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% Interim specs of METAFONT start on the next page

\font\ninerm=amr9
\let\mc=\ninerm % medium caps for names like PASCAL
\font\logo=manfnt % font used for the METAFONT logo
\def\MF{{\logo META}\-{\logo FONT}}
\font\tenss=amss10 % for `The METAFONTbook'
\def\today{\ifcase\month\or
  January\or February\or March\or April\or May\or June\or
  July\or August\or September\or October\or November\or December\fi
  \space\number\day, \number\year}

\def\newsection #1. #2\par
  {\medbreak\noindent{\bf #1.\enspace #2\par}
  \nobreak\smallskip\noindent}
\def\oct#1{\hbox{\rm\'{}\kern-.2em\it#1\/\kern.05em}} % octal constant
\def\<#1>{{$\,\langle$\rm#1$\rangle\,$}}
\def\is{$\;\longrightarrow\;$}
\def\alt{$\;\mid\;$}
\def\andalso{\hskip5em \alt\futurelet\next\andalsocontinued}
\def\andalsocontinued{\ifx\next\.$\;$\fi}
\def\syntaxlines#1{$$\openup1\jot
  \halign{\hbox to\displaywidth{\indent##\hfil}\cr#1}$$}
\def\.#1{\hbox{\tt#1}}
\def\syntaxbreak{\noalign{\smallbreak}}
\def\Bigbreak{\par\ifdim\lastskip<16pt
  \removelastskip\penalty-200\vskip 16pt plus 5pt minus 4pt\fi}
\sfcode`\:=\sfcode`\;

\line{{\bf Low-level \MF}\hfil as of \today}
\rightline{Beware: These specifications change daily!}
\bigskip\bigskip\noindent
This is a preliminary description of what the new \MF\ language will look
like at the lowest level. Please forgive the author for the terseness of
this document; there
hasn't been time to explain things yet. Also please remember that the
low-level language is not what \MF\ programmers will usually be writing;
it is intended as a vehicle for defining nicer high-level languages.
\MF\ users will almost always work with a set of macros and other definitions
called a ``base'' file; the {\tt PLAIN} base will be defined in
{\tenss The \MF book}, in a fashion similar to the way {\tt PLAIN} format
has been defined in {\sl The \TeX book}.

\newsection 1. The lowest level: Tokens.

\MF\ is governed by sequences of {\it tokens}, which it gets either by
reading a file or by regurgitating a list of tokens that were previously
read. So we can understand tokens by understanding what happens when
\MF\ reads from a file. A file is a sequence of lines of text, where
each line of text is a sequence of zero or more characters. The characters
are assumed to be those of standard ASCII (codes \oct{040} through
\oct{176} in Appendix~C of {\sl The \TeX book}). Any other characters that
might appear in the file are flagged as errors,
except that certain systems may make allowances for certain characters.
[For example, the {\mc WAITS} implementation places codes \oct{030},
\oct{032}, \oct{034}, and \oct{035} into the same class as equal signs,
because the special keys for those two-character combinations on {\mc
WAITS} keyboards are too tempting to ignore.]

Each line of text is converted into zero or more tokens according to the
following rules, repeated until no more characters remain on the line:

\smallskip
\item{1)} If the next character is a space, or if it's a period that isn't
followed by a decimal digit or a period, ignore~it and move on.

\item{2)} If the next character is a percent sign, ignore it and also
ignore everything else that remains on the current line. (Percent signs
allow you to put comments in your file that are unseen by \MF.)

\item{3)} If the next character is a decimal digit or a period that's
followed by a decimal digit, the next token is called a {\it numeric
token}. It is the longest sequence of contiguous characters starting
at the current place that satisfies the following syntax:
\syntaxlines{\<numeric token>\is\<digit string>\alt.\<digit string>
  \alt\<digit string>.\<digit string>\cr
\<decimal digit>\is\.0\alt\.1\alt\.2\alt\.3\alt\.4\alt\.5\alt\.6\alt
  \.7\alt\.8\alt\.9\cr
\<digit string>\is\<decimal digit>\alt\<digit string>\<decimal digit>\cr}
Numeric tokens are interpreted according to ordinary decimal notation;
the value of the number must be less than 4096. \MF\ converts decimal
fractions to the nearest multiple of $2^{-16}$.

\item{4)} If the next character is a double-quote mark
(\thinspace{\tt\char`"}\thinspace), the next token is called a {\it string
token}. It consists of all characters following the double-quote up to
but not including the next double-quote on the current line. There must be
at least one more double-quote remaining on the line, otherwise you
get an error message.

\item{5)} If the next character is a left parenthesis, a right parenthesis,
a comma, or a semicolon, the next token is that single character.

\item{6)} Otherwise the next token consists of the next character together
with all immediately following characters of the same class.

\smallskip\noindent
Rules 1--5 tell what to do for 17 of the 95 possible ASCII characters
that might be next. The most interesting rule is number~6, which depends
on a breakdown of the remaining 78 ASCII characters into 12 {\it
classes\/} as shown in Table~1.  Two characters are in the same class if
and only if they belong to the same row in the class~table.

\topinsert
$$\vbox{\halign{\hfil\tt#\hfil&\qquad#\hfil\cr
\hidewidth
ABCDEFGHIJKLMNOPQRSTUVWXYZ\char`\_abcdefghijklmnopqrstuvwxyz\hidewidth\cr
<=>:|\cr
`'\cr
+-\cr
/*\char`\\\cr
!?\cr
\#\&@\$\cr
\char`\^\char`\~\cr
[\cr
]\cr
\char`\{\char`\}\cr
.&(see rules 1, 3, 6)\cr
,&(see rule 5)\cr
;&(see rule 5)\cr
(&(see rule 5)\cr
)&(see rule 5)\cr
"&(see rule 4)\cr
0123456789&(see rule 3)\cr
\%&(see rule 2)\cr}}$$
{\bf Table 1.}\enspace The visible ASCII characters, divided into classes.
Characters in the bottom eight rows are subject to special rules as
indicated.
\endinsert

For example, the (ridiculous) line
$$\hbox{\tt xx3.1.6..[[a+-bc\char`\_d.e] ]"a string \%"
  <>\char`\$1."+-""" \% forget this}$$
produces 17 tokens: `\.{xx}', `\.{3.1}' (which is numeric), `\.{.6}' (another
numeric), `\.{..}', `\.{[[}', `\.a', `\.{+-}', `\.{bc\char`\_d}', `\.e',
`\.]', `\.]', `\.{a string \%}' (which is indeed a string),
`\.{<>}', `\.\$', `\.{1}' (another numeric token), `\.{+-}' (a string, hence
different from the other~`\.{+-}'), and `' (an empty string).
Notice that three of the spaces and two of the periods were deleted
by rule~1.

\newsection 2. The next lowest level: Variables.

But what do tokens mean? Well, numeric tokens stand for numbers and string
tokens stand for strings, but the other tokens are just arbitrary symbols
that can stand for almost anything. Let's say that tokens of the third kind
are {\it symbolic tokens}.

Some of the symbolic tokens have predefined ``primitive'' meanings when
\MF\ begins its operations, but it is possible to change the meaning of
any symbolic token. The `\.{let}' command does this; one simply
says `\.{let}' \<symbolic token>=\<symbolic token>'.
For example, you can even make a left parenthesis
denote the same thing as `\.+', if you want to confuse everybody
who tries to read your code.

Symbolic tokens are further subdivided into two categories based on their
current meaning. If the token currently stands for one of \MF's
primitives, or for a macro that was not defined with \.{vardef}, we shall
call it a {\it spark\/}; otherwise we call it a {\it tag}.  Thus, almost
every token you can think of is initially a tag, available for use as a
name, except those that were needed to define \MF's fundamental
operations. Such pre-reserved tokens can be redefined and used as names,
if you want to use them in your own way; but you probably won't have to,
since they're generally words that don't make desirable names.

Tags are used for the variables in \MF\ programs. These variables can
be structured, like arrays and records in more conventional programming
languages; for example, `\.{x32a}' might be a variable that would be written
`\.{x[32].a}' in {\mc PASCAL}. A variable identifier has the following
syntax:
\syntaxlines{\<variable>\is\<tag>\<suffix>\alt\<internal quantity>\cr
\<suffix>\is\<empty>\alt\<suffix>\<subscript>\alt\<suffix>\<tag>
 \alt\<suffix>\<internal quantity>\cr
\<subscript>\is\<numeric token>\alt\.[\<numeric expression>\.]\cr}
A \<suffix> is taken to be as long as possible; i.e., if a \<suffix> is
followed by a \<subscript> or a \<tag>, the \<suffix> will be extended.

Notice the two permissible forms of subscripts: a numeric token can be
written without brackets, or a bracketed expression can be used.
For example, if \.i is a variable whose value is~7, the variable identifiers
`\.{b7}', `\.{b007}', `\.{b[7]}', `\.{b[i]}', and `\.{b[21-2i]}' are
all equivalent. On the other hand, `\.{b.007}' would be different, since
it involves the fractional subscript `\.{.007}'. Also, `\.{b.i}' would
be different; in this case the `\.i' is simply a tag that appears as a suffix,
it's not a subscript.

Incidentally, the `\.[' and `\.]' that appear in the syntax for
\<subscript> stand for any tokens that have \MF's primitive meanings
for left bracket and right bracket, respectively. They aren't necessarily
brackets; indeed, if the tokens `\.[' and `\.]' have been redefined,
they no longer can be used to produce subscripts. Similar remarks
apply to all of the tokens in all of the rules below. \MF\ doesn't look
at the form of a token; only the current meaning is relevant.

