\input texinfo
@setfilename apl.info
@documentencoding UTF-8
@settitle GNU APL

@c ============================================================================
@c ====== Part 2: Summary Description and Copyright ===========================
@c ============================================================================

@copying
This is the manual for GNU APL, an implementation of ISO standard 13751
"Programming Language APL, Extended"

Copyright @copyright{} 2013 Free Software Foundation, Inc.
@end copying

@dircategory GNU programming tools
@direntry
* APL: (apl).                  the programming language APL - ISO 13751.

@end direntry

@c ============================================================================
@c ====== Part 3: Titlepage, Contents, Copyright ==============================
@c ============================================================================

@titlepage
@title APL Manual

@c The following two commands start the copyright page.
@page
@vskip 0pt plus 1filll
@insertcopying
@end titlepage

@c Output the table of contents at the beginning.
@contents

@c ============================================================================
@c ====== Part 4: ‘Top’ Node and Master Menu ==================================
@c ============================================================================

@ifnottex
@node Top
@top GNU APL

This manual briefly documents GNU APL, an interpreter for APL as described
in ISO standard 13751, aka. "Programming Language APL, Extended".

This manual for GNU APL can be distributed under the terms of the
 GNU Free Documentation License, *Note Chapter 6::.

This manual does NOT describe APL itself; there exist a number of good books
and texts about APL. We would like to refer the reader to the following:

    ISO Standard for APL: @*
    www.math.uwaterloo.ca/~ljdickey/apl-rep/docs/is13751.pdf

    More pointers to APL resources on the Web: @*
    ftp://rtfm.mit.edu/pub/usenet-by-group/comp.lang.apl/APL_language_FAQ

@end ifnottex

@menu
* Chapter 1::    Installing and Starting GNU APL
* Chapter 2::    Design Decisions
* Chapter 3::    Non-standard GNU APL Features
* Chapter 4::    Limitations and Missing Features
* Chapter 5::    Internationalization
* Chapter 6::    Libraries Contributed by GNU APL Users
* Chapter 7::    Licenses for GNU APL and this Manual
@end menu

@c ============================================================================
@c ====== Part 5: The Body of the Document ====================================
@c ============================================================================

@c ----------------------------------------------------------------------------
@node Chapter 1
@chapter Installing and Starting GNU APL

@section Installing APL

APL is built and installed like this:

@itemize
@item download the tar file containing GNU APL, from
 @uref{ftp://ftp.gnu.org/gnu/apl} or from one of its mirrors
 (see @uref{http://www.gnu.org/prep/ftp.html}), and
untar the file.

@item read (and follow) the instructions given in file README in the unpacked
directory
@end itemize

For the experienced, but impatient reader: it is the usual sequence

@itemize
@item ./configure

@item make

@item make install
@end itemize

On success, an executable file called 'apl' will have been produced
in the sub-directory 'src'.

File README contains further instructions about the installation GNU APL.

@section Starting APL

Last things first: before explaining how to start APL, it is important to
remember how to stop (i.e. exit) it. Neither ^C nor ^D will stop APL
 - they serve other purposes. Instead, you leave APL with the command
 )OFF (on a separate line) like this:

      )OFF

If APL is computing a function (and possibly caught in an endless loop),
then you may have to press ^C (called ATTENTION in APL) in order to
return to APL's command mode and then give the )OFF command.

Having that said, APL is started like every other program - entering its
name and optional command line parameters, for example:

$ apl

or:

$ apl ---id 1001

GNU APL is script-able; a text file whose first line looks like this (assuming
the APL interpreter binary is called 'apl' and is located in the current
directory):

#! apl 

or (if the APL interpreter binary is not in the current directory but in
/mypath/apl):

#! /mypath/apl

The path to the 'apl' binary can be missing (like in the first example),
relative, or absolute (second example). The exact details of how the first
line of a GNU APL script shall look like varies slightly among operating
systems. Please consult the info (or man) pages for 'path_resolution' and/or
'execve' on your operating system. After the the name of the binary, optional
GNU APL command line options, usually --script, can be provided.

The text file must, of course, have execute permission, and should be ASCII
or, more likely, UTF-8 encoded. The APL characters in the script
shall be those defined in the Unicode character set (most of them in the
U+2200 - U+23FF range).

@section Command Line Options

GNU APL understands the following command line options:

@itemize @bullet

@item
@option{-C new_root}

perform chroot("new_root") followed by chdir("/"). This restricts the access
of the the process running GNU APL to files in or below directory new_root, and
it also changes the current directory (which could have resided above new_root
before the chroot() was executed).

The -C option is intended to be a security
feature for GNU APL interpreters that are facing a hostile environment like
the public internet.

NOTES:
@itemize @bullet

@item
For -C to work, new_root needs to contain minimal set of binaries, in
particular a shell, and possibly libraries needed by the shell. Consult
'info chroot invocation' for issues to consider and common pitfalls.

@item
GNU APL processes the -C option (i.e. it calls chroot("new_root")) before
all other command line options. As a consequence, file names in other command
line options pf GNU APL are also affected by -C. That means that the file names
are interpreted relative to new_root and not relative to the root of the
process that is starting GNU APL.

@item
GNU APL may automatically start other processes such as APserver and friends
after processing the -C option. These processes (and the libraries that they
depend on) should reside in the proper directory below new_root. For example,
with the default configuration of GNU APL, GNU APL installs itself in
/usr/local/bin and also expects APserver in the same directory. After -C
new_root. however, /usr/local/bin is no longer accessible and one would need to copy /usr/local/bin/APserver to new_root/usr/local/bin/APserver

@item
Depending on your platform, the process using -C may need root privileges.

@end itemize

@item
@option{--cfg}

show ./configure options that were used to configure GNU APL, and exit.

@item
@option{--[no]Color}

start with ]COLOR ON [OFF].

@item
@option{-d}

run the APL interpreter (or APL script) in the background (i.e. as a daemon).
For this to work you need to provide some input to the background process, e.g.
via the -f option.

@item
@option{--emacs}

run in (old) Emacs mode.

@item
@option{--emacs_arg arg}

run in (new) Emacs mode with argument arg.


@item
@option{-f file}

read input from \fIfile\fP rather than from the keyboard. When the end of
the file is reached, input is switched back to the keyboard. 
If you want to terminate the APL interpreter after executing the file,
then use )OFF as last line in the file.

@item
@option{--gpl}

show GNU APL license (GPL) and exit.

@item
@option{-L wsname}

)LOAD wsname on start-up.

@item
@option{--LX expr}

execute expr first. This can be used, for example, to load some library
or workspace at start-up.

@item
@option{-h}, @option{--help}

print all command line options with a brief hint what they do.

@item
@option{--id proc}

use processor ID proc for this interpreter. If no ID is provided, then the
first unused ID > 1000 is taken by this interpreter and the ID becomes used
as long as the interpreter runs. Processor IDs are used by shared variables
to identify share partners.

@item
@option{-l num}

turn logging facility num ON (if dynamic logging is configured). The logging
facility for start-up messages can be turned on even when dynamic logging is
not configured.

@item
@option{--echoCIN}
copy the input line (after editing) to stdout. For creating session logs.

@item
@option{--noCIN}

do not echo stdin to stdout. Almost a must for scripting (unless you
troubleshoot a script).

@item
@option{--noCONT}

do not load a SETUP or CONTINUE workspace on start-up.

@item
@option{--OFF}

This option causes GNU APL to perform an automatic )OFF command after the
last line of the last input file (as per -f option) was executed.

@item
@option{--PW COLS}

set the initial value of ⎕PW to COLS (min. 30, max. 10000)

@item
@option{--[no]SV}

do [not] start APserver (a shared variable server) on start-up. This disables
communication with other workspaces or auxiliary processors through
shared variables.

@item
@option{-p N}

use profile number N in preferences files.

@item
@option{--par pproc}

use processor parent ID pproc (default: no parent ID).

@item
@option{--rawCIN}

do not emit ESC sequences. Normally ESC sequences are emitted for colored
output and during line editing. In scripts, however, ESC sequences usually
not wanted and can be turned off with this option.

@item
@option{-s}, @option{--script}

this option is an abbreviation for:
 @option{--silent} @option{--noCIN} @option{--noCONT} @option{-f -}
which is a typical combination of options for APL scripts.

@item
@option{-q}, @option{--silent}

suppress printing of the GNU APL welcome message. Useful for scripts.

@item
@option{--safe}

disable shared variables and native functions


@item
@option{--show_bin_dir}

display the binary directory (where, according to ./configure,  the programs
apl, APserver, AP100, and AP210 are supposed to be installed. Then exit.

@item
@option{--show_doc_dir}

display the directory where, according to ./configure,  documentation files
for GNU APL are installed. Then exit.


@item
@option{--show_etc_dir}

display the system configuration directory where, according to ./configure,
the preferences file for GNU APL is installed. Then exit.


@item
@option{--show_lib_dir}

display the library directory where, according to ./configure, shared
library files and the workspaces shipped with GNU APL are installed. Then exit.


@item
@option{--show_src_dir}

display the source directory where, according to ./configure, GNU APL
was compiled. Then exit. This can be used, for example, by native functions\
that are built outside the GNU APL source tree to find GNU APL header files
that are needed to compile the native function.


@item
@option{--show_all_dirs}

display all the directories above. Then exit.


@item
@option{-T testcases ...}
run testcases. Testcases are text files that contain both input to the APL
interpreter and the expected response from the interpreter. The output from
the interpreter is compared with the expected output in the testcase file(s)
and differences are marked. In addition a summary file is created that tells
whether or not each of the testcases was successful.

@item

@option{--TM mode}

test mode. This option how the interpreter shall behave
when running a number of testcases (as specified with the @option{-T} option)

@option{--TM 0} (default) run all testcases and exit after the last testcase.

@option{--TM 1} like @option{--TM 0} if no error was detected.
However, if one of the testcases has failed, then the interpreter
does not exit so that the user can investigate the state of APL
(SI, variable values, etc.).

@option{--TM 2} like @option{--TM 1}, but stay in the interpreter even if
all testcases have passed. This can be useful in order to quickly bring
the interpreter into a specific state and continue manual troubleshooting
from that state.

@option{--TM 3} like @option{--TM 1}, but stop testcase execution after the
first failed testcase (i.e. do not exit).

@option{--TM 4} like @option{--TM 3}, but exit after the first failed
testcase. The is useful for automatic regression tests, where no errors
are expected.

@item
@option{--TR}

executes test case files in random order.

@item
@option{--TS}

Normally, when the interpreter is run with the @option{-T} option,
then an existing summary.log file is overridden without notice.
This option causes new test results to be appended to a possibly
existing summary.log instead of overriding it.

@item
@option{-v}, @option{--version},

show version information and exit.

@item
@option{-u UID}

run as user with UID 0. This option can only be used by the root user (who
then wants to run as a different user).

@item
@option{-w milli}

wait milli milliseconds at start-up. Useful to give other programs that are
started together with this interpreter time to initialize themselves.

@item
@option{--}

end of command line options for the interpreter. GNU APL provides the system
variable ⎕ARG that returns all command line options with which the GNU APL
interpreter was invoked (similar to variable argv in main(int argv,
char * argv[]) in C/C++). Option ---- can be used to separate command line
options for the APL interpreter from command line options understood by APL
applications.

Thus,

@code{(⎕ARG ⍳ ⊂'--') ↑ ⎕ARG} returns the options for the APL interpreter, while

@code{(⎕ARG ⍳ ⊂'--') ↓ ⎕ARG} returns the options for the APL application.

All command line options after @code{--} are ignored by the interpreter
(except making them available in ⎕ARG).

@end itemize

@section Config File for GNU APL

The default values for some of the command line options discussed in the
previous section can be set in a configuration file for GNU APL. The name
of the configuration file is 'preferences' and it should live in one of
the following directories:

@itemize

@item
in the sub-directory gnu-apl.d of the system configuration directory, or

@item
in the sub-directory .config/gnu-apl of the user's home directory (as per
$HOME).

@end itemize

The system configuration directory is usually /etc or /usr/local/etc and is
configurable via @option{./configure --sysconfdir}. An empty (i.e. all
settings commented out) preferences file is being installed in the
system configuration directory when GNU APL is installed. You can edit
it or use it as a template to see which options can be controlled.

If file 'preferences' exists in both directories, then the settings in
$HOME/.gnu-apl/preferences override settings in, for example,
/etc/gnu-apl.d/preferences.

Command line options in turn override settings in 'preferences' files.

@section File Names and Paths

The GNU APL interpreter is a binary file named apl. It is usually
installed in directory /usr/bin/ or in /usr/local/bin/. The location
where apl is installed can be changed via ./configure options
(see file INSTALL).

GNU APL understands 4 file types:

@enumerate
@item APL workspaces that can be manipulated with the )LOAD, )SAVE,
 )COPY, and )DROP commands. APL workspaces are XML files and must have a
 file extension of .xml in order to be accepted by GNU APL. APL workspaces
 can only be exchanged between machines that all run GNU APL.

@item APL exchange files can be manipulated with the )IN and )OUT
 commands. APL exchange files are text files in ⎕TF format defined by IBM
 (basically APL expressions that create variables or functions)
 and must have a file extension of .atf in order to be accepted by GNU APL.
 APL exchange files can be exchanged between machines running APL interpreters from
 different vendors. The ⎕TF format can be easily emulated on machines not
 providing compatible )IN and )OUT commands.

@item APL scripts consist of APL commands and APL expressions (including
 function definition via ∇) like they would be entered by the user.
 APL scripts should have a file extension of .apl but other extensions
 are also accepted by GNU APL. APL scripts are, for example, the files
 expected for the -f command line option. A workspace can be written in this
 format with the )DUMP command.

@item APL testcase files are similar to APL scripts, but in addition to
 the APL commands and expression they also contain the expected output from
 from the commands 
 APL testcase files normally have have a file extension of .tc for normal
 (functional) testcases and .pt for performance testcases.
 APL testcase files are, for example, the files expected for the
 -T command line option.

@end enumerate

The following APL commands are related to file names:

)LOAD [lib] name[.xml]

)SAVE [lib] [name[.xml]]

)COPY [lib] [name[.xml]]

)PCOPY [lib] [name[.xml]]

)DROP [lib] [name[.xml]]

)IN   [lib] name[.atf]

)PIN   [lib] name[.atf]

)OUT  [lib] name[.atf]

)DUMP [lib] [name[.apl]]

)LIB  [lib]

)LIBS [new-lib-root]

)WSID       [name]

The rules how file names are constructed from the argument(s) of an APL
command are:

@enumerate
@item command arguments shown in brackets are optional.

@item lib is a number from 0 to 9. If lib is not present then 0 is taken
as default.

@item if the name is optional and missing then the workspace ID (the name
set with )WSID) is used.

@item if the file extension (i.e. .xml or .atf) is missing then it is
appended automatically to name.
@end enumerate

If the name starts with '/' then it is taken as an absolute path to
the file (an absolute file name) and no further computation is done
with the name.

Otherwise name is a relative path which is relative to some directory
library-root and a sub-directory of library-root that is determined by
the lib number. The library numbers 0-9 correspond to the following
directories:

    0: library-root/workspaces/

    1: library-root/wslib1/

    2: library-root/wslib2/

    ...

    9: library-root/wslib9/

The command )LIBS without arguments shows the mapping between library
numbers and paths. The command )LIBS with an argument sets a new lib-root.

The command )LIB [lib] shows the files in library (i.e. directory) lib.

The directory library-root is computed as follows when the interpreter starts:

If an environment variable APL_LIB_ROOT is defined, then its value is used
as library-root. Otherwise the path from the current directory (".") up to
the root directory ("/") is searched until a directory containing two
files 'workspaces' and 'wslib1' is found. Normally 'workspaces' and 'wslib1'
are directories, but for the computation of library-root files suffice.

If such a directory is found, then it is used as library-root; otherwise the
current directory (i.e. ".") is used and converted to an absolute path.

For example, if library-root is "." then the command

)LOAD 2 test

will try to load the workspace file

./wslib2/test.xml

Using a library root implies that all 10 library directories are contained
in the same directory. This is good enough for single-user environments but
is often not adequate for multi-user environments where some directories
are not writable by users and different users have different home directories.

For that reason the above library root scheme can be overridden by the
GNU APL configuration files (preferences). In these files you can uncomment
any of the LIBREF-0 to LIBREF-9 settings (which correspond to library
numbers 0 to 9) and provide your own paths. The library numbers NOT overridden
in a 'preferences' file still follow the library root scheme.

@c ----------------------------------------------------------------------------
@node Chapter 2
@chapter Design Decisions

The ISO standard leaves a few things unspecified and GNU APL may behave
differently than other APL interpreters.

@section APL symbols that can be functions or operators

There are 4 APL symbols / ⌿ \ and ⍀ that can be functions or operators,
depending on their context (i.e. depending on the APL tokens left of them).
Neither the ISO standard nor the otherwise excellent IBM APL2 language
reference manual explain the rules that decide whether, for example /, should
mean 'function compress' or 'operator reduce'. In simple cases the meaning of
/ is obvious: +/B means 'operator reduce' while 1/B means 'function compress'.

The following example may explain the problem:

@verbatim
     ÷  /  \  2      ⍝ case (i)
2
   (÷  /) \  2       ⍝ case (ii)
2
   ÷ (/  \) 2        ⍝ case (iii)
0.5
@end verbatim

In (i) and (ii) / is an operator thanks to ÷ left of it while in (iii) / is
a function bound to operator \.

Both (ii) and (iii) are valid interpretations of (i). The ISO standard
defined the result after the decision if / should be treated as function or
as operator was made but says nothing about how to decide that.

The APL2 language reference gives additional information about such aspects
(binding strength between token) but the ambiguity related to / ⌿ \ and ⍀
is not resolved by these rules.

The first decision to make is at which point in time the role of / and friends
shall be decided. The options are:

(a) when the statement is tokenized and parsed (call that moment '⎕FX time'
 similar to compile-time for compiler languages), or

(b) when a statement is executed (call that 'run-time'), or

(c) theoretically a combination of (a) and (b)

The advantage of (a) is less run-time overhead which is important because / is
probably the most frequently used APL operator. As will be explained below
there are cases where (a) fails. The advantage of (b), at first glance,
seems to be that it always gives the correct result (more precisely: the
expected result because 'correct' would require a valid specification). A
closer look reveals, however, that this is only true for the most simple cases
but not in general.

To give you an idea where (b) becomes tricky is this (there are more of
that kind):

      A[FOO]/B   ⍝ where FOO could define A via ⎕FX or do A←

It is still possible to resolve the last example at run time, but the parser
would become far more complex to do that. The same holds for (c).

For these reasons the decision was made in favor of (a) with a syntactic
tweak to handle the (single) case where (a) fails. In principle the symbol
left of, for instance, / decides if / should be a function or an operators.
The matter can become more complex if index brackets or parentheses are
involved. The algorithm used in GNU APL for classifying / and friend is
(simplified) this:

1. / ⌿ \ and ⍀ are tokenized as operators

2. Scan the tokenized statement from left to right to find / ⌿ \ or ⍀

3. If a / ⌿ \ or ⍀ is found, go backwards until a constant, or a function,
   or a user-defined  name is found:
3a. if a constant, a function, or a user-defined name is found then →4
3b. if ) is seen then skip over it, That is, a parenthesized expression is
    entered.
3c. if ] is seen then skip until the corresponding [ is found, That is an
    index list or axis is skipped over.
3d. otherwise: SYNTAX ERROR

4. decide the role of / \ ⌿ or ⍀ based on the kind of token that was found
   in 3a:
4a. function: leave / as operator as initially tokenized
4b. constant: change / from operator to function (compress)
4c. see below

This works fine except in case 4c. which cannot be resolved at ⎕FX time. For
this case we introduce the following convention:

A user-defined name is assumed to be a function (and hence / is an operator)
unless the name (and nothing else) is enclosed in parentheses. For example:

@verbatim
       A  / B    ⍝ A is function, therefore / is operator

      (A) / B    ⍝ A is value, therefore / is function
@end verbatim

This rule is moderately compatible with ISO and APL2; in APL2 (A) would be
redundant parentheses so in that case there would be a small incompatibility
between GNU APL and IBM APL2.

