Index: doc/user/Makefile
===================================================================
--- doc/user/Makefile	(revision 53ba273db2dfa4a4d251429b05f17a6400ed7f1e)
+++ doc/user/Makefile	(revision e55ca0532660df6b168cbfe023499f87bda57a53)
@@ -1,7 +1,7 @@
 ## Define the appropriate configuration variables.
 
-TeXLIB = .::
+TeXLIB = .:../bibliography/:../LaTeXmacros/:
 LaTeX  = TEXINPUTS=${TeXLIB} && export TEXINPUTS && latex
-BibTeX = BSTINPUTS=${TeXLIB} && export BSTINPUTS && bibtex
+BibTeX = BIBINPUTS=${TeXLIB} && export BIBINPUTS && bibtex
 
 ## Define the text source files.
@@ -43,5 +43,6 @@
 	dvips $< -o $@
 
-${basename ${DOCUMENT}}.dvi : Makefile ${GRAPHS} ${PROGRAMS} ${PICTURES} ${FIGURES} ${SOURCES} ${basename ${DOCUMENT}}.tex ${basename ${DOCUMENT}}.bib /usr/local/bibliographies/pl.bib
+${basename ${DOCUMENT}}.dvi : Makefile ${GRAPHS} ${PROGRAMS} ${PICTURES} ${FIGURES} ${SOURCES} ${basename ${DOCUMENT}}.tex \
+		../LaTeXmacros/common.tex ../LaTeXmacros/indexstyle ../bibliography/cfa.bib
 	# Conditionally create an empty *.ind (index) file for inclusion until makeindex is run.
 	if [ ! -r ${basename $@}.ind ] ; then touch ${basename $@}.ind ; fi
@@ -53,5 +54,5 @@
 	-${BibTeX} ${basename $@}
 	# Make index from *.aux entries and input index at end of document
-	makeindex -s indexstyle ${basename $@}.idx
+	makeindex -s ../LaTeXmacros/indexstyle ${basename $@}.idx
 	${LaTeX} ${basename $@}.tex
 	# Run again to get index title into table of contents
Index: doc/user/indexstyle
===================================================================
--- doc/user/indexstyle	(revision 53ba273db2dfa4a4d251429b05f17a6400ed7f1e)
+++ 	(revision )
@@ -1,2 +1,0 @@
-preamble ""
-postamble ""
Index: doc/user/user.tex
===================================================================
--- doc/user/user.tex	(revision 53ba273db2dfa4a4d251429b05f17a6400ed7f1e)
+++ doc/user/user.tex	(revision e55ca0532660df6b168cbfe023499f87bda57a53)
@@ -11,6 +11,6 @@
 %% Created On       : Wed Apr  6 14:53:29 2016
 %% Last Modified By : Peter A. Buhr
-%% Last Modified On : Wed Apr  6 17:37:39 2016
-%% Update Count     : 34
+%% Last Modified On : Fri Apr  8 11:40:53 2016
+%% Update Count     : 42
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
@@ -43,8 +43,4 @@
 % Names used in the document.
 
-\newcommand{\CFA}{C$\mathbf\forall$\xspace}	% set language symbolic name
-\newcommand{\CFL}{Cforall\xspace}		% set language text name
-\newcommand{\CC}{C\kern-.1em\hbox{+\kern-.25em+}\xspace} % CC symbolic name
-\def\c11{ISO/IEC C} % C11 name (cannot have numbers in latex command name)
 \newcommand{\CS}{C\raisebox{-0.9ex}{\large$^\sharp$}\xspace}
 
