4 @c A menu is needed before every deeper *section nesting of @nodes
5 @c Run M-x texinfo-all-menus-update
6 @c to automagically fill in these menus
7 @c before saving changes
11 @chapter Advanced Topics
14 When translating the input to notation, there are number of distinct
15 phases. We list them here:
17 @c todo: moved from refman.
19 The purpose of LilyPond is explained informally by the term `music
20 typesetter'. This is not a fully correct name: not only does the
21 program print musical symbols, it also makes aesthetic decisions.
22 Symbols and their placements are @emph{generated} from a high-level
23 musical description. In other words, LilyPond would be best described
24 by `music compiler' or `music to notation compiler'.
26 LilyPond is linked to GUILE, GNU's Scheme library for extension
27 programming. The Scheme library provides the glue that holds together
28 the low-level routines and separate modules which are written in C++.
30 When lilypond is run to typeset sheet music, the following happens:
32 @item GUILE Initialization: various scheme files are read
33 @item parsing: first standard @code{ly} initialization files are read, and
34 then the user @file{ly} file is read.
35 @item interpretation: the music in the file is processed ``in playing
36 order'', i.e. the order that you use to read sheet music, or the
37 order in which notes are played. The result of this step is a typesetting
41 The typesetting specification is solved: positions and formatting is
44 @item the visible results ("virtual ink") are written to the output file.
47 During these stages different types of data play the the main role:
48 during parsing, @strong{Music} objects are created. During the
49 interpretation, @strong{contexts} are constructed, and with these
50 contexts a network of @strong{graphical objects} (``grobs'') is
51 created. These grobs contain unknown variables, and the network forms a
52 set of equations. After solving the equations and filling in these
53 variables, the printed output is written to an output file.
55 These threemanship of tasks (parsing, translating, typesetting) and
56 data-structures (music, context, graphical objects) permeates the entire
57 design of the program.
65 The LY file is read, and converted to a list of @code{Scores}, which
66 each contain @code{Music} and paper/midi-definitions. Here @code{Music},
67 @code{Pitch} and @code{Duration} objects are created.
69 @item Interpreting music
70 @cindex interpreting music
72 All music events are "read" in the same order as they would be played
73 (or read from paper). At every step of the interpretation, musical
74 events are delivered to
75 interpretation contexts,
77 which use them to build @code{Grob}s (or MIDI objects, for MIDI output).
79 In this stage @code{Music_iterators} do a traversal of the @code{Music}
80 structure. The music events thus encountered are reported to
81 @code{Translator}s, a set of objects that collectively form interpretation
89 At places where line breaks may occur, clefs and bars are prepared for
90 a possible line break.
96 In this stage, all information that is needed to determine line breaking
99 @item Break calculation:
101 The lines and horizontal positions of the columns are determined.
105 Relations between all grobs are modified to reflect line breaks: When a
106 spanner, e.g. a slur, crosses a line-break, then the spanner is "broken
107 into pieces", for every line that the spanner is in, a copy of the grob
108 is made. A substitution process redirects all grob-reference so that
109 each spanner grob will only reference other grobs in the same line.
113 All vertical dimensions and spanning objects are computed, and all grobs
114 are output, line by line. The output is encoded in the form of
119 The data types that are mentioned here are all discussed in this
124 @c FIXME: Note entry vs Music entry at top level menu is confusing.
128 * Interpretation context::
129 * Syntactic details::
133 @c . {Output formats}
135 @section Output formats
137 LilyPond can output processed music in different output formats. They
138 can be used by invoking lilypond directly, i.e. not through ly2dvi,
139 and supplying the @code{-f} command line option. See also
140 @ref{Invoking LilyPond}.
144 * PostScript output::
146 * ASCIIScript output::
151 @subsection @TeX{} output
152 @cindex @TeX{} output
154 LilyPond will use @TeX{} by default. Even if you want to produce
155 PostScript output for viewing or printing, you should normally have
156 LilyPond produce @TeX{} first. The .tex output must be processed by
157 @TeX{} (@strong{not} La@TeX{}) to generate a .dvi. Then, @file{Dvips}
158 is used to generate PostScript. Alternatively, @file{ly2dvi} can be
159 used to generate the .dvi for you.