@c ----------------------------------------------------------------------------
@node    Chapter 3
@chapter Non-standard GNU APL Features

@menu
* Section 3.1::   APL Scripting
* Section 3.2::   Axis argument in defined functions
* Section 3.3::   Colored Output
* Section 3.4::   Comparison Rules
* Section 3.5::   Complex Numbers
* Section 3.6::   Debug Commands
* Section 3.7::   Direct Functions (Lambdas)
* Section 3.8::   ]DOXY Command
* Section 3.9::   )DUMP Command
* Section 3.10::  History and TAB completion
* Section 3.11::  Logging Facilities
* Section 3.12::  Rational Numbers
* Section 3.13::  Hex Numbers
* Section 3.14::  User-defined Commands
* Section 3.15::  Monadic ⊢ and ⊣, dyadic ⊢ with Axis
* Section 3.16::  Bit-wise Logical Functions ⊤∧, ⊤∨, ⊤⍲, and ⊤⍱
* Section 3.17::  Dyadic ⎕CR
* Section 3.18::  Dyadic ⎕FX (Native Functions)
* Section 3.19::  ⎕ARG  - Interpreter command line arguments
* Section 3.20::  ⎕DLX  - Knuth's Dancing Links Algorithm
* Section 3.21::  ⎕ENV  - Environment Variable
* Section 3.22::  ⎕FIO  - File I/O Functions
* Section 3.23::  ⎕FFT  - Fast Fourier Transform
* Section 3.24::  ⎕GTK  - GTK Interface
* Section 3.25::  ⎕PLOT - Plot Data
* Section 3.26::  ⎕PS   - Print Style
* Section 3.27::  ⎕RE   - Regular Expressions
* Section 3.28::  ⎕SQL  - SQL Database Interface
* Section 3.29::  ⎕SI   - State Indicator
* Section 3.30::  ⎕SYL  - System limits
@end menu

There are a few possibly useful features in GNU APL:

@node    Section 3.1
@section APL Scripting

As already mentioned, it is possible to write APL scripts. Similar to other
script languages, an APL script is a text file whose first line is a
"shebang line", i.e. a line starting with @option{#!}, followed by the
absolute path to the interpreter (in our case the GNU APL binary), followed
by command line arguments that are passed on to the interpreter. In our case
the shebang line could be, for example:

@verbatim
    #! /usr/local/bin/apl --id 1010
@end verbatim

There are essentially two ways to run an APL script: redirecting the script
file to stdin of the interpreter or making the script executable and indicate
apl as the script interpreter (followed by some command line arguments for
apl).

@subsection redirect the script file the stdin of the GNU APL interpreter

A file, say SCRIPT.apl, can be redirected to apl by redirection of the shell:

@verbatim
    apl < SCRIPT.apl
@end verbatim

Alternatively, the command line option -f of apl can be used:

@verbatim
    apl -f SCRIPT.apl
@end verbatim

Both ways of redirecting the file are almost identical; in the first case
redirection was performed by the shell running apl, while in the second case
the redirecting of the file was performed by apl itself.

@subsection Make the script file executable

Alternatively the script can be made executable, mentioning apl as the
interpreter for the script (see also @option{'man 2 execve'}). For this to
work, the first line of the script must have a special format

@verbatim
    #! /usr/local/bin/apl --script
@end verbatim

@option{--script} prevents: printing of a welcome banner, 
echoing of stdin to stdout, automatic loading of a )CONTINUE workspaces,
 and prevents starting of a thread for shared variable communication.

If the path to the interpreter is relative (which might be useful if you
do not know in advance where the APL interpreter will be installed) then
it must be in $PATH of the shell that runs the script.

@subsection How command line arguments are handled

As we have seen, GNU APL can be started directly (by entering the name
of the GNU APL binary on the command line of a shell, or indirectly by
entering the name of a script that provides the name of the GNU APL binary
on the first line of the script. In the latter case, the shell uses function
execve() to start APL, and one can provide additional arguments that are
passed on to APL. We briefly discuss both cases:

0. General Remark

There is a convention in GNU APL that command line options (and
possibly option arguments) that occur left of '----' are options directed
to (and understood by) the APL interpreter while options right of '----' are
passed to the APL application (and their exact format is defined by the
application). The command line options that were used to start APL can be
retrieved with ⎕ARG.

Example 1: APL started directly

We start APL with some command line options and display them with ⎕ARG.
The command line options for the interpreter are --silent, --id, and 1010,
while the options app1 and app2 are for the APL application:

@verbatim
$ apl --silent -l 37 -- app1 app2
    ⊃⎕ARG
apl     
--silent
-l      
37      
--      
app1    
app2    
@end verbatim

Example 2: APL started indirectly

Starting APL indirectly means that there is a script (a text file with execute
permission) that contains APL code and has a special first line as described
above. There are now two sets of command line options: those passed to the
script and those on the first line of the scripts. When the script is started,
possibly with command line arguments, then the command line arguments entered
by the user are combined with the arguments on the first line of the script
in a way that is described in 'man 2 execve'.

Assume the script file SCRIPT.apl contains this (the file is shipped
with GNU APL):

@verbatim
#! /usr/local/bin/apl --id 1010 --script

      ⊃⎕ARG      ⍝ show command line options
      )OFF      ⍝ leave the interpreter

@end verbatim

Assume further that the script is started like this:

@verbatim
$ ./SCRIPT.apl sarg1 sarg2
@end verbatim

Then the following output, which shows the order of command line options
as seen by ⎕ARG, is produced:

@verbatim
   ⊃⎕ARG
/usr/local/bin/apl
--script          
./SCRIPT.apl      
sarg1             
sarg2 
@end verbatim

This tells us that the different names are constructed by execve() in the
following order:

1. Interpreter name (the first name in the script file, here: /usr/local/bin/apl)

2. Optional Interpreter arguments (here: ----script)

3. Script filename (here: ./SCRIPT.apl)

4. Script arguments (here: sarg1 sarg2)

CAUTION: as discussed in 'man 2 execve' the interpretation of the optional
interpreter arguments (2. above) is system specific and possibly not portable.
For that reason the optional interpreter argument should not be missing (you
can use ---- to provide at least one argument) and also not more than one
argument. On GNU/Linux systems the following first lines of the script are
understood:

@verbatim
/usr/local/bin/apl
/usr/local/bin/apl --
/usr/local/bin/apl -s
/usr/local/bin/apl --script
/usr/local/bin/apl -s --
/usr/local/bin/apl --script --
@end verbatim

The recommended form is: /usr/local/bin/apl ----script

Note that '----' and options that follow it ARE NOT shown in ⎕ARG if they
are given on the first line of the script, while '----' and options that follow
on the script command line ARE shown. There is no point in passing application
options in the script file via the command line to apl; instead you can use
them directly in the script.

Using '----' as last argument on the first line of the script file prevents any
of the options given to the script to be interpreted as APL options; all
such options are passed to the application via ⎕ARG.

@subsection Helpful Features for Scripting

In order to be really useful for scripting, three more features have been added:

* ⎕ARG: access to the command line arguments given to the interpreter
* ⎕ENV: access to the environment variables of the process running the
        interpreter, and
* ⎕INP: Here-Document-alike function for creating large text variables

The system variable ⎕ARG contains all command line arguments passed to the
interpreter. In the initial example above this would be a nested 3-element
vector:

@verbatim
    /usr/local/bin/apl --id 1010
@end verbatim

A feature particularly useful for CGI scripting (where some information is
passed to the APL script via environment variables) is the monadic system
function ⎕ENV B. ⎕ENV B returns all environment variables whose name
starts with B. If ⍴B is 0, like:

@verbatim
    ⎕ENV ''
@end verbatim

then all environment variables are returned.
The result of ⎕ENV is a N-by-2 matrix.
The first column is the name of the environment variable.
The second column is the value of the variable.
The number N of environment variables returned obviously depends on
the number of environment variables whose name begins with the prefix
given in B. B is case sensitive, but by convention the names of environment
are uppercase.

If you need to create a longer text, like the body of a web page, then you
would normally construct it like this:

@verbatim
BODY ← ⊂ 'First line'
BODY ← BODY , ⊂ 'Second line'
BODY ← BODY , ⊂ 'Third line'
   ...
@end verbatim

That is not very handy for longer texts. Instead you can write the following
in an APL script:

@verbatim
BODY←⎕INP 'END-OF-⎕INP'
First line
Second line
Third line
   ...
END-OF-⎕INP
@end verbatim

This works like "Here documents" in bash. The right argument of ⎕INP is
the end of text marker, ⎕INP also has a dyadic form where the left argument
specifies an escape sequence from text to apl and back to the text, similar
to PHP scripts:

'<?apl' '?>' ⎕INP 'END-OF-⎕INP'
First line
Time is now: <?apl ⍕⎕TS ?>
Third line
...
END-OF-⎕INP

@subsection Multi-Line Strings

Another feature of GNU APL to simplify the creation of values that contain
longer texts are strings that span several lines. One consequence of how ⎕INP
works is that the strings read by ⎕INP always originate in stdin of the
interpreter. In immediate execution mode (and therefore also in APL scripts)
stdin is the next lines entered by the user (interactive APL sessions) or
the next lines in the script file (in APL scripts). Often, however, a
programmer wants to specify long strings inside a defined function and not
on the top-level of an APL script. That renders ⎕SI almost useless for
defined functions.

In order to provide a way for defining long strings inside defined functions,
multi-line strings were introduced. They come in two flavors: old-style
and new-style.

@subsubsection Old-style Multi-Line Strings

Old-style multi-line strings were the first attempt to provide long strings for
defined functions. These strings are not allowed in immediate execution mode
because could easily be entered by mistake (by simply forgetting the
terminating " or ' of a string) and that would have obscured the traditional
behavior of immediate execution mode.

An  old-style multi-line string starts at the last " in a line of a defined
function that has line with an odd number of " characters.  It continues over
the subsequent function lines until the next ". The result is a nested APL
value containing one nested string per line involved.

For example:
@verbatim

∇Z←FOO
 Z←"ABC
 DEF
 GHIJK"
∇

4 ⎕CR FOO
┏→━━━━━━━━━━━━━━━━━━━━┓
┃┏→━━┓ ┏→━━━┓ ┏→━━━━━┓┃
┃┃ABC┃ ┃ DEF┃ ┃ GHIJK┃┃
┃┗━━━┛ ┗━━━━┛ ┗━━━━━━┛┃
┗∊━━━━━━━━━━━━━━━━━━━━┛
@end verbatim

If the first string is empty then the nested value starts with an empty
string, but completely empty lines in the defined function are being ignored:

@verbatim
∇Z←FOO
 Z←"
ABC
 DEF

  GHIJK"
∇

4 ⎕CR FOO
┏→━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃┏⊖┓ ┏→━━┓ ┏→━━━┓ ┏→━━━━━━┓┃
┃┃ ┃ ┃ABC┃ ┃ DEF┃ ┃  GHIJK┃┃
┃┗━┛ ┗━━━┛ ┗━━━━┛ ┗━━━━━━━┛┃
┗∊━━━━━━━━━━━━━━━━━━━━━━━━━┛
@end verbatim

@subsubsection New-style Multi-Line Strings

Even though the combination of ⎕INP for immediate execution and multi-line
strings for defined functions achieved the goal of specifying large amounts
of text in a simple manner, its  was certainly not very intuitive or elegant
to have different approaches for different APL modes.

This was leading to the new-style multi-line strings. They adopted the triple
quote (""") syntax know from e.g. the Python language. The syntax of new-style
multi-line strings cleaner: empty lines are handled more consistently and the
string lines are completely separated from the APL code lines.
More importantly, new-style multi-line strings work alike in immediate
execution mode, in scripts, and in defined functions. New-style strings are a
little different and more restrictive than their old-style companions:

* the starting """ must be placed at the end of an APL code line, i.e. no
  mixing of APL code and string content on the same line. In old-style strings
   the APL line on which the string started became part of the string while
   in new-style strings the strings begins at the following line.

* the ending """ must be placed at the end of a separate lines with only spaces
  allowed before the """ (to vertically align it with the leading """ if so
  desired). In old-style strings the text up to the termination " is part of
  the string while in new-style strings it is not.

* Neither the starting nor the ending line become nested strings of the result,
  and every line can be clearly identified as being either APL code or else
  string text.

Example:
@verbatim
 4 ⎕CR """
ABC
 DEF

  GHIJK
       """
┏→━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃┏→━━┓ ┏→━━━┓ ┏⊖┓ ┏→━━━━━━┓┃
┃┃ABC┃ ┃ DEF┃ ┃ ┃ ┃  GHIJK┃┃
┃┗━━━┛ ┗━━━━┛ ┗━┛ ┗━━━━━━━┛┃
┗∊━━━━━━━━━━━━━━━━━━━━━━━━━┛
@end verbatim

When entering a new-style multi-line strings then the prompt is prepended by
→ to indicate that a Multi-Line String is being entered.

⎕INP and old-style strings will coexist for s while, but may disappear at some
point in time.

@subsection Script Example

Note that the two different ways of running an APL script have an impact on
how ⎕ARG looks like. If stdin is redirected then there is only one (possibly
empty) set of command line options. Otherwise there are two set of command line
options: command line options for the apl interpreter and command line options
for the script.

Consider the following simple script called SCRIPT.apl in directory workspaces:

@verbatim
#! /usr/local/bin/apl --script

⊃⎕ARG    ⍝ show command line options
)OFF    ⍝ leave the interpreter
@end verbatim

If SCRIPT.apl is redirected to stdin of the APL interpreter:

@verbatim
 /usr/local/bin/apl --silent <  ../workspaces/SCRIPT.apl

 or

 /usr/local/bin/apl --silent -f ../workspaces/SCRIPT.apl
@end verbatim

then the first line @option{#! /usr/local/bin/apl --script} of file SCRIPT.apl 
is merely a comment (GNU APL accepts both the traditional APL character
⍝ and the character # as start of a comment). The @option{--script} option
is therefore ignored and the following mix of input and output is
shown on the screen. The input from the script is indented by the
usual APL prompt of 6 blanks, while the output of the APL interpreter
is not indented.

@verbatim
      #! /usr/local/bin/apl --script
      
      ⎕ARG      ⍝ show command line options
      )OFF      ⍝ leave the interpreter


@end verbatim

If we run the same script directly:

@verbatim
../workspaces/SCRIPT.apl
@end verbatim

Then we get:

@verbatim

 /usr/local/bin/apl --script ../workspaces/SCRIPT.apl 

@end verbatim

The @option{--script} implies @option{--noCIN} so that the

input lines for the interpreter are no longer echoed to the output.
That is most likely what you want when writing a script.

Also, the first line of the script is no longer ignored as a comment,
but controls the command line argument (and thus ⎕ARG) of the interpreter.
The additional command line argument @option{../workspaces/SCRIPT.apl}
comes from function execve (see 'man 2 execve').

If we provide an argument, say SCRIPTARG, to SCRIPT.apl:

@verbatim
../workspaces/SCRIPT.apl SCRIPTARG
@end verbatim

then it shows up at the end of ⎕ARG:

@verbatim

 /usr/local/bin/apl --script ../workspaces/SCRIPT.apl SCRIPTARG 

@end verbatim

A final note on scripting in GNU APL is that the ∇-editor works slightly
differently when it is used in a script. If a user edits an APL function
interactively then an attempt to open an existing function with a full
header gives a DEFN ERROR:

@verbatim

      ∇Z←FOO B
[1] ∇
      
            ∇Z←FOO B
DEFN ERROR+
      ∇Z←FOO B
             ^
      )MORE
attempt to ∇-open existing function with new function header

@end verbatim

In contrast to a user who can react to the DEFN ERROR, a script cannot detect
this situation and would continue to push lines (which were intended to be
the body of the defined function) into the APL interpreter. That would most
likely cause a fairly undesirable behavior.  For example, if the lines of
defined function start with line numbers (like [1], [2], ...) then every
such line would give a SYNTAX ERROR, and other errors can be expected as
well.

For that reason, if the ∇-editor is used in a script and attempts to redefine
an existing defined function then the existing function is simply overridden
with the new one and no DEFN ERROR is raised.

@node    Section 3.2
@section Axis argument in defined functions

Defined functions and operators (including lambdas) accept an axis argument.
For example:

@verbatim

∇Z←Average[X] B
 Z←(+/[X]B) ÷ (⍴B)[X]
∇

      Average[1] 5 5⍴⍳25
11 12 13 14 15

      Average[2] 5 5⍴⍳25
3 8 13 18 23

@end verbatim

Syntactically, the axis is used in the same way as for primitive functions
and operators.

There are no constraints on the axis such as being integers. Therefore you
can use an axis as a third function argument. Keep in mind, however, that
doing so will make your APL code incompatible with other APL interpreters.
Use this feature carefully!


@node    Section 3.3
@section Colored Output

The APL interpreter gets its input from the standard input (stdin),
which is normally connected to the user's keyboard,
but can also be a file if APL scripting, the @option{-f} option,
 or the @option{-T} option is used.

The APL interpreter prints its results on either the standard output (stdout)
for normal APL output, or to the error output (stderr) for additional
trouble-shooting information.

You can print the 3 channels stdin, stdout, and stderr in different colors
by means of the debug command ]XTERM. Command ]XTERM ON enables colored
output while ]XTERM OFF disables it (for example to avoid annoying ANSI
Escape sequences when forwarding stdout or stderr to a file).

By default colored output assumes a terminal (-emulation) that understands
ANSI (or VT100) Escape sequences. The xterm that comes with most recent
GNU/Linux distributions is a perfect choice supporting both colors and
UTF-8 (Unicode) encoded character I/O.

Non-ANSI terminals, as well as other colors than the default ones, can be
configured in the 'preferences' file.  The 'preferences' file also
contains a description of all possible color settings.


@node    Section 3.4
@section Comparison Rules

Both IBM APL2 and the ISO standard require that the arguments of <, ≤, ≥, and
> (but not = or ≠) are integer or real numbers, and that the argument of monadic
⍋ or ⍒ is a vector of integer or real numbers. In contrast GNU APL also allows
the comparison of characters and numbers or the comparison of complex numbers
according to the following, more general, rules.

Let A and B two APL values to be compared. The first comparison below that
succeeds (i.e. returns a result) is then the result of comparing A and B.
 
1. If (⍴⍴A) < (⍴⍴B) then A < B. And vice versa.

2. If (⍴A) < (⍴B) then A < B. And vice versa.

3. Otherwise ⍴A and ⍴B are equal. If all corresponding ravel elements of A
   and B are equal (i.e. tolerantly equal within ⎕CT as defined in the ISO
   standard) then A = B. Otherwise let A1 and B1 the first corresponding
   ravel elements of A and B with A1≠B1.

4. If A1 and B1 are both character values and (⎕UCS A1) < (⎕UCS B1) then
   A < B. And vice versa.

5. If A1 is a character and B1 is numeric, then A < B. And vice versa.

6. If A1 and B1 are both numeric values then:

6a. If (9○A1) < (9○B1) then A < B. And vice versa.

6a. Otherwise if (11○A1) < (11○B1) then A < B. And vice versa.

Another way of describing the rules above is that the comparison of two values
is comprised of sub-comparisons of certain properties of the values in the
following order:

@itemize
@item ranks of the values
@item shapes of the values
@item type (character vs. numeric) of the values,
@item Unicodes of character values,
@item real parts of numeric values,
@item imaginary parts of numeric values,
@end itemize

Note: Rules 1. and 2. above are only relevant for comparisons made in the
context of sorting (i.e. for ⍋ or ⍒). This is because for =, ≠, <, ≤, ≥,
or > either a RANK ERROR or a LENGTH ERROR is raised if the ranks or shapes
of A and B do not match:

@verbatim
      (9 8) < (1 2 3)
LENGTH ERROR
      9 8<1 2 3
      ^  ^

      ⍋(9 8) (1 2 3)
1 2
@end verbatim

The reason for comparing complex numbers first by their real parts and then
by their imaginary part and not, for example, first by their magnitude and
then by their angle is that the chosen order gives more consistent results
when comparing near-complex numbers or their true real companions. For
example, a magnitude first comparison of complex numbers would make ¯1 < ¯2J∈
for a near-complex ¯2J∈ but ¯1 > ¯2 for a true real ¯2.


@node    Section 3.5
@section Complex Numbers

Complex numbers are fully supported.


@node    Section 3.6
@section Debug Commands

Besides the classical commands like )LOAD or )SAVE there are a number of
debug commands that start with ] rather than ).
Regular commands start with ) and print their output on stdout.
Debug commands start with ] and print their output on stderr. Normally
you cannot easily distinguish between stdout and stderr, but another
feature, colored output, uses different colors for stdout and stderr.

Type )HELP or ]HELP in the interpreter for a list of all commands available.


