MirBSD manpage: 22.trofftut(USD)

A TROFF Tutorial                                         USD:22-1

                        A TROFF Tutorial

                       Brian W. Kernighan
               (updated for 4.3BSD by Mark Seiden)

                     AT&T Bell Laboratories
                  Murray Hill, New Jersey 07974


          troff is a text-formatting program for typesetting
     on the UNIX- operating system. This device  is  capable
     of  producing  high quality text; this paper is an
     example of troff output.

          The phototypesetter itself normally runs with
     four  fonts,  containing  roman,  italic  and bold
     letters (as on this page), a full greek  alphabet,
     and a substantial number of special characters and
     mathematical symbols. Characters can be printed in
     a range of sizes, and placed anywhere on the page.

          troff  allows  the  user  full  control  over
     fonts,  sizes, and character positions, as well as
     the usual features of a formatter  -  right-margin
     justification, automatic hyphenation, page titling
     and numbering, and so on. It also provides macros,
     arithmetic  variables  and  operations, and condi-
     tional testing, for complicated formatting tasks.

          This document is an introduction to the  most
     basic use of troff. It presents just enough infor-
     mation to enable the user to do simple  formatting
     tasks  like  making viewgraphs, and to make incre-
     mental changes to existing packages of troff  com-
     mands.  In most respects, the UNIX formatter nroff
     and  a  more  recent  version  (device-independent
     troff)  are  identical  to  the  version described
     here, so this document also serves as  a  tutorial
     for them as well.

-  UNIX  is a registered trademark of AT&T Bell Labora-
tories in the USA and other countries.

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1. Introduction

     troff [1] is a text-formatting program,  written  originally
by  J. F. Ossanna, for producing high-quality printed output from
the phototypesetter on the UNIX operating system.  This  document
is an example of troff output.

     The single most important rule of using troff is not to  use
it  directly,  but through some intermediary. In many ways, troff
resembles an assembly language - a remarkably powerful and flexi-
ble  one  -  but  nonetheless  such  that many operations must be
specified at a level of detail and in a form that is too hard for
most people to use effectively.

     For two special applications, there are programs  that  pro-
vide  an  interface  to  troff for the majority of users. eqn [2]
provides an easy to learn language for  typesetting  mathematics;
the  eqn  user need know no troff whatsoever to typeset mathemat-
ics. tbl [3] provides the same convenience for  producing  tables
of arbitrary complexity.

     For  producing  straight  text  (which  may   well   contain
mathematics  or  tables),  there are a number of `macro packages'
that define formatting rules and operations for  specific  styles
of documents, and reduce the amount of direct contact with troff.
In particular, the `-ms' [4], PWB/MM [5], and `-me' [6]  packages
for  internal  memoranda  and external papers provide most of the
facilities needed for a  wide  range  of  document  preparation.-
(This  memo  was  prepared  with `-ms'.) There are also
packages for viewgraphs, for simulating the older  roff
formatters,  and  for other special applications. Typi-
cally you will find these packages easier to  use  than
troff  once you get beyond the most trivial operations;
you should always consider them first.

     In the few cases where existing packages don't do the  whole
job,  the  solution  is not to write an entirely new set of troff
instructions from scratch, but to make  small  changes  to  adapt
packages that already exist.

     In accordance with this philosophy of letting  someone  else
do  the  work,  the  part of troff described here is only a small
part of the whole, although it tries to concentrate on  the  more
useful  parts.  In  any case, there is no attempt to be complete.
Rather, the emphasis is on showing how to do simple  things,  and
how  to make incremental changes to what already exists. The con-
tents of the remaining sections are:

  2.Point sizes and line spacing
  3.Fonts and special characters
- Most Berkeley Unix sites only have -ms and -me.

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  4.Indents and line length   5.Tabs   6.Local  motions:  Drawing
 lines   and  characters   7.Strings   8.Introduction  to  macros
  9.Titles, pages and numbering 10.Number  registers  and  arith-
 metic  11.Macros  with arguments 12.Conditionals 13.Environments
 14.Diversions    Appendix: Typesetter character set

The troff described here is the C-language version supplied  with
UNIX Version 7 and 32V as documented in [1].

     To use troff you have to prepare not only  the  actual  text
you want printed, but some information that tells how you want it
printed. (Readers who use roff will find the approach  familiar.)
For  troff  the  text  and  the  formatting information are often
intertwined quite intimately. Most commands to troff  are  placed
on  a line separate from the text itself, beginning with a period
(one command per line). For example,

     Some text.
     .ps 14
     Some more text.

will change the `point size', that is, the size  of  the  letters
being printed, to `14 point' (one point is 1/72 inch) like this:

     Some text. Some more text.

     Occasionally, though, something special occurs in the middle
of a line - to produce

     Area = i̅i̅r2

you have to type

     Area = \(*p\fIr\fR\|\s8\u2\d\s0

(which we will explain shortly). The  backslash  character  \  is
used  to introduce troff commands and special characters within a
line of text.

2. Point Sizes; Line Spacing

     As mentioned above, the command .ps sets the point size. One
point  is  1/72 inch, so 6-point characters are at most 1/12 inch
high, and 36-point characters are 1/2 inch. There  are  15  point
sizes, listed below.

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 6 point: Pack my box with five dozen liquor jugs.
 7 point: Pack my box with five dozen liquor jugs.
 8 point: Pack my box with five dozen liquor jugs.
 9 point: Pack my box with five dozen liquor jugs.
 10 point: Pack my box with five dozen liquor
 11 point: Pack my box with five dozen
 12 point: Pack my box with five dozen
 14 point: Pack my box with five

 16 point 18 point 20 point

 22 24 28 36

     If the number after .ps is not one of these legal sizes,  it
is  rounded  up to the next valid value, with a maximum of 36. If
no number follows .ps, troff reverts to the previous size,  what-
ever  it  was.  troff begins with point size 10, which is usually
fine. The original of this document (on 8.5 by 11 inch paper)  is
in 9 point.

     The point size can also be changed in the middle of  a  line
or even a word with the in-line command \s. To produce

     UNIX runs on a PDP-11/45


     \s8UNIX\s10 runs on a \s8PDP-\s1011/45

As above, \s should be followed by a  legal  point  size,  except
that  \s0 causes the size to revert to its previous value. Notice
that \s1011 can be understood correctly as `size 10, followed  by
an 11', if the size is legal, but not otherwise. Be cautious with
similar constructions.