Variables can be of many types:
\syntaxlines{\<type>\is\.{numeric}\alt\.{string}\alt\.{boolean}\alt
\.{path}\alt\.{pen}\alt\.{picture}\alt\.{transform}\alt\.{pair}\cr}
To specify a type other than \.{numeric}, you simply give a type
declaration that lists the relevant identifiers. For example, the declaration
$$\hbox{\tt pair right, left, a.zz}$$
says that `\.{right}', `\.{left}', and `\.{a.zz}' will be variables of type
\.{pair}, so that equations like
$$\hbox{\tt right = -left = 2a.zz = (1,0)}$$
can be given later. These equations, incidentally, define
$\.{right}=(1,0)$, $\.{left}=(-1,0)$, and $\.{a.zz}=(.5,0)$.

The declaration of an array variable is independent of all the subscript
values; all subscripts in the declaration are therefore given in a
special collective form. For example,
$$\hbox{\tt path p[], x[]arc, f[][]}$$
declares all variables of the form \.{p[i]} and \.{x[i]arc} and \.{f[i][j]}
to be of type \.{path}. This declaration doesn't affect the types of
variables like \.p or \.{p3arc}. \MF\ considers a declaration
like `\.{path}~\.{p3}' to be illegal, since it falsely implies that only
\.{p3} (not \.{p2}) is a path; subscripts in a type declaration must
be collective.

Here are the formal syntax rules:
\syntaxlines{\<declaration>\is\<type>\<declaration list>\cr
\<declaration list>\is\<declared variable>\alt
  \<declaration list>\.,\<declared variable>\cr
\<declared variable>\is\<symbolic token>\<declared suffix>\cr
\<declared suffix>\is\<empty>\alt\<declared suffix>\.{[]}\cr
\andalso\<declared suffix>\<tag>\alt\<declared suffix>\<internal quantity>\cr}
A variable that hasn't been declared is automatically of type \.{numeric},
but its value is undefined until it appears in an equation. Declarations
destroy all previous values; thus, a declaration like `\.{numeric}~\.x'
isn't redundant, since it removes any existing value that \.x may have
had, of whatever type.  Incidentally, this declaration doesn't affect
other values like \.{x2} or \.{x2arc} or \.{x.x} that might coexist with~\.x.

\newsection 3. The next lowest level: Expressions.

The declaration `\.{delimiters} \<symbolic token>\<symbolic token>'
declares a pair of tokens to be matching delimiters. For example, the
\.{PLAIN} base says `\.{delimiters}~\.{()}' so that parentheses do
the usual thing. Any distinct symbolic tokens can be defined to act
as delimiters, and many different pairs of delimiters can be
in use simultaneously.

There are eight kinds of expressions in \MF, corresponding to the
eight types numeric, string, etc. The full syntax is quite long,
but most of it falls into a simple pattern: There are four levels
of precedence called the primary level (tightest binding), the
secondary level (next tightest), the tertiary level (next loosest),
and the expression level (loosest); they're something like freshmen,
sophomores, juniors, and seniors. If $\alpha$, $\beta$, and
$\gamma$ are types, most of the syntax rules are of the following
general form:
\syntaxlines{\<$\alpha$ primary>\is\<$\alpha$ variable>\alt
 \<$\alpha$ constant>\cr
\andalso\<left delimiter>\<$\alpha$ expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<$\alpha$ expression> \.{endgroup}\cr
\andalso\<operator that takes type $\beta$ to type $\alpha$>
 \<$\beta$ primary>\cr
\syntaxbreak
\<$\alpha$ secondary>\is\<$\alpha$ primary>\cr
\andalso\<$\beta$ secondary>\<multiplicative operator taking types $\beta$ and
 $\gamma$ to type $\alpha$>\<$\gamma$ primary>\cr
\syntaxbreak
\<$\alpha$ tertiary>\is\<$\alpha$ secondary>\cr
\andalso\<$\beta$ tertiary>\<additive operator taking types $\beta$ and
 $\gamma$ to type $\alpha$>\<$\gamma$ secondary>\cr
\syntaxbreak
\<$\alpha$ expression>\is\<$\alpha$ tertiary>\cr
\andalso\<$\beta$ expression>\<external operator taking types $\beta$ and
 $\gamma$ to type $\alpha$>\<$\gamma$ tertiary>\cr}
These schematic rules don't give the whole story, but they give the
general structure of the plot.

The complete syntax appears below, as a set of rules that can be used as a
summary of all the primitive features that \MF\ provides within
expressions. (We shall see later that macros can be used to extend the
language; hence this list doesn't really exhaust the possibilities.)
\syntaxlines{\<expression>\is
\<boolean expression>\alt
 \<string expression>\alt
 \<path expression>\cr
\andalso \<pen expression>\alt
 \<picture expression>\alt
 \<transform expression>\cr
\andalso \<numeric expression>\alt
 \<pair expression>\cr
\<primary>\is
\<boolean primary>\alt
 \<string primary>\alt
 \<path primary>\cr
\andalso \<pen primary>\alt
 \<picture primary>\alt
 \<transform primary>\cr
\andalso \<numeric primary>\alt
 \<pair primary>\alt\<future pen primary>\cr
\<secondary>\is
\<boolean secondary>\alt
 \<string secondary>\alt
 \<path secondary>\cr
\andalso \<pen secondary>\alt
 \<picture secondary>\alt
 \<transform secondary>\cr
\andalso \<numeric secondary>\alt
 \<pair secondary>\alt\<future pen secondary>\cr
\<tertiary>\is
\<boolean tertiary>\alt
 \<string tertiary>\alt
 \<path tertiary>\cr
\andalso \<pen tertiary>\alt
 \<picture tertiary>\alt
 \<transform tertiary>\cr
\andalso \<numeric tertiary>\alt \<pair tertiary>\cr}

\Bigbreak
\noindent Boolean expressions:
\syntaxlines{\<boolean primary>\is
 \<boolean variable>\alt \.{true}\alt\.{false}\cr
\andalso\<left delimiter>\<boolean expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<boolean expression> \.{endgroup}\cr
\andalso \.{known}\<primary>\alt\.{cycle}\<primary>\alt
 \<type>\<primary>\cr
\andalso \.{odd}\<numeric primary>\cr
\andalso\.{charexists}\<numeric primary>\cr
\andalso \.{not}\<boolean primary>\cr
\syntaxbreak
\<boolean secondary>\is\<boolean primary>\cr
\andalso \<boolean secondary>\.{and}\<boolean primary>\cr
\syntaxbreak
\<boolean tertiary>\is\<boolean secondary>\cr
\andalso \<boolean tertiary>\.{or}\<boolean secondary>\cr
\syntaxbreak
\<boolean expression>\is\<boolean tertiary>\cr
\andalso\<numeric expression>\<relation>\<numeric tertiary>\cr
\andalso\<string expression>\<relation>\<string tertiary>\cr
\andalso\<pair expression>\<relation>\<pair tertiary>\cr
\andalso\<boolean expression>\<relation>\<boolean tertiary>\cr
\<relation>\is\.<\alt\.{<=}\alt\.>\alt\.{>=}\alt\.=\alt\.{<>}\cr}

\Bigbreak
\noindent String expressions:
\syntaxlines{\<string primary>\is
 \<string variable>\alt \<string token>\cr
\andalso\<left delimiter>\<string expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<string expression> \.{endgroup}\cr
\andalso \.{jobname}\alt\.{readstring}\alt\.{str}\<suffix>\cr
\andalso \.{char}\<numeric primary>\alt\.{decimal}\<numeric primary>\cr
\andalso \.{substring}\<pair expression>\.{of}\<string primary>\cr
\syntaxbreak
\<string secondary>\is\<string primary>\cr
\syntaxbreak
\<string tertiary>\is\<string secondary>\cr
\syntaxbreak
\<string expression>\is\<string tertiary>\cr
\andalso\<string expression>\.\&\<string tertiary>\cr}

\Bigbreak
\noindent Path expressions:
\syntaxlines{\<path primary>\is
 \<path variable>\cr
\andalso\<left delimiter>\<path expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<path expression> \.{endgroup}\cr
\andalso \.{reverse}\<path primary>\alt\.{makepath}\<pen primary>
 \alt\.{makepath}\<future pen primary>\cr
\andalso \.{subpath}\<pair expression>\.{of}\<path primary>\cr
\syntaxbreak
\<path secondary>\is\<path primary>\alt\<path secondary>\<transform>\cr
\syntaxbreak
\<path tertiary>\is\<path secondary>\cr
\syntaxbreak
\<path subexpression>\is\<path tertiary>\alt\<pair tertiary>\cr
\andalso\<path subexpression>\<path join>\<path tertiary>\cr
\syntaxbreak
\<path join>\is\<direction specifier>\<basic path join>\<direction specifier>\cr
\<direction specifier>\is\<empty>\alt
 \.{\char`\{curl}\<numeric expression>\.{\char`\}}\cr
\andalso\.{\char`\{}\<pair expression>\.{\char`\}}\alt
  \.{\char`\{}\<numeric expression>,\<numeric expression>\.{\char`\}}\cr
\syntaxbreak
\<basic path join>\is\.\&\alt\.{..}\alt\.{..}\<tension>\.{..}
  \alt\.{..}\<controls>\.{..}\cr
\<tension>\is\.{tension}\<tension amount>\alt
 \.{tension}\<tension amount>\.{and}\<tension amount>\cr
\<tension amount>\is\<numeric primary>\alt\.{atleast}\<numeric primary>\cr
\<controls>\is\.{controls}\<pair primary>\alt
 \.{controls}\<pair primary>\.{and}\<pair primary>\cr
\<path expression>\is\<path subexpression>\alt
\<path subexpression>\<direction specifier>\cr
\andalso \<path subexpression>\<path join>\.{cycle}\cr}

\Bigbreak
\noindent Picture expressions:
\syntaxlines{\<picture primary>\is
 \<picture variable>\alt\.{nullpicture}\cr
\andalso\<left delimiter>\<picture expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<picture expression> \.{endgroup}\cr
\andalso\<plus or minus>\<picture primary>\cr
\syntaxbreak
\<picture secondary>\is\<picture primary>\alt\<picture secondary>\<transform>\cr
\syntaxbreak
\<picture tertiary>\is\<picture secondary>\cr
\andalso \<picture tertiary>\<additive op>\<picture secondary>\cr
\<picture expression>\is\<picture tertiary>\cr}