@node    Section 3.7
@section Direct Functions (Lambdas)

GNU APL supports direct functions (aka. lambdas), but only in a rather
limited form.

@subsection Named Lambdas

A statement of the form

@verbatim
      FUN ← { body_statement } 
@end verbatim

creates a named lambda. body_statement can contain variable names ⍺ and ⍵
as well as function names ⍶ and ⍹ which are replaced by the actual arguments
of the lambda. If both ⍺ and ⍵ are present in body_statement then the lambda
is dyadic. If only ⍵ is present then it is monadic, and if neither ⍺ nor ⍵ is
present then the lambda is niladic.

Likewise, if ⍶ and ⍹ are present then the lambda is a dyadic operator. If only
 ⍶ is present then it is a monadic operator, and if neither ⍶ nor ⍹ is present
then the lambda is a normal function.

GNU APL supports an axis argument in normal user defined functions and
operators. In lambda expressions the Greek letter χ (Chi) is the variable
name for an axis argument.

The way a named lambda is implemented in GNU APL is that the expression

@verbatim
      FUN ← { body_expression }
@end verbatim

is translated to a two-line function ⎕FX 'lambda_header' 'body_expression'.

For example:

@verbatim
      )FNS

      SUM ← { ⍺ + ⍵ }

      )FNS
SUM

      ∇SUM[⎕]∇
[0] λ←⍺ SUM ⍵
[1] λ← ⍺ + ⍵ 

@end verbatim

The lambda_header is automatically deduced from the presence or absence
of the variable names (⍺, ⍵, and χ) and function names (⍶ and ⍹) in the
body_expression and from whether the body_expression is empty (no λ←) or
not (with λ←).

It is possible to specify local variables that work exactly like their
companions in normal defined functions. Please note that this is different
from some other APL interpreters which treat all variables in lambda bodies
as local variables. The syntax for specifying local variables is the same
as for the header in normal defined functions: they are added at the end
with semicolons as separators. In the above example one could add local
variables C and D like this:

@verbatim
      SUM ← { ⍺ + ⍵ ;C;D }

      ⎕CR 'SUM'
λ←⍺ λ1 ⍵;C;D 
λ← ⍺ + ⍵     

@end verbatim

If a named lambda is created inside a function, then the name of the lambda
(i.e. the name left of ← @{ ... @}) can be made a local variable of the
function in which the named lambda is created. This creates a lambda with
local scope.

Please note that the above only describes the current implementation of named
lambda in GNU APL. A consequence of that implementation is that the symbols
⍺, ⍵, ⍶, ⍹, and λ are pretty much behaving like user defined variables. In
particular, they can be used outside named or unnamed lambdas. However, that
may change in the future and therefore such use of ⍺, ⍵, ⍶, ⍹, and λ outside
is certainly a bad idea.

@subsection Unnamed Lambdas

An unnamed lambda is an expression inside @{ @} but without assigning it to a
name. This is often used together with the EACH operator.
For example:

@verbatim

      { ⍴ , ⍵ } ¨ 'a' 'ab' 'abc'
 1  2  3 

@end verbatim

Unnamed lambdas are automatically local in scope (similar to labels). They can
be passed as function arguments to operators. However, unnamed lambdas are NOT
inserted into the symbol table of the interpreter. They are therefore not
visible to functions like ⎕CR or by the ∇-editor. Occasionally the names λ1,
λ2, ... may show up in commands like )SIS. These names are automatically
generated for unnamed lambdas in order to provide a name in places where a
function name is needed.

@subsection Limitations of Lambdas

There are a number of features related to lambdas that are present in other
APL interpreters but that are NOT implemented in GNU APL. This includes
multiple statements, guards, lexical scoping, and probably more.

@node    Section 3.8
@section ]DOXY Command

A particularly useful debug command is ]Doxy. It dumps the current workspace
in brows-able HTML format with listings of defined functions and hyperlinks
between them.

@smallexample
]DOXY                   ⍝ write documentation to /tmp/WS-NAME/*
]DOXY dest              ⍝ write documentation to dest/WS-NAME/*
@end smallexample

The starting point for browsing the documentation are the files:

@smallexample
/tmp/WS-NAME/index.html         ⍝ for ]DOXY without arguments, resp.
dest/WS-NAME/index.html         ⍝ for e.g. ]DOXY dest
@end smallexample

The index.html files above usually corresponds to the following URIs in your
browser:

@smallexample
file:///tmp/WS-NAME   resp.
file:///absolute-path-to-dest/WS-NAME
@end smallexample

In the above examples is WS-NAME the )WSID of the workspace in which the ]DOXY
command was executed.

One can (and should make it a habit to) insert special comments into defined
function which are copied into proper places inside the documentation that is
generated by the ]DOXY command. These "Doxy" comments begin with ⍝⍝ (as opposed
to  "normal" APL comments that start with a single ⍝. Doxy comments are
typically one-liners that briefly explain what a function is supposed to do.

For example:

@verbatim
∇Z←A SUM B
 ⍝⍝ Return the sum of A and B          ← ]DOXY comment:  (double ⍝)
 ⍝  A: numeric                         ← "normal" APL comments (single ⍝) ...
 ⍝  B: numeric
 Z←A + B
∇
@end verbatim


@node    Section 3.9
@section )DUMP Command

GNU APL has a command )DUMP that saves a workspace to disk, similar to command
 )OUT.  The difference to command )OUT is the file format being produced.
While )OUT produces a file in IBM's workspace interchange format (aka. an
.atf file), )DUMP produces a file in GNU APL's script format (i.e. readable
APL statements). Files written with )DUMP can be edited with normal text
editors (vi, Emacs), read back with "apl -f", or made executable (see
scripting).


@node    Section 3.10
@section History and TAB completion

Until GNU APL 1.4 / SVN 465, GNU APL used libreadline for interactive user
input. libreadline did provide two useful features: tab expansion (the tab
key would expand file names) and history (the cursor up/down keys would recall
previously entered lines).

Since SVN 465 libreadline was removed and the standard TAB expansion and
history of libreadline were replaced by more context sensitive (i.e. APL
aware) implementations:

1. Instead of simply recalling the last line entered by the user, there are
   now different histories for different input contexts:

1a. The input history in immediate execution recalls the last line entered
 in immediate execution (and not, for example, lines entered in function
 editing mode or ⍞ input.

1b. Likewise, ⍞ recalls the last line entered for ⍞-input

1c. ⎕ recalls the last line entered for ⎕-input

1d. In the ∇-editor, the other function lines of the function being edited
can be recalled. This is far more handy than the ∇-editor commands for
recalling function lines (and which are not fully supported in GNU APL).

2. Instead of always TAB-completing file names, the tab character now
  understands different TAB-completion contexts:

2a. Input starting with . or / is completed as a filename like readline did.

2b. Input starting with ) or ] is completed as command name name or, to some
   extent, as command arguments.

2c. Input starting with ⎕ is completed as a system function name or a
    system variable name.

2d. Input starting with letters, ∆, or ⍙ is completed as a user defined
    function or variable name.


@node    Section 3.11
@section Logging Facilities

The APL interpreter has over 30 logging facilities. Each logging facility
can be ON (and then produces some logging output on stderr) or OFF. The
decision which logging facility shall be ON and which shall be  OFF can be
made at compile time (of the APL interpreter) or at run-time. 

If the decision is made at compile time - we call that static logging - then
it cannot be changed later on. Otherwise - we call that dynamic logging -
there is a debug command ]LOG that allows to turn logging facilities to be
turned ON or OFF.

@subsection Static Logging

By default the logging facilities that shall be turned ON are defined
statically. To change the logging facilities that shall be turned ON,
you can edit the file src/Logging.def which defines the different logging
facilities. The first argument of macro log_def() tells if the logging
facility shall be ON (1) or OFF (0).

Static logging results in a faster interpreter than dynamic logging because
the decision if something shall be logged or not is made at compile time
and not at run-time.

If you benchmark the APL interpreter, then ./configure Static Logging by
NOT setting DYNAMIC_LOG_WANTED=yes.

@subsection Dynamic Logging

Dynamic Logging is intended for trouble-shooters of GNU APL, but also for
those who are interested in the internals of GNU APL. Dynamic Logging is
enabled by setting DYNAMIC_LOG_WANTED=yes when running ./configure.

If Dynamic Logging is enabled, then the already mentioned file
src/Logging.def determines the initial setting of each logging facility.

The command

 ]LOG

(without arguments) then shows all logging facilities and their current
state. The command

]LOG N

toggles the state of logging facility N from OFF to ON and back.


@node    Section 3.12
@section Rational Numbers

GNU APL has limited support for rational numbers. Instead of dividing integers
(and possibly causing rounding errors), integer quotients are kept undivided
internally until some function requires a conversion to a floating point
(double) value.

Currently only +, -, ×, and ÷ preserve rational numbers where possible, but
this list may grow in the future. Monadic + (a no-op for non-complex numbers)
explicitly converts rational numbers to floating point numbers.

A quotient is internally stored as a 64-bit numerator and a 64-bit denominator.
In some cases arithmetic with rational numbers is faster than with doubles, but
in most cases it is slower.

For that reason support for rational numbers is disabled by default and must
be enabled via ./configure (see README-2-configure).


@node    Section 3.13
@section Hex Numbers

GNU APL supports sedecimal numbers. They start with $ and can be uppercase or
lowercase:

@verbatim
      $2a
42

      $2A
42

@end verbatim

@node    Section 3.14
@section User-defined Commands

There is a simple mechanism to define additional APL commands. This mechanism
is intended to introduce new commands by APL libraries. Like system commands,
user-define commands can only be executed in immediate execution mode and not
from user-defined functions or from ⍎. It is not intended to extend the
functionality of user-defined commands beyond what is being described in the
following.

A user-defined command ]NEW_COMMAND is created with the debug command
]USERCMD like this:

@verbatim
      ]USERCMD ]NEW_COMMAND APL_FUNCTION [mode]
@end verbatim

APL_FUNCTION is an APL function that will be called when the command is
entered in immediate execution mode. The entire line entered by the user,
starting at ]NEW_COMMAND, is the right argument of APL_FUNCTION. If mode is
missing (or 0) then APL_FUNCTION is called monadically. If mode is 1 then
APL_FUNCTION is called dyadically; the left argument is a vector of strings
that is the left argument broken down into individual argument strings.

The function APL_FUNCTION that implements a command need not exist when the
command is created.

A single user-defined command ]UCMD, or all user-defined commands can
be deleted like this:

@verbatim
      ]USERCMD REMOVE ]UCMD
      ]USERCMD REMOVE-ALL
@end verbatim

@node    Section 3.15
@section Monadic ⊢ and ⊣, dyadic ⊢ with Axis

Monadic ⊢ is the identity function. It returns its (committed or non-committed)
right argument as a non-committed value.

Conversely, monadic ⊣ (called @b{Hide} in GNU APL) discards its (committed or
non-committed) right argument and returns a committed integer scalar 0. 

For the most part there is no difference between a committed value (= a value
that was assigned to a variable, including ⎕ and ⍞) and a non-committed value.
The point where it does make a difference is when the value the final result
of a statement (as opposed to an intermediate result inside a statement). In
that situation (and only there) a non-committed value is being printed while
a committed value is not.

You can use ⊢ is a similar fashion as ⎕← at the left end of a statement,
in order to print a value even though it was previously assigned to a
variable.

The main motivation for ⊣ is that, at least in GNU APL, lambdas always return
a value. However, if a lambda is used only for the sake of its side effects, say
to print something, then the value returned by the lambda is often of no
interest and only messes up the APL output. In that situation ⊣ can be used
to suppress the printing of undesired return values from lambdas.

In earlier GNU APL versions, ⊣B and ⊢B would both return B; with ⊣ as committed
value and with ⊢ as non-committed value. But since the only real-life purpose
of ⊣ is to suppress the printing of B, the implementation of ⊣ was changed to
returning an committed integer scalar 0 instead of committed B. That reduced
the run-time of ⊣B from O(,B) to O(1). Also, ⊢B is marginally faster than ⎕←B.

Dyadic ⊢ with axis is a selection function that generalizes ⊣ and ⊢.

Let @b{Z←A[X] B}. Then:

@itemize
@item if X is a one-element vector and ↑X is 0 then Z ≡ A,
@item if X is a one-element vector and ↑X is 1 then Z ≡ B,
@item otherwise X selects corresponding items of A resp. B if the correspondent
 elements of X are 0 or 1 respectively. In that case, the shapes of A and B
 must match the shape of X, but one-element A or B are scalar extended to the
 shape of X.
@end itemize

Example:
@verbatim

      A←2 3⍴'abcdef'
      B←2 3⍴⍳6
      X←2 3⍴0 1 0 1 0
      A ⊢[X] B
a 2 c
4 e 6

   A ⊢[X] '*'
a*c

  '*' ⊢[X] B
* 2 *
4 * 6

@end verbatim


@node    Section 3.16
@section Bit-wise Logical Functions ⊤∧, ⊤∨, ⊤⍲, ⊤⍱, T≠, and T=

The APL functions And (∧), Or (∨), Nand (⍲), and Nor (⍱) operate primarily on
Boolean integers. Primarily means that the the LCM variant for ∧
and the GCD variant for ∨ are not considered in this context. (The LCM and
GCD variants are defined in the ISO standard and supported in GNU APL but
not in IBM APL2).

However, probably more often than not one needs to compute Boolean functions
between the bits of arbitrary (non-Boolean) integers and not between entire
Boolean integers 0 or 1. Although that is possible to do in standard APL,
the procedure is fairly awkward and, more importantly, inefficient:

@itemize
@item
convert every integer argument X to a 64-item Boolean vector X←(64⍴2)⊤X,
@item
call the Boolean function ∧, ∨, ⍲, ⍱, =, or ≠ with the converted arguments,
and
@item
convert the Boolean result vector R back to the integer result Z←2⊥R
@end itemize

Note: for Boolean arguments the APL functions ≠ resp. = can be used to compute
the more customary Boolean functions XOR and XNOR. In this context = and ≠ are
treated as Boolean functions even though they accept non-Boolean arguments,

For example (using  5 ⎕CR (4⍴256)⊤X to display X in hex):

@verbatim
      5 ⎕CR (4⍴256)⊤   A←$ABBADEAD
ABBADEAD
      5 ⎕CR (4⍴256)⊤   B←$00FF00FF
00FF00FF

      5 ⎕CR (4⍴256)⊤   2⊥ ((64⍴2)⊤A) ∧ (64⍴2)⊤B
00BA00AD

@end verbatim

With the bit-wise @b{And} (∣∧) the same can be achieved in a simpler fashion
and far more efficiently:

@verbatim
      ⍝ Traditional AND
      5 ⎕CR (4⍴256)⊤   A←$ABBADEAD
ABBADEAD
      5 ⎕CR (4⍴256)⊤   B←$00FF00FF
00FF00FF

      ⍝ bit-wise AND
      5 ⎕CR (4⍴256)⊤   A ⊤∧ B
00BA00AD
@end verbatim

@subsection Dyadic ⊤∧, ⊤∨, ⊤⍲, ⊤⍱, ⊤=, and ⊤≠

The dyadic forms of @b{⊤∧}, @b{⊤∨}, @b{⊤⍲}, and @b{⊤⍱} are simply the bit-wise
variants of their Boolean companions:

@verbatim
      A ⊤∧ B    ←→    2⊥ ((64⍴2)⊤A) ∧ (64⍴2)⊤B      ⍝ aka. AND
      A ⊤∨ B    ←→    2⊥ ((64⍴2)⊤A) ∨ (64⍴2)⊤B      ⍝ aka. OR
      A ⊤⍲ B    ←→    2⊥ ((64⍴2)⊤A) ⍲ (64⍴2)⊤B      ⍝ aka. NAND
      A ⊤⍱ B    ←→    2⊥ ((64⍴2)⊤A) ⍱ (64⍴2)⊤B      ⍝ aka. NOR
      A ⊤≠ B    ←→    2⊥ ((64⍴2)⊤A) ≠ (64⍴2)⊤B      ⍝ aka. XOR
      A ⊤= B    ←→    2⊥ ((64⍴2)⊤A) = (64⍴2)⊤B      ⍝ aka. NXOR or XNOR
@end verbatim

@subsection Monadic ⊤∨ and ⊤⍱

@b{⊤∧} and @b{⊤⍲}  have no monadic form, but @b{⊤∧}, @b{⊤∨}, and @b{⊤⍱} do.
Formally monadic @b{⊤∨} resp, @b{⊤⍱} are dyadic @b{⊤∨} resp, @b{⊤⍱} with
a left argument of 0:

@verbatim
      ⊤∨ B    ←→    0 ⊤∨ B      ⍝ real B to nearby integer
      ⊤⍱ B    ←→    0 ⊤⍱ B      ⍝ bit-wise Not
@end verbatim

Even though Or-ing a Boolean vector with 0 itself has no effect, the
monadic ⊤∨ and ⊤⍱ are still useful due to their side effects: conversion
from near-integer float values to integers (monadic @b{⊤∨} and inversion
of the bits (monadic @b{⊤⍱}, The latter is needed since ∼ has a monadic
form and as a consequence ⊤∼ was not an option for a bit-wise @b{Not}
function.

Monadic @b{⊤⍱ B} is the bit-wise @b{Not} function of its argument:

      ⊤⍱ B    ←→    2⊥ ~(64⍴2)⊤B

Monadic @b{⊤∨ B} converts near-integer values B into true integers:

@verbatim
      26 ⎕CR    1            ⍝ integer
16
      26 ⎕CR    1.1          ⍝ real
32
      26 ⎕CR    1÷1          ⍝ integer
16
      26 ⎕CR    1.1÷1.1      ⍝ real
32
      26 ⎕CR    ⊤∨ 1.1÷1.1   ⍝ integer
16
@end verbatim

That also works for complex numbers with a near-zero imaginary part:

@verbatim
      26 ⎕CR    1.1J0÷1.1      ⍝ real
32
      26 ⎕CR    ⊤∨ 1.1J0÷1.1      ⍝ integer
16
@end verbatim

As a matter of fact, @b{⊤∨} works for all near-Gaussian complex numbers,
but the effect is not visible with 26 ⎕CR since Gaussian and non-Gaussian
complex numbers have the same cell type in GNU APL.

@subsection Monadic ⊤∧

The ISO standard defines two different concepts to decide if a real number R
is close to an integer I,
@itemize
@item
the real number R is said to be @b{near} to integer I if the absolute
value of I-R is smaller than some small constant called the @b{integer
tolerance} in ISO and @b{system tolerance} in IBM APL2. The @b{integer
tolerance} is typically platform dependent (1E¯10 in GNU APL).

@item
the real number R is said to be @b{equal to integer I within ⎕CT} if the
absolute value of (I-R)/I is smaller than ⎕CT.
@end itemize

The first concept is an absolute distance from a real R to a nearby integer I
while the second concept is a relative distance (larger numbers are allowed to
be farther away from a nearby integer than smaller numbers). The two concepts
differ in the same way that absolute and relative errors do.

Now, all bit-wise functions described so far use the first concept, i,e,
if their their arguments are real or complex, then the smallest distance to
a (nearby) integer must not exceed the @b{integer tolerance}. In some contexts
that could be difficult to achieve and for that reason GNU APL provides
monadic ⊤∧ which works like ⊤∨ except that the permitted distance from a
nearby integer is now controlled by ⎕CT rather than by the integer tolerance.

All bit-wise logical functions throw a DOMAIN ERROR if an argument is not close
enough to an integer. integer tolerance is typically smaller than ⎕CT and
in that case is ⊤∧ little more tolerant than ⊤∨ regarding the distance to
nearby integers. In addition ⊤∧ gives the user (via ⎕CT) more control over
the permitted tolerance for real numbers in the neighborhood of integers.

@subsection Character Arguments for Monadic ⊤⍱ and Dyadic ⊤∧, ⊤∨, ==, and ≠≠

Some of the bit-wise operations are allowed to have characters as their right
argument. If the right argument is a character then the result is a character
as well. This can be useful for masking purposes such as extracting the lower
7 bits of 8-bit bytes containing ASCII characters.

The characters involved are treated as 32 bit quantities:

@verbatim
      5 ⎕CR 'A'
41
      5 ⎕CR ⊤⍱'A'                       ⍝ Note that 5 ⎕CR ANDs with $FF
BE

      256 256 256 256⊤ ⎕UCS ⊤⍱ 'A'      ⍝ ⊤⍱ 'A' is FFFFFFBE
255 255 255 190
      256 256 256 256⊤$FFFFFFBE
255 255 255 190
@end verbatim

@node    Section 3.17
@section Dyadic ⎕CR

The ⎕CR function has an optional left argument that selects one of several
formatting styles and conversion functions in addition to the well-known
monadic form.

