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August 3, 2021

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:

More pointers to APL resources on the Web:

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1 Installing and Starting GNU APL

1.1 Installing APL

APL is built and installed like this:

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

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.

1.2 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:


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


$ 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).

1.3 Command Line Options

GNU APL understands the following command line options:

1.4 Configuration 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:

The system configuration directory is usually /etc or /usr/local/etc and is configurable via ./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.

1.5 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:

  1. 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.
  2. 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.
  3. 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.
  4. 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.

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:

  1. command arguments shown in brackets are optional.
  2. lib is a number from 0 to 9. If lib is not present then 0 is taken as default.
  3. if the name is optional and missing then the workspace ID (the name set with )WSID) is used.
  4. if the file extension (i.e. .xml or .atf) is missing then it is appended automatically to name.

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


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 un-comment 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.

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2 Non-standard GNU APL Features

There are a few hopefully useful features in GNU APL:

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2.1 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 #!, 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:

    #! /usr/local/bin/apl --id 1010

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).

2.1.1 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:

    apl < SCRIPT.apl

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

    apl -f SCRIPT.apl

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.

2.1.2 Make the script file executable

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

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

--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.

2.1.3 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:

$ apl --silent -l 37 -- app1 app2

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):

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

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

Assume further that the script is started like this:

$ ./SCRIPT.apl sarg1 sarg2

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


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:

/usr/local/bin/apl --
/usr/local/bin/apl -s
/usr/local/bin/apl --script
/usr/local/bin/apl -s --
/usr/local/bin/apl --script --

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.

2.1.4 Helpful Features for Scripting

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

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:

    /usr/local/bin/apl --id 1010

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:

    ⎕ENV ''

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; by convention the names of environment are all uppercase.

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

BODY ← ⊂ 'First line'
BODY ← BODY , ⊂ 'Second line'
BODY ← BODY , ⊂ 'Third line'

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

First line
Second line
Third line

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

2.1.5 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. 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:


┃┏→━━┓ ┏→━━━┓ ┏→━━━━━┓┃
┃┃ABC┃ ┃ DEF┃ ┃ GHIJK┃┃
┃┗━━━┛ ┗━━━━┛ ┗━━━━━━┛┃

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:



┃┏⊖┓ ┏→━━┓ ┏→━━━┓ ┏→━━━━━━┓┃
┃┃ ┃ ┃ABC┃ ┃ DEF┃ ┃  GHIJK┃┃
┃┗━┛ ┗━━━┛ ┗━━━━┛ ┗━━━━━━━┛┃
┗∊━━━━━━━━━━━━━━━━━━━━━━━━━┛ 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:


 4 ⎕CR """

┃┏→━━┓ ┏→━━━┓ ┏⊖┓ ┏→━━━━━━┓┃
┃┃ABC┃ ┃ DEF┃ ┃ ┃ ┃  GHIJK┃┃
┃┗━━━┛ ┗━━━━┛ ┗━┛ ┗━━━━━━━┛┃

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

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

2.1.6 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:

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

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

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

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


 /usr/local/bin/apl --silent -f ../workspaces/SCRIPT.apl

then the first line #! /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 --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.

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

If we run the same script directly:


Then we get:

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

The --script implies --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 ../workspaces/SCRIPT.apl comes from function execve (see ’man 2 execve’).

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

../workspaces/SCRIPT.apl SCRIPTARG

then it shows up at the end of ⎕ARG:

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

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:

      ∇Z←FOO B
[1] ∇
            ∇Z←FOO B
      ∇Z←FOO B
attempt to ∇-open existing function with new function header

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.

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2.2 Axis argument in defined functions

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

∇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

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!

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2.3 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 -f option, or the -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.

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2.4 Comparison Rules

Both IBM APL2 and the ISO standard require that the arguments of <, ≤, ≥, and > (but not of = or ≠) are integer or real numbers, and, as a consequence, that the argument of ⍋ 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. Then the final result of comparing A and B is the first decision (i.e. A < B, A > B, or A = B) made when following the rules below:

  1. Comparison by rank: if (⍴⍴A) < (⍴⍴B) then A < B. And vice versa.
  2. Comparison by shape: if (⍴A) < (⍴B) then A < B. And vice versa. The first different shape item decides.
  3. Comparison of ravel elements: at this point ⍴A ≡ ⍴B. 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. If A1 < B1 then A < B and vice versa. The comparison A1 < B1 is made according to the following rules 4. - 7. below.

  4. Comparison by depth:
  5. Comparison by Unicode: if A1 and B1 are both character values and (⎕UCS A1) < (⎕UCS B1) then A < B. And vice versa.
  6. Comparison by type: If A1 is a character and B1 is numeric, then A < B. And vice versa.
  7. Comparison by numeric value: if A1 and B1 are both numeric values then:
  8. Otherwise: A = B.

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:

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:

      (9 8) < (1 2 3)
      9 8<1 2 3
      ^  ^

      ⍋(9 8) (1 2 3)
1 2

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 ¯2 < ¯1 < ¯2J0E¯20 for the near-complex number ¯2J0E¯20.

CAUTION: The comparison of two strings (i.e. nested character vectors) may give unexpected results because shorter strings come before longer strings. For example, ’Zoo’ comes before ’Adam’ even though one might expect the opposite.

      Z[⍋Z ← 'Adam' 'Zoo']
 Zoo Adam 

      Z[⍋Z ← 'Adam' 'Zora']
 Adam Zora

This pitfall can be avoided by enforcing the same length for all strings being compared or sorted. A simple way to achieve that is the use of ⊂[2]⊃ like this (assuming IO←1):

      Z[⍋Z ← ⊂[2]⊃ 'Adam' 'Zoo']
 Adam Zoo  

      Z[⍋Z ← ⊂[2]⊃ 'Adam' 'Zora']
 Adam Zora

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2.5 Complex Numbers

Complex numbers are fully supported.

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2.6 Debug Commands

In addition to the classical APL commands like )LOAD or )SAVE, GNU APL has a number of debug commands for debugging purposes. Regular APL 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 GNU APL feature, colored output, uses different colors for stdout and stderr.

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

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2.7 Direct Functions (Lambdas)

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

2.7.1 Named Lambdas

A statement of the form

      FUN ← { body_statement } 

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

      FUN ← { body_expression }

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

For example:


      SUM ← { ⍺ + ⍵ }


[0] λ←⍺ SUM ⍵
[1] λ← ⍺ + ⍵ 

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:

      SUM ← { ⍺ + ⍵ ;C;D }

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

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.

2.7.2 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:

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

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.

2.7.3 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.

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2.8 ]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.