\Bigbreak
\noindent Pen expressions:
\syntaxlines{\<pen primary>\is
 \<pen variable>\alt\.{nullpen}\cr
\andalso\<left delimiter>\<pen expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<pen expression> \.{endgroup}\cr
\<future pen primary>\is
\.{pencircle}\alt
\.{makepen}\<path primary>\cr
\syntaxbreak
\<pen secondary>\is\<pen primary>\cr
\<future pen secondary>\is\<future pen primary>\alt
  \<future pen secondary>\<transform>\cr
\andalso\<pen secondary>\<transform>\cr
\syntaxbreak
\<pen tertiary>\is\<pen secondary>\alt\<future pen secondary>\cr
\syntaxbreak
\<pen expression>\is\<pen tertiary>\cr}

\Bigbreak
\noindent Transform expressions:
\syntaxlines{\<transform primary>\is
 \<transform variable>\cr
\andalso\<left delimiter>\<transform expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<transform expression> \.{endgroup}\cr
\syntaxbreak
\<transform secondary>\is\<transform primary>\alt
  \<transform secondary>\<transform>\cr
\<transform>\is\.{rotated}\<numeric primary>\alt
\.{slanted}\<numeric primary>\alt\.{scaled}\<numeric primary>\cr
\andalso\.{shifted}\<pair primary>\alt
\.{transformed}\<transform primary>\cr
\andalso\.{xscaled}\<numeric primary>\alt
\.{yscaled}\<numeric primary>\alt
\.{zscaled}\<pair primary>\cr
\syntaxbreak
\<transform tertiary>\is\<transform secondary>\cr
\syntaxbreak
\<transform expression>\is\<transform tertiary>\cr}

\Bigbreak
\noindent Numeric expressions:
\syntaxlines{\<numeric primary>\is
 \<numeric variable>\alt\<numeric token primary>\alt\.{normaldeviate}\cr
\andalso\<expression parameter>\alt\<internal quantity>\cr
\andalso\<left delimiter>\<numeric expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<numeric expression> \.{endgroup}\cr
\andalso\.{oct}\<string primary>\alt\.{hex}\<string primary>
\alt\.{ASCII}\<string primary>\cr
\andalso\.{length}\<string primary>\alt\.{length}\<path primary>\cr
\andalso\.{length}\<pair primary>\alt\.{length}\<numeric primary>\cr
\andalso\<pair part specifier>\<pair primary>
\alt\<transform part specifier>\<transform primary>\cr
\andalso\<unary operator>\<numeric primary>
\alt\.{angle}\<pair primary>\cr
\andalso\.{totalweight}\<picture primary>
\alt\.{turningnumber}\<path primary>\cr
\andalso\.{directiontime}\<pair expression>\.{of}\<path primary>\cr
\<pair part specifier>\is\.{xpart}\alt\.{ypart}\cr
\<transform part specifier>\is \.{xxpart}\alt\.{xypart}\alt
\.{yxpart}\alt\.{yypart}\alt \.{xpart}\alt\.{ypart}\cr
\<scalar multiplication operator>\is
 \.+\alt\.-\cr
\andalso\<numeric token primary not followed by \.+ or \.- or numeric token>\cr
\<numeric token primary>\is\<numeric token
  not followed by `\./$\langle$numeric token$\rangle$'\thinspace>\cr
\andalso \<numeric token>\./\<numeric token>\cr
\<unary operator>\is\<scalar multiplication operator>\cr
\andalso\.{sqrt}\alt\.{mexp}\alt\.{mlog}\alt\.{sind}\alt\.{cosd}\alt
\.{floor}\alt\.{uniformdeviate}\cr
\syntaxbreak
\<numeric secondary>\is\<numeric primary>\cr
\andalso\<numeric secondary>\<multiplicative op>\<numeric primary>\cr
\andalso\<numeric secondary>\.[\<numeric expression>\.,
  \<numeric expression>\.]\cr
\<multiplicative op>\is\.*\alt\./\cr
\syntaxbreak
\<numeric tertiary>\is\<numeric secondary>\cr
\andalso\<numeric tertiary>\<additive op>\<numeric secondary>\cr
\andalso\<numeric tertiary>\<pythagorean additive op>\<numeric secondary>\cr
\<additive op>\is\.+\alt\.-\cr
\<pythagorean additive op>\is\.{++}\alt\.{+-+}\cr
\syntaxbreak
\<numeric expression>\is\<numeric tertiary>\cr}

\Bigbreak
\noindent Pair expressions:
\syntaxlines{\<pair primary>\is
 \<pair variable>\cr
\andalso\<left delimiter>\<numeric expression>\.,
  \<numeric expression>\<right delimiter>\cr
\andalso\<left delimiter>\<pair expression>\<right delimiter>\cr
\andalso\.{begingroup} \<statement list> \<pair expression> \.{endgroup}\cr
\andalso\.{point}\<numeric expression>\.{of}\<path primary>\cr
\andalso\.{precontrol}\<numeric expression>\.{of}\<path primary>\cr
\andalso\.{postcontrol}\<numeric expression>\.{of}\<path primary>\cr
\andalso\.{penoffset}\<pair expression>\.{of}\<pen primary>\cr
\andalso\.{penoffset}\<pair expression>\.{of}\<future pen primary>\cr
\andalso\<scalar multiplication operator>\<pair primary>\cr
\syntaxbreak
\<pair secondary>\is\<pair primary>\cr
\andalso\<pair secondary>\<multiplicative op>\<numeric primary>\cr
\andalso\<numeric secondary>\.*\<pair primary>\cr
\andalso\<numeric secondary>\.[\<pair expression>\.,\<pair expression>\.]\cr
\andalso\<pair secondary>\<transform>\cr
\syntaxbreak
\<pair tertiary>\is\<pair secondary>\cr
\andalso\<pair tertiary>\<additive op>\<pair secondary>\cr
\andalso\<path tertiary>\.{intersectiontimes}\<path secondary>\cr
\syntaxbreak
\<pair expression>\is\<pair tertiary>\cr}

  One of the most important consequences of these rules is that \MF\
always knows the type of the expression it is dealing with. For example,
a \<pair variable> is a variable that has been declared to have type
\.{pair}; such a variable will be recognized as a \<pair expression>
and not as any other kind of expression. There are only a few exceptions:
(1)~A \<pair tertiary> can be a \<path subexpression>; but it
is considered to be only a \<pair tertiary> unless the \<path
subexpression> interpretation is mandatory, i.e., unless followed by
`\.{\char`\{}', `\.{..}', or `\.{\&}'. The boolean expression `\.{path((0,0))}'
is false.  (2)~A \<boolean expression> like `\.{x=y}' that involves the
equality relation looks something like an equation. \MF\ will consider an
equals sign to be a \<relation> unless the expression to its left occurs
at the very beginning of a statement, or just after an equals sign
or `\.{:=}' in an equation or assignment.
(3)~Similarly, a \<type> that occurs at the beginning of a statement
is not considered to be part of a \<boolean primary>; it is considered to
be the beginning of a type declaration.
(4)~After a \<path join>, the `\.{cycle}' operator is not considered
to be part of a \<boolean primary>.

\newsection 4. Macro definitions.

\MF's most powerful way to produce new high-level constructions is to make
one token stand for a combination of other tokens. One easy way to
make this happen is to say
$$\hbox{\.{def} \<symbolic token> \.=
  \<replacement text> \.{enddef};}$$
this is called a {\it definition}.  For example, the definition
$$\hbox{\tt def -- = - - enddef}$$
simply says that the token `\.{--}' is to be replaced by two
consecutive `\.-' tokens. Here's an even more trivial definition:
$$\hbox{\tt def \char`\\\ = enddef;}$$
it causes a single backslash token to be replaced by nothing at all.
(\MF\ actually has this definition built in, because it makes
the use of \MF\ analogous to the use of \TeX, especially in command
lines when you're running the program.)

More interesting definitions include parameters that are replaced by
arguments when the token appears later. In this way definitions provide
the capabilities of subroutines as well as the features of simple macro
expansion.  It's convenient for the sake of brevity to give the general
rules first, and examples later---even though good expository technique
would go the other way; so here's more syntax:
\syntaxlines{\<definition>\is\<definition heading>\.=\<replacement
  text>\.{enddef}\cr
\<definition heading>\is\.{def}\<symbolic token>\<parameter heading>\cr
\andalso\.{vardef}\<defined variable>\<parameter heading>\cr
\<parameter heading>\is\<parameter list>
  \<undelimited parameter heading>\cr
\<parameter list>\is\<empty>\alt\<parameter list>\<parameter declaration>\cr
\<parameter declaration>\is\<left delimiter>\<parameter type>
  \<parameter tokens>\<right delimiter>\cr
\<parameter type>\is\.{expr}\alt\.{text}\alt\.{suffix}\cr
\<parameter tokens>\is\<tag>\alt\<parameter tokens>\.,\<tag>\cr
\<defined variable>\is\<declared variable>\alt
  \<declared variable>\.{@\#}\cr}
For example, the parameter list
$$\hbox{\tt (suffix i,j)(text foo)(expr */*)}$$
introduces four parameter
tokens `\.i', `\.j', `\.{foo}', and `\.{*/*}'; they will be
treated specially whenever they occur within the \<replacement
text>.

The \<replacement text> is any sequence of tokens that is balanced with
respect to unquoted \.{def} and \.{enddef} tokens.
This rule needs some explanation:
There's a primitive operation (initially called \.{quote}) that
inhibits special interpretation of whatever token follows it in a
replacement text. A few
tokens are treated specially when \MF\ is scanning the replacement text of
a definition, unless they've been quoted:

\smallskip\item{1)}\.{def}, \.{vardef}, \.{primarydef}, \.{secondarydef},
and \.{tertiarydef}, which introduce definitions inside definitions.