     Relative size changes are also legal and useful:


temporarily decreases the size, whatever it is,  by  two  points,
then  restores  it. Relative size changes have the advantage that
the size difference is independent of the starting  size  of  the
document.  The  amount  of the relative change is restricted to a
single digit.

     The other parameter that determines what the type looks like
is  the  spacing between lines, which is set independently of the
point size. Vertical spacing is measured from the bottom  of  one
line  to  the bottom of the next. The command to control vertical
spacing is .vs. For running text, it is usually best to  set  the

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vertical  spacing  about  20% bigger than the character size. For
example, so far in this document, we have used ``9 on 11'',  that

     .ps 9
     .vs 11p

If we changed to

     .ps 9
     .vs 9p

the running text would look like this. After  a  few  lines,  you
will  agree it looks a little cramped. The right vertical spacing
is partly a matter of taste, depending on how much text you  want
to squeeze into a given space, and partly a matter of traditional
printing style. By default, troff uses 10 on 12.

     Point size and vertical spacing make a  substantial  differ-
ence in the amount of text per square inch. This is 12 on 14.

     Point size and vertical spacing make a  substantial  differ-
ence in the amount of text per square inch. For example, 10 on 12
uses about twice as much space as 7 on 8. This is 6 on  7,  which
is  even smaller. It packs a lot more words per line, but you can
go blind trying to read it.

     When used without arguments, .ps and .vs revert to the  pre-
vious size and vertical spacing respectively.

     The command .sp is used to get extra  vertical  space.  Una-
dorned, it gives you one extra blank line (one .vs, whatever that
has been set to). Typically, that's more or less than  you  want,
so  .sp  can  be followed by information about how much space you
want -

     .sp 2i

means `two inches of vertical space'.

     .sp 2p

means `two points of vertical space'; and

     .sp 2

means `two vertical spaces' - two of whatever .vs is set to (this
can  also  be  made explicit with .sp 2v); troff also understands
decimal fractions in most places, so

     .sp 1.5i

is a space of 1.5 inches. These same scale factors  can  be  used

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after .vs to define line spacing, and in fact after most commands
that deal with physical dimensions.

     It should be noted  that  all  size  numbers  are  converted
internally  to `machine units', which are 1/432 inch (1/6 point).
For most purposes, this is enough resolution that you don't  have
to  worry about the accuracy of the representation. The situation
is not quite so good vertically, where resolution is  1/144  inch
(1/2 point).

3. Fonts and Special Characters

     troff and the typesetter allow four different fonts  at  any
one time. Normally three fonts (Times roman, italic and bold) and
one collection of special characters are permanently mounted.

  abcdefghijklmnopqrstuvwxyz 0123456789
  abcdefghijklmnopqrstuvwxyz 0123456789
  abcdefghijklmnopqrstuvwxyz 0123456789

The greek, mathematical symbols and  miscellany  of  the  special
font are listed in Appendix A.

     troff prints in roman unless told otherwise. To switch  into
bold, use the .ft command

     .ft B

and for italics,

     .ft I

To return to roman, use .ft R; to return to  the  previous  font,
whatever  it  was,  use either .ft P or just .ft. The `underline'


causes the next input line to print in italics. .ul can  be  fol-
lowed  by  a  count  to indicate that more than one line is to be

     Fonts can also be changed within a line or word with the in-
line command \f:

     boldface text

is produced by

     \fBbold\fIface\fR text

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If you want to do this so the previous font, whatever it was,  is
left undisturbed, insert extra \fP commands, like this:

     \fBbold\fP\fIface\fP\fR text\fP

Because only the immediately previous  font  is  remembered,  you
have  to  restore  the previous font after each change or you can
lose it. The same is true of .ps and .vs  when  used  without  an

     There are other fonts available besides  the  standard  set,
although  you can still use only four at any given time. The com-
mand .fp tells troff what fonts are  physically  mounted  on  the

     .fp 3 H

says that the Helvetica font is mounted on position 3. (The  com-
plete list of font sizes and styles depends on your typesetter or
laser printer.) Appropriate .fp commands  should  appear  at  the
beginning of your document if you do not use the standard fonts.

     It is possible to make a document relatively independent  of
the  actual  fonts used to print it by using font numbers instead
of names; for example, \f3  and  .ft 3  mean  `whatever  font  is
mounted  at  position  3',  and thus work for any setting. Normal
settings are roman font on 1, italic on 2, bold on 3, and special
on 4.

     There is also a way to get `synthetic' bold fonts  by  over-
striking letters with a slight offset. Look at the .bd command in

     Special characters have four-character names beginning  with
\(, and they may be inserted anywhere. For example,

     1/4 + 1/2 = 3/4

is produced by

     \(14 + \(12 = \(34

In particular, greek letters are all of the form \(*-, where - is
an  upper  or  lower  case roman letter reminiscent of the greek.
Thus to get

     ≥̅((x|) -> oo

in bare troff we have to type

     \(*S(\(*a\(mu\(*b) \(-> \(if

That line is unscrambled as follows:

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     \(*S      ≥̅
     (         (
     \(*a      (
     \(mu      x
     \(*b      |
     )         )
     \(->      ->
     \(if      oo

A complete list of these special names occurs in Appendix A.

     In eqn [2] the same effect can be achieved with the input

     SIGMA ( alpha times beta ) -> inf

which is less concise, but clearer to the uninitiated.

     Notice that each four-character name is a  single  character
as far as troff is concerned - the `translate' command

     .tr \(mi\(em

is perfectly clear, meaning

     .tr --

that is, to translate - into -.

     Some characters are automatically  translated  into  others:
grave   `   and  acute   '  accents (apostrophes) become open and
close single quotes `'; the combination of ``...''  is  generally
preferable  to  the  double quotes "...". Similarly a typed minus
sign becomes a hyphen -. To print an explicit - sign, use \-.  To
get a backslash printed, use \e.

4. Indents and Line Lengths

     troff starts with a line length of 6.5  inches,  which  some
people  think  is  too  wide for 81/2x11 paper. To reset the line
length, use the .ll command, as in

     .ll 6i

As with .sp, the actual length can be specified in several  ways;
inches are probably the most intuitive.

     The maximum line length provided by the  typesetter  is  7.5
inches, by the way. To use the full width, you will have to reset
the default physical left margin (``page offset''), which is nor-
mally  slightly  less  than  one  inch  from the left edge of the
paper. This is done by the .po command.