]DOXY                   ⍝ write documentation to /tmp/WSNAME/*
]DOXY dest              ⍝ write documentation to dest/WSNAME/*

The starting point for browsing the documentation are the files:

/tmp/WSNAME/index.html         ⍝ for ]DOXY without arguments, resp.
dest/WSNAME/index.html         ⍝ for e.g. ]DOXY dest

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

file:///tmp/WSNAME   resp.

In the above examples is WSNAME 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:

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

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2.9 Commands )COPY_ONCE, )DUMP, and DUMP-HTML

In standard APL, workspaces are processed with the standard commands )LOAD, )COPY, and )SAVE. GNU APL provides additional commands to process workspaces.

2.9.1 )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).

2.9.2 )DUMP-HTML Command

The )DUMP-HTML command is similar to the )DUMP command. The output format is similar to the )DUMP command, the difference is that those characters\ that need HTML-escaping (e.g. ’<’ becomes &lt;, ’>’ becomes ’&gt;) are being HTML-escaped. The output of the )DUMP-HTML command can therefore be directly used by a web server to display workspace listings (in order to share the code).

The files written with command )DUMP-HTML have the extension .html.

In addition to the APL code, the .html files produced have a short HTML <head> section template. The user should replace the fields marked with ?????? with proper values (for the author, the copyright owner, and a short description) before publishing the page.

2.9.3 )COPY_ONCE Command

Command )COPY_ONCE copies all objects (variables, functions and operators) from some other workspace into the current workspace similar to )COPY. However, )COPY_ONCE does this only once; a second invocation of )COPY_ONCE with the same workspace (and the same library reference number) is silently being ignored. This speeds up the )COPYing of libraries that occur in several )DUMPed or )SAVEd workspace.

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2.10 ]NEXTFILE and ]PUSHFILE Commands

2.10.1 ]NEXTFILE

The debug command ]NEXTFILE, when used in an APL script file, terminates the processing of that file and continues processing in the next script file (if any) or else enters immediate execution mode. Unlike )OFF (which terminates the interpreter), ]NEXTFILE does not terminate the interpreter but only changes its input source to the next script file (if there is one remaining) and enters immediate execution only if all scripts were processed.

The user may, for example, want to use the space near the end of the script to add longer comments (as to what the script does, how it works, how it is used, etc.) without the need to prepend every line with ⍝ or #.

For example:


⍝ see documentation at the end of this file



This workspace does the following...

2.10.2 ]PUSHFILE

The debug command ]PUSHFILE is similar to ]NEXTFILE in that it terminates the processing of the current script file. Unlike ]NEXTFILE, ]PUSHFILE does not proceed to the next script file but enters a new immediate execution context in which the user can interact with the interpreter. This context can be processes input until a ]NEXTFILE command is given. After the ]NEXTFILE that leaves the immediat execution context processing proceeds at the next line after the ]PUSHFILE command.

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2.11 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.

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2.12 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.

2.12.1 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.

2.12.2 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


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


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

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2.13 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).

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2.14 Hex Numbers

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



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2.15 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:


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:


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2.16 Structured Variables and Associative Arrays

GNU APL has implemented two features that are closely related because, under the hood, they share the same implementation: structured variables and associative arrays.

2.16.1 Structured Variables

A structured variable is an APL variable that contains several related but otherwise independent sub-variables aka members. Such structured variables can be convenient for passing many related arguments to a function, or for returning multiple results from a function.

The different sub-variables of a structured variable are accessed by the (top-level) name of the variable followed by a non-empty sequence of member names, separated by ’.’. In the following we will use uppercase names for structured variables and lowercase names for their members. For example:


is a structured variable PERSON, which has a member address, and PERSON.address is a structured (sub-)variable of PERSON which has a member street.

For a structured variable and all its sub-variables, the usual rules for normal variables apply. They can be created, erased, and even passed as arguments to functions.

A structured variable is created by assigning a value to one of its members. For example:

      PERSON.firstname ← 'Jane'   ⍝ create variable PERSON with member 'firstname'
      PERSON.lastname  ← 'Doe'    ⍝ add a second member 'lastname' to PERSON

The depth of a newly created member can be more than one. In this case the intermediate members are created automatically. For example:

      PERSON.address.street ←  '42 Main Street'   ⍝ implicitly creates PERSON.address

Empty structured variables can be created with 38 ⎕CR:

      EMPTY ← 38 ⎕CR CAPACITY ← 32

Note: A structured variable is automatically expanded when new members are added to it. From time to time this expansion exceeds the space allocated for the members of the variable and then the existing members need to be copied into a new, larger structure. The overhead caused by this reorganization can be avoided by specifying a sufficiently large capacity when the structure is created (with 38 ⎕CR).

An entire structured variable can be erased with ⎕EX or with\ )ERASE just like other variables. That erases the variable along with all its members. In addition to erasing an entire structured variable, individual members at any depth can also be erased with ⎕EX or )ERASE:

      )ERASE PERSON.address      ⍝ OK, PERSON.address exists
      )ERASE PERSON.address      ⍝ error: PERSON.address does not exist anymore

After having been created, the members of a structured variable can be referenced and overridden just like normal variables:

      PERSON.address.street ←  '42 Main Street'   ⍝ create member address.street
      PERSON.address.street   ⍝ reference member address.street of PERSON
42 Main Street

      PERSON.address.street ←  '44 Main Street'   ⍝ override address.street
44 Main Street

The members of a structured variable form a tree of (sub-) variables, similar to the file system on a computer. This tree has:

Due to their tree-like structure, structured variables need to be printed somewhat different than normal APL variables. For example:

.firstname: ┌→───┐

.lastname: ┌→──┐

.address.street: ┌→─────────────┐
                 │44 Main Street│

Only the leafs of a deeply structured variable can have values and, as a precaution, assigning a value to a non-leaf (including the root) raises a DOMAIN ERROR:

      B.b.c←'leaf-Abc'        ⍝ OK, since B.b.c will be a leaf
      B.b←42                  ⍝ will fail since B.b is not a leaf
       ^ ^
member access: cannot override non-leaf member A.b
)ERASE or ⎕EX that member first.

      )ERASE B.b
      B.b ← 'leaf-Ab'         ⍝ now OK, since B.b will now become a (new) leaf


On the other hand, assigning a structured variable to the leaf of another structured variable is valid and concatenates the members:

      )ERASE A
      A.b.c ← 'leaf-Abc'      ⍝ variable A with leaf A.b.c
      C.d.e ← 'leaf-cde'      ⍝ variable C with leaf C.d.e
      A.b.c ← C               ⍝ override leaf A.b.c of A

The file src/testcases/ contains the examples above (and more)

2.16.2 Associative Arrays

APL arrays are primarily indexed with numbers (or arrays of numbers), which is also the most efficient method. Many other languages provide, in either addition or else alternatively, a method to index arrays by keys, where the keys are frequently characters strings. Such arrays are commonly referred to as associative arrays.