Calling ⎕CR monadically without an axis and with an empty right argument
shows a list of all functions provided by ⎕CR:

@verbatim
      ⎕CR ''
@end verbatim

Say a @b{byte vector} is an integer vector with numbers having a (signed or
unsigned) 8-bit value (i.e. a value from -128 to 255 inclusive). Such byte
vectors are frequenctly used arguments and results of ⎕FIO functions.

Let Z←A ⎕CR B.

Then the left argument A of ⎕CR selects one of several sub-functions of ⎕CR:

A=0-4 or 7-9, or 29: various formatting styles (boxed, APL input/output, etc.).
Just try them out.

A=5 resp. A=6: convert byte vector B to a string of uppercase resp. lowercase
hex digits. Every byte in B becomes 2 characters in Z.

A=10: convert variable named in B to an APL expression producing it.

A=11: convert value B to byte vector Z in CDR ("Common Data Representation",
an IBM standard) format (similar to 3 ⎕TF).

A=12: convert byte vector Z in CDR format to value Z.

A=13: convert hex string B to byte vector Z.

If a conversion has an inverse conversion (like 12 being the inverse of 11)
then the inverse conversion can be expressed as the negative of the conversion
number. For example, 12 ⎕CR B is the same as ¯11 ⎕CR B.

A=14: conversion 11 followed by conversion 13 (Value to hex string in
CDR format)

A=15: conversion 13 followed by conversion 12 (hex string in CDR format
to Value)

A=16: encode byte vector B into Z (base64 encoding, RFC 4648)

A=17: decode base64 vector B into byte vector Z (base64 encoding, RFC 4648)

A=18: convert text vector B into byte vector Z (UTF8 encoding, RFC 3629) 

A=19: convert byte vector B into text vector Z (UTF8 encoding, RFC 3629)

A=20-25: like 3,4,7-9 but using a formatting similar to NARS APL ⎕FMT
(showing the axis lengths as numbers instead of → and ↓)

A=26: Z is the cell types of the ravel elements of B (2: character,
16: integer, 32: real number, 64: complex number.

A=27: Z[I] is the primary data representation (for example the real part 
of a complex number, or the numerator of a rational number) of B[I].

A=28: Z[I] is the additional data representation (for example the imaginary
part of a complex number, or the denominator of a rational number) of B[I].

A=30: Z is B with all top-level elements conformed to a common rank and
shape (as required by the ⍤ operator). This conversion is primarily used 
internally bu the GNU APL interpreter.

A=31 or A=32: These conversions are used internally by ⎕INP.

A=33: convert tagged byte vector to a TLV (Tag/Length/Value) buffer. The TLV
buffer can be sent over a byte stream (socket) and easily decoded at the other
end. Say B = B[1], B[2], ..., B[n] such that B1 is an Integer (the tag) and
B[j] is a character in the range 0.255 for j > 1. Let Z←33 ⎕CR B with
Z = Z[1], Z[2], ... Z[m]. Then Z[1 2 3 4] is the 4 byte tag, Z[5 6 7 8]
is the 4 byte data length (n-1) == (m - 8) and 1↓B == 8 ↓ Z. In other words,
the first 4 bytes of Z are the tag in big endian byte order, the next 4 bytes
are the length of B except the tag, and the rest of Z is B except the tag.

Example:
@verbatim
      Tag←55   ⍝ hex 37
      5 ⎕CR 33 ⎕CR Tag,'Value'
000000370000000556616C7565
@end verbatim

A=34: this is the inverse of 33 ⎕CR. The intended use for 33 ⎕CR and 34 ⎕CR
is the transmission of a tagged byte vector over e.g a TCP socket:

  Sender                                          Receiver
  ------                                          --------
  T,Data →→→ 33 ⎕CR T,Data   →→→TCP connection→→→   34 ⎕CR T,Data →→→ T,Data

Example:
@verbatim
      34 ⎕CR ¯5 ⎕CR '000000370000000556616C7565'
55 Value
@end verbatim

The TLVs constructed by 33 ⎕CR can be sent back-to-back over a TCP connection
or similar in such a way that the receiver knows exactly after which byte
a TLV ends, which is perfect for connections over which data is sent
sporadically.  33 ⎕CR and 34 ⎕CR are particularly useful for encoding and
decoding TLV byte buffers exchanged between GNU APL and processes that were
forked by GNU APL with ⎕FIO[57] (aka. fork() and execve()).

Most dyadic ⎕CR variants whose argument B is expected to be a byte vector throw:

@enumerate
@item RANK ERROR if 1≠⍴⍴B
@item DOMAIN ERROR if one of the B[j] is not a proper byte value
@end enumerate

A proper byte value is either an integer in the range -128...255 including,
or a (Unicode) character with a code point between U+FF80 and U+FFFF
(including, corresponding to a negative signed char in C/C++) or between
U+0000...U+00FF (including, corresponding to an unsigned char or to a signed
positive char in C/C++). Real, Complex, or rational numbers are never proper
byte values even if their value is close to an integer. Nor are nested APL
values or values being assigned.

@node    Section 3.18
@section  Dyadic ⎕FX (Native Functions)

A Native Function is a function that can be called in APL like a normal user
defined APL function, but is implemented in C++.

A native function is created with A ⎕FX B. A is a string that is the
path of a shared library and B is the name of the function in APL.

The GNU APL package contains a shared library file_io.so that contains the
implementation of a native function for reading and writing files (fopen(),
fclose(), ...), For example:

@verbatim
      ⍝ fix native function in lib_file_io.so as FILE_IO
      ⍝
      'lib_file_io.so' ⎕FX 'FILE_IO'
FILE_IO

      ⍝ show overview of sub-functions in FILE_IO
      ⍝
      FILE_IO ''
   Functions provided by this library.
   Assumes 'lib_file_io.so'  ⎕FX  'FUN'

   Legend: e - error code
           i - integer
           h - file handle (integer)
           s - string
           A1, A2, ...  nested vector with elements A1, A2, ...

           FUN     ''    print this text on stderr
        '' FUN     ''    print this text on stdout
           FUN[ 0] ''    print this text on stderr
        '' FUN[ 0] ''    print this text on stdout

   Zi ←    FUN[ 1] ''    errno (of last call)
   Zs ←    FUN[ 2] Be    strerror(Be)
   Zh ← As FUN[ 3] Bs    fopen(Bs, As) filename Bs mode As
   Zh ←    FUN[ 3] Bs    fopen(Bs, "r") filename Bs
      ...
@end verbatim

Recent versions of GNU APL have replaced the native FILE_IO function above by
the system function ⎕FIO. ⎕FIO need not be ⎕FX'ed and is otherwise backward
compatible to the native function. New function numbers are, however, only
added to ⎕FIO and not to the old native function FILE_IO. The parameters of
the functions are described in the man pages for, e.g. strerror, fopen, ...
and are fairly obvious.

Many functions in FILE_IO have byte vectors as arguments or return byte 
vectors. A byte vector is an integer vector whose numbers fit into a byte
(so they are integers between -128 and 255). Often ⎕UCS and the functions in
dyadic ⎕CR are used to convert such byte vectors to/from, for example,
Unicode strings.

The GNU APL package also contains other shared libraries as templates
for your own native functions. Copy one of the files
 src/native/template_F0.cc (for
niladic native functions), src/native/template_F12.cc (for nomadic native
functions), src/native/template_OP1.cc (for monadic native operators),
or src/native/template_OP2/cc (for dyadic native operators) to your own
.cc file and adjust src/native/Makefile.am accordingly.

Note: The )IN and )OUT commands of GNU APL support native functions, but
in order to do so they have to use dyadic ⎕FX. This renders the workspace
interchange file (.atf files) written by )OUT incompatible with all other
APL interpreters if the workspace contains native functions. The )OUT 
command prints a warning when the )OUT command is used with a
workspace that contains native functions.

Note: As of GNU APL 1.6, the native function FILE_IO has been turned into the
system function ⎕FIO. The syntax of ⎕FIO is the same as for FILE_IO. The
)CLEAR workspace command will close all open files. 


@node    Section 3.19
@section ⎕ARG - Interpreter command line arguments

⎕ARG contains the command line arguments with which GNU APL was invoked.
@xref{Section 3.1}.


@node    Section 3.20
@section ⎕DLX - Knuth's Dancing Links Algorithm

⎕DLX is an implementation of Donald Knuth's Dancing Links Algorithm (called
DLX by Knuth himself, but is sometimes also referred to as Knuth's Algorithm X)
⎕DLX is a generic backtracking machinery that can be used to dramatically
simplify problems like the 8 queens problem on a chess board or sudokus.

The monadic form of ⎕DLX, i.e. ⎕DLX B, is a shortcut for 0 ⎕DLX B. It
computes the first solution for the constraint matrix B.

The dyadic form of ⎕DLX, i.e. A ⎕DLX B, has a integer scalar A as left argument
which determines the details of the computation as follows:

A > 0: The algorithm tries to find all solutions, but stops when A solutions
have been found. This is handy while debugging code using ⎕DLX. The
result is a nested vector with one vector item per solution.

A = 0: The algorithm stops when the first solution was found. In this case
the solution is a simple (non-nested) numeric vector.

A = ¯1: like A > 0 but finding all solutions

A = ¯2: like A = 0 but instead of returning the first solution, the number of
solutions (i.e. 0 or 1), the number of backtracks, and the number of
link dances is returned as a 3-element numeric vector.

A = ¯3: like A = ¯1 but instead of returning all solutions, the number of
solutions, the number of backtracks, and the number of
link dances is returned as a 3-element numeric vector.

A = ¯4: A number of single step in Knuth's Algorithm are performed. Let e.g.
A←¯4 r1 r2 r3. Then Z←A ⎕DLX B is the matrix B after 3 steps r1, r2, and r3
have been performed. r1, r2, and r3 are valid (as per ⎕IO) row numbers of B,
and a step with a given row changes B as follows:
@itemize
@item
the given row is set to 0 (this row becomes part of the final result),
@item
all other rows that have a 1 or a 2 in the same column as B are set to 0
(these 1s or 2s in the other rows conflict with the 1 or 2 in the given row
and are therefore removed from B), and
@item
all columns that have no 1s or 2s left are removed from B (these columns have
a 1 or 2 in B and the constraint is therefore satisfied).
@end itemize
The purpose of ¯4 ⎕DLX is:
@itemize
@item
To demonstrate how Knuth's algorithm works, and/or
@item
To preset some initial values in B. For example one can first initialize
the constraints for an empty Sudoku (which is the same matrix for all Sudokus)
and then enter the initial digits of a particular Sudoku using 4 ⎕DLX. If there are, say, 20 initial digits in the Sudoku then A has 21 elements (¯4 plus the
20 rows representing the 20 initial digits. The result of ¯4 ⎕DLX B has the
same number of rows as B (with some rows now cleared), but fewer columns than B.
@end itemize

The right argument B of ⎕DLX B or A ⎕DLX B is a constraints matrix whose
columns consist of either 0s and 1s (called a primary column) or 0s and 2s
(called secondary columns). The 0s, 1s and 2s can be the integers 0, 1, or 2,
characters '0', '1', or '2' respectively, or ' ' meaning '0'. The character
representation is useful when B becomes large and shall be printed because
the spaces in the numerical variant will not be printed. In the following,
B is assumed to be numeric.

Let Z←A ⎕DLX B, and let R be a solution in Z, that is, Z itself (A = 0) or
R is Z[k] for some k if A ≠ 0. And let S←+⌿B[R].

Then S = s1 s2 s3, ... sN where N is the number of columns in B and sj=1
if j is a primary column of B and sj∈0 1 if j is a secondary column of B.

In other words, ⎕DLX B computes a subset of the rows of B in such a way that
for every column j of B exactly one (for primary column j) or at most one
(for a secondary column) of the rows in a solution has its j'th element set
to 1 and all other words set their j'th element set to 0.

In yet other words, for every solution returned by ⎕DLX B, a 1 in one row
prevents all other rows that also have a 1 in that column, and all rows
together have exactly one 1 in every primary column and at most one 1 in
every secondary column. In the absence of secondary columns, the problem
solved by ⎕DLX is also known as the "exact cover problem"

If all that sounds weird and useless, consider the following APL program
for finding all solutions of the 8 Queens problem on a chess board (which
probably every programmer has programmed at some point in time):

@verbatim
      RC←8↑'1' ◊ D←15↑¯8↑'2'   ⍝ helpers for constructing Q8
      ⍝     rows   cols   diag1    diag2
      Q8←⊃{(R⌽RC),(C⌽RC),((C-R)⌽D),((¯7-R+C)⌽D)⊣(R C)←-8 8⊤⍵-⎕IO} ¨ ⍳64
      Z←¯1 ⎕DLX Q8
      {⎕UCS (65+⌊⍵÷8)(49+8∣⍵←⍵-⎕IO)} ¨ ⊃Z[1 2 3 92] ⍝ solutions 1, 2, and 92
 A1 B6 C8 D3 E7 F4 G2 H5 
 A1 C5 F4 H3 D8 G6 B7 E2 
 A8 D6 H4 G7 C1 F5 B3 E2 

@end verbatim

Obviously Z contains solutions for the 8 Queens problem; the total number of
solutions is well known to be 92 and we showed only the first two and the
last solution above.

The constraint matrix Q8 is the key to success. The matrix has 64 rows - one
row for every field of the chess board. And it has 8 + 8 + 15 + 15 columns.
The first 8 columns of Q8 are constraints that prevent more than one Queen
to be placed in the same row of the chess board (the argument ⍵ is the field
number counting from left to right and from bottom to top).
The next 8 columns of Q8 are constraints that prevent more than one Queen
to be placed in the same column of the chess board.

If we would call ⎕DLX with only these constraints, i.e. ⎕DLX T8←64 16↑Q8,
then we would get the solutions of the 8 tower problem. However, we continue
and add 15 more constraints for each of the two diagonals. The resulting
constraint matrix Q8 is this:

@verbatim
      Q8

1       1              2                     2
1        1              2                   2 
1         1              2                 2  
1          1              2               2   
1           1              2             2    
1            1              2           2     
1             1              2         2      
1              1              2       2       
 1      1             2                     2 
 1       1             2                   2  
 1        1             2                 2   
 1         1             2               2    
 1          1             2             2     
 1           1             2           2      
 1            1             2         2       
 1             1             2       2        
  1     1            2                     2  
  1      1            2                   2   
  1       1            2                 2    
  1        1            2               2     
  1         1            2             2      
  1          1            2           2       
  1           1            2         2        
  1            1            2       2         
   1    1           2                     2   
   1     1           2                   2    
   1      1           2                 2     
   1       1           2               2      
   1        1           2             2       
   1         1           2           2        
   1          1           2         2         
   1           1           2       2          
    1   1          2                     2    
    1    1          2                   2     
    1     1          2                 2      
    1      1          2               2       
    1       1          2             2        
    1        1          2           2         
    1         1          2         2          
    1          1          2       2           
     1  1         2                     2     
     1   1         2                   2      
     1    1         2                 2       
     1     1         2               2        
     1      1         2             2         
     1       1         2           2          
     1        1         2         2           
     1         1         2       2            
      1 1        2                     2      
      1  1        2                   2       
      1   1        2                 2        
      1    1        2               2         
      1     1        2             2          
      1      1        2           2           
      1       1        2         2            
      1        1        2       2             
       11       2                     2       
       1 1       2                   2        
       1  1       2                 2         
       1   1       2               2          
       1    1       2             2           
       1     1       2           2            
       1      1       2         2             
       1       1       2       2              
@end verbatim

To see how, for example, the first solution looks like and how it relates
to the constraints matrix Q8:

@verbatim

      ⍝ the rows in Q8 of the first solution
      ⍝
      Z[1]
 1 14 24 27 39 44 50 61 

      ⍝ the first solution translated back into the problem domain
      ⍝
      {⎕UCS (65+⌊⍵÷8)(49+8∣⍵←⍵-⎕IO)} ¨ ⊃Z[1]
 A1 B6 C8 D3 E7 F4 G2 H5 

      ⍝ the constraints of the rows of the first solution
      ⍝
      Q8[⊃Z[1];]
1       1              2                     2
 1           1             2           2      
  1            1            2       2         
   1      1           2                 2     
    1         1          2         2          
     1     1         2               2        
      1  1        2                   2       
       1    1       2             2           

      ⍝ all primary contraints met?
      ⍝
      +⌿ ' '≠ Q8[⊃Z[1];] 
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 0 0 1 1 1 1 1 1 
      1 0 0 0 0 1

@end verbatim


And that's it: call ⎕DLX to get the solution(s). In general all problems that
can be solved by ⎕DLX contain 3 steps:

@itemize @bullet
@item translate the problem into a constraints matrix B,
@item Z←⎕DLX B, and
@item translate the result Z back into the problem domain.
@end itemize

Another application of ⎕DLX is solving sudokus. The constraints matrix is
a little more complicated, but the principle is the same.


@node    Section 3.21
@section ⎕ENV - Environment Variables

⎕ENV contains the environment variables of the process that is running
GNU APL. @xref{Section 3.1}.


@node    Section 3.22
@section ⎕FIO - File I/O Functions

As of GNU APL 1.6, the native function FILE_IO has been replaced by the
system function ⎕FIO. ⎕FIO normally takes a numeric axis argument which
selects one of many different functions, most of which are contained in
the standard C library. The arguments for these function are usually the same
as the corresponding C function and the man page for each functions describes
the meaning of the arguments.

For example, ⎕FIO[3] corresponds to fopen() and 'man fopen' explains what fopen does (opening a file).

Calling ⎕FIO monadically without an axis and with an empty right argument
shows a list of all functions provided by ⎕FIO:

@verbatim
      ⎕FIO ''
   Functions provided by ⎕FIO...

   Legend: a - address family, IPv4 address, port (or errno)
           d - table of dirent structs
           e - error code (integer as per errno.h)
           h - file handle (integer)
           i - integer
           n - names (nested vector of strings)
           s - string
           u - time divisor: 1       - second
                             1000    - milli second
                             1000000 - micro second
           y4 - seconds, wday, yday, dst (
           y67- year, mon, day, hour, minute, second, [dst]
           y9 - year, mon, day, hour, minute, second, wday, yday, dst
           A1, A2, ...  nested vector with elements A1, A2, ...