     .po 0

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sets the offset as far to the left as it will go.

     The indent command .in causes the left margin to be indented
by  some  specified amount from the page offset. If we use .in to
move the left margin in, and .ll to move the right margin to  the
left, we can make offset blocks of text:

     .in 0.3i
     .ll -0.3i
     text to be set into a block
     .ll +0.3i
     .in -0.3i

will create a block that looks like this:

     Pater noster qui est in caelis sanctificetur nomen  tuum;
     adveniat  regnum tuum; fiat voluntas tua, sicut in caelo,
     et in terra. ... Amen.

Notice the use of `+' and `-' to specify the  amount  of  change.
These change the previous setting by the specified amount, rather
than just overriding it.  The  distinction  is  quite  important:
.ll +1i  makes  lines one inch longer; .ll 1i makes them one inch

     With .in, .ll and .po, the previous  value  is  used  if  no
argument is specified.

     To indent a single line, use the `temporary indent'  command
.ti.  For  example, all paragraphs in this memo effectively begin
with the command

     .ti 3

Three of what? The default unit for .ti, as for most horizontally
oriented  commands  (.ll, .in, .po), is ems; an em is roughly the
width of the letter `m' in the current point size. (Precisely,  a
em  in  size  p is p points.) Although inches are usually clearer
than ems to people who don't set type for a living,  ems  have  a
place:  they  are  a  measure of size that is proportional to the
current point size. If you want to make text that keeps its  pro-
portions  regardless  of  point  size, you should use ems for all
dimensions. Ems can be specified as scale factors directly, as in
.ti 2.5m.

     Lines can also be  indented  negatively  if  the  indent  is
already positive:

     .ti -0.3i

causes the next line to be moved back three tenths  of  an  inch.
Thus  to  make  a decorative initial capital, we indent the whole
paragraph, then move the letter `P' back with a .ti command:

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      ater noster qui est in caelis sanctificetur nomen  tuum;
        adveniat  regnum  tuum;  fiat  voluntas  tua, sicut in
     caelo, et in terra. ... Amen.

Of course, there is also some trickery to  make  the  `P'  bigger
(just a `\s36P\s0'), and to move it down from its normal position
(see the section on local motions).

5. Tabs

     Tabs (the ASCII `horizontal tab' character) can be  used  to
produce  output  in columns, or to set the horizontal position of
output. Typically tabs are used only in unfilled text. Tab  stops
are  set  by default every half inch from the current indent, but
can be changed by the .ta command. To set stops every  inch,  for

     .ta 1i 2i 3i 4i 5i 6i

     Unfortunately the stops are left-justified  only  (as  on  a
typewriter),  so lining up columns of right-justified numbers can
be painful. If you have many numbers, or if you need more compli-
cated table layout, don't use troff directly; use the tbl program
described in [3].

     For a handful of numeric columns, you can do  it  this  way:
Precede  every  number  by  enough blanks to make it line up when

     .ta 1i 2i 3i
       1 tab   2 tab   3
      40 tab  50 tab  60
     700 tab 800 tab 900

Then change each leading blank into the  string  \0.  This  is  a
character  that  does not print, but that has the same width as a
digit. When printed, this will produce

       1         2         3
      40        50        60
     700       800       900

     It is also possible to fill up tabbed-over space  with  some
character other than blanks by setting the `tab replacement char-
acter' with the .tc command:

     .ta 1.5i 2.5i
     .tc \(ru       (\(ru is "_")
     Name tab Age tab

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   Name___________ Age _____

To reset the tab replacement character to a blank, use  .tc  with
no  argument.  (Lines  can  also  be  drawn  with the \l command,
described in Section 6.)

     troff also provides a very general mechanism called `fields'
for  setting  up  complicated  columns. (This is used by tbl). We
will not go into it in this paper.

6. Local Motions: Drawing lines and characters

     Remember `Area = i̅i̅r2' and the big `P' in  the  Paternoster.
How  are they done? troff provides a host of commands for placing
characters of any size at any place. You can  use  them  to  draw
special  characters  or  to  tune  your  output  for a particular
appearance. Most of these commands are straightforward, but messy
to read and tough to type correctly.

     If you won't use eqn, subscripts and superscripts  are  most
easily  done  with  the  half-line local motions \u and \d. To go
back up the page half a point-size, insert a \u  at  the  desired
place;  to go down, insert a \d. (\u and \d should always be used
in pairs, as explained below.) Thus

     Area = \(*pr\u2\d


     Area = i̅i̅r2

To make the `2' smaller, bracket it with \s-2...\s0. Since \u and
\d  refer  to  the current point size, be sure to put them either
both inside or both outside the size changes, or you will get  an
unbalanced vertical motion.

     Sometimes the space given by  \u  and  \d  isn't  the  right
amount. The \v command can be used to request an arbitrary amount
of vertical motion. The in-line command


causes motion up or down the page  by  the  amount  specified  in
`(amount)'. For example, to move the `P' down, we used

  .in +0.6i (move paragraph in)
  .ll -0.3i (shorten lines)
  .ti -0.3i (move P back)
  \v'2'\s36P\s0\v'-2'ater noster qui est
  in caelis ...

A minus sign causes upward motion, while no sign or a  plus  sign

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means down the page. Thus \v'-2' causes an upward vertical motion
of two line spaces.

     There are many other ways to specify the amount of motion -


and so on are all legal. Notice that the scale specifier i  or  p
or  m  goes inside the quotes. Any character can be used in place
of the quotes; this is also true  of  all  other  troff  commands
described in this section.

     Since troff does not take within-the-line  vertical  motions
into  account  when  figuring out where it is on the page, output
lines can have unexpected positions if the left  and  right  ends
aren't  at  the  same vertical position. Thus \v, like \u and \d,
should always balance upward vertical motion in a line  with  the
same amount in the downward direction.

     Arbitrary horizontal motions are  also  available  -  \h  is
quite  analogous  to  \v, except that the default scale factor is
ems instead of line spaces. As an example,


causes a backwards motion of a tenth of an inch. As  a  practical
matter,  consider  printing  the  mathematical  symbol  `>>'. The
default spacing is too wide, so eqn replaces this by


to produce >>.