APL has no associative array per se, but the structured variables in GNU APL can be used for the same purpose. The only limitation is (currently) that the keys need to be character strings (as opposed to arbitrary APL values).

That is, in GNU APL an associative array

As long as the strings that are used as keys follow the same rules as APL variable names (no leading digit, no ’.’ etc.), a structured variable can also be indexed with a string. That can be useful if keys are being computed or passed as function arguments. However, unlike indexing of APL arrays with numbers, only one key per (bracket-) index is permitted.

   A.key ← 42
   A['key' 'key']   ⍝ not allowed even though 'key' is a valid member
      D['key' 'key']

Strings that do not follow the rules for variable names can be used with bracket index, but not with the .member syntax:

      ASSOC ← 38 ⎕CR 8
      KEY←''   ⍝ works, but avoid such keys
43   ⍝ won't work: '' is a single key, but is 2 keys
member access: structure ASSOC has no member key←44   ⍝ works: 2 (nested) keys
      ASSOC['']   ⍝ works: one key containing '.'

This is because above is being tokenized by the APL parser into [ASSOC] [key] [dot], while ’’ is a single key. The example above (with different values for and for ASSOC[’’] demonstrates why such keys are better avoided.

Even though (one) bracket index can only access the top-level members of a structured variable, repeated bracket index (or dyadic PICK) can be used to access deeper nesting levels:

      D['b.c']   ⍝ will fail
member access: member b.c was not found. The valid members are:

      D['b']['c']   ⍝ will work

      ⍝ alternatively: use PICK
      'b' 'c' ⊃ D   ⍝ fails: 'b' 'c' is 'ab'
      "b" "c" ⊃ D   ⍝ works

In the above examples each bracket index (or each element of PICK) discards the current top-level structure and descends into the structured sub-variable of the chosen member. In this case PICK is more efficient since repeated bracket index creates copies of the intermediate structured sub-variables.

If a variable is used as a structured variable then the number of its members is typically small (since every member name occurs explicitly in the APL code that uses it). If a variable is used as an associative array, then the member names are typically being computed and the number of members can become rather large (like the different key values in a database). When such a variable (i.e. with many members) reaches its capacity, then finding a member (when the array is indexed), or finding an unused place in the variable (when a new member is added) becomes slower and slower. The GNU APL implementation has addressed this by hashing into the variable (based on the member name) instead of, for example, sequentially allocating the members. This is very fast under normal circumstances, but becomes as slow as sequential allocation when the number of members in the variable reaches its current capacity. For this reason, if a structured variable is used as an associative array, e.g. as a database, then it is better to not rely on the (automatic) reorganization of the variable, but to create the variable with a large enough (with 38 ⎕CR) from the beginning.

If that is not possible (because the (performance-) problem has occurred after the variable was created, then one can manually increase the capacity like this:

      TMP ← 39 ⎕CR ASSOC_ARRAY   ⍝ save ASSOC_ARRAY as normal APL array
      ⊣ ⎕EX 'ASSOC_ARRAY'        ⍝ erase it so that it can be assigned
      ASSOC_ARRAY ← 38 ⎕CR TMP   ⍝ new associative array with ≥ twice the size

As a rule of thumb, associative arrays will be fast as long their capacity is more than twice the number of their members. The expression ASSOC_ARRAY[;1] returns all keys (= members) of ASSOC_ARRAY, therefore the number of members is ⍴ASSOC_ARRAY[;1] and the capacity is ↑⍴ASSOC_ARRAY.

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2.17 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 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 Z←A[X] B. Then:


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

   A ⊢[X] '*'

  '*' ⊢[X] B
* 2 *
4 * 6

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2.18 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:

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):

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

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

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

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

      ⍝ bit-wise AND
      5 ⎕CR (4⍴256)⊤   A ⊤∧ B

2.18.1 Dyadic ⊤∧, ⊤∨, ⊤⍲, ⊤⍱, ⊤=, and ⊤≠

The dyadic forms of ⊤∧, ⊤∨, ⊤⍲, and ⊤⍱ are simply the bit-wise variants of their Boolean counterparts:

      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

2.18.2 Monadic ⊤∨ and ⊤⍱

⊤∧ and ⊤⍲ do not have a monadic form, but ⊤∧, ⊤∨, and ⊤⍱ do. Formally monadic ⊤∨ resp, ⊤⍱ are dyadic ⊤∨ resp, ⊤⍱ with a left argument of 0:

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

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 ⊤∨ and inversion of the bits (monadic ⊤⍱, The latter is needed since ∼ has a monadic form and as a consequence ⊤∼ was not an option for a bit-wise Not function.

Monadic ⊤⍱ B is the bit-wise Not function of its argument:

⊤⍱ B ←→ 2⊥ ~(64⍴2)⊤B

Monadic ⊤∨ B converts near-integer values B into true integers:

      26 ⎕CR    1            ⍝ integer
      26 ⎕CR    1.1          ⍝ real
      26 ⎕CR    1÷1          ⍝ integer
      26 ⎕CR    1.1÷1.1      ⍝ real
      26 ⎕CR    ⊤∨ 1.1÷1.1   ⍝ integer

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

      26 ⎕CR    1.1J0÷1.1      ⍝ real
      26 ⎕CR    ⊤∨ 1.1J0÷1.1      ⍝ integer

As a matter of fact, ⊤∨ 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.

2.18.3 Monadic ⊤∧

The ISO standard defines two different concepts to decide if a real number R is close to an integer I,

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 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.

2.18.4 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:

      5 ⎕CR 'A'
      5 ⎕CR ⊤⍱'A'                       ⍝ Note that 5 ⎕CR ANDs with $FF

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

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2.19 Generalized ⍳

2.19.1 Generalized monadic ⍳

The standard function Interval (Z←⍳B) requires its argument B to be a scalar or a length 1 vector. The result Z←⍳B then contains all possible indices of values which have shape B.

Generalized monadic ⍳ extends this concept to integer vectors B with more than 1 element. The result Z←⍳B again contains all possible indices of a value which has shape B, but the rank of B can now be more than 1. The items of Z are nested integer vectors as opposed to integer scalars in the standard case.

2.19.2 Generalized dyadic ⍳

The standard function Index Of (Z←A⍳B) requires its left argument A to be a scalar or a vector of rank 1. The items of the result Z are the (first) positions (= indices) of the corresponding items of B in A (for the items found in A) or else ⎕IO+⍴A (which is an invalid index of A) for the items of B that are not found in A.