\item{2)}\.{enddef}, which ends the replacement text unless it is matched
by a preceding \.{def}-like token as listed in rule~1.

\item{3)}a parameter token (like `\.i' or `\.{*/*}' in the example above),
which is replaced by a special internal token that will tell \MF\ to
substitute an argument when this token is encountered again.

\item{4)}\.{quote}, which disables any special interpretation of the
immediately following token; this token doesn't survive in the
replacement text, unless of course it has been quoted.

\item{5)}\.{\#@}, \.@, and \.{@\#}, which will be replaced respectively by
the prefix, the name, and the suffix of this macro when it's used.
(This rule applies only to \.{vardef} macros; and \.{@\#} is replaced only
when the \<defined variable> in the definition heading ends with \.{@\#}.)

\smallskip\noindent
Rule 5 is the only unusual one, but the examples below should make it clear.
The mnemonic for distinguishing \.{\#@} from \.{@\#} is that the \.@ sign
represents where the macro is ``at,'' and the other sign retrieves the
tokens that either precede or follow the ``at'' position.

It may be worthwhile to reiterate the fact that these rules don't
really apply to the specific tokens \.{enddef}, \.{quote}, \.{\#@}, \.@, and
\.{@\#}; they apply to tokens whose meaning (at the time \MF\ is
recording the definition) is the same as the primitive meaning that those
other tokens had when \MF\ was started up. In particular, if the meanings
of \.{enddef}, \.{quote}, \.{\#@}, \.@, and \.{@\#} have changed at the time of
definition recording, no quoting is actually necessary. But some other
token had better have received the meaning of \.{enddef}, or the definition
will never end!

A defined quantity that has parameters must be supplied with corresponding
{\sl arguments\/} when it is used.  The arguments are enclosed in
delimiters (usually parentheses). It's also possible to use a comma
between arguments; in this context a comma can be thought of as an
abbreviation for \<right delimiter>\<left delimiter> with respect to the
delimiter pair that preceded the comma.

The argument corresponding to a parameter of type \.{expr} can be any
\<expression>.  This expression is effectively parenthesized before it is
substituted into the replacement text, hence it occurs as a \<primary> in
expressions.  Expression parameters are evaluated as much as possible
before the macro is invoked, but they need not have ``known'' values. They
should not appear on the left of `\.{:=}' operations.

The argument corresponding to a parameter of type \.{suffix} can be any
\<suffix>.  Subscripts in that suffix, if any, will have been evaluated
and replaced by (signed) numeric tokens of the corresponding value, before
the argument is actually substituted into the replacement text.

The argument corresponding to a parameter of type \.{text} is any sequence
of tokens that are balanced with respect to the enclosing delimiters.
This means that text arguments cannot be followed by commas. For example,
a list of three arguments can usually be given either as `\.{(a,b,c)}'
or `\.{(a,b)(c)}' or `\.{(a)(b,c)}' or `\.{(a)(b)(c)}'; but only the
second and last of these alternatives is permitted when the second
argument corresponds to a text parameter. Since delimiters need not
be parentheses, a text argument need not be balanced with respect
to parentheses; but it's usually not a good idea to play with
unbalanced parentheses unless you have a really special reason. Text
arguments are not ``evaluated'' at the time of a macro call; they are
simply stored away, and substituted for the corresponding parameter when
it shows up in the replacement text.

The defined quantity in a \.{vardef} can be any \<defined variable>, not simply
a \<tag>; for example, you can define `\.{a[]b@\#}'. What does this mean? Well,
it means that a supposed variable name like `\.{a35b42c.d}' becomes a
macro call instead. The prefix that gets substituted for \.{\#@} in the
replacement text will be `\.{a35}' in this example; the name that gets
substituted for \.@ will be `\.b'; and the suffix that gets substituted
for \.{@\#} will be `\.{42c.d}'. In simpler cases the prefix and suffix
are empty. If there's no \.{@\#} at the end of the \<defined variable>,
the suffix part is always empty. For example, after a definition of
\.{a[]b}, the text `\.{a35b42c.d}' will be interpreted as simply `\.{a35b}'
and \MF\ will not look ahead for a suffix.

One of the important definitions in the \.{PLAIN} base is
$$\hbox{\tt vardef z@\# = (x@\#,y@\#) enddef};$$
it converts variable names like `\.{z20}' and `\.{z[i]r}' into
`\.{(x20,y20)}' and `\.{(x[i]r,y[i]r)}', respectively, making it
possible to give convenient names to the components of a pair
variable without explicitly defining \.z as a pair variable.
Consider also the definition
$$\hbox{\tt vardef p[]slope=(\#@dx,\#@dy) enddef};$$
this converts, e.g., `\.{p5slope}' into `\.{(p5dx,p5dy)}'.

\MF\ actually puts \.{begingroup...endgroup} around the replacement text of
\.{vardef}'ed macros, in order to make them variable-like.
Thus, `\.{z20}' really stands for `\.{begingroup}~\.{(x20,y20)}~\.{endgroup}'.

Here now are a few more examples, as promised. The first one
is intended to set up a triple of points that represent the position
of a broad pen. For example, `\.{penpos(3,20,45)}' will stand for pen
position~3 at which the pen is 20~pixels broad and inclined at an
angle of $45^\circ$; there will be three points \.{z3}, \.{z3l}, and
\.{z3r}, representing the middle of the pen, its left edge, and its
right edge. Here's one way to define \.{penpos} accordingly:
$$\vcenter{\halign{\tt#\hfil\cr
def penpos(suffix i)(expr l,theta)=\cr
\ \ \ \ \ z.i.r-z.i.quote l = (l,0) rotated theta;\cr
\ \ \ \ \ z.i = .5[z.i.quote l, z.i.r] enddef\cr}}$$
Now the tokens `\.{penpos(4,15,d+90)}' will expand into
`\.{z4r-z4l=(15,0)rotated135;} \.{z4=.5[z4l,z4r]}', if \.{d=45}. It
wouldn't have been necessary to quote any of the appearances of `\.l' if
another name had been chosen for the parameter. For example,
$$\vcenter{\halign{\tt#\hfil\cr
def penpos(suffix i)(expr length,theta)=\cr
\ \ \ \ \ z.i.r-z.i.l = (length,0) rotated theta;\cr
\ \ \ \ \ z.i = .5[z.i.l, z.i.r] enddef\cr}}$$
would have been simpler. The \.{quote} operation has been provided
mostly to permit definitions within definitions, not to compensate for
poorly chosen parameter names.

The following example illustrates the use of a text parameter.
$$\vcenter{\halign{\tt#\hfil\cr
def label(text t)=\cr
\ \ \ \ \ forsuffixes \$=t:\ autolabel(z\$,"point"\&str\$); endfor\cr}}$$
The expansion of `\.{label(1,[i+1],7a)}' will be
$$\hbox{\tt forsuffixes \$=1,[i+1],7a:\
  autolabel(z\$,"point"\&str\$); endfor}$$
and this, in turn, is a macro-like construction that essentially expands into
$$\hbox{\tt autolabel(z1,"point1"); autolabel(z2,"point2");
  autolabel(z7a,"point7a");}$$
if \.{i=1}, after which the `\.{autolabel}' and `\.z' macros expand the
text even more.

Going back to the syntax for \<parameter heading>, you'll note that there's
something called an \<un\-delim\-ited parameter heading> that hasn't yet been
explained. Well, here's the missing syntax:
\syntaxlines{\<undelimited parameter heading>\is\<empty>\alt
 \.{primary}\<tag>\alt\.{secondary}\<tag>\alt\.{tertiary}\<tag>\cr
\andalso\.{expr}\<tag>\alt\.{expr}\<tag>\.{of}\<tag>\cr
\andalso\.{suffix}\<tag>\alt\.{text}\<tag>\cr}
In this case the macro works just as usual, but its arguments are parsed
like the components of expressions or statements; no delimiters are required.
The first undelimited argument may be preceded by an optional
`\.=' or `\.{:=}' (except in the case of undelimited text arguments).
When `\.{primary}\<tag>' is given, the argument is a \<primary>; when
`\.{expr}\<tag>' is given, the argument is an \<expression>;
and `\.{expr}\<tag>\.{of}\<tag>' parses the first argument as an
expression and the second as a primary. This essentially extends the
syntax of \MF\ expressions so that additional operators are provided.
An undelimited text argument runs until the end of the current statement;
more precisely, until the next semicolon or
\.{endgroup} or \.{end} that is not nested inside \.{begingroup..endgroup}.

For example, plain \MF\ defines rounding as follows:
$$\hbox{\tt vardef round primary x = floor(x+.5) enddef};$$
it's not necessary to put parenthesis around the argument when that
argument is a numeric primary as in `\.{round 1.5u}'. And here's
a slightly more complex example that rounds its argument to a ``good''
value with respect to a given ``pen width'' \.{w[i]}:
$$\vcenter{\halign{\tt#\hfil\cr
vardef good[] primary x=\cr
\ \ begingroup save t;\cr
\ \ if odd w@: t=(floor x)+.5;\cr
\ \ else: t=round x;\cr
\ \ fi; t endgroup enddef\cr}}$$
Now, for example, if \.{w3=4.9} and \.{x10=15.2}, the result of
`\.{good3 x10}' will be 15.5.