     Frequently \h is used with the `width function' \w  to  gen-
erate  motions  equal  to the width of some character string. The


is a number equal to the width of `thing' in machine units (1/432
inch). All troff computations are ultimately done in these units.
To move horizontally the width of an `x', we can say


As we mentioned above, the default scale factor for all  horizon-
tal  dimensions is m, ems, so here we must have the u for machine
units, or the motion produced will be far  too  large.  troff  is
quite  happy  with  the nested quotes, by the way, so long as you
don't leave any out.

     As a live example of this kind of construction, all  of  the

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command  names  in  the text, like .sp, were done by overstriking
with a slight offset. The commands for .sp are


That is, put out `.sp', move left by the  width  of  `.sp',  move
right 1 unit, and print `.sp' again. (Of course there is a way to
avoid typing that much input for each command name, which we will
discuss in Section 11.)

     There are also several special-purpose  troff  commands  for
local  motion.  We  have  already seen \0, which is an unpaddable
white space of the same width as a digit. `Unpaddable' means that
it  will never be widened or split across a line by line justifi-
cation and filling. There is also \(blank), which is  an  unpadd-
able  character  the  width  of  a  space, \|, which is half that
width, \^, which is one quarter of the width of a space, and  \&,
which  has  zero width. (This last one is useful, for example, in
entering a text line which would otherwise begin with a `.'.)

     The command \o, used like

     \o'set of characters'

causes (up to 9) characters to be  overstruck,  centered  on  the
widest. This is nice for accents, as in

  syst\o"e\(ga"me t\o"e\(aa"l\o"e\(aa"phonique

which makes

     syst`me t'l'phonique

The accents are \(ga and \(aa, or \` and \'; remember  that  each
is just one character to troff.

     You can make your own overstrikes with another special  con-
vention,  \z,  the zero-motion command. \zx suppresses the normal
horizontal motion after  printing  the  single  character  x,  so
another character can be laid on top of it. Although sizes can be
changed within \o, it centers the characters on the  widest,  and
there  can be no horizontal or vertical motions, so \z may be the
only way to get what you want:


is produced by

     .sp 2

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The .sp is needed to leave room for the result.

     As another example, an extra-heavy semicolon that looks like

     .  instead of  ;  or  ;

can be constructed with a big comma and a big period above it:


`0.25m' is an experimentally-derived constant.

     A more ornate overstrike is given by the bracketing function
\b, which piles up characters vertically, centered on the current
baseline. Thus we can get big brackets,  constructing  them  with
piled-up smaller pieces:

     | |
     | | x | |
           | |

by typing in only this:

\b'\(lt\(lk\(lb' \b'\(lc\(lf' x \b'\(rc\(rf' \b'\(rt\(rk\(rb'

     troff also provides a convenient facility for  drawing  hor-
izontal  and  vertical  lines  of arbitrary length with arbitrary
characters. \l'1i'  draws  a  line  one  inch  long,  like  this:
__________. The length can be followed by the character to use if
the _ isn't appropriate; \l'0.5i.'  draws  a  half-inch  line  of
dots:  ......  The  construction \L is entirely analogous, except
that it draws a vertical line instead of horizontal.

7. Strings

     Obviously if a paper contains a large number of  occurrences
of  an  acute accent over a letter `e', typing \o"e\'" for each '
would be a great nuisance.

     Fortunately, troff provides a way in which you can store  an
arbitrary  collection  of  text in a `string', and thereafter use
the string name as a shorthand for its contents. Strings are  one
of  several  troff mechanisms whose judicious use lets you type a
document with less effort and organize it so that extensive  for-
mat changes can be made with few editing changes.

     A reference to a string is replaced  by  whatever  text  the
string  was defined as. Strings are defined with the command .ds.
The line

     .ds e \o"e\'"

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defines the string e to have the value \o"e\'"

     String names may be either one or two characters  long,  and
are  referred  to by \*x for one character names or \*(xy for two
character names. Thus to get t'l'phone, given the  definition  of
the string e as above, we can say t\*el\*ephone.

     If a string must begin with blanks, define it as

     .ds xx "      text

The double quote signals the beginning of the  definition.  There
is no trailing quote; the end of the line terminates the string.

     A string may  actually  be  several  lines  long;  if  troff
encounters  a \ at the end of any line, it is thrown away and the
next line added to the current one. So you can make a long string
simply by ending each line but the last with a backslash:

     .ds xx this \
     is a very \
     long string

     Strings may be defined in terms of other strings, or even in
terms  of themselves; we will discuss some of these possibilities

8. Introduction to Macros

     Before we can go much further in troff, we need to  learn  a
bit  about  the  macro facility. In its simplest form, a macro is
just a shorthand notation quite similar to a string.  Suppose  we
want  every  paragraph  to start in exactly the same way - with a
space and a temporary indent of two ems:

     .ti +2m

Then to save typing, we would like to  collapse  these  into  one
shorthand line, a troff `command' like


that would be treated by troff exactly as

     .ti +2m

.PP is called a macro. The way we tell troff what .PP means is to
define it with the .de command:

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     .de PP
     .ti +2m

The first line names the macro (we used  `.PP'  for  `paragraph',
and  upper  case so it wouldn't conflict with any name that troff
might already know about). The last line .. marks the end of  the
definition.  In  between  is  the  text, which is simply inserted
whenever troff sees the `command' or macro call


A macro can contain any mixture of text and formatting commands.

     The definition of .PP has to precede its  first  use;  unde-
fined  macros  are simply ignored. Names are restricted to one or
two characters.

     Using macros for commonly occurring sequences of commands is
critically  important. Not only does it save typing, but it makes
later changes much easier. Suppose we decide that  the  paragraph
indent  is  too  small,  the  vertical space is much too big, and
roman font should be forced. Instead of changing the whole  docu-
ment, we need only change the definition of .PP to something like

     .de PP \" paragraph macro
     .sp 2p
     .ti +3m
     .ft R

and the change takes effect everywhere we used .PP.

     \" is a troff command that causes the rest of the line to be
ignored.  We  use it here to add comments to the macro definition
(a wise idea once definitions get complicated).

     As another example of macros, consider these two which start
and  end a block of offset, unfilled text, like most of the exam-
ples in this paper:

     .de BS \" start indented block
     .in +0.3i
     .de BE \" end indented block
     .in -0.3i

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Now we can surround text like

     Copy to
     John Doe
     Richard Roberts
     Stanley Smith

by the commands .BS and .BE, and it  will  come  out  as  it  did
above.  Notice that we indented by .in +0.3i instead of .in 0.3i.
This way we can nest our uses of .BS and BE to get blocks  within

     If later on we decide that the indent should be  0.5i,  then
it  is  only  necessary to change the definitions of .BS and .BE,
not the whole paper.