Generalized dyadic ⍳ extends this concept to find the (first) indices of the corresponding items of B in A (in ravel order) where the rank of A is > 1. Each item of the result Z is then either a nested integer vector (if the item was found) or - different from the standard case (!) - the empty vector ⍬ if the item was not found).

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2.20 ⌹[X] - QR Factorization

Z←⌹[X] B computes a QR factorization of the real or complex matrix B. The axis argument X is used to clear near-0 matrix items to exactly 0.0 during the computation. Set X←⎕CT if unsure.

The result Z is a triple (QT R Ri)←Z with the following properties. Let ⍴B=(M, N).

* QT is an orthogonal M×M matrix, i.e QT-1 = QTT, resp. QT +.× ⍉QT is the M×M identity matrix IM (with IM←∘.=⍨⍳M).

* R is an upper triangular M×N matrix, i.e. R[m;n] = 0 for n < m, and

* Ri is the inverse of R, i.e. Ri +.× R is the identity matrix IN.

* (⍉QT) +.× R = B.

Note that, unlike in standard QR factorizations, the matrix QT returned by ⌹[X] is already inverted (i.e. transposed since QT is orthogonal). The reason is that the algorithm used can transpose Q with no extra cost and usually the first step after a QR factorization is to transpose the returned Q matrix. This first transpose step is therefore not needed.

Example 1 (real B)

      ⎕←B←3 3⍴ 1 1 3 2 4 2 4 8 7
1 1 3
2 4 2
4 8 7

      (QT R Ri)←⌹[⎕CT]B
      Q←⍉QT   ⍝ recover the non-transposed Q

      4 ⎕CR 0 4⍕ Q
↓ .2182  .9759 ¯.0000┃
┃ .4364 ¯.0976 ¯.8944┃
┃ .8729 ¯.1952  .4472┃

      ⍝ verify that Q is orthogonal
      4 ⎕CR 0 4⍕ Q +.×⍉Q
↓ 1.0000 ¯.0000  .0000┃
┃ ¯.0000 1.0000  .0000┃
┃  .0000  .0000 1.0000┃

      ⍝ verify that R is upper triangle
      4 ⎕CR 0 4⍕ R
↓ 4.5826 8.9469 7.6376┃
┃  .0000 ¯.9759 1.3663┃
┃ ¯.0000 ¯.0000 1.3416┃

       ⍝ verify that B is Q +.× R   i.e. B is (⍉Q) +.× R
       Q +.× R
1 1 3
2 4 2
4 8 7

      ⍝ verify that Ri is the inverse of R
      4 ⎕CR 0 4⍕ Ri +.×R
↓ 1.0000 ¯.0000  .0000┃
┃  .0000 1.0000  .0000┃
┃  .0000  .0000 1.0000┃

Example 2 (complex over-determined B)

⎕←B←5 4⍴4J6 6J3 5J10 3J2 8J10 3J4 5J10 5J8 3J1 2J3 4J5 1J3 1J4 9J9 9J6 2J7 2J10 7J6 9J8 10J10

      (QT R)←⌹[⎕CT]B
      Q←⍉QT   ⍝ recover the non-transposed Q

      4 ⎕CR 0 4⍕ Q
↓ .4107J¯.0310  .0621J¯.1742  .9124J¯.1121  .3710J.3755  ¯.2148J.0626 ┃
┃ .7219J¯.1180 ¯.5950J.0697  ¯.2629J.4735  ¯.7179J¯.4253 ¯.1979J.2738 ┃
┃ .1338J¯.1213  .0880J.2603   .3667J¯.0282 ¯.1833J.3784  1.0188J.0717 ┃
┃ .2271J.0623   .9071J.0968   .0575J.2496  ¯.5003J.2494  ¯.1208J¯.0703┃
┃ .5538J.1806   .1779J¯.3283 ¯.6232J¯.3575  .8260J¯.3033  .0605J¯.2291┃

      ⍝ verify that Q is orthogonal
      4 ⎕CR 0 4⍕ Q +.×⍉Q
↓ 1.0000J.0000   .0000J¯.0000 ¯.0000J¯.0000 ¯.0000J¯.0000  .0000J.0000 ┃
┃  .0000J¯.0000 1.0000J.0000   .0000J.0000   .0000J.0000   .0000J¯.0000┃
┃ ¯.0000J¯.0000  .0000J.0000  1.0000J¯.0000  .0000J¯.0000 ¯.0000J.0000 ┃
┃ ¯.0000J¯.0000  .0000J.0000   .0000J¯.0000 1.0000J.0000  ¯.0000J.0000 ┃
┃  .0000J.0000   .0000J¯.0000 ¯.0000J.0000  ¯.0000J.0000  1.0000J.0000 ┃

      ⍝ verify that R is upper triangle...
      4 ⎕CR 0 4⍕ R
↓ 8.5870J15.2557 10.1036J10.9309 13.5055J18.7452 10.0961J15.2530┃
┃  .0000J.0000    8.7353J5.5589   9.2429J.4120    2.5086J.7539  ┃
┃ ¯.0000J.0000     .0000J.0000   ¯2.4869J4.4115  ¯5.9788J¯6.0801┃
┃ ¯.0000J.0000    ¯.0000J.0000    ¯.0000J.0000    7.4038J¯3.9492┃
┃  .0000J.0000     .0000J.0000     .0000J.0000    ¯.0000J.0000  ┃

       ⍝ verify that B is Q +.× R   i.e. B is (⍉Q) +.× R
       Q +.× R
4J6  6J3 5J10  3J2
8J10 3J4 5J10  5J8
3J1  2J3 4J5   1J3
1J4  9J9 9J6   2J7
2J10 7J6 9J8  10J10

Please note as well that QR factorization is currently experimental. So please double-check its results before using it in production code.

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2.21 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:

      ⎕CR ''

Say a 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 frequently 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.


      Tag←55   ⍝ hex 37
      5 ⎕CR 33 ⎕CR Tag,'Value'

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


      34 ⎕CR ¯5 ⎕CR '000000370000000556616C7565'
55 Value

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:

  1. RANK ERROR if 1≠⍴⍴B
  2. DOMAIN ERROR if one of the B[j] is not a proper byte value

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.

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2.22 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 that contains the implementation of a native function for reading and writing files (fopen(), fclose(), ...), For example:

      ⍝ fix native function in as FILE_IO
      '' ⎕FX 'FILE_IO'

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

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/ (for niladic native functions), src/native/ (for nomadic native functions), src/native/ (for monadic native operators), or src/native/template_OP2/cc (for dyadic native operators) to your own .cc file and adjust src/native/ 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.