The following example defines a transform that is like a given one but
fixes the origin:
$$\hbox{\tt vardef unshifted primary t =
  t shifted-((0,0) transformed t) enddef}$$
And here's an absolute-value operator that works on pairs and numbers:
$$\vcenter{\halign{\tt#\hfil\cr
def abs primary x =\cr
\ \ if pair x: (xpart x ++ ypart x)\cr
\ \ elseif numeric x: if x<0: (-x) else: x fi\cr
\ \ else: x fi\cr
\ \ enddef\cr}}$$

It's also possible to define macros that act as infix operators:
\syntaxlines{\<infix definition>\is
 \<level indicator>\<tag>\<symbolic token>\<tag>\.=%
  \<replacement text>\.{enddef}\cr
\<level indicator>\is\.{primarydef}\alt
 \.{secondarydef}\alt\.{tertiarydef}\cr}
For example,
$$\hbox{\tt secondarydef x++y = sqrt(x*x+y*y) enddef}$$
would be a way to define the \.{++} operator. (However, \MF's built-in
\.{++} is much better, because it won't overflow when \.{x*x} or \.{y*y}
are out of range.) Exponentiation can be defined by
$$\hbox{\tt primarydef x**y = mexp(y*mlog x) enddef}$$
but such a definition blows up when $x<0$ and $y=2$. Here's a better way:
$$\vcenter{\halign{\tt#\hfil\cr
primarydef x**y =\cr
\ \ begingroup save t;\cr
\ \ if y=2: t=x*x; \% that's the most common case\cr
\ \ elseif x>0: t=mexp(y*mlog x);\cr
\ \ elseif y=floor y: t=1;\cr
\ \ \ \ if y>=0: for n=1 step 1 until y:  t:=t*x endfor;\cr
\ \ \ \ else: for n=-1 step -1 until y: t:=t/x endfor;\cr
\ \ \ \ fi;\cr
\ \ else: errmessage("Undefined power " \& decimal x \& "**" \& decimal y);\cr
\ \ \ \ t=1;\cr
\ \ fi; t endgroup enddef\cr}}$$
The \<level indicator> indicates how the arguments should be parsed
within \MF\ expressions.  If it is `\.{primarydef}', the first argument is
parsed as a secondary and the second as a primary; if it is
`\.{secondarydef}', the first argument is parsed as a tertiary and the
second as a secondary; if it is `\.{tertiarydef}', the first argument is
parsed as an expression and the second as a tertiary.

Here is a way to define the sum of two transforms:
$$\vcenter{\halign{\tt#\hfil\cr
secondarydef x transum y =\cr
\ \ begingroup save t; transform t;\cr
\ \ (0,1) transformed t = (0,1) transformed x + (0,1) transformed y;\cr
\ \ (1,0) transformed t = (1,0) transformed x + (1,0) transformed y;\cr
\ \ (0,0) transformed t = (0,0) transformed x + (0,0) transformed y;\cr
\ \ t endgroup enddef\cr}}$$

A symbolic token whose current meaning was defined in a \.{def} or an
infix definition is not usable as a \<tag> in a variable; it has become
a spark. But the symbolic tokens defined by \.{vardef} are like
variables, except that their suffixes no longer carry values. For example,
after making the definitions above, it is obviously impossible to refer
to a variable called `\.{x.transum}' or `\.{good3y}'; but `\.{x.good}'
would be OK.

\newsection 5. Conditions and loops.

\MF\ also handles a few other things with a macro-like behavior, in the
sense that they effectively change the text that reaches \MF's ``stomach.''
The first of these allows you to select between different pieces of program:
\syntaxlines{\<conditional>\is\.{if}\<boolean expression>\.:%
  \<conditional text>\<alternatives>\.{fi}\cr
\<alternatives>\is\<empty>\alt\.{else:}\<conditional text>\cr
\andalso\.{elseif}\<boolean expression>:\<conditional text>\<alternatives>\cr}
Conditionals are expanded whenever macros would be expanded, as in \TeX;
in particular, conditionals are permitted in the middle of expressions and
commands. When you write
$$\hbox{\tt if $\beta_1$: \<text$_1$> elseif $\beta_2$: \<text$_2$>
  elseif $\beta_3$: \<text$_3$> else: \<text$_4$> fi}$$
\MF\ will evaluate $\beta_1$ first; if it's true, \<text$_1$> will be
interpreted and everything else from \.{elseif} to \.{fi} will be ignored.
But if $\beta_1$ is false, \<text$_1$> will be ignored and $\beta_2$
will be evaluated in a similar fashion. Ultimately if $\beta_1$, $\beta_2$,
and~$\beta_3$ all turn out to be false, \<text$_4$> will be read.

The conditional texts inside a conditional construction are arbitrary
sequences of tokens that are balanced with respect to \.{if} and \.{fi}.

There's also a general iteration facility:
\syntaxlines{\<iteration>\is\.{for}\<symbolic token>\<gets>\<expression list>%
  \.:\<iterated text>\.{endfor}\cr
\andalso\.{for}\<symbolic token>\<gets>\<arithmetic progression>%
  \.:\<iterated text>\.{endfor}\cr
\andalso\.{forsuffixes}\<symbolic token>\<gets>\<suffix list>%
  \.:\<iterated text>\.{endfor}\cr
\andalso\.{forever}\.:\<iterated text>\.{endfor}\cr
\<gets>\is\.=\alt\.{:=}\cr
\<expression list>\is\<expression>\alt\<expression list>\.,\<expression>\cr
\<suffix list>\is\<suffix>\alt\<suffix list>\.,\<suffix>\cr
\<arithmetic progression>\is\<initial value and step size>%
  \.{until}\<numeric expression>\cr
\<initial value and step size>\is\<numeric expression>\.{step}%
  \<numeric expression>\cr
\<exit clause>\is\.{exitif}\<boolean expression>\.;\cr}
Here \<iterated text> is any sequence of tokens that is balanced with
respect to unquoted appearances of \.{for}/\.{forsuffixes}/\.{forever}
and \.{endfor} delimiters.

These iterative statements have the conventional meaning of similar
constructions in other languages, but it is necessary to spell out the
rules precisely because each language has certain quirks. The statement
$$\hbox{\tt forsuffixes s = $\sigma_1$,$\sigma_2$,$\sigma_3$:
  \<text> endfor}$$
is equivalent to
$$\hbox{\tt \<text($\sigma_1$)> \<text($\sigma_2$)> \<text($\sigma_3$)>}$$
where \<text($\sigma$)> means that the value of suffix $\sigma$ is inserted
in place of the token~\.s in the text. It's just as if \.s were a \.{suffix}
parameter to a macro; subscripts in $\sigma_1$, $\sigma_2$, and~$\sigma_3$
are evaluated before the replacement is done. Similarly
$$\hbox{\tt for e = $\epsilon_1$,$\epsilon_2$,$\epsilon_3$: \<text> endfor}$$
is equivalent to
$$\hbox{\tt \<text($\epsilon_1$)> \<text($\epsilon_2$)>
  \<text($\epsilon_3$)>}$$
with \.e treated as an \.{expr} parameter.

Arithmetic progressions are similar but the rules are slightly more fussy.
The statement
$$\hbox{\tt for n = 1 step 2 until 7: \<text> endfor}$$
is equivalent to
$$\hbox{\tt for n = 1,3,5,7: \<text> endfor}$$
but
$$\hbox{\tt for n = 1 step 2 until 0: \<text> endfor}$$
skips over the text entirely. In general
$$\hbox{\tt for n = $\nu_1$ step $\nu_2$ until $\nu_3$: \<text> endfor}$$
causes \MF\ to evaluate the expressions (once and for all) and then to
form an arithmetic progression of values as follows:
If $\nu_2>0$ and $\nu_1>\nu_3$, or if $\nu_2<0$ and $\nu_1<\nu_3$,
the sequence is empty; otherwise the sequence is $\nu_1$ followed by the
sequence that would be obtained if $\nu_1+\nu_2$ were substituted
for~$\nu_1$. (In particular, if $\nu_2=0$ the sequence is $\nu_1$,
$\nu_1$, $\nu_1$, \dots\ repeated endlessly.)

In all of these instances the iteration index (i.e., the tokens
\.s, \.e, and \.n in our examples) are treated as macro parameters
inside the \<iterated text>; they have no connection with similarly named
variables elsewhere in the program. For example, if you say
$$\hbox{\tt n=0; for n=1: m=n; endfor; show m,n}$$
you will find that \.{m=1} and \.{n=0}.

Nested iterations like the following are possible:
$$\vcenter{\halign{\tt#\hfil\cr
for i=1 step 1 until n:\cr
\ for j=i+1 step 1 until n: a[i][j]=a[j][i]; endfor; endfor\cr}}$$
But \MF\ can't do such things with super efficiency; in this example,
it has to scan and redefine and undefine the inner \.{for} loop
\.n~times.

The `\.{forever}' construction iterates the text repeatedly, and you
may well wonder how this could possibly be useful. Well, there's a way to
get out of a loop without terminating it normally. When \MF\ encounters
the construction
$$\hbox{\.{exitif}\<boolean expression>\.;}$$
as it interprets an iterated text, it will conclude the iteration
immediately if the boolean expression is true.

There are a few other things that transform program text something like
macro expansion. The construction `\.{expandafter}\<token>\<token>'
expands the second token before the first, as in \TeX. The construction
`\.{scantokens}\<string primary>' converts the string primary to a
sequence of tokens as if it were a line of characters read from a file.

If \MF\ encounters the construction `\.{input} \<filename>' while reading
a file, it will begin to read from the specified file instead (and will
resume the previous file later). This operation is permitted only when
\MF\ is scanning a line of characters that have not yet been converted to
tokens; otherwise the file name might be garbaged by the tokenizing process.
(You can use \.{input} inside macros by saying, e.g., `\.{scantokens}
\.{"input} \<filename>\.{"}.)
The command `\.{endinput}' tells \MF\ to cease reading a particular file
at the end of the current line. As in \TeX, the syntax of file names
is system dependent, and both of these commands are performed only
when they are ``expanded'' like macros and conditionals.

Here's a somewhat silly program that illustrates a few of these ideas:
$$\vcenter{\halign{\tt#\hfil\cr
Yes=1; No=0;\cr
forever: message "Are you happy? ";\cr
\ result:=scantokens readstring;\cr
\ exitif known result;\cr
\ message "(Please type Yes or No.)";\cr
endfor;\cr}}$$
The user is assumed to be cooperative; lots of potential responses
in this example would get \MF\ incredibly mixed up. There is a
safer alternative:
$$\vcenter{\halign{\tt#\hfil\cr
string answer;\cr
forever: message "Are you happy? ";\cr
\ answer:=readstring;\cr
\ exitif answer="Yes";\cr
\ exitif answer="No";\cr
\ message "(Please type Yes or No.)";\cr
endfor;\cr}}$$

\newsection 6. Statements and commands.