9. Titles, Pages and Numbering

     This is an area where things get tougher, because nothing is
done for you automatically. Of necessity, some of this section is
a cookbook, to be copied literally until you get some experience.

     Suppose you want a title at the top  of  each  page,  saying
left top center topright top
In roff, one can say

  .he 'left top'center top'right top'
  .fo 'left bottom'center bottom'right bottom'

to get headers and footers automatically  on  every  page.  Alas,
this  doesn't work so easily in troff, a serious hardship for the
novice. Instead you have to do a lot of specification (or  use  a
macro package, which makes it effortless).

     You have to say what the actual title  is  (easy);  when  to
print  it  (easy  enough); and what to do at and around the title
line (harder). Taking these in reverse order, first we  define  a
macro  .NP (for `new page') to process titles and the like at the
end of one page and the beginning of the next:

     .de NP
     'sp 0.5i
     .tl 'left top'center top'right top'
     'sp 0.3i

To make sure we're at the top of a page, we issue a `begin  page'
command  'bp,  which  causes a skip to top-of-page (we'll explain
the ' shortly). Then we space down half an inch, print the  title
(the use of .tl should be self explanatory; later we will discuss
parameterizing the titles), space another 0.3 inches,  and  we're

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     To ask for .NP at the bottom of each page, we  have  to  say
something  like `when the text is within an inch of the bottom of
the page, start the processing for a new page.' This is done with
a `when' command .wh:

     .wh  -1i  NP

(No `.' is used before NP; this is simply the name  of  a  macro,
not a macro call.) The minus sign means `measure up from the bot-
tom of the page', so `-1i' means `one inch from the bottom'.

     The .wh command appears in the input outside the  definition
of .NP; typically the input would be

     .de NP
     .wh -1i NP

     Now what happens? As text is actually  being  output,  troff
keeps  track  of  its  vertical position on the page, and after a
line is printed within one inch from the bottom, the .NP macro is
activated.  (In  the  jargon,  the .wh command sets a trap at the
specified place, which is `sprung' when that  point  is  passed.)
.NP  causes  a  skip to the top of the next page (that's what the
'bp was for), then prints the title with the appropriate margins.

     Why 'bp and 'sp instead of .bp and .sp? The answer  is  that
.sp  and  .bp, like several other commands, cause a break to take
place. That is, all the input text collected but not yet  printed
is  flushed  out  as soon as possible, and the next input line is
guaranteed to start a new line of output. If we had used  .sp  or
.bp  in  the .NP macro, this would cause a break in the middle of
the current output line when a new page is  started.  The  effect
would  be  to print the left-over part of that line at the top of
the page, followed by the next input line on a new  output  line.
This  is  not  what  we  want. Using ' instead of . for a command
tells troff that no break is to take  place  -  the  output  line
currently  being filled should not be forced out before the space
or new page.

     The list of  commands  that  cause  a  break  is  short  and

     .bp   .br   .ce   .fi   .nf   .sp   .in   .ti

All others cause no break, regardless of whether you use a . or a
'. If you really need a break, add a .br command at the appropri-
ate place.

     One other thing to beware of - if you're changing  fonts  or
point sizes a lot, you may find that if you cross a page boundary
in an unexpected font or size, your titles come out in that  size

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and font instead of what you intended. Furthermore, the length of
a title is independent of the current line length, so titles will
come  out  at  the default length of 6.5 inches unless you change
it, which is done with the .lt command.

     There are several ways to fix the problems  of  point  sizes
and fonts in titles. For the simplest applications, we can change
.NP to set the proper size and font for the title,  then  restore
the previous values, like this:

  .de NP
  'sp 0.5i
  .ft R   \" set title font to roman
  .ps 10  \" and size to 10 point
  .lt 6i  \" and length to 6 inches
  .tl 'left'center'right'
  .ps     \" revert to previous size
  .ft P   \" and to previous font
  'sp 0.3i

     This version of .NP does not work if the fields in  the  .tl
command  contain size or font changes. To cope with that requires
troff's `environment' mechanism, which we will discuss in Section

     To get a footer at the bottom of a page, you can modify  .NP
so  it  does some processing before the 'bp command, or split the
job into a footer macro invoked at the bottom margin and a header
macro  invoked  at the top of the page. These variations are left
as exercises.

     Output page numbers are computed automatically as each  page
is  produced  (starting  at 1), but no numbers are printed unless
you ask for them explicitly. To get page numbers printed, include
the  character  %  in the .tl line at the position where you want
the number to appear. For example

     .tl ''- % -''

centers the page number inside hyphens, as on this page. You  can
set  the page number at any time with either .bp n, which immedi-
ately starts a new page numbered n, or with .pn n, which sets the
page number for the next page but doesn't cause a skip to the new
page. Again, .bp +n sets the page  number  to  n  more  than  its
current value; .bp means .bp +1.

10. Number Registers and Arithmetic

     troff has a facility for doing arithmetic, and for  defining
and using variables with numeric values, called number registers.

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Number registers, like strings and macros, can be useful in  set-
ting  up  a document so it is easy to change later. And of course
they serve for any sort of arithmetic computation.

     Like strings, number registers have  one  or  two  character
names.  They  are set by the .nr command, and are referenced any-
where by \nx (one character name) or \n(xy (two character name).

     There are quite a few  pre-defined  number  registers  main-
tained by troff, among them % for the current page number; nl for
the current vertical position on the page; dy, mo and yr for  the
current  day,  month and year; and .s and .f for the current size
and font. (The font is a number from 1 to 4.) Any of these can be
used  in  computations like any other register, but some, like .s
and .f, cannot be changed with .nr.

     As an example of the use of number  registers,  in  the  -ms
macro  package  [4],  most  significant parameters are defined in
terms of the values of  a  handful  of  number  registers.  These
include  the  point  size for text, the vertical spacing, and the
line and title lengths. To set the point size and vertical  spac-
ing for the following paragraphs, for example, a user may say

     .nr PS 9
     .nr VS 11

The paragraph macro .PP is defined (roughly) as follows:

     .de PP
     .ps \\n(PS\" reset size
     .vs \\n(VSp\" spacing
     .ft R     \" font
     .sp 0.5v  \" half a line
     .ti +3m

This sets the font to Roman and the point size and  line  spacing
to whatever values are stored in the number registers PS and VS.