           ⎕FIO     ''    print this text on stderr
        '' ⎕FIO     ''    print this text on stdout
           ⎕FIO[ 0] ''    print this text on stderr
        '' ⎕FIO[ 0] ''    print this text on stdout

   Zi ←    ⎕FIO[ 1] ''    errno (of last call)
   Zs ←    ⎕FIO[ 2] Be    strerror(Be)
   Zh ← As ⎕FIO[ 3] Bs    fopen(Bs, As) filename Bs mode As
   Zh ←    ⎕FIO[ 3] Bs    fopen(Bs, "r") filename Bs

File I/O functions:

   Ze ←    ⎕FIO[ 4] Bh    fclose(Bh)
   Ze ←    ⎕FIO[ 5] Bh    errno (of last call on Bh)
   Zi ←    ⎕FIO[ 6] Bh    fread(Zi, 1, 5000, Bh) 1 byte per Zi
   Zi ← Ai ⎕FIO[ 6] Bh    fread(Zi, 1, Ai, Bh) 1 byte per Zi
   Zi ← Ai ⎕FIO[ 7] Bh    fwrite(Ai, 1, ⍴Ai, Bh) 1 byte per Ai
   Zi ←    ⎕FIO[ 8] Bh    fgets(Zi, 5000, Bh) 1 byte per Zi
   Zi ← Ai ⎕FIO[ 8] Bh    fgets(Zi, Ai, Bh) 1 byte per Zi
   Zi ←    ⎕FIO[ 9] Bh    fgetc(Zi, Bh) 1 byte
   Zi ←    ⎕FIO[10] Bh    feof(Bh)
   Zi ←    ⎕FIO[11] Bh    ferror(Bh)
   Zi ←    ⎕FIO[12] Bh    ftell(Bh)
   Zi ← Ai ⎕FIO[13] Bh    fseek(Bh, Ai, SEEK_SET)
   Zi ← Ai ⎕FIO[14] Bh    fseek(Bh, Ai, SEEK_CUR)
   Zi ← Ai ⎕FIO[15] Bh    fseek(Bh, Ai, SEEK_END)
   Zi ←    ⎕FIO[16] Bh    fflush(Bh)
   Zi ←    ⎕FIO[17] Bh    fsync(Bh)
   Zi ←    ⎕FIO[18] Bh    fstat(Bh)
   Zi ←    ⎕FIO[19] Bh    unlink(Bc)
   Zi ←    ⎕FIO[20] Bh    mkdir(Bc, 0777)
   Zi ← Ai ⎕FIO[20] Bh    mkdir(Bc, AI)
   Zi ←    ⎕FIO[21] Bh    rmdir(Bc)
   Zi ← A  ⎕FIO[22] 1     printf(         A1, A2...) format A1
   Zi ← A  ⎕FIO[22] 2     fprintf(stderr, A1, A2...) format A1
   Zi ← A  ⎕FIO[22] Bh    fprintf(Bh,     A1, A2...) format A1
   Zi ← Ac ⎕FIO[23] Bh    fwrite(Ac, 1, ⍴Ac, Bh) 1 Unicode per Ac, Output UTF8
   Zh ← As ⎕FIO[24] Bs    popen(Bs, As) command Bs mode As
   Zh ←    ⎕FIO[24] Bs    popen(Bs, "r") command Bs
   Ze ←    ⎕FIO[25] Bh    pclose(Bh)
   Zs ←    ⎕FIO[26] Bs    return entire file Bs as byte vector
   Zs ← As ⎕FIO[27] Bs    rename file As to Bs
   Zd ←    ⎕FIO[28] Bs    return content of directory Bs
   Zn ←    ⎕FIO[29] Bs    return file names in directory Bs
   Zs ←    ⎕FIO 30        getcwd()
   Zn ← As ⎕FIO[31] Bs    access(As, Bs) As ∈ 'RWXF'
   Zh ←    ⎕FIO[32] Bi    socket(Bi=AF_INET, SOCK_STREAM, 0)
   Ze ← Aa ⎕FIO[33] Bh    bind(Bh, Aa)
   Ze ←    ⎕FIO[34] Bh    listen(Bh, 10)
   Ze ← Ai ⎕FIO[34] Bh    listen(Bh, Ai)
   Za ←    ⎕FIO[35] Bh    accept(Bh)
   Ze ← Aa ⎕FIO[36] Bh    connect(Bh, Aa)
   Zi ←    ⎕FIO[37] Bh    recv(Bh, Zi, 5000, 0) 1 byte per Zi
   Zi ← Ai ⎕FIO[37] Bh    recv(Bh, Zi, Ai, 0) 1 byte per Zi
   Zi ← Ai ⎕FIO[38] Bh    send(Bh, Ai, ⍴Ai, 0) 1 byte per Ai
   Zi ← Ac ⎕FIO[39] Bh    send(Bh, Ac, ⍴Ac, 0) 1 Unicode per Ac, Output UTF8
   Zi ←    ⎕FIO[40] B     select(B_read, B_write, B_exception, B_timeout)
   Zi ←    ⎕FIO[41] Bh    read(Bh, Zi, 5000) 1 byte per Zi
   Zi ← Ai ⎕FIO[41] Bh    read(Bh, Zi, Ai) 1 byte per Zi
   Zi ← Ai ⎕FIO[42] Bh    write(Bh, Ai, ⍴Ai) 1 byte per Ai
   Zi ← Ac ⎕FIO[43] Bh    write(Bh, Ac, ⍴Ac) 1 Unicode per Ac, Output UTF8
   Za ←    ⎕FIO[44] Bh    getsockname(Bh)
   Za ←    ⎕FIO[45] Bh    getpeername(Bh)
   Zi ← Ai ⎕FIO[46] Bh    getsockopt(Bh, A_level, A_optname, Zi)
   Ze ← Ai ⎕FIO[47] Bh    setsockopt(Bh, A_level, A_optname, A_optval)
   Ze ← As ⎕FIO[48] Bh    fscanf(Bh, As)
   Zs ←    ⎕FIO[49] Bs    return entire file Bs as nested lines
   Zs ← LO ⎕FIO[49] Bs    ⎕FIO[49] Bs and pipe each line through LO.
   Zi ←    ⎕FIO[50] Bu    gettimeofday()
   Zy4←    ⎕FIO[51] By67  mktime(By67)  Note: Jan 2, 2017 is: 2017 1 2 ...
   Zy9←    ⎕FIO[52] Bi    localtime(Bi) Note: Jan 2, 2017 is: 2017 1 2 ...
   Zy9←    ⎕FIO[53] Bi    gmtime(Bi)    Note: Jan 2, 2017 is: 2017 1 2 ...
   Zi ←    ⎕FIO[54] Bs    chdir(Bs)
   Ze ← As ⎕FIO[55] Bh    sscanf(Bs, As) As is the format string
   Zs ← As ⎕FIO[56] Bs    write nested lines As to file named Bs

Benchmarking functions:

           ⎕FIO[200] Bi    clear statistics with ID Bi
   Zn ←    ⎕FIO[201] Bi    get statistics with ID Bi
           ⎕FIO[202] Bs    get monadic parallel threshold for primitive Bs
        Ai ⎕FIO[202] Bs    set monadic parallel threshold for primitive Bs
           ⎕FIO[203] Bs    get dyadic parallel threshold for primitive Bs
        Ai ⎕FIO[203] Bs    set dyadic parallel threshold for primitive Bs

@end verbatim


A new feature of ⎕FIO (which is not available with the native function FILE_IO)
is ⎕FIO[49]. ⎕FIO[49] is a monadic operator which takes a monadic conversion
function as function argument. For example:

@smallexample
Z←F ⎕FIO[49] 'filename'
@end smallexample

reads the file named filename line by line. For every line read, the conversion
function F is called and the result returned by F is enclosed and stored in Z.
In other words,

@smallexample
Z←F ⎕FIO[49] 'filename'
@end smallexample

does:

@smallexample
Z F¨Z←⎕FIO[49] 'filename'
@end smallexample


@node    Section 3.23
@section ⎕FFT - Fast Fourier Transform

For those interested in signal processing and the like, GNU APL provides ⎕FFT:

The monadic form ⎕FFT B is a shortcut for the dyadic form 0 ⎕FFT B. It computes
the FFT of complex or real B without applying a window function.

The dyadic form A ⎕FFT B provides more control over what ⎕FFT computes. A is
an integer scalar which falls into one of three ranges.

The first range from ¯15 to ¯10 does not compute an FFT, but returns the result
of multiplying B with one of several window functions, that are frequently
used in the context of FFTs. The result has same shape as B and can be used for
analyzing or troubleshooting FFTs:

@itemize
@item A=¯10: no FFT, return the Hann window applied to B
@item A=¯11: no FFT, return the Hamming window applied to B
@item A=¯12: no FFT, return the Blackman window applied to B
@item A=¯13: no FFT, return the Blackman-Harris window applied to B
@item A=¯14: no FFT, return the Blackman-Nuttal window applied to B
@item A=¯15: no FFT, return the Flat-Top window applied to B
@end itemize

The second range around 0 contains the computation of the forward and inverse
FFTs:

@itemize
@item  0 ⎕FFT B returns the "normal" (aka. forward) FFT of the numeric array B.
@item ¯1 ⎕FFT B returns the inverse FFT of the numeric array B.
@end itemize

The third range from 10 to 15 corresponds to the first range and first
multiplies B with a window function and then computes the FFT:

@itemize
@item A=2: FFT(B × Hann window)
@item A=3: FFT(B × Hamming window)
@item A=4: FFT(B × Blackman window)
@item A=5: FFT(B × Blackman-Harris window)
@item A=6: FFT(B × Blackman-Nuttal window)
@item A=7: FFT(B × Flat-Top window)
@end itemize

⍴⍴B can be 1 (one-dimensional FFT, the most common case) or more. The
implementation of ⎕FFT uses libfftw3, aka. "The fastest Fourier Transform in
the West". GNU APL checks the presence of libfftw3 when it is ./configured.
If libfftw3 is present then ⎕FFT will hopefully return the expected result;
if not then a DOMAIN ERROR will be raised when ⎕FFT is being used.

⎕FFT honors the presence of /etc/fftw/wisdom (see man fftw-wisdom) to speed
up the computations performed by ⎕FFT. Creating /etc/fftw/wisdom will take a
few hours, though, so that creating it will not pay off for most mortals.

@node    Section 3.24
@section ⎕GTK - GTK Interface

GTK (Gimp Toolkit) is a rather powerful library for creating graphical user
interfaces (GUIs). ⎕GTK makes a subset of the almost 10000 functions in the
different GTK libraries available to GNU APL programs. With ⎕GTK a GNU APL
program can, for example, replace the somewhat crude ⎕ or ⍞ input methods
of standard APL with a more intuitive GUI.

The details of using ⎕GTK would go far beyond the scope of this info manual
and has therefore been put into a separate document.
See: @b{HOWTOs/Quad-GTK.html}.

@node    Section 3.25
@section ⎕PLOT - Plot Data

⎕PLOT is a function for visualizing numerical APL values. The values to be
plotted are provided as the right argument of ⎕PLOT while the optional
left argument controls details of the output, such as the plot window size,
colors for lines and grids, etc.

The general syntax of ⎕PLOT is:

@verbatim
   ⎕PLOT ''      ⍝ show a list of attrinutes and their default values
   H←⎕PLOT B     ⍝ plot B with all attributes set to their default values
   H←A ⎕PLOT B   ⍝ plot B with some of the default attributes overridden
   ⎕PLOT H       ⍝ close the plot window with handle H
   ⎕PLOT  0      ⍝ verbosity: OFF (do not print attribute values)
   ⎕PLOT ¯1      ⍝ verbosity: ON (print attribute values before plotting)
   ⎕PLOT ¯2      ⍝ verbosity: DEBUG (also print debug information)
@end verbatim

@subsection The Plot Data B

The Plot Data B can be a vector (in that case a single plot line is being
plotted) or a matrix (in that case one plot line per matrix row is being
plotted, by default in different colors). Each data item has to be numeric
and represents one point in the plot. The points that are adjacent in a row
of the matrix are connected by lines. By default plotted points and the lines
connecting them have the same color. However, all colors used, all diameters
of points, and all thicknesses of the lines can be controlled by overriding
the default values (dyadic A ⎕PLOT B).

@subsubsection Complex Plot Data

If a data item B[N] or B[row;N] is @b{complex}, say B[N] = x + iy. then it is
placed (after some scaling) at position (x, y) of the plot. The X-range
[Xmin ... Xmax] of the plot is then determined by the real parts of B,
and the Y-range [Ymin ... Ymax] of the plot is determined by the imaginary
parts of B. That is:

@verbatim
Xmin ← ⌊/,9○B    ⍝ smallest real part of B
Xmax ← ⌈/,9○B    ⍝ largest real part of B
Ymin ← ⌊/,11○B   ⍝ smallest imaginary part of B
Ymax ← ⌈/,11○B   ⍝ largest imaginary part of B
@end verbatim

Example (plot a circle (actually: a regular 20-gon)):

@verbatim
      ⎕PLOT +⌿1 0J1×[1]1 2 ∘.○ (0,⍳2×N) × ○÷N←10
@end verbatim

produces this plot window (only visible in the HTML version of this document;
in text mode see file @b{doc/PLOT_circle.png}):

@image {PLOT_circle}

@subsubsection Real Plot Data

On the other hand, if a data item B[N] or B[row;N] is @b{real}, then it is
placed at position (N, x) of the plot. The X-range is then\
[⎕IO ... ⎕IO + ¯1↑⍴B] and the Y-range [Ymin ... Ymax] of the plot is
determined by the values parts of B. That is:

@verbatim
Xmin ← ⎕IO         ⍝ smallest real part of B
Xmax ← ⎕IO + ⌈/B   ⍝ largest real part of B
Ymin ← ⌊/,B        ⍝ smallest value in B
Ymax ← ⌈/,B        ⍝ largest value in B
@end verbatim

In theory one can also mix real and complex values, even though doing so makes
little sense.

Example:

@verbatim
      ⎕PLOT ⎕PLOT 0 1 ¯1 2 ¯2 3 ¯3
@end verbatim

produces this plot window (only visible in the HTML version of this document;
in text mode see file @b{doc/PLOT_zigzag.png}):

@image {PLOT_zigzag}

@subsection The Plot Attributes A

As can be displayed by ⎕PLOT "" there is quite a number of attributes that
control how the resulting plot looks like:

@verbatim
      ⎕PLOT ''

   ⎕PLOT Usage:

   ⎕PLOT B     plot B with default attribute values
   A ⎕PLOT B   plot B with attributes A

   A is a nested vector of strings.
   Each string has the form "Attribute: Value"
   Colors are specified either as #RGB or as #RRGGBB or as RR GG BB)
   The attributes understood and their defaults are:

   1. Global (plot window) Attributes:

caption:            GNU APL PLOT   (plot window caption)
pa_width:           600 pixel      (plotarea width)
pa_height:          400 pixel      (plotarea height)
pa_border_L:        30 pixel       (pixels left of the plotarea)
pa_border_R:        20 pixel       (pixels right of the plotarea)
pa_border_T:        25 pixel       (pixels above the plotarea)
pa_border_B:        25 pixel       (pixels below the plotarea)
gridx_style:        1              (X grid style (0-2))
gridx_pixels:       44 pixel       (pixels between X grid lines)
gridy_style:        1              (Y grid style (0-2))
gridy_pixels:       33 pixel       (pixels between Y grid lines)
border_width:       10 pixel       (width of the window border)
canvas_color:       #FFFFFF        (background color of the plot window)
gridX_color:        #000000        (color of the X-grid lines)
gridX_line_width:   1 pixel        (thickness of the X-grid lines)
gridY_color:        #000000        (color of the Y-grid lines)
gridY_line_width:   1 pixel        (thickness of the Y-grid lines)
legend_X:           50 pixel       (the X position of the legend)
legend_Y:           50 pixel       (the Y position of the legend)
legend_dY:          15 pixel       (the distance between legend lines)
legend_lX:          50 pixel       (the length of the legend lines)

   2. Local (plot line N) Attributes:

line_color-N:       #00FF00        (the color of plot line N)
line_width-N:       3 pixel        (the thickness of plot line N)
point_color-N:      #00FF00        (the color of the plot points)
point_size-N:       8 pixel        (the diameter of the plot points)
legend_name-N:                     (the name of plot line N in the legend)

@end verbatim

There are 2 kinds of attributes: global attributes that affect the entire plot,
and local (per-line) attributes that affect one of the plot lines (which
corresponds to one row of B). The most convenient way to specify multiple
attributes in one go is to use multi-line strings.

For example (plot 2 lines of 10 random numbers each, named "random row 1" and
"random row 2"):

@verbatim
      Data ← ?2 10⍴10   ⍝ two rows of random data
      Attributes  ← """
legend_name-0: Random Row 1
legend_name-1: Random Row 2
                    """
      Attributes ⎕PLOT Data
@end verbatim

@subsection Plot Window Handling

Each call of ⎕PLOT with some plot data B opens a separate window in the X
server (which implies that ⎕PLOT requires X). That window runs in its own
thread until it is being closed. A window can be closed in different ways:

* By the user clicking on the close button (at the top-right) of the window, or
* By the user opening the drop down menu of the window (at the top left of the
  window) and selecting the option named "Close", or
* from APL by calling 

@node    Section 3.26
@section ⎕PS - Print Style

⎕PS is an integer vector that currently (read: SVN 982) contains two integers
which control some details of how APL values are being printed. The default
value of ⎕PS is 0 0. ⎕PS is a session variable which survives )LOADing of
workspaces

⎕PS[1] = 0: print rational quotients a normal floating point numbers

⎕PS[1] = 1: print rational quotients as A÷B

Note: ⎕PS[1] has only an effect if rational numbers were ./configured.

⎕PS[2] = 0: no "boxing" of APL values

⎕PS[2] > 0: "boxing" of APL values according to ⎕PS[2].

Setting ⎕PS[2] has the same effect as the debug command ]BOXING and uses
the same values.

Note: For compatibility with older workspaces, Assigning a single value to
⎕PS assigns that value to ⎕PS[2] and sets ⎕PS[1] to 0.


@node    Section 3.27
@section ⎕RE - Regular Expressions

⎕RE is a function that provides access to a subset of libpcre2, which is a
powerful regular expression matching library. "pcre" is an acronym for "Perl
compatible regular expressions". libpcre2 is Copyright (c) 1997-2017
University of Cambridge, England.

@subsection Preconditions

libpcre2 is NOT shipped with GNU APL but must be installed before the GNU APL
./configure script is executed. The ./configure script tries to locate libpcre2
and enables ⎕RE if the library (and its header files) are found.

If ./configure does not find libpcre2, then ⎕RE will raise a SYNTAX ERROR when
⎕RE is used in an APL program.

@subsection Syntax

⎕RE has two forms. The short form (without an axis argument) is intended to
cover the most likely use cases of ⎕RE, while the long form gives more control
over the format of the result produced by ⎕RE:

@verbatim
Z ← A ⎕RE B      (short form, no axis)
Z ← A ⎕RE[X] B   (long form, with axis X)
@end verbatim

The short form is equivalent to the long form with an empty axis:

@verbatim
    A ⎕RE B   ←→   A ⎕RE[''] B
@end verbatim

It therefore suffices to explain the long form. The long form has 3 different
arguments A, B, and X.

@subsection The Regular Expression A

A is a simple character vector which is expected to be a regular expression
as defined for the libpcre2 library. ⎕RE passes its left argument A unmodified
to libpcre2. The format of A ranges from very simple REs to very complex REs.
In fact, regular expressions are a language of their own, and it is impossible
to describe them here. The user of ⎕RE is referred to the description that
comes with libpcre2.

See in particular:

man pcre2pattern

@subsection The String(s) B Being Matched

B is either (1) a simple character vector (which is then also passed unmodified
to libpcre2) or (2) a (nested) APL array containing only simple character
vectors.

In the case (2) the result of ⎕RE is conceptually the same as if the EACH
operator had been applied to ⎕RE:

@verbatim
    A ⎕RE B   ←→   A ⎕RE ¨ B
@end verbatim

The libpcre2 first compiles A into an internal representation that improves
the matching (of B) speed. As a consequence, if several strings are matched
with the same regular expression A, then it is (sometimes considerably) faster
to call ⎕RE once with several nested than to call calling ⎕RE multiple times
with the same A but different Bs. This is in particular the case when longer
text files with many lines is being matched.

If multiple (nested) strings B are used then A is compiled once and after that
the different ⊃B[i] in B are passed unmodified to libpcre2. In that
case the result is nested and (⍴B) ≡ (⍴A ⎕RE[X] B). We can therefore limit
the description to the case where B is a simple character vector.

Any string B that is passed to libpcre2 is called "Subject" in the
libpcre2 documentation.

@subsection The Flags X

Without any flags (or with an empty flag string X) ⎕RE returns the first
match of the regular expression A in the string B. The flags will change
this behavior in order to adapt various aspects of the matching to satisfy
different requirements that the user of ⎕RE may have. The X argument of
⎕RE is a character vector where each character is a flag. The different flag
characters are either flags understood by (and then passed unmodified to)
libpcre2 or flags understood by ⎕RE itself (and then not passed to libpcre2).

@subsubsection libpcre2 flags: i, m, s, and x

The libpcre2 flags accepted by ⎕RE are: i, m, s, and x. They correspond to the
following libpcre2 flags:

@itemize
@item i: PCRE2_CASELESS   (case insensitive matching)
@item m: PCRE2_MULTILINE  (matching across multiple lines)
@item s: PCRE2_DOTALL     (dot (.) also matches CR/LF)
@item x: PCRE2_EXTENDED   (see 'man pcre2pattern')
@end itemize

Please also consult the libpcre2 documentation for a description of these flags.

@subsubsection The APL output format flags ↓, ⊂, and /

⎕RE provides different output formats, some of which are tailored to different
APL functions. There are currently 4 different output formats:

@itemize
@item no flag: ⎕RE returns the matching sub-string of B

@item ↓ flag:  ⎕RE returns the position and the length of the matched sub-string of B,
The result does not depend on ⎕IO and can be used by ↓ and ↑ to cut out the
matched pieces.