A \MF\ program is a sequence of statements separated by semicolons and
followed by \.{end}. More precisely, the syntax
\syntaxlines{\<program>\is\<statement list> \.{end}\cr
\<statement list>\is\<empty>\alt\<statement>\.;\<statement list>\cr}
defines a \<program> in terms of a \<statement>.

But what are statements? Well, they are of various kinds. An ``equation''
states that two expressions are supposed to be equal. An ``assignment''
assigns the value of an expression to a variable. A ``declaration''
states that certain variables will have a certain type.
A ``definition'' defines a macro.  A ``title''
gives a descriptive name to the character that is to follow.
And a ``command'' orders \MF\ to do some specific operation, immediately.
\syntaxlines{\<statement>\is\<equation>\alt\<assignment>\alt
 \<declaration>\alt\<definition>\alt\<title>\alt\<command>\cr
\andalso\.{begingroup} \<statement list> \<statement> \.{endgroup}\cr
\<equation>\is\<expression>\.=\<right-hand side>\cr
\<assignment>\is\<variable>\.{:=}\<right-hand side>\cr
\<right-hand side>\is\<expression>\alt\<equation>\alt\<assignment>\cr
\<title>\is\<string expression>\cr}
We have already given the syntax and rules for \<declaration> and
\<definition>; the syntax for each of the various kinds of \<command>
appears below.

Multiple equations and assignments are performed from right to left.
For example,
$$\hbox{\tt x+1=y:=y+1=z:=1/2x=z+2}$$
first equates \.{.5x} to \.{z+2}, then assigns this common value to \.z,
then equates \.z to \.{y+1}, then assigns this to \.y, and finally
equates \.y to \.{x+1}. This, of course, is more complicated than anything
a person ought to write, but it is still instructive to see what it means.
Let's suppose that \.x, \.y, and \.z have not appeared in any equations
or assignments before this point. Then `\.{1/2x=z+2}' makes \.x an
independent variable and gives \.z the value \.{.5x-2}. The next
assignment wipes this out and gives \.z the value \.{.5x} instead.
Then \.{y+1} is equated to \.z, so \.y becomes equal to \.{.5x-1};
but the subsequent assignment wipes out \.y's former value and
makes it \.{.5x}. Finally, the equation \.{x+1=y} becomes \.{x+1=.5x},
so \.x is set to $-2$; this causes \.y and \.z to become equal to~$-1$.

A numeric variable is either ``independent'' or ``dependent'' or ``known.''
Before it receives a value it is independent; later it may be expressed as
a linear combination of independent variables (e.g., `\.{.5x-2}'); and
eventually its value ought to become precisely known, so that we can do
something with it. Every equation that \MF\ encounters is transformed
into a linear combination of independent variables that is equated to zero.
An independent variable whose coefficient is greatest, in absolute value,
is chosen to depend on the others; this variable becomes dependent
or known. Notice that each equation reduces the number of independent
variables by one, unless the equation is redundant (e.g., `\.{x=x}')
or inconsistent (e.g., `\.{0=1}'). Thus if you have $n$ independent variables,
you should give $n$ equations in order to define their values.

Each component of a pair or transform variable is, similarly,
independent or dependent or known. An equation between pair expressions
is equivalent to two equations (one for the $x$~part, and one for the
$y$~part). Similarly, an equation between transform expressions is
equivalent to six equations. \MF\ won't complain if one or more of these
equations prove to be redundant, although it does report an error if
two unequal expressions of type \.{numeric} have been equated.

The other five types of variables can appear in equations, but only
in simple ways. A boolean, string, pen, picture, or path variable is
either ``unknown'' or ``known.'' Unknown variables of these types should
appear only by themselves on one side or the other of an equation. If, for
example, \.{s[]} is an array of strings, \MF\ will be able to deduce from
$$\hbox{\tt s1=s2; s3=s4; s1=s3; s2="gosh";}$$
that \.{s4} equals \.{"gosh"}. But \MF\ will {\it not\/} be able to
deduce from the equation \.{"h"\&s5="heck"} that \.{s5="eck"}.

\MF\ prefers equations to assignments. If you find yourself using
assignments a lot, you are probably not getting the best results;
you're still locked into old-style ``imperative'' programming languages,
poor soul.

So much for equations and assignments. A \<title> is a string that
is simply ignored as if it were a comment, except in two circumstances:
If \.{tracingtitles>0}, the title is displayed on the user's terminal
when it is encountered. And if \.{proofing>0}, the title is written
into the output so that it can be displayed as a caption on
the proofsheet that follows.

The quantities \.{tracingtitles} and \.{proofing}, just mentioned,
are special internal variables of \MF, by which it is possible to interact
with the system in a variety of ways. Here is a complete
list of \MF's internal variables, together with a brief indication
of their meanings:
$$\tabskip\centering
\halign to\hsize{\tt#\hfil\quad\tabskip0pt&#\hfil\tabskip\centering\cr
tracingtitles&show titles online when they appear\cr
tracingequations&show each variable when it becomes known via an equation\cr
tracingcapsules&show capsules as well as variables\cr
tracingchoices&show the control points chosen for paths\cr
tracingspecs&show subdivision of paths into octants before digitizing\cr
tracingpens&show details of pens that are made\cr
tracingcommands&show commands and operations before they are performed\cr
tracingmacros&show macros before they are expanded\cr
tracingedges&show digitized edges as they are computed\cr
tracingoutput&show digitized edges as they are output\cr
tracingstats&log the memory usage at end of job\cr
tracingonline&show long diagnostics on terminal as well as in the log file\cr
year&the current year (e.g., 1984)\cr
month&the current month (e.g, 3 $\equiv$ March)\cr
day&the current day of the month\cr
time&the number of minutes since midnight when this job started\cr
charcode&the number of the next character to be output\cr
charfam&the class of the next character to be output\cr
charwd&the width of the next character to be output\cr
charht&the height of the next character to be output\cr
chardp&the depth of the next character to be output\cr
charic&the italic correction of the next character to be output\cr
chardx&horizontal device displacement of the next character, in pixels\cr
chardy&vertical device displacement of the next character, in pixels\cr
designsize&the unit of measure used for \.{charwd...charic}, in points\cr
hppp&the number of horizontal pixels per point\cr
vppp&the number of vertical pixels per point\cr
pausing&positive to display lines before they are executed\cr
proofing&positive for proof mode, negative if there's no output at all\cr
fontmaking&positive if font metric output is to be produced\cr
showstopping&positive if \.{show} commands are to stop like errors\cr
smoothing&positive if certain glitches are to be removed automatically\cr
autorounding&positive to fix horizontal/vertical curve points;
 $>1$ for diagonals\cr
granularity&the number of pixels per ``large'' pixel\cr
warningcheck&positive for warnings when variables get large values\cr
turningcheck&positive to reorient clockwise paths;
 $>1$ to flag strange ones\cr}$$
All of these quantities are numeric, and initially zero (except for
\.{year}, \.{month}, \.{day}, and \.{time}, which are initialized to
the time the run began). Plain \MF\ sets \.{smoothing:=1} and
\.{autorounding:=2}, because such adjustments are usually desirable.
You can use any of these quantities
in expressions or on the left-hand side of assignments---they show up
under the heading \<internal quantity> in the syntax rules above---but
when you assign a new value to them it should be numeric and ``known.''

\medbreak
All of the remaining statements of \MF\ are called {\it commands}, and they
will be listed here in a more or less arbitrary order. Macros and
conditionals and such things are not expanded in commands when the
next token is being defined or used in some unusual way; but expansion
usually happens unless there's a good reason for not doing so.

\def\@{\bigskip\textindent{$\bullet$}}
\@A {\it save command\/} has the syntax
\syntaxlines{\<save command>\is\.{save}\<symbolic token list>\cr
\<symbolic token list>\is\<symbolic token>\alt
 \<symbolic token list>\.,\<symbolic token>\cr}
This tells \MF\ to put the current meaning of the symbolic tokens into
a safe place, and to restore those meanings at the end of the current
group. Each token in the list becomes undefined, as if it had never appeared
before; in particular, it loses any ``primitive'' meaning that
would have prevented it from being used as a \<tag>.

\@An {\it interim command\/}
$$\hbox{\.{interim}\<internal quantity>\.{:=}\<right-hand side>}$$
acts like an ordinary assignment, but the previous value of the internal
quantity is saved away, to be restored at the end of the current group.

\@The {\it let command\/}
$$\hbox{\.{let}\<symbolic token>\.=\<symbolic token>}$$
assigns the current meaning of the right-hand token as the current
meaning of the left-hand token. For example, after
`\.{let} \.{diamonds=forever}', the token `\.{diamonds}' will introduce
loops. If the left-hand token was the
first token in any variable names, those variables all disappear.
If the right-hand token was the first token in any variable names,
those variables still have their old names; the left-hand token
will act like an undefined variable in that case. (The purpose of
\.{let} is to redefine primitive meanings, not variable names.)

Note: If the right-hand symbol is one of a pair of matching delimiters,
the subsequent behavior of the left-hand symbol is undefined. For
example, it's a bad idea to say `\.{let[[=(;} \.{let]]=)}'.

\@The {\it shipout command\/}
$$\hbox{\.{shipout}\<picture expression>}$$
puts the pixels of positive weight, as defined by the given picture,
into a generic font output file, where they will be the image associated
with character number \.{charcode+256*charfam}. (However, no output is done
if \.{proofing<0}.) This command also saves the \.{charwd}, \.{charht},
\.{chardp}, \.{charic}, and \.{chardw} values and associates them with
the current \.{charcode} number modulo~256. (The \.{charcode}, \.{charfam},
and \.{chardw} values are rounded to integers before \.{shipout} uses them.)