@@ -52,170 +48,5 @@
 
 % Bespoke macros used in the document.
-
-\makeatletter
-% allow escape sequence in lstinline
-%\usepackage{etoolbox}
-%\patchcmd{\lsthk@TextStyle}{\let\lst@DefEsc\@empty}{}{}{\errmessage{failed to patch}}
-
-\renewcommand\small{%
-   \@setfontsize\small{8.5}{11}%
-   \abovedisplayskip 8.5pt \@plus 3pt \@minus 4pt
-   \abovedisplayshortskip \z@ \@plus 2pt
-   \belowdisplayshortskip 4pt \@plus 2pt \@minus 2pt
-   \def\@listi{\leftmargin\leftmargini
-               \topsep 4pt \@plus 2pt \@minus 2pt
-               \parsep 2pt \@pluspt \@minuspt
-               \itemsep \parsep}%
-   \belowdisplayskip \abovedisplayskip
-}
-\usepackage{relsize}            % must be after change to small
-
-\renewcommand{\labelitemi}{{\raisebox{0.25ex}{\footnotesize$\bullet$}}}
-\renewenvironment{itemize}{\begin{list}{\labelitemi}{\topsep=5pt\itemsep=5pt\parsep=0pt}}{\end{list}}
-
-%  Reduce size of section titles
-\renewcommand\section{\@startsection{section}{1}{\z@}{-3.0ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\large\bfseries}}
-\renewcommand\subsection{\@startsection{subsection}{2}{\z@}{-2.5ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\normalsize\bfseries}}
-\renewcommand\subsubsection{\@startsection{subsubsection}{3}{\z@}{-2.5ex \@plus -1ex \@minus -.2ex}{1.0ex \@plus .2ex}{\normalfont\normalsize\bfseries}}
-\renewcommand\paragraph{\@startsection{paragraph}{4}{\z@}{-2.0ex \@plus -1ex \@minus -.2ex}{-1em}{\normalfont\normalsize\bfseries}}
-
-% index macros
-\newcommand{\italic}[1]{\emph{\hyperpage{#1}}}
-\newcommand{\definition}[1]{\textbf{\hyperpage{#1}}}
-\newcommand{\see}[1]{\emph{see} #1}
-
-% Define some commands that produce formatted index entries suitable for cross-references.
-% ``\spec'' produces entries for specifications of entities.  ``\impl'' produces entries for their
-% implementations, and ``\use'' for their uses.
-
-%  \newcommand{\bold}[1]{{\bf #1}}
-%  \def\spec{\@bsphack\begingroup
-%             \def\protect##1{\string##1\space}\@sanitize
-%             \@wrxref{|bold}}
-\def\impl{\@bsphack\begingroup
-          \def\protect##1{\string##1\space}\@sanitize
-          \@wrxref{|definition}}
-\newcommand{\indexcode}[1]{{\lstinline$#1$}}
-\def\use{\@bsphack\begingroup
-         \def\protect##1{\string##1\space}\@sanitize
-         \@wrxref{|hyperpage}}
-\def\@wrxref#1#2{\let\thepage\relax
-    \xdef\@gtempa{\write\@indexfile{\string
-    \indexentry{#2@{\lstinline$#2$}#1}{\thepage}}}\endgroup\@gtempa
-    \if@nobreak \ifvmode\nobreak\fi\fi\@esphack}
-%\newcommand{\use}[1]{\index{#1@{\lstinline$#1$}}}
-%\newcommand{\impl}[1]{\index{\protect#1@{\lstinline$\protect#1$}|definition}}
-
-% inline text and lowercase index: \Index{inline and lowercase index text}
-% inline text and as-in index: \Index[as-is index text]{inline text}
-% inline text but index with different as-is text: \Index[index text]{inline text}
-\newcommand{\Index}{\@ifstar\@sIndex\@Index}
-\newcommand{\@Index}[2][\@empty]{\lowercase{\def\temp{#2}}#2\ifx#1\@empty\index{\temp}\else\index{#1@{\protect#2}}\fi}
-\newcommand{\@sIndex}[2][\@empty]{#2\ifx#1\@empty\index{#2}\else\index{#1@{\protect#2}}\fi}
-
-\newcommand{\newtermFontInline}{\emph}
-\newcommand{\newterm}{\@ifstar\@snewterm\@newterm}
-\newcommand{\@newterm}[2][\@empty]{\lowercase{\def\temp{#2}}{\newtermFontInline{#2}}\ifx#1\@empty\index{\temp}\else\index{#1@{\protect#2}}\fi}
-\newcommand{\@snewterm}[2][\@empty]{{\newtermFontInline{#2}}\ifx#1\@empty\index{#2}\else\index{#1@{\protect#2}}\fi}
-\makeatother
-
-% blocks and titles
-\newenvironment{quote2}{%
-	\list{}{\lstset{resetmargins=true}\leftmargin=\parindent\rightmargin\leftmargin}%
-	\item\relax
-}{%
-	\endlist
-}% quote2
-\newenvironment{rationale}{%
-  \begin{quotation}\noindent$\Box$\enspace
-}{%
-  \hfill\enspace$\Box$\end{quotation}
-}%
-\newcommand{\define}[1]{\emph{#1\/}\index{#1}}
-\newcommand{\rewrite}{\(\Rightarrow\)}
-\newcommand{\rewriterules}{\paragraph{Rewrite Rules}~\par\noindent}
-\newcommand{\examples}{\paragraph{Examples}~\par\noindent}