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2.23 ⎕ARG - Interpreter command line arguments

⎕ARG contains the command line arguments with which GNU APL was invoked. See Section 2.1.

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2.24 ⎕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:

The purpose of ¯4 ⎕DLX is:

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):

      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 

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:


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              

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

      ⍝ the rows in Q8 of the first solution
 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
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

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

Another application of ⎕DLX is solving sudokus. The constraints matrix is a little more complicated, but the principle is the same. GNU APL is shipped with two workspaces: sudoku.apl (which solves sudokus without using ⎕DLX) and sudoku_DLX.apl (which solves sudokus using ⎕DLX).

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2.25 ⎕ENV - Environment Variables

⎕ENV contains the environment variables of the process that is running GNU APL. See Section 2.1.

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2.26 ⎕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:

      ⎕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

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:

Z←F ⎕FIO[49] 'filename'

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,

Z←F ⎕FIO[49] 'filename'


Z F¨Z←⎕FIO[49] 'filename'

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2.27 ⎕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:

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

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:

⍴⍴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.

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2.28 ⎕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: HOWTOs/Quad-GTK.html.

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2.29 ⎕JSON - JSON Parsing

GNU APL provides ⎕JSON for decoding and encoding JSON strings and files. A (valid) JSON string is mapped to an APL value as follows:

2.29.1 Monadic ⎕JSON

Z←⎕JSON B converts the string B into an APL value according to the mapping above. If that fails then command )MORE provides information about the error and where in B the error was detected.

2.29.2 Dyadic ⎕JSON

Z←A ⎕JSON B performs one of the following conversions:

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2.30 ⎕MAP - Map Value

⎕MAP changes the ravel items of its right argument according to a mapping table provided as its left argument. Let Z←A ⎕MAP B.

The left argument A of ⎕MAP must be a N×2 matrix. Each 2-element row of A specifies a separate mapping. That is, the elements of B which are found in A[;1] are replaced by the corresponding element in A[;2]. The shape of the result Z is the shape of the right argument B.


      ⍝ the map A
      ⊢A←5 2⍴'eEwWaAzZ92'
eE    ⍝ map 'e' → 'E'
wW    ⍝ map 'w' → 'W'
aA    ⍝ map 'a' → 'A'
zZ    ⍝ map 'z' → 'Z'
92    ⍝ map '9' → '2'

      ⍝ the value B being mapped

      ⍝ the result of A ⎕MAP B
      A ⎕MAP B


      A←5 2⍴'eEwWaAzZ92'
      B←'Hal' 'low' 'een'   ⍝ nested B
      4 ⎕CR A ⎕MAP B        ⍝ non-recursive (none of the keys in A[;1] matches)
┃┏→━━┓ ┏→━━┓ ┏→━━┓┃
┃┃Hal┃ ┃low┃ ┃een┃┃
┃┗━━━┛ ┗━━━┛ ┗━━━┛┃

      4 ⎕CR (⊂A) ⎕MAP B   ⍝ recursive (some simple keys in A[;1] match)
┃┏→━━┓ ┏→━━┓ ┏→━━┓┃
┃┃HAl┃ ┃loW┃ ┃EEn┃┃
┃┗━━━┛ ┗━━━┛ ┗━━━┛┃

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2.31 ⎕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:

   ⎕PLOT ''      ⍝ show a list of attributes 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)
   ⎕PLOT ¯3      ⍝ close all plot windows

2.31.1 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). Complex Plot Data

If a data item B[N] or B[row;N] is 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:

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

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

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

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

PLOT_circle Real Plot Data

On the other hand, if a data item B[N] or B[row;N] is 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:

Xmin ← ⎕IO             ⍝ smallest real part of B
Xmax ← ¯1 + ⎕IO + ⍴B   ⍝ largest real part of B
Ymin ← ⌊/,B            ⍝ smallest value in B
Ymax ← ⌈/,B            ⍝ largest value in B


      ⎕PLOT 0 1 ¯1 2 ¯2 3 ¯3

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


NOTE: In theory one can also mix real and complex values, even though doing so makes little sense. If at least one item of the plot data B is complex, then all real items in B are taken as complex with imaginary part 0.

2.31.2 The Plot Attributes A

As can be displayed with ⎕PLOT ” there are a number of attributes that control how the resulting plot will look like:


      ⎕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)
filename:                          (output file name)
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)

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"):

      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

If the global attribute "filename" is given, then the plot is not only being displayed in an X window on the screen but also written to a file with the name provided as attribute value. The file format is bitmap (typical file extension: .bmp) which can then eaily converted to other graphic formats such as .png or .jpg with tools like ’convert’ from package imagemagick.

For example:

      ⊣ ( ⊂ "filename: /tmp/bitmap.bmp" ) ⎕PLOT 1 3 1 4 2

writes the plot of a a zigzag curve to file /tmp/bitmap.bmp (note: ⎕PLOT with attribute filename overrides existing files without a warning. Lack of permissions to write the file raises a DOMAIN ERROR with )MORE providing details.

2.31.3 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 plot window can be closed in different ways:

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2.32 ⎕PS - Print Style

⎕PS is an integer vector that currently (read: as of 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.

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2.33 ⎕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.

2.33.1 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.

2.33.2 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:

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

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

    A ⎕RE B   ←→   A ⎕RE[''] B

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

2.33.3 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

2.33.4 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:

    A ⎕RE B   ←→   A ⎕RE ¨ B

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.

2.33.5 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). 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:

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

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

      ⍝ return matched string
      4 ⎕CR 'f..' ⎕RE[''] '__foo___fun____fox'

      ⍝ 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┃

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. 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:

      4 ⎕CR 'f..' ⎕RE[''] '__foo___fun____fox'
      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┃

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. 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:

       4 ⎕CR 'g..' ⎕RE[''] '__foo___fun____fox'
       'g..' ⎕RE['E'] '__foo___fun____fox'
      'g..' ⎕RE['E']'__foo___fun____fox'
      ^            ^
No match

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:

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

2.33.6 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:

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

Matching all instead of only the first then gives:

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

The same for the pos+len output format:

      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┃┃┃
┃┃    ┗━━━┛ ┗━━━┛┃ ┃    ┗━━━┛ ┗━━━━┛┃ ┃     ┗━━━━┛ ┗━━━━┛┃┃
┃┗∊━━━━━━━━━━━━━━┛ ┗∊━━━━━━━━━━━━━━━┛ ┗∊━━━━━━━━━━━━━━━━━┛┃

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2.34 ⎕RVAL - Random APL value

The standard way to produce random numbers is the primitive function ? aka. Roll. Roll returns a simple random array whose ravel elements are positive integers chosen in a (pseudo-) random fashion. While this is sufficient for many applications, one sometimes needs APL values whose randomness not only affects the ravel elements themselves, but also other aspects like:

Such values can be produced with system function ⎕RVAL. The main use case for ⎕RVAL is the production of test data for the interpreter, but ⎕RVAL might be useful for other purposes as well.