\@The {\it special commands\/} $$\hbox{\.{special}\<string expression>\alt
\.{numspecial}\<numeric expression>}$$ specify non-pixel information that
is shipped to the generic output file, if \.{proofing} is nonnegative.
Such special information is unrestricted, although it should follow
conventions that are understood by the software that reads the output;
such conventions may grow up over the years after \MF\ has been
``frozen,'' so that there will always be an easy way to make extensions.
Initially the \.{PLAIN} base will use \.{special} and \.{numspecial} to
implement some conventions that provide rudimentary proof outputs; for
example, the \.{autolabel} operation in one of the examples above will
expand into a sequence of \.{special} and \.{numspecial} commands.

\@The {\it drawing command\/} does \MF's main duty:
\syntaxlines{\<drawing command>\is\.{addto}\<picture variable>
 \.{also}\<picture expression>\cr
\andalso\.{addto}\<picture variable>\.{contour}\<path expression>\<with list>\cr
\andalso
 \.{addto}\<picture variable>\.{doublepath}\<path expression>\<with list>\cr
\<with list>\is\<empty>\alt\<with list>\<with clause>\cr
\<with clause>\is\.{withpen}\<pen expression>\cr
\andalso\.{withweight}\<numeric expression>\cr}
The amount of weight should be $-3$, $-2$, $-1$, 1, 2, or 3.
A \.{contour} should be a cyclic path; a \.{doublepath} is a contour
obtained by going from the beginning to the end and then back to the beginning.
When a pen is specified, the envelope of the contour is used.
The effect of this command is to add the specified weight to each pixel
inside the specified contour or envelope. (Complications arise if the
path ``winds around'' some points more than once; such pixels are
``colored'' more than once. The manual will explain this further.)

\@Arrays of pixels can be modified and ``standardized'' by the {\it cull
command}, which looks like this:
\syntaxlines{\<cull command>\is\.{cull}\<picture variable>
  \<keep or drop>\<pair expression>\cr
\andalso\<cull command>\.{withweight}\<numeric expression>\cr
\<keep or drop>\is\.{keeping}\alt\.{dropping}\cr}
Each pixel whose weight is included in or excluded from the given closed
interval is replaced by a pixel of the specified weight,
and all other pixels get weight zero. For example,
$$\hbox{\tt cull pic dropping (-4095,0)}$$
zeros out all pixels of negative weight and changes pixels of weight $>2$
to weight~1. The interval must be such that
pixels of weight zero remain of weight zero.

\@The {\it display commands\/} provide online graphic output:
\syntaxlines{\<openwindow command>\is\.{openwindow}\<window number>
 \<screen rectangle>\.{at}\<pair expression>\cr
\<window number>\is\<numeric expression>\cr
\<screen rectangle>\is\.{from}\<pair expression>\.{to}\<pair expression>\cr
\<display command>\is\.{display}\<picture variable>\.{inwindow}\<window
  number>\cr}
A window number must be between 0 and 15. The statement
$$\hbox{\.{openwindow} $k$ \.{from} $(r_0,c_0)$ \.{to}
 $(r_1,c_1)$ \.{at} $(x,y)$}$$
associates a rectangular area of the user's screen with \MF's pixels.
The $(r,c)$ coordinates are row and column numbers on the screen,
considering the top row and left column to be number zero; note that this
is quite different from the Cartesian coordinates used elsewhere in \MF.
The values will all be rounded to integers. Point $(x,y)$ of \MF's
raster will be equated to the upper left corner of the rectangle, i.e.,
to the upper left corner of the pixel in screen column~$c_0$ of screen
row~$r_0$.  The window itself contains $r_1-r_0$ rows and $c_1-c_0$
columns; thus, $(r_1,c_1)$ is the screen pixel diagonally just southeast of
the lower right corner of the window, but it is not in the window itself.
A window can be opened any number of times (hence moved to different
locations on the screen, if desired), but it must be opened at least once
before it is used in a \.{display} command.
Opening a window blanks the corresponding screen rectangle.
The effect of overlapping windows is undefined, because \MF\ does not
always update pixels that have previously been displayed in a window area.

\@The {\it protection commands\/}
$$\hbox{\.{outer}\<symbolic token list>\alt\.{inner}\<symbolic token list>}$$
apply or remove a ``protection tag'' to the given tokens. If a token
tagged \.{outer} occurs when \MF\ is skipping over tokens at high speed,
the program will stop and insert an appropriate delimiter, since \.{outer}
tokens are supposed to occur only at ``quiet'' times. (Unquiet times
occur when \MF\ is skipping tokens because of a false conditional,
or because it is reading the replacement text of a macro
or iteration definition, or because it is scanning a text parameter to
a macro, or because it is flushing erroneous tokens that were found
at the end of a statement.) Without such protection, a missing right
delimiter could cause \MF\ to eat up your whole program before any
error was detected; the protections keep such errors localized.
Changing the protection tag has no other effect on a token's meaning.

\@The {\it show commands\/} provide diagnostic output:
\syntaxlines{\<show command>\is\.{show} \<expression list>\cr
\andalso\.{showvariable} \<symbolic token list>\cr
\andalso\.{showtoken} \<symbolic token list>\cr
\andalso\.{showstats}\cr
\andalso\.{showdependencies}\cr}
The first of these displays the value of each expression, in turn.
The \.{showvariable} command gives the structure of all variables that begin
with a given name, together with their values in an abbreviated form;
this allows you to see which of its subscripts and attributes have
occurred. The \.{showtoken} command gives the current meaning
of a token (i.e., whether it is a primitive or not).
The \.{showstats} command tells you how much of \MF's internal memory is
currently being used.
And \.{showdependencies} tells you about every dependent variable
that is currently not known.
 In each case \MF\
pauses to allow subsequent interaction, as if an error had occurred,
if \.{showstopping} is positive;
but the ``error message'' is simply `\.{OK}'.

\@The {\it mode commands\/} control error recovery interaction; they
are the same as in \TeX:
$$\hbox{\.{batchmode}\alt\.{nonstopmode}
 \alt\.{scrollmode}\alt\.{errorstopmode}}$$

\@The command `\.{randomseed} \.{:=} \<numeric expression>'
initializes the random number generator to a specific value. If you
do this you can guarantee consistent results in different runs;
otherwise \MF\ uses \.{day+time/256/256} as the seed value, so
you will rarely get the same pseudo-random results twice.

\@The token `\.{dump}' can be substituted for `\.{end}', if a special
version of \MF\ is being used. This stores the macros defined so
far, so that they can be loaded as a base file. (It is analogous
to \TeX's \.{\char`\\dump} command.)

\@The command `\.{everyjob}\<symbolic token>' tells \MF\ that
the designated token should be inserted first, just before the
input file is read, when a job starts. (This is meaningful only
in a base file that will be loaded at the beginning of a run;
it is analogous to \TeX's \.{\char`\\everyjob} command.)

\@The command `\.{message}\<string expression>' displays the string
on the user's terminal, beginning with a new line. And
`\.{errmessage}\<string expression>' displays the string in
\MF's error message format, then stops as if an error had occurred.
And `\.{errhelp}\<string expression>' displays the string if the
user asks for help on the next \.{errmessage} error, unless the
string is empty.

\@The `\.{delimiters}\<symbolic token>\<symbolic token>' command
has already been described.

\@The command `\.{newinternal}\<symbolic token list>' defines each symbolic
token to act like an internal quantity (i.e., like `\.{pausing}',
`\.{proofing}', etc.); the values of these internal quantities are set to
zero initially.

\@The {\it font metric commands\/} specify information that \MF\ will pass
to a special output file for font metric data if \.{fontmaking} is
positive.  The syntax of these commands is explained in the appendix.
(The idea is to specify information for ligatures, kerns, extensible
characters, and character lists, as well as certain esoteric data that
goes in the \.{TFM} header.)

\@Finally, there's the {\it empty command}, which consists
of no tokens and causes \MF\ to do nothing. This may seem useless,
but actually it's very handy: You can always feel safe when you put
extra semicolons between statements (e.g., in conditionals or iterations).

\vfill\eject

\newsection Appendix: Font metric commands.

A special series of commands is available to specify data that will go in
the \.{TFM} output file if `\.{fontmaking}' is positive. To fully
understand these commands you should understand the conventions of font
metric files; see, for example, the listing of \TeX82 or the \TeX ware
report.
\syntaxlines{\<font metric command>\is\.{charlist}\<byte list>\cr
\andalso\.{extensible}\<byte>\.: \<top byte>\., \<mid byte>\., \<bot
  byte>\., \<rep byte>\cr
\andalso\.{headerbyte}\<numeric expression>\.:\<byte list>\cr
\andalso\.{fontdimen}\<numeric expression>\.:\<expression list>\cr
\andalso\.{ligtable}\<ligtable program sequence>\cr
\<byte list>\is\<byte>\alt\<byte list>\.,\<byte>\cr
\<byte>\is\<numeric expression>\alt\<string expression>\cr
\<top byte>\is\<byte>\cr
\<mid byte>\is\<byte>\cr
\<bot byte>\is\<byte>\cr
\<rep byte>\is\<byte>\cr
\<ligtable program sequence>\is\<ligtable step>\cr
\andalso\<ligtable program sequence>\., \<ligtable step>\cr
\<ligtable step>\is\<ligature replacement>\alt\<kern specification>\cr
\andalso\<byte>\.:\<ligtable step>\cr
\<ligature replacement>\is\<byte>\.{=:}\<byte>\cr
\<kern specification>\is\<byte>\.{kern}\<numeric expression>\cr}
A \<byte> specifies an eight-bit number; it is either a numeric
expression---which should have a known value between 0 and~255, inclusive,
when rounded to the nearest integer---or it is a string expression for
a string of length~1. In the latter case it denotes the ASCII code
of that string character. For example, `\.{"A"}' and `\.{64.61}' both
specify the byte value~65.