     Why are there two backslashes? This is the  eternal  problem
of  how  to  quote a quote. When troff originally reads the macro
definition, it peels off one backslash to see what's coming next.
To  ensure  that another is left in the definition when the macro
is used, we have to put in two backslashes in the definition.  If
only  one backslash is used, point size and vertical spacing will
be frozen at the time the macro is defined, not when it is used.

     Protecting by an extra layer of backslashes is  only  needed
for  \n,  \*,  \$  (which  we haven't come to yet), and \ itself.
Things like \s, \f, \h, \v, and  so  on  do  not  need  an  extra
backslash,  since they are converted by troff to an internal code
immediately upon being seen.

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     Arithmetic expressions can appear anywhere that a number  is
expected. As a trivial example,

     .nr PS \\n(PS-2

decrements PS by 2. Expressions can use the arithmetic  operators
+,  -,  *,  /, % (mod), the relational operators >, >=, <, <=, =,
and != (not equal), and parentheses.

     Although the  arithmetic  we  have  done  so  far  has  been
straightforward,  more  complicated  things  are somewhat tricky.
First, number registers hold only integers. troff arithmetic uses
truncating  integer  division,  just like Fortran. Second, in the
absence of parentheses, evaluation is done left-to-right  without
any operator precedence (including relational operators). Thus


becomes `-1'. Number registers can occur anywhere in  an  expres-
sion, and so can scale indicators like p, i, m, and so on (but no
spaces). Although integer division causes truncation, each number
and  its  scale  indicator  is  converted to machine units (1/432
inch) before any arithmetic is done, so 1i/2u evaluates  to  0.5i

     The scale indicator u often has to appear when you  wouldn't
expect  it  -  in  particular, when arithmetic is being done in a
context that implies horizontal or vertical dimensions. For exam-

     .ll 7/2i

would seem obvious enough - 31/2 inches. Sorry. Remember that the
default  units for horizontal parameters like .ll are ems. That's
really `7 ems / 2  inches',  and  when  translated  into  machine
units, it becomes zero. How about

     .ll 7i/2

Sorry, still no good - the `2' is `2 ems', so  `7i/2'  is  small,
although not zero. You must use

     .ll 7i/2u

So again, a safe rule is to attach a  scale  indicator  to  every
number, even constants.

     For arithmetic done within a .nr command, there is no impli-
cation  of horizontal or vertical dimension, so the default units
are `units', and 7i/2 and 7i/2u mean the same thing. Thus

     .nr ll 7i/2
     .ll \\n(llu

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does just what you want, so long as you don't forget the u on the
.ll command.

11. Macros with arguments

     The next step is to define macros that can change  from  one
use to the next according to parameters supplied as arguments. To
make this work, we need two things: first,  when  we  define  the
macro, we have to indicate that some parts of it will be provided
as arguments when the macro is called. Then  when  the  macro  is
called we have to provide actual arguments to be plugged into the

     Let us illustrate by defining a macro .SM  that  will  print
its  argument  two points smaller than the surrounding text. That
is, the macro call

     .SM TROFF

will produce TROFF.

     The definition of .SM is

     .de SM

Within a macro definition, the symbol  \\$n  refers  to  the  nth
argument  that the macro was called with. Thus \\$1 is the string
to be placed in a smaller point size when .SM is called.

     As a slightly more complicated version, the following defin-
ition  of  .SM  permits  optional second and third arguments that
will be printed in the normal size:

     .de SM

Arguments not provided when the macro is called  are  treated  as
empty, so

     .SM  TROFF  ),

produces TROFF), while

     .SM  TROFF  ).  (

produces (TROFF). It is convenient to reverse the order of  argu-
ments because trailing punctuation is much more common than lead-

     By the way, the number of arguments that a macro was  called
with is available in number register .$.

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     The following macro .BD is the one used to  make  the  `bold
roman'  we  have  been  using for troff command names in text. It
combines horizontal motions,  width  computations,  and  argument

  .de BD

The \h and \w commands need no extra backslash, as  we  discussed
above. The \& is there in case the argument begins with a period.

     Two backslashes are needed with the \\$n  commands,  though,
to protect one of them when the macro is being defined. Perhaps a
second example will make this clearer. Consider  a  macro  called
.SH  which  produces  section  headings rather like those in this
paper, with the sections numbered automatically, and the title in
bold in a smaller size. The use is

     .SH  "Section title ..."

(If the argument to a macro is to contain blanks, then it must be
surrounded  by  double  quotes,  unlike  a string, where only one
leading quote is permitted.)

     Here is the definition of the .SH macro:

     .nr SH 0   \" initialize section number
     .de SH
     .sp 0.3i
     .ft B
     .nr SH \\n(SH+1\" increment number
     .ps \\n(PS-1\" decrease PS
     \\n(SH.  \\$1\" number. title
     .ps \\n(PS \" restore PS
     .sp 0.3i
     .ft R

The section number is kept in number register SH, which is incre-
mented  each  time just before it is used. (A number register may
have the same name as a macro without conflict but a  string  may

     We used \\n(SH instead of \n(SH and \\n(PS instead of \n(PS.
If  we  had used \n(SH, we would get the value of the register at
the time the macro was defined, not at the time it was  used.  If
that's  what  you  want,  fine, but not here. Similarly, by using
\\n(PS, we get the point size at the time the macro is called.

     As an example that does not involve numbers, recall our  .NP
macro which had a

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     .tl 'left'center'right'

We could make these into parameters by using instead

     .tl '\\*(LT'\\*(CT'\\*(RT'

so the title comes from three strings called LT, CT  and  RT.  If
these are empty, then the title will be a blank line. Normally CT
would be set with something like

     .ds  CT  - % -

to give just the page number between hyphens (as on  the  top  of
this  page),  but a user could supply private definitions for any
of the strings.

12. Conditionals

     Suppose we want the .SH macro to leave two extra  inches  of
space  just  before section 1, but nowhere else. The cleanest way
to do that is to test inside the .SH macro  whether  the  section
number  is  1,  and add some space if it is. The .if command pro-
vides the conditional test that we can add just before the  head-
ing line is output:

    .if \\n(SH=1 .sp 2i   \" first section only

     The condition after the .if can be any arithmetic or logical
expression. If the condition is logically true, or arithmetically
greater than zero, the rest of the line is treated as if it  were
text  -  here  a  command.  If the condition is false, or zero or
negative, the rest of the line is skipped.