2.34.1 General

In general, monadic ⎕RVAL B, returns a single random APL value Z, while dyadic A RVAL B is used to control the properties of subsequently generated random APL values returned by monadic ⎕RVAL.

The typical use of ⎕RVAL is to firzt call A ⎕RVAL B zero or more times to override individual default properties of the subsequently produced values, followed by one or more calls of monadic ⎕RVAL B.

The default properties, i.e. the properties used unless they were overridden by A ⎕RVAL B are:

Rank:  0
Shape: 1 1 1 1 1 1 1 1 (unused since Rank = 0)
Type:  0 1 0 0 0       (only integers
Max. Depth: 4

The default properties therefore return an integer scalar for every call of ⎕RVAL B.

2.34.2 Dyadic ⎕RVAL

The left argument A of A ⎕RVAL B determines which aspect of the subsequent random APL values shall be controlled. A is an integer scalar: 0 ⎕RVAL B: Control of the underlying random number generator

⎕RVAL uses the standard C function random_r(). For this reason ⎕RVAL is only available on platforms which use glibc, for example all GNU/Linux system.

Every random number generator has a state (similar to ⎕RL for ’?’). While the primitive ? keeps its state in ⎕RL, i.e. in the workspace, ⎕RVAL has no associated system variable like ⎕RL which keeps its state. Instead, the user needs to store the state of ⎕RVAL in a workspace variable if the workspace shall be stored and continued at a later point. This rarely happens, therefore no effort was spent for implementing another system variable. For the same reason, the state of ⎕RVAL survives )CLEAR.

The current state of ⎕RVAL’s random number generator can be retrieved with:

      STATE ← 0 ⎕RVAL ''

The state changes with every call of monadic ⎕RVAL. The random number generator can later be restored to the same state like this:

      0 ⎕RVAL STATE

Restoring the state is needed when the same sequence of random value shall be generated again. The random number generators of ? and ⎕RVAL are indepentent; generating a random number or random value with one does not change the state of the other. 1 ⎕RVAL B: Control of the ranks

The rank of subsequently generated random values can be controlled with 1 ⎕RVAL B as follows.

1 ⎕RVAL always returns its previous setting (i.e. before applying B). An empty B, e.g. 1 ⎕RVAL ⍬ will not change anything and can be used to query the current setting for 1 ⎕RVAL.

Examples: 2 ⎕RVAL B: Control of the shapes

The shapes of subsequently generated random values can be controlled with 2 ⎕RVAL B as follows.

B must be a vector of positive or negative integers. Vectors longer than MAX_RANK + 1 will give a LENGTH ERROR while vectors shorter than MAX_RANK + 1 will be filled with 1 until the length of B becomes MAX_RANK + 1.

If an element Bi of the resulting shape B = B1 ... BMAXRANK is ≥ 0 then the corresponding axis i will have a fixed length of Bi. If Bi < 0 then the length of that axis will be chosen at random with a probability of 1÷Bi. Note that the same B can still produce different shapes even if all Bi are ≥ 0 (i.e. if the rank is also chosen at random).

2 ⎕RVAL always returns its previous setting (i.e. before applying B). An empty B, e.g. 2 ⎕RVAL ⍬, will not change anything and can be used to query the current setting for 2 ⎕RVAL.


1 ⎕RVAL 2        ⍝ produce matrices
2 ⎕RVAL 3 ¯10    ⍝ the first axis of every matrix will have length 3, and
                 ⍝ the last axis of every matrix will vary between 0 and 10

This will produce scalars, vectors with a fixed length of 3 and matrices with 3 rows and between 0 and 10 columns. 3 ⎕RVAL B: Control of the data types

The types (i.e. CHARACTER, INTEGER, REAL, COMPLEX, or NESTED) of subsequently generated random values can be controlled with 3 ⎕RVAL B as follows.

B must be a vector with up to 5 positive numbers, corresponding to the types. Shorter vectors are filled with 0 (the corresponding types will not occur) and longer vectors will raise a LENGTH error.

Once the type was chosen, th ravel item will be:

3 ⎕RVAL always returns its previous setting (i.e. before applying B). An empty B, e.g. 3 ⎕RVAL ⍬ will not change anything and can be used to query the current setting for 3 ⎕RVAL.


      1 ⎕RVAL 2         ⍝ produce matrices
      2 ⎕RVAL 3 3       ⍝ produce 3×3 matrices
      3 ⎕RVAL 0 50 50   ⍝ produce a mix of integer and real values
      ⎕RVAL ''
¯975954163190248487                   0.5892132425
7677327503669503253 2152001972871424768 4 ⎕RVAL B: Control of a maximum depth

If the probability of generating a nested value is > 0 then the depth of random values can become arbitrarily large and could therefore exceed the system limit for the depth of the random value being produced. This can be prevented by setting a maximum depth for every value generated. ⎕RVAL sets the probability of the deepest allowed depth to 0.

4 ⎕CR B expects B to be a positive integer which is deepest allowed depth;

An empty B, e.g. 4 ⎕RVAL ⍬, will not change anything and can be used to query the current setting for 4 ⎕RVAL. monadic ⎕RVAL B: Return a new random value

Calling ⎕RVAL monadically produces one new random APL value.

The properties of that next value can be controlled by the dyadic calls of ⎕RVAL as described above. If no prior dyadic call of ⎕RVAL was made then the properties have the following defaults:

      1 ⎕RVAL ⍬    ⍝ rank (scalar)

      2 ⎕RVAL ⍬    ⍝ shape (not used since rank = 0)
1 1 1 1 1 1 1 1

      3 ⎕RVAL ⍬    ⍝ types (integer)
0 1 0 0 0

      4 ⎕RVAL ⍬    ⍝ max. depth (not used since probasbility of NESTED = 0)

That is, by default ⎕RVAL ⍬ produces random integer scalars.

It is sometimes convenient to be able to change the properties of the next random value without modifying (and later restoring) the properties with dyadic ⎕RVAL. This can be achieved with monadic ⎕RVAL with non-empty B.

Let 4=⍴B. Then

   Z←⎕RVAL B does essentially:

   B[1]←1 ⎕RVAL B[1]
   B[2]←2 ⎕RVAL B[2]
   B[3]←3 ⎕RVAL B[3]
   B[4]←4 ⎕RVAL B[4]

   Z←⎕RVAL ''

   B[1]←1 ⎕RVAL B[1]
   B[2]←2 ⎕RVAL B[2]
   B[3]←3 ⎕RVAL B[3]
   B[4]←4 ⎕RVAL B[4]

If 4>⍴B then the missing properties are not changed.