-\newcommand{\semantics}{\paragraph{Semantics}~\par\noindent}
-\newcommand{\constraints}{\paragraph{Constraints}~\par\noindent}
-\newcommand{\predefined}{\paragraph{Predefined Identifiers}~\par\noindent}
-
-% BNF macros
-\def\syntax{\paragraph{Syntax}\trivlist\parindent=.5in\item[\hskip.5in]}
-\let\endsyntax=\endtrivlist
-\newcommand{\lhs}[1]{\par{\emph{#1:}}\index{#1@{\emph{#1}}|italic}}
-\newcommand{\rhs}{\hfil\break\hbox{\hskip1in}}
-\newcommand{\oldlhs}[1]{\emph{#1: \ldots}\index{#1@{\emph{#1}}|italic}}
-\newcommand{\nonterm}[1]{\emph{#1\/}\index{#1@{\emph{#1}}|italic}}
-\newcommand{\opt}{$_{opt}$\ }
-
-% adjust varioref package with default "section" and "page" titles, and optional title with faraway page numbers
-% \VRef{label} => Section 2.7, \VPageref{label} => page 17
-% \VRef[Figure]{label} => Figure 3.4, \VPageref{label} => page 17
-\renewcommand{\reftextfaceafter}{\unskip}
-\renewcommand{\reftextfacebefore}{\unskip}
-\renewcommand{\reftextafter}{\unskip}
-\renewcommand{\reftextbefore}{\unskip}
-\renewcommand{\reftextfaraway}[1]{\unskip, p.~\pageref{#1}}
-\renewcommand{\reftextpagerange}[2]{\unskip, pp.~\pageref{#1}--\pageref{#2}}
-\newcommand{\VRef}[2][Section]{\ifx#1\@empty\else{#1}\nobreakspace\fi\vref{#2}}
-\newcommand{\VPageref}[2][page]{\ifx#1\@empty\else{#1}\nobreakspace\fi\pageref{#2}}
-
-% Go programming language
-\lstdefinelanguage{Golang}%
-  {morekeywords=[1]{package,import,func,type,struct,return,defer,panic, recover,select,var,const,iota,},%
-   morekeywords=[2]{string,uint,uint8,uint16,uint32,uint64,int,int8,int16, int32,int64,
-		bool,float32,float64,complex64,complex128,byte,rune,uintptr, error,interface},%
-   morekeywords=[3]{map,slice,make,new,nil,len,cap,copy,close,true,false, delete,append,real,imag,complex,chan,},%
-   morekeywords=[4]{for,break,continue,range,goto,switch,case,fallthrough,if, else,default,},%
-   morekeywords=[5]{Println,Printf,Error,},%
-   sensitive=true,%
-   morecomment=[l]{//},%
-   morecomment=[s]{/*}{*/},%
-   morestring=[b]',%
-   morestring=[b]",%
-   morestring=[s]{`}{`},%
-}
-
-% CFA based on ANSI C
-\lstdefinelanguage{CFA}[ANSI]{C}%
-{morekeywords={_Alignas,_Alignof,__alignof,__alignof__,asm,__asm,__asm__,_At,_Atomic,__attribute,__attribute__,auto,
-    _Bool,catch,catchResume,choose,_Complex,__complex,__complex__,__const,__const__,disable,dtype,enable,__extension__,
-	fallthru,finally,forall,ftype,_Generic,_Imaginary,inline,__label__,lvalue,_Noreturn,otype,restrict,_Static_assert,
-	_Thread_local,throw,throwResume,trait,try,typeof,__typeof,__typeof__,},
-  moredelim=**[is][\color{red}]{`}{`},
-}%
-
-\lstset{
-language=CFA,
-columns=flexible,
-basicstyle=\sf\relsize{-1},
-tabsize=4,
-xleftmargin=\parindent,
-escapechar=@,
-mathescape=true,
-keepspaces=true,
-showstringspaces=false,
-showlines=true,
-aboveskip=6pt,
-belowskip=4pt,
-literate={\\`}{\raisebox{0.3ex}{\ttfamily\upshape \hspace*{-2pt}`}}1, % escape \`, otherwise used to highlight in red
-%extendedchars=true,
-}%
-
-\makeatletter
-% replace/adjust listings characters that look bad in sanserif
-\lst@CCPutMacro
-\lst@ProcessOther{"22}{\lst@ttfamily{"}{\raisebox{0.3ex}{\ttfamily\upshape "}}} % replace double quote
-\lst@ProcessOther{"27}{\lst@ttfamily{'}{\raisebox{0.3ex}{\ttfamily\upshape '\hspace*{-2pt}}}} % replace single quote
-\lst@ProcessOther{"2D}{\lst@ttfamily{-}{\ttfamily\upshape -}} % replace minus
-\lst@ProcessOther{"3C}{\lst@ttfamily{<}{\texttt{<}}} % replace less than
-\lst@ProcessOther{"3E}{\lst@ttfamily{<}{\texttt{>}}} % replace greater than
-\lst@ProcessOther{"5E}{\raisebox{0.4ex}{$\scriptstyle\land\,$}} % replace circumflex
-\lst@ProcessOther{"5F}{\lst@ttfamily{\char95}{{\makebox[1.2ex][c]{\rule{1ex}{0.1ex}}}}} % replace underscore
-\lst@ProcessOther{"60}{\lst@ttfamily{`}{\raisebox{0.3ex}{\ttfamily\upshape \hspace*{-2pt}`}}} % replace backquote
-\lst@ProcessOther{"7E}{\raisebox{0.3ex}{$\scriptstyle\sim\,$}} % replace tilde
-%\lst@ProcessOther{"7E}{\raisebox{-.4ex}[1ex][0pt]{\textasciitilde}} % lower tilde
-\@empty\z@\@empty
-\makeatother
+\input{common}
 