163 Titling is not generated unless you use @file{ly2dvi}.
166 @node PostScript output
167 @subsection PostScript output
168 @cindex PostScript output
169 @cindex direct PostScript output
171 LilyPond can produce PostScript directly, without going through @TeX{}.
172 Currently, this is mainly useful if you cannot use TeX, because direct
173 PostScript output has some problems; see Bugs below.
176 $ lilypond -fps foo.ly
178 Now processing: `foo.ly'
180 Interpreting music...[3]
181 Preprocessing elements...
182 Calculating column positions...
183 paper output to foo.ps...
185 $ cat /usr/share/lilypond/pfa/feta20.pfa foo.ps | lpr
191 Text font selection is broken.
193 The .ps file does not contain the .pfa font files. To print a .ps
194 created through direct postscript output, you should prepend the
195 necessary .pfa files to LilyPond's .ps output, or upload them to the
196 printer before printing.
198 The line height calculation is broken, you must set @var{lineheight} in
199 the paperblock if you have more than one staff in your score, e.g.
204 % Set line height to 40 staff spaces
210 @subsection Scheme output
211 @cindex Scheme output
213 In the typesetting stage, LilyPond builds a page description, which is
214 then written to disk in postscript, @TeX{} or ASCII art. Before it is
215 written, the page description is represented as Scheme expressions. You
216 can also dump these Scheme expressions to a file, which may be
217 convenient for debugging output routines. This is done with the Scheme
221 $ lilypond -fscm foo.ly
223 Now processing: `foo.ly'
225 Interpreting music...[3]
226 Preprocessing elements...
227 Calculating column positions...
228 paper output to foo.scm...
231 ;;; Usage: guile -s x.scm > x.tex
232 (primitive-load-path 'standalone.scm)
236 $ guile -s foo.scm > foo.tex
240 @node ASCIIScript output
241 @subsection ASCIIScript output
242 @cindex ASCIIScript output
246 LilyPond can output ASCII Art. This is a two step process, LilyPond
247 produces an ASCII description file, dubbed ASCIIScript (extension
248 @file{.as}). ASCIIScript has a small and simple command set that
249 includes font selection, character and string printing and line drawing
250 commands. The program @file{as2text} is used to translate an .as file
253 To produce ASCII Art, you must include an ASCII Art paper definition
254 file in your .ly, one of:
256 \include "paper-as5.ly"
257 \include "paper-as9.ly"
260 Here's an example use for ASCII Art output (the example file
261 @file{as-email.ly} is included in the LilyPond distribution), the staff
262 symbol has been made invisible:
265 $ lilypond -fas as-email.ly
267 Now processing: `as-email.ly'
269 Interpreting music...[3]
270 Preprocessing elements...
271 Calculating column positions... [2]
272 paper output to as-email.as...
274 $ as2text as-email.as 2>/dev/null
277 /| | | | | |\ |\ |\ |\ |\ |
278 / |_ 3 | | | | 5 | )| )| )| )| )|
279 | /| \ 8 * * * | 8 * * * * * |
289 The ASCII Art fonts are far from complete and not very well designed.
290 It's easy to change the glyphs, though; if you think you can do better,
291 have a look at @file{mf/*.af}.
293 Lots of resizable symbols such as slurs, ties and tuplets are missing.
295 The poor looks of most ASCII Art output and its limited general
296 usefulness gives ASCII Art output a low priority; it may be
297 dropped in future versions.
301 @subsection Sketch output
303 @uref{http://sketch.sourceforge.net,Sketch} is a Free vector drawing
304 program. LilyPond includes bare bones output for Sketch version
308 @cindex vector drawing
309 @cindex drawing program
312 @node Interpretation context
313 @section Interpretation context
316 * Creating contexts::
318 * Context properties::
319 * Engravers and performers::
320 * Changing context definitions::
321 * Defining new contexts::
325 Interpretation contexts are objects that only exist during a run of
326 LilyPond. During the interpretation phase of LilyPond (when it prints
327 "interpreting music"), the music expression in a @code{\score} block is
328 interpreted in time order. This is the same order that humans hear and
331 During this interpretation, the interpretation context holds the
332 state for the current point within the music. It contains information
336 @item What notes are playing at this point?
337 @item What symbols will be printed at this point?
338 @item What is the current key signature, time signature, point within
342 Contexts are grouped hierarchically: A @internalsref{Voice} context is
343 contained in a @internalsref{Staff} context (because a staff can contain
344 multiple voices at any point), a @internalsref{Staff} context is contained in
345 @internalsref{Score}, @internalsref{StaffGroup}, or @internalsref{ChoirStaff} context.