@item ⊂ flag:  ⎕RE returns an integer vector suitable as the left argument of 
   partition (⊂)

@item / flag:  ⎕RE returns an Boolean vector suitable as the left argument of 
   compress (/)
@end itemize

The following examples may better explain the nature of the output flags:

@verbatim
      ⍝ return matched string
      4 ⎕CR 'f..' ⎕RE[''] '__foo___fun____fox'
┏→━━┓
┃foo┃
┗━━━┛

      ⍝ return possition and length
      4 ⎕CR 'f..' ⎕RE['↓'] '__foo___fun____fox'
┏→━━┓
┃2 3┃
┗━━━┛

      ⍝ return left argument of ⊂
      4 ⎕CR 'f..' ⎕RE['⊂'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

      ⍝ return left argument of /
      4 ⎕CR 'f..' ⎕RE['/'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
@end verbatim

In the absence of a 'g' flag (see below) the results of output formats
⊂ and / are identical; if 'g' is present, however, then they may differ.

@subsubsection the ⎕RE global flag g

The default behavior of ⎕RE is to return only the first match in B.
The 'g' flag causes ⎕RE to return all matches. For example:

@verbatim
      4 ⎕CR 'f..' ⎕RE[''] '__foo___fun____fox'
┏→━━┓
┃foo┃
┗━━━┛
      4 ⎕CR 'f..' ⎕RE['g'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━┓
┃┏→━━┓ ┏→━━┓ ┏→━━┓┃
┃┃foo┃ ┃fun┃ ┃fox┃┃
┃┗━━━┛ ┗━━━┛ ┗━━━┛┃
┗∊━━━━━━━━━━━━━━━━┛

      4 ⎕CR 'f..' ⎕RE['↓'] '__foo___fun____fox'
┏→━━┓
┃2 3┃
┗━━━┛
      4 ⎕CR 'f..' ⎕RE['↓g'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━┓
┃┏→━━┓ ┏→━━┓ ┏→━━━┓┃
┃┃2 3┃ ┃8 3┃ ┃15 3┃┃
┃┗━━━┛ ┗━━━┛ ┗━━━━┛┃
┗∊━━━━━━━━━━━━━━━━━┛

      4 ⎕CR 'f..' ⎕RE['⊂'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
      4 ⎕CR 'f..' ⎕RE['⊂g'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃0 0 1 1 1 0 0 0 2 2 2 0 0 0 0 3 3 3┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛

      4 ⎕CR 'f..' ⎕RE['/'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃0 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
      4 ⎕CR 'f..' ⎕RE['/g'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃0 0 1 1 1 0 0 0 1 1 1 0 0 0 0 1 1 1┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
@end verbatim

Please note that the 'g' flag increments the depth of the result of the output
formats string and position/length, but not of the result of output formats
partition and compress.

@subsubsection the ⎕RE error flag E

The default behavior of ⎕RE is to return an empty result if no match of
the regular expression A is found in B. It is sometimes more convenient to
raise an error if no match is found. This can be achieved with the E flag:

@verbatim
       4 ⎕CR 'g..' ⎕RE[''] '__foo___fun____fox'
┏⊖┓
┃0┃
┗━┛
       'g..' ⎕RE['E'] '__foo___fun____fox'
DOMAIN ERROR+
      'g..' ⎕RE['E']'__foo___fun____fox'
      ^            ^
      )more
No match
@end verbatim

The 'E' flag has no effect if the 'g' flag is also given because in that case
it is natural to check the length of the result:

@verbatim
       'g..' ⎕RE['Eg'] '__foo___fun____fox'

@end verbatim

@subsection Complex Matches

The regular expressions considered so far were simple, which means that they
did not have (regular) sub-expressions. In other words, the regular expression
A did not contain non-literal (unquoted) parentheses. However, the libpcre2
allows sub-expressions and ⎕RE follows suit to a certain extent. If A contains
sub-expressions, then the result A ⎕RE becomes deeper, and the structure of
the result is determined by the structure of the parentheses in A.

The result of a general regular expression A is recursively constructed by ⎕RE
as follows:

1. If A contains no sub-expressions then the result is constructed as described
   in the previous sections.

2. If A contains sub-expressions, say A1, ... An, then the result is a (nested)
   vector with N+1 elements where the first element is the entire match (which
   contains the sub-matches) and the following elements are the next-level
   sub-matches.

Since the sub-matches are contained in their parent matches, it makes no sense
to handle sub-matches in the partition and compress output formats. For the
string and pos+len formats, the following examples may give an insight as to
how the results look like.

The regular expression A ← 'f(.)(.)' used in the example below is a top-level
regular expression which contains two 1-character sub-expressions (.).
The result is therefore the top-level match plus two 1-character sub-matches:

@verbatim
      4 ⎕CR 'f(.)(.)' ⎕RE[''] '__foo___fun____fox'
┏→━━━━━━━━━━━━┓
┃┏→━━┓ ┏→┓ ┏→┓┃
┃┃foo┃ ┃o┃ ┃o┃┃
┃┗━━━┛ ┗━┛ ┗━┛┃
┗∊━━━━━━━━━━━━┛
@end verbatim

Matching all instead of only the first then gives:

@verbatim
      4 ⎕CR 'f(.)(.)' ⎕RE['g'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃┏→━━━━━━━━━━━━┓ ┏→━━━━━━━━━━━━┓ ┏→━━━━━━━━━━━━┓┃
┃┃┏→━━┓ ┏→┓ ┏→┓┃ ┃┏→━━┓ ┏→┓ ┏→┓┃ ┃┏→━━┓ ┏→┓ ┏→┓┃┃
┃┃┃foo┃ ┃o┃ ┃o┃┃ ┃┃fun┃ ┃u┃ ┃n┃┃ ┃┃fox┃ ┃o┃ ┃x┃┃┃
┃┃┗━━━┛ ┗━┛ ┗━┛┃ ┃┗━━━┛ ┗━┛ ┗━┛┃ ┃┗━━━┛ ┗━┛ ┗━┛┃┃
┃┗∊━━━━━━━━━━━━┛ ┗∊━━━━━━━━━━━━┛ ┗∊━━━━━━━━━━━━┛┃
┗∊∊━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
@end verbatim

The same for the pos+len output format:

@verbatim
      4 ⎕CR 'f(.)(.)' ⎕RE['↓'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━┓
┃2 3 ┏→━━┓ ┏→━━┓┃
┃    ┃3 1┃ ┃4 1┃┃
┃    ┗━━━┛ ┗━━━┛┃
┗∊━━━━━━━━━━━━━━┛
      4 ⎕CR 'f(.)(.)' ⎕RE['↓g'] '__foo___fun____fox'
┏→━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃┏→━━━━━━━━━━━━━━┓ ┏→━━━━━━━━━━━━━━━┓ ┏→━━━━━━━━━━━━━━━━━┓┃
┃┃2 3 ┏→━━┓ ┏→━━┓┃ ┃8 3 ┏→━━┓ ┏→━━━┓┃ ┃15 3 ┏→━━━┓ ┏→━━━┓┃┃
┃┃    ┃3 1┃ ┃4 1┃┃ ┃    ┃9 1┃ ┃10 1┃┃ ┃     ┃16 1┃ ┃17 1┃┃┃
┃┃    ┗━━━┛ ┗━━━┛┃ ┃    ┗━━━┛ ┗━━━━┛┃ ┃     ┗━━━━┛ ┗━━━━┛┃┃
┃┗∊━━━━━━━━━━━━━━┛ ┗∊━━━━━━━━━━━━━━━┛ ┗∊━━━━━━━━━━━━━━━━━┛┃
┗∊∊━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
@end verbatim



@node    Section 3.28
@section ⎕SQL - SQL Database Interface

As of GNU APL 1.6, the native function SQL has been replaced by the
system function ⎕SQL, described below.

@verbatim 
      ⎕SQL[0]''
Available function numbers:
type  ⎕SQL[1] file      - open a database file, return reference ID for it
      ⎕SQL[2] ref       - close database
query ⎕SQL[3,db] params - send SQL query
query ⎕SQL[4,db] params - send SQL update
      ⎕SQL[5] ref       - begin a transaction
      ⎕SQL[6] ref       - commit current transaction
      ⎕SQL[7] ref       - rollback current transaction
      ⎕SQL[8] ref       - list tables
ref   ⎕SQL[9] table     - list columns for table
@end verbatim

@verbatim
      type  ⎕SQL[1] file
@end verbatim

Connect to database of type L using connection arguments R.

L must be a string indicating the database type. Currently supported
values are 'postgresql' and 'sqlite'.

R is the connection parameters which depends on the type of
database:

  - For type≡'sqlite': the argument is string pointing to the
    database file.

  - For type≡'postgresql', the argument is a standard connect
    string as described in the PostgreSQL documentation.

This function returns a database handle that should be used when
using other SQL functions. This value should be seen as an opaque
handle. It is, however, guaranteed that the handle is a scalar
value.

@verbatim
      ⎕SQL[2] ref
@end verbatim

Disconnect from database R.

R is the database handle that should be disconnected. After this
function has been called, no further operations are to be performed
on this handle. Future calls to SQL∆Connect may reuse previously
disconnected handles.

@verbatim
      query ⎕SQL[3,db] params
@end verbatim

Execute a select statement and return the result table.

The axis parameter indicates the database handle.

L is a select statement to be executed. Positional parameters can
be supplied by specifying a question mark "?" in the statement.

R is an array containing the values for the positional parameters.
If the array is of rank 2, the statement will be executed multiple
times with each row being the values for each call.

The return value is a rank-2 array representing the result of the
select statement. Null values are returned as ⍬ and empty strings
are returned as ''.

@verbatim
      query ⎕SQL[4,db] params
@end verbatim

Execute an SQL statement that does not return a result.

This function is identical to SQL∆Select with the exception that it
is used on statements which do not return a result table.

@verbatim
      ⎕SQL[5] ref
@end verbatim

Begin a transaction.

@verbatim
      ⎕SQL[6] ref
@end verbatim

Commit a transaction.

@verbatim
      ⎕SQL[7] ref
@end verbatim

Rolls back the current transaction.

@verbatim
      ⎕SQL[8] ref
@end verbatim

Return an array containing the name of all tables.

@verbatim
      ref   ⎕SQL[9] table
@end verbatim

Return an array containing information about the columns in the
given table. Currently, the column layout is as follows:

  Name
  Type

More columns containing extra information may be added in a future
release.


@node    Section 3.29
@section ⎕SI - State Indicator

⎕SI returns aspects of the current State Indicator, similar to the standard
command )SI. This can be used, for example, to create debug functions similar
to the assert() macro in C/C++:

@verbatim

∇Assert B;COND;LOC;VAR
 →(1≡B)⍴0
 ' '
 COND←7↓,¯2 ⎕SI 4
 LOC←,¯2 ⎕SI 3
 '************************************************'
 ' '
 '*** Assertion (', COND, ') failed at ',LOC
 ''

 ⍝ show stack
 ⍝
 ' '
 'Stack:'
 7 ⎕CR ⊃¯1↓⎕SI 3
 ' '
 '************************************************</pre>'
 →
∇

@end verbatim

⎕SI is a system function whose right argument specifies which aspect of
the State indicator shall be returned:

⎕SI 1: The name of the context. That is either the name of a user defined
function, or ◊ for an immediate execution context, or ⍎ for an execute
context.

⎕SI 2: The line number (of a defined function) or 0 for immediate execution
and execute.

⎕SI 3: The function name and line number in square brackets, like foo[3]

⎕SI 4: Either the statement text of the function line or the error text of
 an error that has occurred on the line

⎕SI 5: The program counter (= token number counted from the start of the
function text

⎕SI 6: the parse mode of the context (immediate execution, execute, or
defined function).

If no left argument is provided then the result of ⎕SI is a vector with
one entry per State Indicator level (and hence ⍴⎕SI B is the depth of the SI).

If a left argument A is provided then specifies a particular level of the SI
instead of the entire SI. A should be an integer scalar. If A is positive
then the level is counted from the oldest entry to the latest, while negative
A count from the latest to the oldest level.

For example, ¯1 ⎕SI refers to the currently executing context, ¯2 ⎕SI is
the caller, and so on.


@node    Section 3.30
@section ⎕SYL - System limits

System variable ⎕SYL shows a number of system limits when referenced:

@verbatim
      ⎕SYL
 SI depth limit          (0 = no limit)                    0 
 number of values limit  (0 = no limit)                    0 
 total ravel bytes limit (0 = no limit)                    0 
 current SI depth                                          1 
 current number of values                                 54 
 current total ravel bytes                              9072 
 max. rank for APL values                                  8 
 min. ⎕PW                                                 30 
 max. ⎕PW                                               1000 
 min. ⎕PP                                                  1 
 max. ⎕PP                                                 16 
 max. input line length                                 2000 
 hash table size (obsolete)                            65536 
 max. shared variable name length                         64 
 max. length of filenames (paths)                       4096 
 max. # of shared variables (obsolete)                    64 
 max. number of APs                                       16 
 max. operators per statement                             16 
 largest integer                         9000000000000000000 
 smallest integer                       ¯9000000000000000000 
 largest numeric exponent                                308 
 max. shared variable size (bytes)                     65000 
 max. cores (per ./configure)                              0 
 max. cores (per max_cores())                              1 
 current cores (per core_count())                          1 
 print length limit (0 = no limit)                         0 
@end verbatim

Most system limits are read-only; attempting to assign ⎕SYL will result
in a SYNTAX ERROR. Indexed assignment to ⎕SYL will result in an
INDEX ERROR unless the limit is writable. Some read-only limits can
be changed at compile-time via ./configure

@subsection ⎕SYL[1 2 3 4 5 6;]

The first three limits are writable; their purpose is to stop execution
if:

@enumerate
@item The SI stack of the interpreter reaches a limit, or
@item The number of APL values created reaches a limit, or
@item The memory size of APL values created reaches a limit.
@end enumerate

Whenever a writable limit is reached, a corresponding LIMIT ERROR
is reported and the limit is reset to 0 (meaning no limit) in order
to prevent that the interpreter gets locked up.

The main use of ⎕SYL is to troubleshoot infinite recursion in user-defined
function that would otherwise cause the machine to start swapping or to
become non-responding.

Example (stop execution if function call stack exceeds 20):

@verbatim
      ⎕SYL[1;2]←20
@end verbatim

Note that small APL values (up to a configurable number of ravel elements)
count as values (in the number of values limit), but not in the total ravel
bytes limit (the ravel does not allocate memory in addition to the
space already in the number of values limit). It is therefore typical to
set the number of values limits and the total ravel bytes limits together.

An attempt to set a too small limit, for example one that is  close to the
current value, is rejected with a DOMAIN ERROR.

@subsection ⎕SYL[7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23;]

These system limits are read-only. Some of them can be changed at
compile time via ./configure. Most others can be changed in the source code
of GNU APL, but doing so is not recommended.

@subsection ⎕SYL[24 25 26;]

These system limits have been added in preparation of multi-core GNU APL.
They are currently not used.

@subsection ⎕SYL[27;]

This is not a limit that raises a limit error. Instead it limits the
size of APL values when printed as statement results. It is fairly easy
in APL to create huge APL values by mistake. During development it can
be useful to limit the amount of data printed. If the ravel length of,
say, VALUE exceeds ⎕SYL[27;2] (i.e. if ⎕SYL[27;2] ≤ ⍴,VALUE) then SH↑VALUE
is printed instead of VALUE. The shape SH is computed like this:

@verbatim

      SH←⍴VALUE
      while (ravel-length(SH) ≥ ⎕SYL[27;2])   { divide longest axis in SH by 2 }

@end verbatim

@c ----------------------------------------------------------------------------
@node Chapter 4
@chapter Limitations and Missing Features

APL is an almost full implementation of the ISO standard 13751.
However, a few limitations exist. See file README-4-compliance for
an up-to-date descriptions of limitations.

@section System Limits

APL integers are 64-bit wide, ranging from
-9200000000000000000 to 9200000000000000000

Due to rounding and similar, some integers can become slightly larger, but
the above limits are guaranteed for some operations (e.g. + and -)

APL floating point values are 64-bit wide, thus ranging from
-8.98E307 to 8.98E307.

APL values have a maximum rank of 8. This value can be increased, however,
by means of ./configure (see README-2-configure).

@section Shared Variables

The system functions and variables for shared variables, i.e. ⎕SVO, ⎕SVR,
⎕SVC, ⎕SVS, ⎕SVQ are implemented.

Communication between two workspaces is supported, but with some
limitations. Two workspaces must run on the same machine in order
to communicate via shared variables.

However, only two auxiliary processors, AP100 and AP210, are provided as
examples for implementing auxiliary processors.

Shared variables for auxiliary processors are provided for some backward
compatibility. In the past - without access to the source code of the APL
interpreter - shared variables were the only method available to extend the
functionality of the interpreter.

With this interpreter - and access to its source code - it is often more
convenient to add your own commands or your own system variables to the
APL interpreter rather that adding auxiliary processors.

@c ----------------------------------------------------------------------------
@node Chapter 5
@chapter Internationalization

GNU APL used to be internationalized by means of GNU gettext, but is not
anymore. 

For APL characters to work properly with keyboards and terminal emulators
(see also README-3-keyboard) it is essential that your LANG environment
variable is correctly set. For German, that would be "de_DE.utf8", like:

$export LANG=de_DE.utf8

A misspelling of the language can cause APL characters to become unavailable,
even if your xmodmap is correct. You can check your setting by executing the
program 'locale'.  If it  shows warnings like these:

locale: Cannot set LC_CTYPE to default locale: No such file or directory
locale: Cannot set LC_MESSAGES to default locale: No such file or directory
locale: Cannot set LC_ALL to default locale: No such file or directory

then something is wrong and you should check your LANG setting and installed
locales.

As far as xterm is concerned, the xterm command line options --u8, --lc, and
--en might solve problems related to the terminal.

@c ----------------------------------------------------------------------------
@node Chapter 6
@chapter Libraries Contributed by GNU APL Users

Since the first release of GNU APL, a number of libraries, but also other
developments, have been made by users of GNU APL. Below are links to these
contributions.

@menu
* Section 6.1::  The GNU APL Community Webpage
* Section 6.2::  Core Libraries
@end menu

@node Section 6.1
@section The GNU APL Community Webpage

The GNU APL project maintains a web page that lists contributions made by
GNU APL users:

@uref{http://www.gnu.org/software/apl/Community.html}

The contributions listed there were collected from emails sent to
bug-apl@@gnu.org

Since the list was started long after bug-apl@@gnu.org was created. It is
therefore quite possible that your contribution is missing. That does not
mean that your contribution was not considered worthwhile to be listed but
more likely that it was overlooked. Just send an email to bug-apl@@gnu.org
to fix that.


@node Section 6.2
@section Core Libraries

There is a small number of libraries that are considered "core" APL because,
for example, the ISO standard requires their functionality, or because other
APL interpreters normally support them.

These libraries are linked via the GNU APL Community web page. In addition
they are stored in the GNU APL SVN repository and also included in the
GNU APL packages that follows their contribution.

Currently the following core libraries exist:

GNU APL Emacs mode     (for Emacs users)           by Elias Mårtenson

SQL interface          (SQLite and Postgres)       by Elias Mårtenson

Component File System  (as required by ISO 13751)  by David B. Lamkins

Component File System  (as required by ISO 13751)  by Blake McBride

SQL

@c ----------------------------------------------------------------------------
@node Chapter 7
@chapter Licenses for this GNU APL Manual and for GNU APL

This manual for GNU APL is licensed under the GNU Free Documentation
License, *Note Section 4.1:: below.

GNU APL itself is licensed under the GNU Public License version 3 or later
(aka GPLv3+), *Note Section 4.2:: below.

@menu
* Section 7.1::  The GNU Free Documentation License
* Section 7.2::  The GNU General Public License
@end menu

@node Section 7.1
@section The GNU Free Documentation License

@c The GNU Free Documentation License.
@center Version 1.3, 3 November 2008

@display
Copyright @copyright{} 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.
@uref{http://fsf.org/}

Everyone is permitted to copy and distribute verbatim copies
of this license document, but changing it is not allowed.
@end display

@enumerate 0
@item
PREAMBLE

The purpose of this License is to make a manual, textbook, or other
functional and useful document @dfn{free} in the sense of freedom: to
assure everyone the effective freedom to copy and redistribute it,
with or without modifying it, either commercially or non-commercially.
Secondarily, this License preserves for the author and publisher a way
to get credit for their work, while not being considered responsible
for modifications made by others.

This License is a kind of ``copyleft'', which means that derivative
works of the document must themselves be free in the same sense.  It
complements the GNU General Public License, which is a copyleft
license designed for free software.

