\doc{The normalize command}
\ref{normalize-command}

The \def{normalize command} provides manual control over the application of
(possibly passive) rewrite rules to (possibly immune) formulas, rewrite rules,
and deduction rules.  It also provides a means of backward inference.

\head{2}{\dlink{../symbols/syntax}{Syntax}}
\begin{verbatim}
\sd{normalize-command} ::= \f{normalize} \s{target} [ \f{with} [ \f{reversed} ] \slink{../misc/names}{names} ]
\sd{target}            ::= \slink{../misc/names}{names} | \f{conjecture}
\end{verbatim}

\head{2}{Examples}
\begin{verbatim}
normalize immune / lemmas with *
normalize conjecture with distributiveLaws
\end{verbatim}

\head{2}{Usage} 

The first version of the \fq{normalize} command
\olink{normalization}{normalizes} the formulas, deduction rules, and rewrite
rules in the \s{target}, whether or not they are immune, using the hardwired
rewrite rules together with the rewrite rules obtained as described below.
Rewrite rules in the \s{target} that are also named by \s{names} are not
normalized.
\p
If \fq{reversed} is present, all named formulas and rewrite rules, whether or
not they are active, that can be oriented from right to left into legal rewrite
rules are used with that orientation.  If \fq{reversed} is not present, all
named rewrite rules and formulas, whether or not they are active, that can be
oriented from left to right are used with that orientation.  If no \s{names}
are given, all rewrite rules and left-to-right orientable formulas are used.
\p
The second version of the \fq{normalize} command normalizes the current
conjecture using the rewrite rules obtained as just described.
\p
The \fq{normalize} command is typically used to ``open up'' definitions using a
set of passive rewrite rules.  When \fq{reversed} is present, the named rewrite
rules should ordinarily be passive to prevent them from immediately undoing the
result of the \fq{normalize} command.  See also the \cflink{rewrite} command.