     It is possible to do more than one command if a condition is
true. Suppose several operations are to be done before section 1.
One possibility is to define a macro .S1 and invoke it if we  are
about to do section 1 (as determined by an .if).

     .de S1
     ---  processing for section 1 ---
     .de SH
     .if \\n(SH=1 .S1

     An alternate way is to use the extended  form  of  the  .if,
like this:

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     .if \\n(SH=1 \{--- processing
     for section 1 ----\}

The braces \{ and \} must occur in the  positions  shown  or  you
will  get  unexpected extra lines in your output. troff also pro-
vides an `if-else' construction, which we will not go into here.

     A condition can be negated by preceding it with  !;  we  get
the same effect as above (but less clearly) by using

     .if !\\n(SH>1 .S1

     There are a handful of other conditions that can  be  tested
with .if. For example, is the current page even or odd?

     .if o .tl 'odd page title''- % -'
     .if e .tl '- % -''even page title'

gives facing pages different titles and page numbers on the  out-
side edge when used inside an appropriate new page macro.

     Two other conditions are t and n, which tell you whether the
formatter is troff or nroff.

     .if t troff stuff ...
     .if n nroff stuff ...

     Finally, string comparisons may be made in an .if:

     .if  'string1'string2'  stuff

does `stuff' if string1 is the same  as  string2.  The  character
separating  the  strings  can  be anything reasonable that is not
contained in either string. The strings themselves can  reference
strings with \*, arguments with \$, and so on.

13. Environments

     As we mentioned, there is a  potential  problem  when  going
across  a page boundary: parameters like size and font for a page
title may well be different from those in effect in the text when
the  page  boundary  occurs. troff provides a very general way to
deal with this and similar situations. There are three  `environ-
ments', each of which has independently settable versions of many
of the parameters associated  with  processing,  including  size,
font,  line  and  title lengths, fill/nofill mode, tab stops, and
even partially collected lines. Thus the titling problem  may  be
readily solved by processing the main text in one environment and
titles in a separate one with its own suitable parameters.

     The command .ev n shifts to environment n; n must be 0, 1 or

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2.  The  command  .ev  with  no  argument returns to the previous
environment. Environment names are  maintained  in  a  stack,  so
calls  for  different environments may be nested and unwound con-

     Suppose we say that the main text is processed  in  environ-
ment  0,  which  is  where  troff  begins by default. Then we can
modify the new page macro .NP to process titles in environment  1
like this:

  .de NP
  .ev 1  \" shift to new environment
  .lt 6i \" set parameters here
  .ft R
  .ps 10
  ... any other processing ...
  .ev    \" return to previous environment

It is also possible to initialize the parameters for an  environ-
ment  outside  the .NP macro, but the version shown keeps all the
processing in one place and is  thus  easier  to  understand  and

14. Diversions

     There are numerous occasions  in  page  layout  when  it  is
necessary  to  store some text for a period of time without actu-
ally printing it. Footnotes are the  most  obvious  example:  the
text of the footnote usually appears in the input well before the
place on the page where it is to be printed is reached. In  fact,
the  place  where it is output normally depends on how big it is,
which implies that there must be a way to process the footnote at
least enough to decide its size without printing it.

     troff provides a mechanism called a diversion for doing this
processing.  Any  part of the output may be diverted into a macro
instead of being printed, and then at some  convenient  time  the
macro may be put back into the input.

     The command .di xy begins a diversion - all subsequent  out-
put  is collected into the macro xy until the command .di with no
arguments is encountered. This terminates the diversion. The pro-
cessed text is available at any time thereafter, simply by giving
the command


The vertical size of the last finished diversion is contained  in
the built-in number register dn.

     As a simple example, suppose we want to implement  a  `keep-
release' operation, so that text between the commands .KS and .KE
will not be split across a page boundary  (as  for  a  figure  or

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table).  Clearly,  when  a  .KS  is encountered, we have to begin
diverting the output so we can find out how big it is. Then  when
a  .KE  is  seen, we decide whether the diverted text will fit on
the current page, and print it either there if it fits, or at the
top of the next page if it doesn't. So:

  .de KS\" start keep
  .br   \" start fresh line
  .ev 1 \" collect in new environment
  .fi   \" make it filled text
  .di XX\" collect in XX

  .de KE\" end keep
  .br   \" get last partial line
  .di   \" end diversion
  .if \\n(dn>=\\n(.t .bp   \" bp if doesn't fit
  .nf   \" bring it back in no-fill
  .XX   \" text
  .ev   \" return to normal environment

Recall that number register nl is the  current  position  on  the
output page. Since output was being diverted, this remains at its
value when the diversion started. dn is the amount of text in the
diversion;  .t (another built-in register) is the distance to the
next trap, which we assume is at the bottom margin of  the  page.
If  the diversion is large enough to go past the trap, the .if is
satisfied, and a .bp is issued. In either case, the diverted out-
put  is  then  brought back with .XX. It is essential to bring it
back in no-fill mode so troff will do no  further  processing  on

     This is not the most general keep-release, nor is it  robust
in  the face of all conceivable inputs, but it would require more
space than we have here to write it in full generality. This sec-
tion is not intended to teach everything about diversions, but to
sketch out enough that you can read existing macro packages  with
some comprehension.


     I am deeply indebted to J. F. Ossanna, the author of  troff,
for his repeated patient explanations of fine points, and for his
continuing willingness to adapt troff to make other uses  easier.
I  am also grateful to Jim Blinn, Ted Dolotta, Doug McIlroy, Mike
Lesk and Joel Sturman for helpful comments on this paper.


[1]  J. F. Ossanna, NROFF/TROFF User's Manual, Bell  Laboratories
     Computing   Science   Technical   Report   54,   1976.   The

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     21.troff(USD) paper.

[2]  B. W. Kernighan, A  System  for  Typesetting  Mathematics  -
     User's  Guide  (Second Edition), Bell Laboratories Computing
     Science Technical Report 17, 1977.

[3]  M. E. Lesk, TBL - A Program to Format Tables,  Bell  Labora-
     tories Computing Science Technical Report 49, 1976.

[4]  M. E. Lesk, Typing Documents  on  UNIX,  Bell  Laboratories,

[5]  J. R. Mashey and D. W. Smith, PWB/MM  -  Programmer's  Work-
     bench Memorandum Macros, Bell Laboratories internal memoran-

[6]  Eric P. Allman, Writing Papers with NROFF using -me, Univer-
     sity of California, Berkeley.