347 Contexts associated with sheet music output are called @emph{notation
348 contexts}, those for sound output are called @emph{performance
349 contexts}. The default definitions of the standard notation and
350 performance contexts can be found in @file{ly/engraver-init.ly} and
351 @file{ly/performer-init.ly}, respectively.
353 @node Creating contexts
354 @subsection Creating contexts
356 @cindex @code{\context}
357 @cindex context selection
359 Contexts for a music expression can be selected manually, using the
360 following music expression.
363 \context @var{contexttype} [= @var{contextname}] @var{musicexpr}
366 This instructs lilypond to interpret @var{musicexpr} within the context
367 of type @var{contexttype} and with name @var{contextname}. If this
368 context does not exist, it will be created.
370 @lilypond[verbatim,singleline]
372 \notes \relative c'' {
373 c4 <d4 \context Staff = "another" e4> f
379 In this example, the @code{c} and @code{d} are printed on the
380 default staff. For the @code{e}, a context Staff called
381 @code{another} is specified; since that does not exist, a new
382 context is created. Within @code{another}, a (default) Voice context
383 is created for the @code{e4}. When all music referring to a
384 context is finished, the context is ended as well. So after the
385 third quarter, @code{another} is removed.
389 @node Default contexts
390 @subsection Default contexts
392 Most music expressions don't need an explicit @code{\context}
393 declaration: they inherit the
394 notation context from their parent. Each note is a music expression, and
395 as you can see in the following example, only the sequential music
396 enclosing the three notes has an explicit context.
398 @lilypond[verbatim,singleline]
399 \score { \notes \context Voice = goUp { c'4 d' e' } }
402 There are some quirks that you must keep in mind when dealing with
405 First, every top level music is interpreted by the Score context, in other
406 words, you may think of @code{\score} working like
409 \context Score @var{music}
413 Second, contexts are created automatically to be able to interpret the
414 music expressions. Consider the following example.
416 @lilypond[verbatim, singleline]
417 \score { \context Score \notes { c'4 ( d' )e' } }
420 The sequential music is interpreted by the Score context initially
421 (notice that the @code{\context} specification is redundant), but when a
422 note is encountered, contexts are setup to accept that note. In this
423 case, a Thread, Voice and Staff are created. The rest of the sequential
424 music is also interpreted with the same Thread, Voice and Staff context,
425 putting the notes on the same staff, in the same voice.
427 This is a convenient mechanism, but do not expect opening chords to work
428 without @code{\context}. For every note, a separate staff is
431 @cindex explicit context
432 @cindex starting with chords
433 @cindex chords, starting with
435 @lilypond[verbatim, singleline]
436 \score { \notes <c'4 es'> }
439 Of course, if the chord is preceded by a normal note in sequential
440 music, the chord will be interpreted by the Thread of the preceding
442 @lilypond[verbatim,singleline]
443 \score { \notes { c'4 <c'4 es'> } }
448 @node Context properties
449 @subsection Context properties
451 Notation contexts have properties. These properties are from
452 the @file{.ly} file using the following expression:
453 @cindex @code{\property}
455 \property @var{contextname}.@var{propname} = @var{value}
458 Sets the @var{propname} property of the context @var{contextname} to the
459 specified Scheme expression @var{value}. All @var{propname} and
460 @var{contextname} are strings, which are typically unquoted.
462 Properties that are set in one context are inherited by all of the
463 contained contexts. This means that a property valid for the
464 @internalsref{Voice} context can be set in the @internalsref{Score} context (for
465 example) and thus take effect in all @internalsref{Voice} contexts.
467 Properties can be unset using the following expression:
469 \property @var{contextname}.@var{propname} \unset
472 @cindex properties, unsetting
473 @cindex @code{\unset}
475 This removes the definition of @var{propname} in @var{contextname}. If
476 @var{propname} was not defined in @var{contextname} (but was inherited
477 from a higher context), then this has no effect.
482 The syntax of @code{\unset} is asymmetric: @code{\property \unset} is not
483 the inverse of @code{\property \set}.