We have designed this License in order to use it for manuals for free
software, because free software needs free documentation: a free
program should come with manuals providing the same freedoms that the
software does.  But this License is not limited to software manuals;
it can be used for any textual work, regardless of subject matter or
whether it is published as a printed book.  We recommend this License
principally for works whose purpose is instruction or reference.

@item
APPLICABILITY AND DEFINITIONS

This License applies to any manual or other work, in any medium, that
contains a notice placed by the copyright holder saying it can be
distributed under the terms of this License.  Such a notice grants a
world-wide, royalty-free license, unlimited in duration, to use that
work under the conditions stated herein.  The ``Document'', below,
refers to any such manual or work.  Any member of the public is a
licensee, and is addressed as ``you''.  You accept the license if you
copy, modify or distribute the work in a way requiring permission
under copyright law.

A ``Modified Version'' of the Document means any work containing the
Document or a portion of it, either copied verbatim, or with
modifications and/or translated into another language.

A ``Secondary Section'' is a named appendix or a front-matter section
of the Document that deals exclusively with the relationship of the
publishers or authors of the Document to the Document's overall
subject (or to related matters) and contains nothing that could fall
directly within that overall subject.  (Thus, if the Document is in
part a textbook of mathematics, a Secondary Section may not explain
any mathematics.)  The relationship could be a matter of historical
connection with the subject or with related matters, or of legal,
commercial, philosophical, ethical or political position regarding
them.

The ``Invariant Sections'' are certain Secondary Sections whose titles
are designated, as being those of Invariant Sections, in the notice
that says that the Document is released under this License.  If a
section does not fit the above definition of Secondary then it is not
allowed to be designated as Invariant.  The Document may contain zero
Invariant Sections.  If the Document does not identify any Invariant
Sections then there are none.

The ``Cover Texts'' are certain short passages of text that are listed,
as Front-Cover Texts or Back-Cover Texts, in the notice that says that
the Document is released under this License.  A Front-Cover Text may
be at most 5 words, and a Back-Cover Text may be at most 25 words.

A ``Transparent'' copy of the Document means a machine-readable copy,
represented in a format whose specification is available to the
general public, that is suitable for revising the document
straightforwardly with generic text editors or (for images composed of
pixels) generic paint programs or (for drawings) some widely available
drawing editor, and that is suitable for input to text formatters or
for automatic translation to a variety of formats suitable for input
to text formatters.  A copy made in an otherwise Transparent file
format whose markup, or absence of markup, has been arranged to thwart
or discourage subsequent modification by readers is not Transparent.
An image format is not Transparent if used for any substantial amount
of text.  A copy that is not ``Transparent'' is called ``Opaque''.

Examples of suitable formats for Transparent copies include plain
ASCII without markup, Texinfo input format, La@TeX{} input
format, SGML or XML using a publicly available
DTD, and standard-conforming simple HTML,
PostScript or PDF designed for human modification.  Examples
of transparent image formats include PNG, XCF and
JPG.  Opaque formats include proprietary formats that can be
read and edited only by proprietary word processors, SGML or
XML for which the DTD and/or processing tools are
not generally available, and the machine-generated HTML,
PostScript or PDF produced by some word processors for
output purposes only.

The ``Title Page'' means, for a printed book, the title page itself,
plus such following pages as are needed to hold, legibly, the material
this License requires to appear in the title page.  For works in
formats which do not have any title page as such, ``Title Page'' means
the text near the most prominent appearance of the work's title,
preceding the beginning of the body of the text.

The ``publisher'' means any person or entity that distributes copies
of the Document to the public.

A section ``Entitled XYZ'' means a named subunit of the Document whose
title either is precisely XYZ or contains XYZ in parentheses following
text that translates XYZ in another language.  (Here XYZ stands for a
specific section name mentioned below, such as ``Acknowledgements'',
``Dedications'', ``Endorsements'', or ``History''.)  To ``Preserve the Title''
of such a section when you modify the Document means that it remains a
section ``Entitled XYZ'' according to this definition.

The Document may include Warranty Disclaimers next to the notice which
states that this License applies to the Document.  These Warranty
Disclaimers are considered to be included by reference in this
License, but only as regards disclaiming warranties: any other
implication that these Warranty Disclaimers may have is void and has
no effect on the meaning of this License.

@item
VERBATIM COPYING

You may copy and distribute the Document in any medium, either
commercially or noncommercially, provided that this License, the
copyright notices, and the license notice saying this License applies
to the Document are reproduced in all copies, and that you add no other
conditions whatsoever to those of this License.  You may not use
technical measures to obstruct or control the reading or further
copying of the copies you make or distribute.  However, you may accept
compensation in exchange for copies.  If you distribute a large enough
number of copies you must also follow the conditions in section 3.

You may also lend copies, under the same conditions stated above, and
you may publicly display copies.

@item
COPYING IN QUANTITY

If you publish printed copies (or copies in media that commonly have
printed covers) of the Document, numbering more than 100, and the
Document's license notice requires Cover Texts, you must enclose the
copies in covers that carry, clearly and legibly, all these Cover
Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on
the back cover.  Both covers must also clearly and legibly identify
you as the publisher of these copies.  The front cover must present
the full title with all words of the title equally prominent and
visible.  You may add other material on the covers in addition.
Copying with changes limited to the covers, as long as they preserve
the title of the Document and satisfy these conditions, can be treated
as verbatim copying in other respects.

If the required texts for either cover are too voluminous to fit
legibly, you should put the first ones listed (as many as fit
reasonably) on the actual cover, and continue the rest onto adjacent
pages.

If you publish or distribute Opaque copies of the Document numbering
more than 100, you must either include a machine-readable Transparent
copy along with each Opaque copy, or state in or with each Opaque copy
a computer-network location from which the general network-using
public has access to download using public-standard network protocols
a complete Transparent copy of the Document, free of added material.
If you use the latter option, you must take reasonably prudent steps,
when you begin distribution of Opaque copies in quantity, to ensure
that this Transparent copy will remain thus accessible at the stated
location until at least one year after the last time you distribute an
Opaque copy (directly or through your agents or retailers) of that
edition to the public.

It is requested, but not required, that you contact the authors of the
Document well before redistributing any large number of copies, to give
them a chance to provide you with an updated version of the Document.

@item
MODIFICATIONS

You may copy and distribute a Modified Version of the Document under
the conditions of sections 2 and 3 above, provided that you release
the Modified Version under precisely this License, with the Modified
Version filling the role of the Document, thus licensing distribution
and modification of the Modified Version to whoever possesses a copy
of it.  In addition, you must do these things in the Modified Version:

@enumerate A
@item
Use in the Title Page (and on the covers, if any) a title distinct
from that of the Document, and from those of previous versions
(which should, if there were any, be listed in the History section
of the Document).  You may use the same title as a previous version
if the original publisher of that version gives permission.

@item
List on the Title Page, as authors, one or more persons or entities
responsible for authorship of the modifications in the Modified
Version, together with at least five of the principal authors of the
Document (all of its principal authors, if it has fewer than five),
unless they release you from this requirement.

@item
State on the Title page the name of the publisher of the
Modified Version, as the publisher.

@item
Preserve all the copyright notices of the Document.

@item
Add an appropriate copyright notice for your modifications
adjacent to the other copyright notices.

@item
Include, immediately after the copyright notices, a license notice
giving the public permission to use the Modified Version under the
terms of this License, in the form shown in the Addendum below.

@item
Preserve in that license notice the full lists of Invariant Sections
and required Cover Texts given in the Document's license notice.

@item
Include an unaltered copy of this License.

@item
Preserve the section Entitled ``History'', Preserve its Title, and add
to it an item stating at least the title, year, new authors, and
publisher of the Modified Version as given on the Title Page.  If
there is no section Entitled ``History'' in the Document, create one
stating the title, year, authors, and publisher of the Document as
given on its Title Page, then add an item describing the Modified
Version as stated in the previous sentence.

@item
Preserve the network location, if any, given in the Document for
public access to a Transparent copy of the Document, and likewise
the network locations given in the Document for previous versions
it was based on.  These may be placed in the ``History'' section.
You may omit a network location for a work that was published at
least four years before the Document itself, or if the original
publisher of the version it refers to gives permission.

@item
For any section Entitled ``Acknowledgements'' or ``Dedications'', Preserve
the Title of the section, and preserve in the section all the
substance and tone of each of the contributor acknowledgements and/or
dedications given therein.

@item
Preserve all the Invariant Sections of the Document,
unaltered in their text and in their titles.  Section numbers
or the equivalent are not considered part of the section titles.

@item
Delete any section Entitled ``Endorsements''.  Such a section
may not be included in the Modified Version.

@item
Do not retitle any existing section to be Entitled ``Endorsements'' or
to conflict in title with any Invariant Section.

@item
Preserve any Warranty Disclaimers.
@end enumerate

If the Modified Version includes new front-matter sections or
appendices that qualify as Secondary Sections and contain no material
copied from the Document, you may at your option designate some or all
of these sections as invariant.  To do this, add their titles to the
list of Invariant Sections in the Modified Version's license notice.
These titles must be distinct from any other section titles.

You may add a section Entitled ``Endorsements'', provided it contains
nothing but endorsements of your Modified Version by various
parties---for example, statements of peer review or that the text has
been approved by an organization as the authoritative definition of a
standard.

You may add a passage of up to five words as a Front-Cover Text, and a
passage of up to 25 words as a Back-Cover Text, to the end of the list
of Cover Texts in the Modified Version.  Only one passage of
Front-Cover Text and one of Back-Cover Text may be added by (or
through arrangements made by) any one entity.  If the Document already
includes a cover text for the same cover, previously added by you or
by arrangement made by the same entity you are acting on behalf of,
you may not add another; but you may replace the old one, on explicit
permission from the previous publisher that added the old one.

The author(s) and publisher(s) of the Document do not by this License
give permission to use their names for publicity for or to assert or
imply endorsement of any Modified Version.

@item
COMBINING DOCUMENTS

You may combine the Document with other documents released under this
License, under the terms defined in section 4 above for modified
versions, provided that you include in the combination all of the
Invariant Sections of all of the original documents, unmodified, and
list them all as Invariant Sections of your combined work in its
license notice, and that you preserve all their Warranty Disclaimers.

The combined work need only contain one copy of this License, and
multiple identical Invariant Sections may be replaced with a single
copy.  If there are multiple Invariant Sections with the same name but
different contents, make the title of each such section unique by
adding at the end of it, in parentheses, the name of the original
author or publisher of that section if known, or else a unique number.
Make the same adjustment to the section titles in the list of
Invariant Sections in the license notice of the combined work.

In the combination, you must combine any sections Entitled ``History''
in the various original documents, forming one section Entitled
``History''; likewise combine any sections Entitled ``Acknowledgements'',
and any sections Entitled ``Dedications''.  You must delete all
sections Entitled ``Endorsements.''

@item
COLLECTIONS OF DOCUMENTS

You may make a collection consisting of the Document and other documents
released under this License, and replace the individual copies of this
License in the various documents with a single copy that is included in
the collection, provided that you follow the rules of this License for
verbatim copying of each of the documents in all other respects.

You may extract a single document from such a collection, and distribute
it individually under this License, provided you insert a copy of this
License into the extracted document, and follow this License in all
other respects regarding verbatim copying of that document.

@item
AGGREGATION WITH INDEPENDENT WORKS

A compilation of the Document or its derivatives with other separate
and independent documents or works, in or on a volume of a storage or
distribution medium, is called an ``aggregate'' if the copyright
resulting from the compilation is not used to limit the legal rights
of the compilation's users beyond what the individual works permit.
When the Document is included in an aggregate, this License does not
apply to the other works in the aggregate which are not themselves
derivative works of the Document.

If the Cover Text requirement of section 3 is applicable to these
copies of the Document, then if the Document is less than one half of
the entire aggregate, the Document's Cover Texts may be placed on
covers that bracket the Document within the aggregate, or the
electronic equivalent of covers if the Document is in electronic form.
Otherwise they must appear on printed covers that bracket the whole
aggregate.

@item
TRANSLATION

Translation is considered a kind of modification, so you may
distribute translations of the Document under the terms of section 4.
Replacing Invariant Sections with translations requires special
permission from their copyright holders, but you may include
translations of some or all Invariant Sections in addition to the
original versions of these Invariant Sections.  You may include a
translation of this License, and all the license notices in the
Document, and any Warranty Disclaimers, provided that you also include
the original English version of this License and the original versions
of those notices and disclaimers.  In case of a disagreement between
the translation and the original version of this License or a notice
or disclaimer, the original version will prevail.

If a section in the Document is Entitled ``Acknowledgements'',
``Dedications'', or ``History'', the requirement (section 4) to Preserve
its Title (section 1) will typically require changing the actual
title.

@item
TERMINATION

You may not copy, modify, sublicense, or distribute the Document
except as expressly provided under this License.  Any attempt
otherwise to copy, modify, sublicense, or distribute it is void, and
will automatically terminate your rights under this License.

However, if you cease all violation of this License, then your license
from a particular copyright holder is reinstated (a) provisionally,
unless and until the copyright holder explicitly and finally
terminates your license, and (b) permanently, if the copyright holder
fails to notify you of the violation by some reasonable means prior to
60 days after the cessation.

Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.

Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License.  If your rights have been terminated and not permanently
reinstated, receipt of a copy of some or all of the same material does
not give you any rights to use it.

@item
FUTURE REVISIONS OF THIS LICENSE

The Free Software Foundation may publish new, revised versions
of the GNU Free Documentation License from time to time.  Such new
versions will be similar in spirit to the present version, but may
differ in detail to address new problems or concerns.  See
@uref{http://www.gnu.org/copyleft/}.

Each version of the License is given a distinguishing version number.
If the Document specifies that a particular numbered version of this
License ``or any later version'' applies to it, you have the option of
following the terms and conditions either of that specified version or
of any later version that has been published (not as a draft) by the
Free Software Foundation.  If the Document does not specify a version
number of this License, you may choose any version ever published (not
as a draft) by the Free Software Foundation.  If the Document
specifies that a proxy can decide which future versions of this
License can be used, that proxy's public statement of acceptance of a
version permanently authorizes you to choose that version for the
Document.

@item
RELICENSING

``Massive Multiauthor Collaboration Site'' (or ``MMC Site'') means any
World Wide Web server that publishes copyrightable works and also
provides prominent facilities for anybody to edit those works.  A
public wiki that anybody can edit is an example of such a server.  A
``Massive Multiauthor Collaboration'' (or ``MMC'') contained in the
site means any set of copyrightable works thus published on the MMC
site.

``CC-BY-SA'' means the Creative Commons Attribution-Share Alike 3.0
license published by Creative Commons Corporation, a not-for-profit
corporation with a principal place of business in San Francisco,
California, as well as future copyleft versions of that license
published by that same organization.

``Incorporate'' means to publish or republish a Document, in whole or
in part, as part of another Document.

An MMC is ``eligible for relicensing'' if it is licensed under this
License, and if all works that were first published under this License
somewhere other than this MMC, and subsequently incorporated in whole
or in part into the MMC, (1) had no cover texts or invariant sections,
and (2) were thus incorporated prior to November 1, 2008.

The operator of an MMC Site may republish an MMC contained in the site
under CC-BY-SA on the same site at any time before August 1, 2009,
provided the MMC is eligible for relicensing.

@end enumerate

@page
@heading ADDENDUM: How to use this License for your documents

To use this License in a document you have written, include a copy of
the License in the document and put the following copyright and
license notices just after the title page:

@smallexample
@group
  Copyright (C)  @var{year}  @var{your name}.
  Permission is granted to copy, distribute and/or modify this document
  under the terms of the GNU Free Documentation License, Version 1.3
  or any later version published by the Free Software Foundation;
  with no Invariant Sections, no Front-Cover Texts, and no Back-Cover
  Texts.  A copy of the license is included in the section entitled ``GNU
  Free Documentation License''.
@end group
@end smallexample

If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts,
replace the ``with@dots{}Texts.''@: line with this:

@smallexample
@group
    with the Invariant Sections being @var{list their titles}, with
    the Front-Cover Texts being @var{list}, and with the Back-Cover Texts
    being @var{list}.
@end group
@end smallexample

If you have Invariant Sections without Cover Texts, or some other
combination of the three, merge those two alternatives to suit the
situation.

If your document contains nontrivial examples of program code, we
recommend releasing these examples in parallel under your choice of
free software license, such as the GNU General Public License,
to permit their use in free software.

@node Section 7.2
@section The GNU GENERAL PUBLIC LICENSE

                    GNU GENERAL PUBLIC LICENSE
                       Version 3, 29 June 2007

 Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
 Everyone is permitted to copy and distribute verbatim copies
 of this license document, but changing it is not allowed.

                            Preamble

  The GNU General Public License is a free, copyleft license for
software and other kinds of works.

  The licenses for most software and other practical works are designed
to take away your freedom to share and change the works.  By contrast,
the GNU General Public License is intended to guarantee your freedom to
share and change all versions of a program--to make sure it remains free
software for all its users.  We, the Free Software Foundation, use the
GNU General Public License for most of our software; it applies also to
any other work released this way by its authors.  You can apply it to
your programs, too.

  When we speak of free software, we are referring to freedom, not
price.  Our General Public Licenses are designed to make sure that you
have the freedom to distribute copies of free software (and charge for
them if you wish), that you receive source code or can get it if you
want it, that you can change the software or use pieces of it in new
free programs, and that you know you can do these things.

  To protect your rights, we need to prevent others from denying you
these rights or asking you to surrender the rights.  Therefore, you have
certain responsibilities if you distribute copies of the software, or if
you modify it: responsibilities to respect the freedom of others.

  For example, if you distribute copies of such a program, whether
gratis or for a fee, you must pass on to the recipients the same
freedoms that you received.  You must make sure that they, too, receive
or can get the source code.  And you must show them these terms so they
know their rights.

  Developers that use the GNU GPL protect your rights with two steps:
(1) assert copyright on the software, and (2) offer you this License
giving you legal permission to copy, distribute and/or modify it.

  For the developers' and authors' protection, the GPL clearly explains
that there is no warranty for this free software.  For both users' and
authors' sake, the GPL requires that modified versions be marked as
changed, so that their problems will not be attributed erroneously to
authors of previous versions.

  Some devices are designed to deny users access to install or run
modified versions of the software inside them, although the manufacturer
can do so.  This is fundamentally incompatible with the aim of
protecting users' freedom to change the software.  The systematic
pattern of such abuse occurs in the area of products for individuals to
use, which is precisely where it is most unacceptable.  Therefore, we
have designed this version of the GPL to prohibit the practice for those
products.  If such problems arise substantially in other domains, we
stand ready to extend this provision to those domains in future versions
of the GPL, as needed to protect the freedom of users.

  Finally, every program is threatened constantly by software patents.
States should not allow patents to restrict development and use of
software on general-purpose computers, but in those that do, we wish to
avoid the special danger that patents applied to a free program could
make it effectively proprietary.  To prevent this, the GPL assures that
patents cannot be used to render the program non-free.

  The precise terms and conditions for copying, distribution and
modification follow.

                       TERMS AND CONDITIONS

  0. Definitions.

  "This License" refers to version 3 of the GNU General Public License.

  "Copyright" also means copyright-like laws that apply to other kinds of
works, such as semiconductor masks.

  "The Program" refers to any copyrightable work licensed under this
License.  Each licensee is addressed as "you".  "Licensees" and
"recipients" may be individuals or organizations.

  To "modify" a work means to copy from or adapt all or part of the work
in a fashion requiring copyright permission, other than the making of an
exact copy.  The resulting work is called a "modified version" of the
earlier work or a work "based on" the earlier work.

  A "covered work" means either the unmodified Program or a work based
on the Program.

  To "propagate" a work means to do anything with it that, without
permission, would make you directly or secondarily liable for
infringement under applicable copyright law, except executing it on a
computer or modifying a private copy.  Propagation includes copying,
distribution (with or without modification), making available to the
public, and in some countries other activities as well.

  To "convey" a work means any kind of propagation that enables other
parties to make or receive copies.  Mere interaction with a user through
a computer network, with no transfer of a copy, is not conveying.

  An interactive user interface displays "Appropriate Legal Notices"
to the extent that it includes a convenient and prominently visible
feature that (1) displays an appropriate copyright notice, and (2)
tells the user that there is no warranty for the work (except to the
extent that warranties are provided), that licensees may convey the
work under this License, and how to view a copy of this License.  If
the interface presents a list of user commands or options, such as a
menu, a prominent item in the list meets this criterion.