 *   The nroff(1) manual page.

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Appendix A: Phototypesetter Character Set (APS-5)

These characters exist in roman, italic, and bold. To get the one
on the left, type the four-character name on the right.

     ff      \(ff    fi      \(fi    fl      \(fl    ffi     \(Fiffl\(Fl
     _ \(ru  - \(em  1/4     \(14    1/2     \(12    3/4     \(34
     (C)     \(co      \(de  - \(dg  ' \(fm  / \(ct
     (R)     \(rg    + \(bu  []      \(sq    - \(hy
                     (In bold, \(sq is [].)

The following are special-font characters:

     +  \(pl   -  \(mi   x  \(mu   -  \(di
     =  \(eq   _  \(==   ≥  \(>=   ≤  \(<=
     /  \(!=   ±  \(+-      \(no   /  \(sl
     ~  \(ap    ̅  \(~=   oc \(pt   \̅/̅ \(gr
     -> \(->   <- \(<-   ^  \(ua   v  \(da
        \(is   `  \(pd   oo \(if   /  \(sr
     (= \(sb   =) \(sp   (̅)̅ \(cu   _)_ \(ca
     (_ \(ib   _) \(ip   -  \(mo   /  \(es
     '  \(aa   `  \(ga   O  \(ci      \(bs
     S  \(sc   =  \(dd   <= \(lh   => \(rh
     |  \(lt   |  \(rt   |  \(lc   |  \(rc
     |  \(lb   |  \(rb   |  \(lf   |  \(rf
     |  \(lk   |  \(rk   |  \(bv      \(ts
     |  \(br   |  \(or   _  \(ul   ~  \(rn
     *  \(**

These four characters also have two-character names. The ' is the
apostrophe on terminals; the ` is the other quote mark.

     '  \'     `  \`     -  \-     _  \_

These characters exist only on the special font, but they do  not
have four-character names:

     "      {      }      <      >      ~      ^      \      #      @

For greek, precede the roman letter by \(* to get the correspond-
ing greek; for example, \(*a is (.



                        December 24, 2022

USD:22-30                                        A TROFF Tutorial

Index                              changing fonts (^ft, #f) 5
                                   changing macros 15
! (negating conditionals) 17       character set 4,5,19
#$ (macro argument) 16             character translation (^tr) 2,6
#*x, #(xy (invoke string macro) 14 columnated output 10
#b (bracketing function) 13        commands 1
#d (subscript) 11                  commands that cause break 9
#f (font change) 5                 conditionals (^if) 16
#h (horizontal motion) 12          constant proportion 7
#nx, #n(xy (number register) 15    default break list 9
#o (overstrike) 13                 define macro (^de) 7
#s (size change) 3                 define string macro (^ds) 14
#u (superscript) 11                drawing lines 11
#v (vertical motion) 11            em 7,11
#w (width function) 12             end of macro (^^) 7
#z (zero motion) 13                even page test (e) 17
'command instead of ^command 9     fill (^fi) 2
% (page number register) 10,15     fonts (^ft) 4,19
^^ (end of macro definition) 7     Greek (#(*-) 5,19
^bp 9,10                           hanging indent (^ti) 12
^br (break) 9                      hints 20
^ce (center) 2                     horizontal motion (#h) 12
^ds (define string macro) 7,14     hp (horizontal position register) 15
^fi (fill) 2                       hyphen 6
^ft (change font) 5                i scale indicator 4
^if (conditional test) 16          indent (^in) 6
^in (indent) 6                     index 21
^lg (set ligatures 5               italic font (.ft I) 4
^ll (line length) 6                italicize (^ul) 6
^nf (nofill) 2                     legal point sizes 3
^nr (set number register) 14       ligatures (ff,fi,fl; ^lg) 5
^pn (page number) 10               line length (^ll) 6
^ps (change point size) 1,3        line spacing (^vs) 3
^sp (space) 4                      local motions (#u,#d,#v,#h,#w,#o,#z,#b) 11 ff
^ss (set space size) 10            m scale indicator 7
^ta (set tab stops) 11             machine units 4,12
^tc (set tab character) 10         macro arguments 15
^tl (title) 9                      macros 7
^tr (translate characters) 2,6     macros that change 15
^ul (italicize) 6                  multiple backslashes 14
^vs (vertical spacing) 3           negating conditionals (!) 17
^wh (when conditional) 9,17        new page macro (NP) 8
accents 6,13                       nl (current vertical position register) 15
apostrophes 6                      nofill (^nf) 2
arithmetic 15                      NROFF test (n) 17
backslash 1,3,5,14,16              nested quotes 12
begin page (^bp) 9                 number registers (^nr,#n) 14
block macros (B1,B2) 8             numbered paragraphs 12
bold font (.ft B) 5                odd page test (o) 17
boustrophedon 12                   order of evaluation 14
bracketing function (##b) 13       overstrike (#o) 13
break (^br) 9                      p scale indicator 3
break-causing commmands 9          page number register (%) 10
centering (^ce) 2                  page numbers (^pn, ^bp) 10

                        December 24, 2022

A TROFF Tutorial                                        USD:22-31

paragraph macro (PG) 7  Pater-
noster  6 point size (^ps) 1,3
previous font (#fP, ^ft  P)  5
previous  point size (#s0,^ps)
3 quotes 6 relative change (±)
6   ROFF  1  ROFF  header  and
footer 8 Roman font (.ft R)  4
scale   indicator  i  4  scale
indicator m 7 scale  indicator
p 3 scale indicator u 12 scale
indicators  in  arithmetic  15
section  heading macro (SC) 15
set space size (^ss) 10 size _
see  point  size space (^sp) 4
space between  lines  (^vs)  3
special characters (#(xx) 5,19
string macros (^ds,#*) 14 sub-
scripts  (#d)  11 superscripts
(#u) 11 tab character (^tc) 11
tabs (^ta) 10 temporary indent
(^ti)   7   titles   (^tl)   8
translate  (^tr)  2,6,12 TROFF
examples 19 TROFF test (t)  17
truncating  division  15  type
faces  _  see  fonts  u  scale
indicator 12 underline (^ul) 6
valid point sizes  3  vertical
motion  (#v) 11 vertical posi-
tion on page 9 vertical  spac-
ing  (^vs)  3  when (^wh) 9,17
width function (#w)  12  width
of  digits 10 zero motion (#z)

                        December 24, 2022

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