485 @node Engravers and performers
486 @subsection Engravers and performers
490 Basic building blocks of translation are called engravers; they are
495 @node Changing context definitions
496 @subsection Changing context definitions
498 @cindex context definition
499 @cindex translator definition
501 The most common way to define a context is by extending an existing
502 context. You can change an existing context from the paper block, by
503 first initializing a translator with an existing context identifier:
507 @var{context-identifier}
510 Then you can add and remove engravers using the following syntax:
512 \remove @var{engravername}
513 \consists @var{engravername}
517 Here @var{engravername} is a string, the name of an engraver in the
521 @lilypond[verbatim,singleline]
525 \translator { \StaffContext
526 \remove Clef_engraver
532 You can also set properties in a translator definition. The syntax is as
535 @var{propname} = @var{value}
536 @var{propname} \set @var{grob-propname} = @var{pvalue}
537 @var{propname} \override @var{grob-propname} = @var{pvalue}
538 @var{propname} \revert @var{grob-propname}
540 @var{propname} is a string, @var{grob-propname} a symbol, @var{value}
541 and @code{pvalue} are Scheme expressions. These type of property
542 assignments happen before interpretation starts, so a @code{\property}
543 command will override any predefined settings.
546 To simplify editing translators, all standard contexts have standard
547 identifiers called @var{name}@code{Context}, e.g. @code{StaffContext},
548 @code{VoiceContext}, see @file{ly/engraver-init.ly}.
550 @node Defining new contexts
551 @subsection Defining new contexts
553 If you want to build a context from scratch, you must also supply the
554 following extra information:
556 @item A name, specified by @code{\name @var{contextname}}.
558 @item A cooperation module. This is specified by @code{\type
565 \type "Engraver_group_engraver"
568 \consists "Staff_symbol_engraver"
569 \consists "Note_head_engraver"
570 \consistsend "Axis_group_engraver"
574 The argument of @code{\type} is the name for a special engraver that
575 handles cooperation between simple engravers such as
576 @code{Note_head_engraver} and @code{Staff_symbol_engraver}. Alternatives
577 for this engraver are the following:
579 @cindex @code{Engraver_group_engraver}
580 @item @code{Engraver_group_engraver}
581 The standard cooperation engraver.
583 @cindex @code{Score_engraver}
585 @item @code{Score_engraver}
586 This is cooperation module that should be in the top level context,
587 and only the top level context.
594 @item @code{\alias} @var{alternate-name}
595 This specifies a different name. In the above example,
596 @code{\property Staff.X = Y} will also work on @code{SimpleStaff}s
598 @item @code{\consistsend} @var{engravername}
599 Analogous to @code{\consists}, but makes sure that
600 @var{engravername} is always added to the end of the list of
603 Some engraver types need to be at the end of the list; this
604 insures they stay there even if a user adds or removes engravers.
605 End-users generally don't need this command.
607 @item @code{\accepts} @var{contextname}
608 Add @var{contextname} to the list of contexts this context can
609 contain in the context hierarchy. The first listed context is the
610 context to create by default.
612 @item @code{\denies}. The opposite of @code{\accepts}. Added for
613 completeness, but is never used in practice.
616 @item @code{\name} @var{contextname}
617 This sets the type name of the context, e.g. @internalsref{Staff},
618 @internalsref{Voice}. If the name is not specified, the translator won't do
622 In the @code{\paper} block, it is also possible to define translator
623 identifiers. Like other block identifiers, the identifier can only
624 be used as the very first item of a translator. In order to define
625 such an identifier outside of @code{\score}, you must do
630 foo = \translator @{ @dots{} @}
637 \translator @{ \foo @dots{} @}
645 @cindex paper types, engravers, and pre-defined translators
648 @node Syntactic details
649 @section Syntactic details
650 @cindex Syntactic details
652 This section describes details that were too boring to be put elsewhere.
656 * Music expressions::
657 * Manipulating music expressions::
666 @subsection Identifiers
670 What has this section got to do with identifiers?
671 It seems more appropriate in the introduction to Chapter 4,
677 All of the information in a LilyPond input file, is internally
678 represented as a Scheme value. In addition to normal Scheme data types
679 (such as pair, number, boolean, etc.), LilyPond has a number of
680 specialized data types,
691 @item Music_output_def
692 @item Moment (rational number)
695 LilyPond also includes some transient object types. Objects of these
696 types are built during a LilyPond run, and do not `exist' per se within
697 your input file. These objects are created as a result of your input
698 file, so you can include commands in the input to manipulate them,
699 during a lilypond run.
702 @item Grob: short for Graphical object.
703 @item Molecule: device-independent page output object,
704 including dimensions. Produced by some Grob functions
705 @item Translator: object that produces audio objects or Grobs. This is
706 not yet user accessible.
707 @item Font_metric: object representing a font.
