteger 5 and 7, then  $\sim a = -6$, $a \wedge b = 5$, $a \vee b = 7$ and $\mbox{xor}(a,b) = 2$.