⎕RVAL 1 (,¯4) (0 1)    ⍝ return a random 0-4 element integer vector
⎕RVAL 2 (2 2) (1 0)    ⍝ return a random 2×2 character array

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2.35 ⎕SQL - SQL Database Interface

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

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
      type  ⎕SQL[1] file

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.

      ⎕SQL[2] ref

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.

      query ⎕SQL[3,db] params

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 ”.

      query ⎕SQL[4,db] params

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.

      ⎕SQL[5] ref

Begin a transaction.

      ⎕SQL[6] ref

Commit a transaction.

      ⎕SQL[7] ref

Rolls back the current transaction.

      ⎕SQL[8] ref

Return an array containing the name of all tables.

      ref   ⎕SQL[9] table

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.

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2.36 ⎕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++:

 ' '
 COND←7↓,¯2 ⎕SI 4
 LOC←,¯2 ⎕SI 3
 ' '
 '*** Assertion (', COND, ') failed at ',LOC

 ⍝ show stack
 ' '
 7 ⎕CR ⊃¯1↓⎕SI 3
 ' '

⎕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.

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2.37 ⎕SYL - System limits

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

 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 

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

2.37.1 ⎕SYL[1 2 3 4 5 6;]

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

  1. The SI stack of the interpreter reaches a limit, or
  2. The number of APL values created reaches a limit, or
  3. The memory size of APL values created reaches a limit.

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):


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.

2.37.2 ⎕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.

2.37.3 ⎕SYL[24 25 26;]

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

2.37.4 ⎕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:

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

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2.38 ⎕XML - XML Parsing

2.38.1 Purpose

GNU APL provides ⎕XML as a means of performing elementary manipulations of APL character strings that are formatted according to the XML standard. The anticipated procedure for such modifications is something like:

      XML_string ← "<A><B><C>Hello</C></B></A>"   ⍝ input data (usually from an .xml file)
      APL ← ⎕XML XML_string       ⍝ convert XML_string to associative array APL
      ABC ← APL.a.b.c             ⍝ retrieve node a.b.c in APL
      APL.a.b.c ← ABC, " World"   ⍝ modify node a.b.c in APL
      Z ← ⎕XML APL                ⍝ convert associative array APL to XML string Z

      ABC   ⍝ the original value of XML.a.b.c
      Z     ⍝ the modified XML string
<A><B><C>Hello World</C></B></A>"

The scope (functionality) of ⎕XML is then:

2.38.2 Some XML Terminology

An XML document is a character string with a standardized format. The characters must be valid XML characters as defined in the XML standard (almost all Unicode characters except most of the ASCII control characters). GNU APL raises a DOMAIN ERROR when an XML document contains invalid XML characters.

The XML document is a sequence of adjacent sub-strings, where each sub-string is:

A markup (sub-)string:

A non-markup (sub-)string:

Non-markup is sometimes referred to as "unstructured text". The producer of an XML document has a principal choice as to where to put the information that the document contains is located: in the unstructured text or in the atttribute values inside the tags. For that reason the XML standard is somewhat picky about keeping the unstructured text as well as attribute values intact and requires that whitespace in non-markup (the only allowed whitspace characters in XML being TAB, CR, LF, and SPACE) is preserved in non-markup strings.

As a consequence, many non-markup strings begin with LF because the preceeding markup was on the previous line and therefore the LF after the preceeding markup is whitespace of the non-markup and therefore needs to be preserved.

Every markup belongs to one of 4 categories:

The XML tags recursively define a tree structure where:

Processing instructions and declarations are typically located at the beginnning of the XML document and at the same level as the root of the tree. defined by the document. Document type declarations are being preserved (so that they can be processed in APL), but are currently ignored by ⎕XML. As a consequence, entity declarations have no effect and only the predefined XML entities (i.e. &, <, >, ’, and ") are recognized (and translated) by ⎕XML.

2.38.3 How ⎕XML maps XML documents to APL Values

The principal mapping between XML strings and APL values is:

Every valid name in XML is also a valid name for an APL variable or structure member. Unfortunately, mapping XML names directly to APL member names cannot work because:

⎕XML solves these issues with a simple naming convention for all member names in the (recursive) associative array that is produced by monadic ⎕XML. Every member name consists of 3 components that together yield a valid APL variable name (and therefore a valid member name that is understood by the APL parser):

Let NN be a sequence of decimal digits. Then only the following 4 synthesized names are produced by ⎕XML:

Every XML name (of a tag or attribute) is also a valid APL name, but valid APL names may also contain the characters ¯, ∆, and ⍙ which are not valid in XML and used in the naming convention above to clearly separate the member names used in APL from the names used in the XML document.

The essence of all this is that everything that belongs to an XML node or document, i.e. the attributes inside a tag, the sub-nodes between a start tag and its corresponding end tag (if any), declarations, etc. will be contained in a single associative array.

Examples of APL member names (assuming ⎕IO←1):

      ⍙1              ⍝ the first member in every XML node. Its value is the node tag.
      ∆1declaration   ⍝ the first member in most XML documents. E.g. <?xml version= ...>
      ∆2text          ⍝ whitespace (LF) between _1∆declaration and _3∆doctype
      ∆3doctype       ⍝ DTD in XML documents that have one. E.g. <!DOCTYPE  ...
      _6Workspace     ⍝ Sub-array for <Workspace ... at position 6.
      ⍙1wsid          ⍝ first attribute wsid from e.g. <Workspace wsid=...
      ⍙2year          ⍝ second attribute year

2.38.4 Monadic ⎕XML

Z ← ⎕XML B converts APL string B that contains a valid XML document to an associative APL array Z and vice versa.

Note: If you convert an associative APL array back to a an XML document, then the result is a possibly very long strings with containing several linefeed characters. That is OK if the string is written to a file, but causes problems when the string is being displayed and longer than ⎕PW. The standard APL folding of output near ⎕PW make the string then look somewhat garbled. This effenct can be suppressed in 2 ways:

  1. set ⎕PW large enough, or
  2. prefix the string with ⊃35⎕CR as in the examples below.

2.38.5 Dyadic ⎕XML

Z ← A ⎕XML B provides a number of convenience functions. Its left argument A is an interger function number, possibly followed by arguments of the function number ↑A.