711 @node Music expressions
712 @subsection Music expressions
714 @cindex music expressions
716 Music in LilyPond is entered as a music expression. Notes, rests, lyric
717 syllables are music expressions, and you can combine music expressions
718 to form new ones, for example by enclosing a list of expressions in
719 @code{\sequential @{ @}} or @code{< >}. In the following example, a
720 compound expression is formed out of the quarter note @code{c} and a
721 quarter note @code{d}:
724 \sequential @{ c4 d4 @}
727 @cindex Sequential music
728 @cindex @code{\sequential}
729 @cindex sequential music
732 @cindex Simultaneous music
733 @cindex @code{\simultaneous}
735 The two basic compound music expressions are simultaneous and
739 \sequential @code{@{} @var{musicexprlist} @code{@}}
740 \simultaneous @code{@{} @var{musicexprlist} @code{@}}
742 For both, there is a shorthand:
744 @code{@{} @var{musicexprlist} @code{@}}
748 @code{<} @var{musicexprlist} @code{>}
750 for simultaneous music.
751 In principle, the way in which you nest sequential and simultaneous to
752 produce music is not relevant. In the following example, three chords
753 are expressed in two different ways:
755 @lilypond[fragment,verbatim,center]
756 \notes \context Voice {
757 <a c'> <b d' > <c' e'>
758 < { a b c' } { c' d' e' } >
763 Other compound music expressions include
766 \transpose @var{pitch} @var{expr}
767 \apply @var{func} @var{expr}
768 \context @var{type} = @var{id} @var{expr}
769 \times @var{fraction} @var{expr}
773 @c . {Manipulating music expressions}
774 @node Manipulating music expressions
775 @subsection Manipulating music expressions
777 The @code{\apply} mechanism gives you access to the internal
778 representation of music. You can write Scheme-functions that operate
779 directly on it. The syntax is
781 \apply #@var{func} @var{music}
783 This means that @var{func} is applied to @var{music}. The function
784 @var{func} should return a music expression.
786 This example replaces the text string of a script. It also shows a dump
787 of the music it processes, which is useful if you want to know more
788 about how music is stored.
790 @lilypond[verbatim,singleline]
791 #(define (testfunc x)
792 (if (equal? (ly-get-mus-property x 'text) "foo")
793 (ly-set-mus-property! x 'text "bar"))
795 (ly-set-mus-property! x 'elements
796 (map testfunc (ly-get-mus-property x 'elements)))
801 \apply #testfunc { c'4_"foo" }
805 For more information on what is possible, see the automatically
806 generated documentation.
809 Directly accessing internal representations is dangerous: the
810 implementation is subject to changes, so you should avoid this feature
813 A final example is a function that reverses a piece of music in time:
815 @lilypond[verbatim,singleline]
816 #(define (reverse-music music)
817 (let* ((elements (ly-get-mus-property music 'elements))
818 (reversed (reverse elements))
819 (span-dir (ly-get-mus-property music 'span-direction)))
820 (ly-set-mus-property! music 'elements reversed)
822 (ly-set-mus-property! music 'span-direction (- span-dir)))
823 (map reverse-music reversed)
826 music = \notes { c'4 d'4( e'4 f'4 }
828 \score { \context Voice {
830 \apply #reverse-music \music
835 More examples are given in the distributed example files in
844 @subsection Span requests
845 @cindex Span requests
847 Notational constructs that start and end on different notes can be
848 entered using span requests. The syntax is as follows:
852 \spanrequest @var{startstop} @var{type}
856 @cindex @code{\start}
859 This defines a spanning request. The @var{startstop} parameter is either
860 -1 (@code{\start}) or 1 (@code{\stop}) and @var{type} is a string that
861 describes what should be started. Much of the syntactic sugar is a
862 shorthand for @code{\spanrequest}, for example,
864 @lilypond[fragment,verbatim,center]
865 c'4-\spanrequest \start "slur"
866 c'4-\spanrequest \stop "slur"
869 Among the supported types are @code{crescendo}, @code{decrescendo},
870 @code{beam}, @code{slur}. This is an internal command. Users are
871 encouraged to use the shorthands which are defined in the initialization
872 file @file{spanners.ly}.
877 @subsection Assignments
880 Identifiers allow objects to be assigned to names during the parse
881 stage. To assign an identifier, you use @var{name}@code{=}@var{value}
882 and to refer to an identifier, you precede its name with a backslash:
883 `@code{\}@var{name}'. @var{value} is any valid Scheme value or any of
884 the input-types listed above. Identifier assignments can appear at top
885 level in the LilyPond file, but also in @code{\paper} blocks.