 \setcounter{secnumdepth}{3}     % number subsubsections
@@ -4573,6 +4404,58 @@
 
 
+\section{Rational Numbers}
+\label{s:RationalNumbers}
+
+Rational numbers are numbers written as a ratio, i.e., as a fraction, where the numerator (top number) and the denominator (bottom number) are whole numbers.
+When creating and computing with rational numbers, results are constantly reduced to keep the numerator and denominator as small as possible.
+
+\begin{lstlisting}
+// implementation
+struct Rational {
+	long int numerator, denominator;					// invariant: denominator > 0
+}; // Rational
+
+// constants
+extern struct Rational 0;
+extern struct Rational 1;
+
+// constructors
+Rational rational();
+Rational rational( long int n );
+Rational rational( long int n, long int d );
+
+// getter/setter for numerator/denominator
+long int numerator( Rational r );
+long int numerator( Rational r, long int n );
+long int denominator( Rational r );
+long int denominator( Rational r, long int d );
+
+// comparison
+int ?==?( Rational l, Rational r );
+int ?!=?( Rational l, Rational r );
+int ?<?( Rational l, Rational r );
+int ?<=?( Rational l, Rational r );
+int ?>?( Rational l, Rational r );
+int ?>=?( Rational l, Rational r );
+
+// arithmetic
+Rational -?( Rational r );
+Rational ?+?( Rational l, Rational r );
+Rational ?-?( Rational l, Rational r );
+Rational ?*?( Rational l, Rational r );
+Rational ?/?( Rational l, Rational r );
+
+// conversion
+double widen( Rational r );
+Rational narrow( double f, long int md );
+
+// I/O
+forall( dtype istype | istream( istype ) ) istype * ?|?( istype *, Rational * );
+forall( dtype ostype | ostream( ostype ) ) ostype * ?|?( ostype *, Rational );
+\end{lstlisting}
+
+
 \bibliographystyle{plain}
-\bibliography{/usr/local/bibliographies/pl.bib}
+\bibliography{cfa}