In the following examples, let

      XML←36 ⎕CR """
<?xml version='1.0' encoding='UTF-8'?>
    <Tag1 name='tag1'>   <!-- first tag -->
      <Subtag name='subag1.1'>   <!-- first subtag -->



2.38.6 XML Queries

The different functions in dyadic ⎕XML are intended to construct XML queries. An XML query extracts information from, or modifies information in, an XML document. XML queries may differ considerably in their details, but usually follow these top-level steps:

  1. Read an XML document into, say, APL (APL←0 ⎕XML B or APL←1 ⎕XML B)
  2. Optionally, display the structure of the document (3, 4, or 5 ⎕XML)
  3. Select a subset of XML nodes (= GNU APL member names, 6 ⎕XML APL)
  4. retrieve or modify the data in the selected XML nodes (with something like MEMBERS←(⊂APL) FUN¨6⎕XML APL←⎕XML followed by MEMBER⊃ )
  5. Optionally, convert the modified XML document back to XML (0 ⎕XML

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3 Limitations and Missing Features

GNU 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.

3.1 System Limits

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

GNU APL integers have a guaranteed range from -9200000000000000000 to 9200000000000000000, which is a slighly smaller range.

A 64-bit integer represents a value between -9223372036854775808L and 9223372036854775807.

If the result of a computation is integer by nature, for example +, -, or × with integer arguments, and falls into the guaranteed range, then the result will be an APL integer. If the result is to large for a 64-bit signed integer then the result will be automatically converted to an APL floating point value. However, if the result is outside the guaranteed range but still within the 64-bit integer range, e.g. between i(excluding) 9200000000000000000 and 9223372036854775807, then GNU APL gives no guarantees as to whether the result will be a 64-bit integer or as a 64-bit floating point (and then loosing precision). This decision is usually function-specific and driven by performance considerations.

APL values have a maximum rank of 8. However, the maximum range can be by means of ./configure (see README-2-configure).

3.2 Shared Variables

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

Communication between two workspaces is supported, but with some limitations. Two workspaces can only communicate via shared variables if they (i.e. their processes) run on the same machine.

However, only two auxiliary processors, AP100 and AP210, are provided as examples of how to implementing auxiliary processors in GNU APL.

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.

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4 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.

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5 Project Structure

The top-level directory of the GNU APL project has a structure like this:

    ├── autom4te.cache
    ├── build
    ├── debian
    ├── debian_tmp
    ├── devel_doc
    ├── doc
    ├── erlang
    ├── gnu-apl.d
    ├── HOWTOs
    ├── html
    ├── m4
    ├── rpm
    ├── src
    ├── support-files
    ├── tools
    ├── websock
    ├── workspaces
    ├── wslib2
    ├── wslib3
    ├── wslib4
    └── wslib5

Most of these directories are contained in the project tar file (e.g. apl-1.8.tar.gz) and some are created during the build of GNU APL. Only the directories in the top-level are shown above.

The GNU APL project follows the standard layout for autoconf/automake projects. The top-level itself contains the files needed by autoconf/automake and a handful of README-XXX files that might be of interest when building GNU APL.

The subdirectories are (in order of decreasing relevance):

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5.1 The subdirectory src

The subdirectory src contains all C++ source files that are needed to build either the GNU APL interpreter itself, or libapl (a library that contains the essential part of GNU APL, but without the interactive REPL loop of the interpreter). During the build, the object files produced by the compiler are also placed in this directory.

The subdirectory src contains further subdirectories for components of GNU APL that are optional and typically require the installation of additional libraries on the build machine. The ./configure script in the top-level directory determines, which optional components shall be included on the build.

    ├── src
        ├── APs                     APs for ⎕SVO and friends
        ├── emacs_mode              dito
        ├── Gtk                     ⎕GTK (graphical user interface)
        ├── native                  templates for native functions
        ├── sql                     ⎕SQL
        ├── testcaseses             dito

GNU APL comes with an automated test suite, the testcases are contained in subdirectory src/testcases

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5.2 The subdirectory support-files

The subdirectory support-file contains a number of configuration files that aim at making a standard keyboard produce APL characters. Details are explained in top-level file README-3-keyboard.

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5.3 The subdirectory doc

The subdirectory doc is used to create this info file in different file formats (.info, .html).

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5.4 The subdirectory HOWTOs

The subdirectory HOWTOs contains some documents that try to explain how some of the non-standard features of GNU APL are supposed to be used. These documents were written for two different audiences: APL programmers and GNU APL hackers. The documents for APL programmers are, by default, installed in directory /usr/local/share/doc/apl by make install while the documents for GNU APL hackers (i.e. C++ programmers or trouble-shooters) are not installed by make install, but rather remain in the source tree.

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5.5 The subdirectories workspaces and wslib2 ... wslib5

These directories (and their content) are, by default, copied to /usr/local/lib/apl by make install. Some subdirectories are empty while others contain small workspaces or libraries for various purposes (mostly demonstrating the use of some non-standard APL features).

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5.6 The subdirectory m4

The subdirectory m4 contains macros used by autoconf and automake. In most cases the top-level ./configure script can be used as is. If a platform on which GNU APL shall be built differs to much from the platform on which the GNU APL project tar file (e.g. apl-1.8.tar.gz) was created, then it might be necessary to re-create the ./configure script on the platform.

Re-creating the ./configure script requires:

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5.7 The subdirectories rpm, debian, and debian_tmp

These subdirectories are templates for building (binary) RPM resp. Debian packages that contain GNU APL. Subdirectory debian_tmp is initially empty and acts as a scratch directory inside which the interpreter is being compiled when a Debian package is built.

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5.8 The subdirectory tools

GNU APL uses generated C++ code. The subdirectory tools contains the source code for the code generator (phrase_gen) and also some other small tools for various purposes. These tools are typically used by GNU APL hackers and are therefore not installed by make install.

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6 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.

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6.1 The GNU APL Community Webpage

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

The contributions listed there were collected from emails sent to

Since the list was started long after 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 to fix that.

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6.2 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


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7 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 7.1:: below.

GNU APL itself is licensed under the GNU Public License version 3 or later (aka GPLv3+), *Note Section 7.2:: below.

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7.1 The GNU Free Documentation License

Version 1.3, 3 November 2008
Copyright © 2000, 2001, 2002, 2007, 2008 Free Software Foundation, Inc.

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

    The purpose of this License is to make a manual, textbook, or other functional and useful document 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.


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    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:

    1. 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.
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    10. 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.
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    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.

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    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.

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    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.”


    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.


    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.

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    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.


    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.


    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

    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.


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    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.

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:

  Copyright (C)  year  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
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If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the “with…Texts.” line with this:

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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.

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GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007

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


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.

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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.

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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.


16. Limitation of Liability.


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.


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 <>.

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 <>.

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 <>.