887 An identifier can be created with any string for its name, but you will
888 only be able to refer to identifiers whose names begin with a letter,
889 being entirely alphabetical. It is impossible to refer to an identifier
890 whose name is the same as the name of a keyword.
892 The right hand side of an identifier assignment is parsed completely
893 before the assignment is done, so it is allowed to redefine an
894 identifier in terms of its old value, e.g.
900 When an identifier is referenced, the information it points to is
901 copied. For this reason, an identifier reference must always be the
902 first item in a block.
906 \paperIdent % wrong and invalid
910 \paperIdent % correct
917 @subsection Lexical modes
918 @cindex Lexical modes
921 @cindex @code{\notes}
922 @cindex @code{\chords}
923 @cindex @code{\lyrics}
925 To simplify entering notes, lyrics, and chords, LilyPond has three
926 special input modes in addition to the default mode: note, lyrics and
927 chords mode. These input modes change the way that normal, unquoted
928 words are interpreted: for example, the word @code{cis} may be
929 interpreted as a C-sharp, as a lyric syllable `cis' or as a C-sharp
930 major triad respectively.
932 A mode switch is entered as a compound music expression
934 @code{\notes} @var{musicexpr}
935 @code{\chords} @var{musicexpr}
936 @code{\lyrics} @var{musicexpr}.
939 In each of these cases, these expressions do not add anything to the
940 meaning of their arguments. They just instruct the parser in what mode
941 to parse their arguments.
943 Different input modes may be nested.
947 @subsection Ambiguities
952 The grammar contains a number of ambiguities. We hope to resolve them at
961 is interpreted as the string identifier assignment. However,
962 it can also be interpreted as making a string identifier @code{\foo}
963 containing @code{"bar"}, or a music identifier @code{\foo} containing
964 the syllable `bar'. The former interpretation is chosen.
966 @item If you do a nested repeat like
978 then it is ambiguous to which @code{\repeat} the
979 @code{\alternative} belongs. This is the classic if-then-else
980 dilemma. It may be solved by using braces.
984 @c . {Lexical details}
985 @node Lexical details
986 @section Lexical details
988 Even more boring details, now on lexical side of the input parser.
998 @subsection Direct Scheme
1002 @cindex Scheme, in-line code
1008 @cindex accessing Scheme
1009 @cindex evaluating Scheme
1012 LilyPond internally uses GUILE, a Scheme-interpreter. Scheme is a
1013 language from the LISP family. You can learn more about Scheme at
1014 @uref{http://www.scheme.org}. It is used to represent data throughout
1015 the whole program. The hash-sign (@code{#}) accesses GUILE directly: the
1016 code following the hash-sign is evaluated as Scheme. The boolean value
1017 @var{true} is @code{#t} in Scheme, so for LilyPond @var{true} looks like
1020 LilyPond contains a Scheme interpreter (the GUILE library) for
1021 internal use. In some places, Scheme expressions also form valid syntax:
1022 wherever it is allowed,
1026 evaluates the specified Scheme code. Example:
1028 \property Staff.TestObject \override #'foobar = #(+ 1 2)
1030 @code{\override} expects two Scheme expressions, so there are two Scheme
1031 expressions. The first one is a symbol (@code{foobar}), the second one
1032 an integer (namely, 3).
1034 In-line scheme may be used at the top level. In this case the result is
1037 Scheme is a full-blown programming language, and a full discussion is
1038 outside the scope of this document. Interested readers are referred to
1039 the website @uref{http://www.schemers.org/} for more information on
1045 @cindex real numbers
1047 Formed from an optional minus sign and a sequence of digits followed
1048 by a @emph{required} decimal point and an optional exponent such as
1049 @code{-1.2e3}. Reals can be built up using the usual operations:
1050 `@code{+}', `@code{-}', `@code{*}', and
1051 `@code{/}', with parentheses for grouping.
1059 A real constant can be followed by one of the dimension keywords:
1060 @code{\mm} @code{\pt}, @code{\in}, or @code{\cm}, for millimeters,
1061 points, inches and centimeters, respectively. This converts the number
1062 a number that is the internal representation of that dimension.
1070 Begins and ends with the @code{"} character. To include a @code{"}
1071 character in a string write @code{\"}. Various other backslash
1072 sequences have special interpretations as in the C language. A string
1073 that contains no spaces can be written without the quotes. Strings can
1074 be concatenated with the @code{+} operator.