  1. Source Code.

  The "source code" for a work means the preferred form of the work
for making modifications to it.  "Object code" means any non-source
form of a work.

  A "Standard Interface" means an interface that either is an official
standard defined by a recognized standards body, or, in the case of
interfaces specified for a particular programming language, one that
is widely used among developers working in that language.

  The "System Libraries" of an executable work include anything, other
than the work as a whole, that (a) is included in the normal form of
packaging a Major Component, but which is not part of that Major
Component, and (b) serves only to enable use of the work with that
Major Component, or to implement a Standard Interface for which an
implementation is available to the public in source code form.  A
"Major Component", in this context, means a major essential component
(kernel, window system, and so on) of the specific operating system
(if any) on which the executable work runs, or a compiler used to
produce the work, or an object code interpreter used to run it.

  The "Corresponding Source" for a work in object code form means all
the source code needed to generate, install, and (for an executable
work) run the object code and to modify the work, including scripts to
control those activities.  However, it does not include the work's
System Libraries, or general-purpose tools or generally available free
programs which are used unmodified in performing those activities but
which are not part of the work.  For example, Corresponding Source
includes interface definition files associated with source files for
the work, and the source code for shared libraries and dynamically
linked subprograms that the work is specifically designed to require,
such as by intimate data communication or control flow between those
subprograms and other parts of the work.

  The Corresponding Source need not include anything that users
can regenerate automatically from other parts of the Corresponding
Source.

  The Corresponding Source for a work in source code form is that
same work.

  2. Basic Permissions.

  All rights granted under this License are granted for the term of
copyright on the Program, and are irrevocable provided the stated
conditions are met.  This License explicitly affirms your unlimited
permission to run the unmodified Program.  The output from running a
covered work is covered by this License only if the output, given its
content, constitutes a covered work.  This License acknowledges your
rights of fair use or other equivalent, as provided by copyright law.

  You may make, run and propagate covered works that you do not
convey, without conditions so long as your license otherwise remains
in force.  You may convey covered works to others for the sole purpose
of having them make modifications exclusively for you, or provide you
with facilities for running those works, provided that you comply with
the terms of this License in conveying all material for which you do
not control copyright.  Those thus making or running the covered works
for you must do so exclusively on your behalf, under your direction
and control, on terms that prohibit them from making any copies of
your copyrighted material outside their relationship with you.

  Conveying under any other circumstances is permitted solely under
the conditions stated below.  Sublicensing is not allowed; section 10
makes it unnecessary.

  3. Protecting Users' Legal Rights From Anti-Circumvention Law.

  No covered work shall be deemed part of an effective technological
measure under any applicable law fulfilling obligations under article
11 of the WIPO copyright treaty adopted on 20 December 1996, or
similar laws prohibiting or restricting circumvention of such
measures.

  When you convey a covered work, you waive any legal power to forbid
circumvention of technological measures to the extent such circumvention
is effected by exercising rights under this License with respect to
the covered work, and you disclaim any intention to limit operation or
modification of the work as a means of enforcing, against the work's
users, your or third parties' legal rights to forbid circumvention of
technological measures.

  4. Conveying Verbatim Copies.

  You may convey verbatim copies of the Program's source code as you
receive it, in any medium, provided that you conspicuously and
appropriately publish on each copy an appropriate copyright notice;
keep intact all notices stating that this License and any
non-permissive terms added in accord with section 7 apply to the code;
keep intact all notices of the absence of any warranty; and give all
recipients a copy of this License along with the Program.

  You may charge any price or no price for each copy that you convey,
and you may offer support or warranty protection for a fee.

  5. Conveying Modified Source Versions.

  You may convey a work based on the Program, or the modifications to
produce it from the Program, in the form of source code under the
terms of section 4, provided that you also meet all of these conditions:

    a) The work must carry prominent notices stating that you modified
    it, and giving a relevant date.

    b) The work must carry prominent notices stating that it is
    released under this License and any conditions added under section
    7.  This requirement modifies the requirement in section 4 to
    "keep intact all notices".

    c) You must license the entire work, as a whole, under this
    License to anyone who comes into possession of a copy.  This
    License will therefore apply, along with any applicable section 7
    additional terms, to the whole of the work, and all its parts,
    regardless of how they are packaged.  This License gives no
    permission to license the work in any other way, but it does not
    invalidate such permission if you have separately received it.

    d) If the work has interactive user interfaces, each must display
    Appropriate Legal Notices; however, if the Program has interactive
    interfaces that do not display Appropriate Legal Notices, your
    work need not make them do so.

  A compilation of a covered work with other separate and independent
works, which are not by their nature extensions of the covered work,
and which are not combined with it such as to form a larger program,
in or on a volume of a storage or distribution medium, is called an
"aggregate" if the compilation and its resulting copyright are not
used to limit the access or legal rights of the compilation's users
beyond what the individual works permit.  Inclusion of a covered work
in an aggregate does not cause this License to apply to the other
parts of the aggregate.

  6. Conveying Non-Source Forms.

  You may convey a covered work in object code form under the terms
of sections 4 and 5, provided that you also convey the
machine-readable Corresponding Source under the terms of this License,
in one of these ways:

    a) Convey the object code in, or embodied in, a physical product
    (including a physical distribution medium), accompanied by the
    Corresponding Source fixed on a durable physical medium
    customarily used for software interchange.

    b) Convey the object code in, or embodied in, a physical product
    (including a physical distribution medium), accompanied by a
    written offer, valid for at least three years and valid for as
    long as you offer spare parts or customer support for that product
    model, to give anyone who possesses the object code either (1) a
    copy of the Corresponding Source for all the software in the
    product that is covered by this License, on a durable physical
    medium customarily used for software interchange, for a price no
    more than your reasonable cost of physically performing this
    conveying of source, or (2) access to copy the
    Corresponding Source from a network server at no charge.

    c) Convey individual copies of the object code with a copy of the
    written offer to provide the Corresponding Source.  This
    alternative is allowed only occasionally and noncommercially, and
    only if you received the object code with such an offer, in accord
    with subsection 6b.

    d) Convey the object code by offering access from a designated
    place (gratis or for a charge), and offer equivalent access to the
    Corresponding Source in the same way through the same place at no
    further charge.  You need not require recipients to copy the
    Corresponding Source along with the object code.  If the place to
    copy the object code is a network server, the Corresponding Source
    may be on a different server (operated by you or a third party)
    that supports equivalent copying facilities, provided you maintain
    clear directions next to the object code saying where to find the
    Corresponding Source.  Regardless of what server hosts the
    Corresponding Source, you remain obligated to ensure that it is
    available for as long as needed to satisfy these requirements.

    e) Convey the object code using peer-to-peer transmission, provided
    you inform other peers where the object code and Corresponding
    Source of the work are being offered to the general public at no
    charge under subsection 6d.

  A separable portion of the object code, whose source code is excluded
from the Corresponding Source as a System Library, need not be
included in conveying the object code work.

  A "User Product" is either (1) a "consumer product", which means any
tangible personal property which is normally used for personal, family,
or household purposes, or (2) anything designed or sold for incorporation
into a dwelling.  In determining whether a product is a consumer product,
doubtful cases shall be resolved in favor of coverage.  For a particular
product received by a particular user, "normally used" refers to a
typical or common use of that class of product, regardless of the status
of the particular user or of the way in which the particular user
actually uses, or expects or is expected to use, the product.  A product
is a consumer product regardless of whether the product has substantial
commercial, industrial or non-consumer uses, unless such uses represent
the only significant mode of use of the product.

  "Installation Information" for a User Product means any methods,
procedures, authorization keys, or other information required to install
and execute modified versions of a covered work in that User Product from
a modified version of its Corresponding Source.  The information must
suffice to ensure that the continued functioning of the modified object
code is in no case prevented or interfered with solely because
modification has been made.

  If you convey an object code work under this section in, or with, or
specifically for use in, a User Product, and the conveying occurs as
part of a transaction in which the right of possession and use of the
User Product is transferred to the recipient in perpetuity or for a
fixed term (regardless of how the transaction is characterized), the
Corresponding Source conveyed under this section must be accompanied
by the Installation Information.  But this requirement does not apply
if neither you nor any third party retains the ability to install
modified object code on the User Product (for example, the work has
been installed in ROM).

  The requirement to provide Installation Information does not include a
requirement to continue to provide support service, warranty, or updates
for a work that has been modified or installed by the recipient, or for
the User Product in which it has been modified or installed.  Access to a
network may be denied when the modification itself materially and
adversely affects the operation of the network or violates the rules and
protocols for communication across the network.

  Corresponding Source conveyed, and Installation Information provided,
in accord with this section must be in a format that is publicly
documented (and with an implementation available to the public in
source code form), and must require no special password or key for
unpacking, reading or copying.

  7. Additional Terms.

  "Additional permissions" are terms that supplement the terms of this
License by making exceptions from one or more of its conditions.
Additional permissions that are applicable to the entire Program shall
be treated as though they were included in this License, to the extent
that they are valid under applicable law.  If additional permissions
apply only to part of the Program, that part may be used separately
under those permissions, but the entire Program remains governed by
this License without regard to the additional permissions.

  When you convey a copy of a covered work, you may at your option
remove any additional permissions from that copy, or from any part of
it.  (Additional permissions may be written to require their own
removal in certain cases when you modify the work.)  You may place
additional permissions on material, added by you to a covered work,
for which you have or can give appropriate copyright permission.

  Notwithstanding any other provision of this License, for material you
add to a covered work, you may (if authorized by the copyright holders of
that material) supplement the terms of this License with terms:

    a) Disclaiming warranty or limiting liability differently from the
    terms of sections 15 and 16 of this License; or

    b) Requiring preservation of specified reasonable legal notices or
    author attributions in that material or in the Appropriate Legal
    Notices displayed by works containing it; or

    c) Prohibiting misrepresentation of the origin of that material, or
    requiring that modified versions of such material be marked in
    reasonable ways as different from the original version; or

    d) Limiting the use for publicity purposes of names of licensors or
    authors of the material; or

    e) Declining to grant rights under trademark law for use of some
    trade names, trademarks, or service marks; or

    f) Requiring indemnification of licensors and authors of that
    material by anyone who conveys the material (or modified versions of
    it) with contractual assumptions of liability to the recipient, for
    any liability that these contractual assumptions directly impose on
    those licensors and authors.

  All other non-permissive additional terms are considered "further
restrictions" within the meaning of section 10.  If the Program as you
received it, or any part of it, contains a notice stating that it is
governed by this License along with a term that is a further
restriction, you may remove that term.  If a license document contains
a further restriction but permits relicensing or conveying under this
License, you may add to a covered work material governed by the terms
of that license document, provided that the further restriction does
not survive such relicensing or conveying.

  If you add terms to a covered work in accord with this section, you
must place, in the relevant source files, a statement of the
additional terms that apply to those files, or a notice indicating
where to find the applicable terms.

  Additional terms, permissive or non-permissive, may be stated in the
form of a separately written license, or stated as exceptions;
the above requirements apply either way.

  8. Termination.

  You may not propagate or modify a covered work except as expressly
provided under this License.  Any attempt otherwise to propagate or
modify it is void, and will automatically terminate your rights under
this License (including any patent licenses granted under the third
paragraph of section 11).

  However, if you cease all violation of this License, then your
license from a particular copyright holder is reinstated (a)
provisionally, unless and until the copyright holder explicitly and
finally terminates your license, and (b) permanently, if the copyright
holder fails to notify you of the violation by some reasonable means
prior to 60 days after the cessation.

  Moreover, your license from a particular copyright holder is
reinstated permanently if the copyright holder notifies you of the
violation by some reasonable means, this is the first time you have
received notice of violation of this License (for any work) from that
copyright holder, and you cure the violation prior to 30 days after
your receipt of the notice.

  Termination of your rights under this section does not terminate the
licenses of parties who have received copies or rights from you under
this License.  If your rights have been terminated and not permanently
reinstated, you do not qualify to receive new licenses for the same
material under section 10.

  9. Acceptance Not Required for Having Copies.

  You are not required to accept this License in order to receive or
run a copy of the Program.  Ancillary propagation of a covered work
occurring solely as a consequence of using peer-to-peer transmission
to receive a copy likewise does not require acceptance.  However,
nothing other than this License grants you permission to propagate or
modify any covered work.  These actions infringe copyright if you do
not accept this License.  Therefore, by modifying or propagating a
covered work, you indicate your acceptance of this License to do so.

  10. Automatic Licensing of Downstream Recipients.

  Each time you convey a covered work, the recipient automatically
receives a license from the original licensors, to run, modify and
propagate that work, subject to this License.  You are not responsible
for enforcing compliance by third parties with this License.

  An "entity transaction" is a transaction transferring control of an
organization, or substantially all assets of one, or subdividing an
organization, or merging organizations.  If propagation of a covered
work results from an entity transaction, each party to that
transaction who receives a copy of the work also receives whatever
licenses to the work the party's predecessor in interest had or could
give under the previous paragraph, plus a right to possession of the
Corresponding Source of the work from the predecessor in interest, if
the predecessor has it or can get it with reasonable efforts.

  You may not impose any further restrictions on the exercise of the
rights granted or affirmed under this License.  For example, you may
not impose a license fee, royalty, or other charge for exercise of
rights granted under this License, and you may not initiate litigation
(including a cross-claim or counterclaim in a lawsuit) alleging that
any patent claim is infringed by making, using, selling, offering for
sale, or importing the Program or any portion of it.

  11. Patents.

  A "contributor" is a copyright holder who authorizes use under this
License of the Program or a work on which the Program is based.  The
work thus licensed is called the contributor's "contributor version".

  A contributor's "essential patent claims" are all patent claims
owned or controlled by the contributor, whether already acquired or
hereafter acquired, that would be infringed by some manner, permitted
by this License, of making, using, or selling its contributor version,
but do not include claims that would be infringed only as a
consequence of further modification of the contributor version.  For
purposes of this definition, "control" includes the right to grant
patent sublicenses in a manner consistent with the requirements of
this License.

  Each contributor grants you a non-exclusive, worldwide, royalty-free
patent license under the contributor's essential patent claims, to
make, use, sell, offer for sale, import and otherwise run, modify and
propagate the contents of its contributor version.

  In the following three paragraphs, a "patent license" is any express
agreement or commitment, however denominated, not to enforce a patent
(such as an express permission to practice a patent or covenant not to
sue for patent infringement).  To "grant" such a patent license to a
party means to make such an agreement or commitment not to enforce a
patent against the party.

  If you convey a covered work, knowingly relying on a patent license,
and the Corresponding Source of the work is not available for anyone
to copy, free of charge and under the terms of this License, through a
publicly available network server or other readily accessible means,
then you must either (1) cause the Corresponding Source to be so
available, or (2) arrange to deprive yourself of the benefit of the
patent license for this particular work, or (3) arrange, in a manner
consistent with the requirements of this License, to extend the patent
license to downstream recipients.  "Knowingly relying" means you have
actual knowledge that, but for the patent license, your conveying the
covered work in a country, or your recipient's use of the covered work
in a country, would infringe one or more identifiable patents in that
country that you have reason to believe are valid.

  If, pursuant to or in connection with a single transaction or
arrangement, you convey, or propagate by procuring conveyance of, a
covered work, and grant a patent license to some of the parties
receiving the covered work authorizing them to use, propagate, modify
or convey a specific copy of the covered work, then the patent license
you grant is automatically extended to all recipients of the covered
work and works based on it.

  A patent license is "discriminatory" if it does not include within
the scope of its coverage, prohibits the exercise of, or is
conditioned on the non-exercise of one or more of the rights that are
specifically granted under this License.  You may not convey a covered
work if you are a party to an arrangement with a third party that is
in the business of distributing software, under which you make payment
to the third party based on the extent of your activity of conveying
the work, and under which the third party grants, to any of the
parties who would receive the covered work from you, a discriminatory
patent license (a) in connection with copies of the covered work
conveyed by you (or copies made from those copies), or (b) primarily
for and in connection with specific products or compilations that
contain the covered work, unless you entered into that arrangement,
or that patent license was granted, prior to 28 March 2007.

  Nothing in this License shall be construed as excluding or limiting
any implied license or other defenses to infringement that may
otherwise be available to you under applicable patent law.

  12. No Surrender of Others' Freedom.

  If conditions are imposed on you (whether by court order, agreement or
otherwise) that contradict the conditions of this License, they do not
excuse you from the conditions of this License.  If you cannot convey a
covered work so as to satisfy simultaneously your obligations under this
License and any other pertinent obligations, then as a consequence you may
not convey it at all.  For example, if you agree to terms that obligate you
to collect a royalty for further conveying from those to whom you convey
the Program, the only way you could satisfy both those terms and this
License would be to refrain entirely from conveying the Program.

  13. Use with the GNU Affero General Public License.

  Notwithstanding any other provision of this License, you have
permission to link or combine any covered work with a work licensed
under version 3 of the GNU Affero General Public License into a single
combined work, and to convey the resulting work.  The terms of this
License will continue to apply to the part which is the covered work,
but the special requirements of the GNU Affero General Public License,
section 13, concerning interaction through a network will apply to the
combination as such.

  14. Revised Versions of this License.

  The Free Software Foundation may publish revised and/or new versions of
the GNU General Public License from time to time.  Such new versions will
be similar in spirit to the present version, but may differ in detail to
address new problems or concerns.

  Each version is given a distinguishing version number.  If the
Program specifies that a certain numbered version of the GNU General
Public License "or any later version" applies to it, you have the
option of following the terms and conditions either of that numbered
version or of any later version published by the Free Software
Foundation.  If the Program does not specify a version number of the
GNU General Public License, you may choose any version ever published
by the Free Software Foundation.

  If the Program specifies that a proxy can decide which future
versions of the GNU General Public License can be used, that proxy's
public statement of acceptance of a version permanently authorizes you
to choose that version for the Program.

  Later license versions may give you additional or different
permissions.  However, no additional obligations are imposed on any
author or copyright holder as a result of your choosing to follow a
later version.

  15. Disclaimer of Warranty.

  THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
ALL NECESSARY SERVICING, REPAIR OR CORRECTION.

  16. Limitation of Liability.

  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
SUCH DAMAGES.

  17. Interpretation of Sections 15 and 16.

  If the disclaimer of warranty and limitation of liability provided
above cannot be given local legal effect according to their terms,
reviewing courts shall apply local law that most closely approximates
an absolute waiver of all civil liability in connection with the
Program, unless a warranty or assumption of liability accompanies a
copy of the Program in return for a fee.

                     END OF TERMS AND CONDITIONS

            How to Apply These Terms to Your New Programs

  If you develop a new program, and you want it to be of the greatest
possible use to the public, the best way to achieve this is to make it
free software which everyone can redistribute and change under these terms.

  To do so, attach the following notices to the program.  It is safest
to attach them to the start of each source file to most effectively
state the exclusion of warranty; and each file should have at least
the "copyright" line and a pointer to where the full notice is found.

    <one line to give the program's name and a brief idea of what it does.>
    Copyright (C) <year>  <name of author>

    This program is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    This program is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with this program.  If not, see <http://www.gnu.org/licenses/>.

Also add information on how to contact you by electronic and paper mail.

  If the program does terminal interaction, make it output a short
notice like this when it starts in an interactive mode:

    <program>  Copyright (C) <year>  <name of author>
    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
    This is free software, and you are welcome to redistribute it
    under certain conditions; type `show c' for details.

The hypothetical commands `show w' and `show c' should show the appropriate
parts of the General Public License.  Of course, your program's commands
might be different; for a GUI interface, you would use an "about box".

  You should also get your employer (if you work as a programmer) or school,
if any, to sign a "copyright disclaimer" for the program, if necessary.
For more information on this, and how to apply and follow the GNU GPL, see
<http://www.gnu.org/licenses/>.

  The GNU General Public License does not permit incorporating your program
into proprietary programs.  If your program is a subroutine library, you
may consider it more useful to permit linking proprietary applications with
the library.  If this is what you want to do, use the GNU Lesser General
Public License instead of this License.  But first, please read
<http://www.gnu.org/philosophy/why-not-lgpl.html>.

@c Local Variables:
@c ispell-local-pdict: "ispell-dict"
@c End:

@c ============================================================================
@c ====== Part 6: The End of the Document =====================================
@c ============================================================================

@c @node Index
@c @unnumbered Index
@c @printindex cp

@bye

