\HeaderA{Logic}{Logical Operators}{Logic}
\aliasA{"!}{Logic}{"!}
\aliasA{\&}{Logic}{.Ramp.}
\aliasA{\&\&}{Logic}{.Ramp..Ramp.}
\aliasA{isTRUE}{Logic}{isTRUE}
\aliasA{xor}{Logic}{xor}
\aliasA{"|}{Logic}{"|}
\aliasA{"|"|}{Logic}{"|"|}
\keyword{logic}{Logic}
\begin{Description}\relax
These operators act on logical vectors.
\end{Description}
\begin{Usage}
\begin{verbatim}
! x
x & y
x && y
x | y
x || y
xor(x, y)

isTRUE(x)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{x, y}] logical vectors, or objects which can be coerced to such
or for which methods have been written.
\end{ldescription}
\end{Arguments}
\begin{Details}\relax
\code{!} indicates logical negation (NOT).

\code{\&} and \code{\&\&} indicate logical AND and \code{|} and \code{||}
indicate logical OR.  The shorter form performs elementwise
comparisons in much the same way as arithmetic operators.  The longer
form evaluates left to right examining only the first element of each
vector.  Evaluation proceeds only until the result is determined.  The
longer form is appropriate for programming control-flow and typically
preferred in \code{\LinkA{if}{if}} clauses.

\code{xor} indicates elementwise exclusive OR.

\code{isTRUE(x)} is an abbreviation of \code{identical(TRUE, x)}, and
so is true if and only if \code{x} is a length-one logical vector with
no attributes (not even names).

Numeric and complex vectors will be coerced to logical values, with
zero being false and all non-zero values being true.  Raw vectors are
handled without any coercion for \code{!}, \code{\&} and \code{|}, with
these operators being applied bitwise (so \code{!} is the 1-complement).

The operators \code{!}, \code{\&} and \code{|} are generic functions:
methods can be written for them individually or via the
\code{\LinkA{Ops}{Ops}}) group generic function.

\code{\LinkA{NA}{NA}} is a valid logical object.  Where a component of
\code{x} or \code{y} is \code{NA}, the result will be \code{NA} if the
outcome is ambiguous.  In other words \code{NA \& TRUE} evaluates to
\code{NA}, but \code{NA \& FALSE} evaluates to \code{FALSE}.  See the
examples below.

See \LinkA{Syntax}{Syntax} for the precedence of these operators: unlike many
other languages (including S) the AND and OR operators do not have the
same precedence (the AND operators are higher than the OR operators).
\end{Details}
\begin{Value}
For \code{!}, a logical or raw vector of the same length as \code{x}.

For \code{|}, \code{\&} and \code{xor} a logical or raw vector. The
elements of shorter vectors are recycled as necessary (with a
\code{\LinkA{warning}{warning}} when they are recycled only \emph{fractionally}).
The rules for determining the attributes of the result are rather
complicated.  Most attributes are taken from the longer argument, the
first if they are of the same length.  Names will be copied from the
first if it is the same length as the answer, otherwise from the
second if that is.  For time series, these operations are allowed only
if the series are compatible, when the class and \code{\LinkA{tsp}{tsp}}
attribute of whichever is a time series (the same, if both are) are
used.  For arrays (and an array result) the dimensions and dimnames
are taken from first argument if it is an array, otherwise the second.

For \code{||}, \code{\&\&} and \code{isTRUE}, a length-one logical vector.
\end{Value}
\begin{References}\relax
Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988)
\emph{The New S Language}.
Wadsworth \& Brooks/Cole.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{TRUE}{TRUE}} or \code{\LinkA{logical}{logical}}.

\code{\LinkA{any}{any}} and \code{\LinkA{all}{all}} for OR and AND on many scalar
arguments.

\code{\LinkA{Syntax}{Syntax}} for operator precedence.
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
y <- 1 + (x <- rpois(50, lambda=1.5) / 4 - 1)
x[(x > 0) & (x < 1)]    # all x values between 0 and 1
if (any(x == 0) || any(y == 0)) "zero encountered"

## construct truth tables :

x <- c(NA, FALSE, TRUE)
names(x) <- as.character(x)
outer(x, x, "&")## AND table
outer(x, x, "|")## OR  table
\end{ExampleCode}
\end{Examples}