Several characters of a font can be linked together in a series by
means of the \.{charlist} command. For example,
$$\.{charlist oct"000", oct"020", oct"022", oct"040", oct"060"}$$
is used in the font \.{amathx} to specify the left parentheses that
\TeX\ uses in displayed math formulas, in increasing order of size.
(Font \.{amathx} is shown on page 432 of {\sl The \TeX book}.)

An extensible character is specified by giving top, middle, bottom,
and repeatable characters that \TeX\ can string together to make
arbitrarily large delimiters. For example, the extensible left
parentheses in \.{amathx} are defined by
$$\.{extensible oct"060": oct"060", 0, oct"100", oct"102";}$$
this says that character code \oct{060} specifies an extensible
delimiter constructed from character number \oct{060} as the top piece,
character number \oct{100} as the bottom piece, and character number
\oct{102} as the piece that should be repeated as often as necessary to
reach a desired size. (In this particular example there is no ``middle''
piece, but characters like braces have a middle piece as well.)

Numeric parameters of a font are specified by saying, e.g.,
$$\.{fontdimen 3: 2.5, 6.5, 0, 4x}$$
which says that parameters 3--6 are to be 2.5, 6.5, zero, and $4x$,
respectively. These are the parameters that \TeX\ calls
\.{\char`\\fontdimen3} through \.{\char`\\fontdimen6}. Byte-valued
parameters in the \.{TFM} header are specified in a similar
way:
$$\.{headerbyte 33: 0, 214, 0, "c"}$$
says that bytes 33--36 of the header (which constitute the ninth
word, since there are four bytes per word) will be 0, 214, 0, and 99.
This can be used for various hacks; for example, it's possible to
override the normal check sum by specifying values of the first four
header bytes. Here is a conventional way to put the name of a font
family into the \.{TFM} header:
$$\vcenter{\halign{\tt#\hfil\cr
def BCPLstring(expr s,max)=\cr
\ \ for l:=if length(s)>max: max else: length(s) fi: l\cr
\ \ for n:=1 step 1 until l: , substring (n-1,n) of s endfor\cr
\ \ for n:=l+1 step 1 until max: , 0 endfor endfor enddef;\cr
def fontfamily expr s=headerbyte 49: BCPLstring(s,19) enddef;\cr
def codingscheme expr s=headerbyte 9: BCPLstring(s,39) enddef;\cr
fontfamily "HELVETICA"; codingscheme "XEROX TEXT";\cr}}$$

Ligatures and kerns are specified by little ``programs'' like the
following:
$$\vcenter{\halign{\tt#\hfil\cr
ligtable "f": "i" =: oct"200", "f" =: oct"201", "/": ")" kern 1.5;\cr
ligtable oct"201": "i" =: oct "202";\cr}}$$
Paraphrased, this cryptic code means:
If character `\.f' is followed by `\.i', replace those two
characters by number \oct{200}; if `\.f' is followed by another `\.f',
replace them both by character number \oct{201}; if `\.f' or `\./' is
followed by a right parenthesis, insert 1.5 points of space between them;
and if \oct{201} is followed by `\.i', replace those two characters by
\oct{202} (which presumably is the ligature `ffi').

A character code should not appear more than once in the following
places: (1)~As one of the bytes of a \.{charlist} that is followed
by a comma; (2)~as the byte in an \.{extensible} recipe that is
followed by a colon; (3)~as a byte in a \.{ligtable} that is
followed by a colon. Each of these usages is mutually exclusive;
for example, only the final character of a \.{charlist} can be
extensible or form a ligature.

\vfill\eject

\newsection Index to primitive tokens.

\medskip
\spaceskip=.16em
\def\\#1  {{\tt#1}\quad}
\line{\vtop{\halign{#\hfil\cr
\\"  1\cr
\\\#@  9\cr
\\\%  1\cr
\\\&  5\cr
\\*  7\cr
\\+  6, 7\cr
\\++{\rm,\thinspace}+-+  7\cr
\\,  7, 8, 12, 16, 20\cr
\\-  6, 7\cr
\\.  1\cr
\\..  5\cr
\\/  7\cr
\\:  12, 20\cr
\\:=  12, 14, 15, 16\cr
\\;  12, 14\cr
\\<  4\cr
\\<=  4\cr
\\<>  4\cr
\\=  4, 8, 11, 14, 17\cr
\\=:  20\cr
\\>  4\cr
\\>=  4\cr
\\@  9\cr
\\@\#  8, 9\cr
\\[  2, 3, 7\cr
\\\char`\\  8\cr
\\]  2, 3, 7\cr
\\\char`\{  5\cr
\\\char`\}  5\cr
\\addto  17\cr
\\also  17\cr
\\and  4, 5\cr
\\angle  6\cr
\\ASCII  6\cr
\\at  18\cr
\\atleast  5\cr
\\autorounding  16\cr
\\batchmode  18\cr
\\begingroup  3, 9, 14\cr
\\boolean  3\cr
\\char  5\cr
\\charcode  15\cr
\\chardp  15\cr
\\chardx  15\cr
\\chardy  15\cr
\\charexists  4\cr
\\charfam  15\cr
\\charht  15\cr
\\charic  15\cr
\\charlist  20\cr
\\charwd  15\cr
\\contour  17\cr
\\controls  5\cr
}}\hfil\vtop{\halign{#\hfil\cr
\\cosd  7\cr
\\cull  17\cr
\\curl  5\cr
\\cycle  4\cr
\\day  15\cr
\\decimal  5\cr
\\def  8\cr
\\delimiters  3\cr
\\designsize  15\cr
\\directiontime  6\cr
\\display  17\cr
\\doublepath  17\cr
\\dropping  17\cr
\\dump  19\cr
\\else  12\cr
\\elseif  12\cr
\\end  14\cr
\\enddef  8, 11\cr
\\endfor  12\cr
\\endgroup  3, 9, 14\cr
\\endinput  13\cr
\\errhelp  19\cr
\\errmessage  19\cr
\\errorstopmode  18\cr
\\everyjob  19\cr
\\exitif  12\cr
\\expandafter  13\cr
\\expr  8, 9\cr
\\extensible  20\cr
\\false  4\cr
\\fi  12\cr
\\floor  7\cr
\\fontdimen  20\cr
\\fontmaking  16\cr
\\for  12\cr
\\forever  12\cr
\\forsuffixes  12\cr
\\from  17\cr
\\granularity 16\cr
\\headerbyte  20\cr
\\hex  6\cr
\\hppp  15\cr
\\if  12\cr
\\inner  18\cr
\\input  13\cr
\\interim  16\cr
\\intersectiontimes  7\cr
\\inwindow  17\cr
\\keeping  17\cr
\\kern  20\cr
\\known  4\cr
\\jobname  5\cr
\\length  6\cr
}}\hfil\vtop{\halign{#\hfil\cr
\\let  16\cr
\\ligtable  20\cr
\\makepath  5\cr
\\makepen  6\cr
\\message  19\cr
\\mexp  7\cr
\\mlog  7\cr
\\month  15\cr
\\newinternal  19\cr
\\nonstopmode  18\cr
\\normaldeviate  6\cr
\\not  4\cr
\\nullpen  6\cr
\\nullpicture  5\cr
\\numeric  3\cr
\\numspecial  16\cr
\\oct  6\cr
\\odd  4\cr
\\of  5, 6, 7, 10\cr
\\openwindow  17\cr
\\or  4\cr
\\outer  18\cr
\\pair  3\cr
\\path  3\cr
\\pausing  15\cr
\\pen  3\cr
\\pencircle  6\cr
\\penoffset  7\cr
\\picture  3\cr
\\point  7\cr
\\postcontrol  7\cr
\\precontrol  7\cr
\\primary  9\cr
\\primarydef  8, 11\cr
\\proofing  15\cr
\\quote  8\cr
\\randomseed  19\cr
\\readstring  5\cr
\\reverse  5\cr
\\rotated  6\cr
\\save  16\cr
\\scaled  6\cr
\\scantokens  13\cr
\\scrollmode  19\cr
\\secondary  9\cr
\\secondarydef  8, 11\cr
\\shifted  6\cr
\\shipout  16\cr
\\show  18\cr
\\showdependencies  18\cr
\\showstats  18\cr
\\showstopping  16\cr
\\showtoken  18\cr
}}\hfil\vtop{\halign{#\hfil\cr
\\showvariable  18\cr
\\sind  7\cr
\\slanted  6\cr
\\smoothing  16\cr
\\special  16\cr
\\sqrt  7\cr
\\step  12\cr
\\str  5\cr
\\string  3\cr
\\subpath  5\cr
\\substring  5\cr
\\suffix  8\cr
\\tension  5\cr
\\tertiary  9\cr
\\tertiarydef  8, 11\cr
\\text  8\cr
\\time  15\cr
\\to  17\cr
\\totalweight  6\cr
\\tracingcapsules  15\cr
\\tracingchoices  15\cr
\\tracingcommands  15\cr
\\tracingedges  15\cr
\\tracingequations  15\cr
\\tracingmacros  15\cr
\\tracingonline  15\cr
\\tracingoutput  15\cr
\\tracingpens  15\cr
\\tracingspecs  15\cr
\\tracingstats  15\cr
\\tracingtitles  15\cr
\\transform  3\cr
\\transformed  6\cr
\\true  4\cr
\\turningcheck  16\cr
\\turningnumber 6\cr
\\uniformdeviate  7\cr
\\until  12\cr
\\vardef  8\cr
\\vppp  15\cr
\\warningcheck  16\cr
\\withpen  17\cr
\\withweight  17\cr
\\xpart  6\cr
\\xscaled  6\cr
\\xxpart  6\cr
\\xypart  6\cr
\\year  15\cr
\\ypart  6\cr
\\yscaled  6\cr
\\yxpart  6\cr
\\yypart  6\cr
\\zscaled  6\cr
}}}
\bye

\vfill\end
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