Specification: BQN system-provided values

This portion of the spec is still potentially subject to major changes.

The symbol is used to access values other than primitives provided by BQN.

All system values described in the BQN specification are optional: an implementation does not have to include any of them. However, if a system value with one of the names given below is included, then it must have the specified behavior. For namespaces this rule applies to individual fields as well: a namespace may be provided with only some of the fields, but a field with one of the given names must behave as specified.


Name Summary
•BQN Evaluate the argument string in an isolated scope
•ReBQN Create a BQN-like evaluation function with options 𝕩
•primitives List of primitives as glyph-value pairs

The left argument to •BQN or the result of •ReBQN, if given, is a list of up to three elements, giving a prefix of •state (see next section) during evaluations of that function. Thus "","xyz"•BQN"•name" returns "xyz".

•ReBQN accepts a namespace 𝕩. The following options are specified if supported:

Option Values (default first)
repl "none", "strict", "loose"
primitives List of glyph-value pairs; default •primitives
system "all", "none", "safe" or list of names
scope "none", "read", "modify" or list of name-setting pairs

The option repl indicates how variables are retained across calls: with "none" they are not saved; with "strict", they are saved and can't be redefined; and with "loose" they may be redefined. Each element in primitives gives the glyph and value for a primitive to be made available. The value must have an operation type and its type determines the primitive's role. system in general gives the list of system values to be made available, with shorthand values to indicate all currently-available ones, none of them, or only a subset that cannot be used to interact with anything outside of the execution context. scope indicates allowed interaction with the scope in which •ReBQN is called (not loaded): with "read" variables may be read and with "modify" they may be read or modified.


Name Summary
•Import Load a script file
•state •path, •name, •args
•args Arguments passed to current file
•path Current file's path
•name Current filename
•wdpath Shell's working directory path
•Exit Leave the top-level running program

•Import loads another BQN script. The script is evaluated in its own isolated scope, and its result is either the result of the last line, or a module if it exports with at the top level. If it is a module, then it must be destructured immediately unless first-class namespaces are possible.

The right argument is a filename, which may be relative or absolute. Relative paths are taken relative to the source file where this instance of •Import was written. The left argument, if given, is the list of arguments that should be passed through to the file as •args. If no left argument is given then ⟨⟩ is used for •args. However, the behavior is different in this case. The same file will only be loaded once in a given BQN program by •Import calls with no left argument: the first such call saves the returned value, even if it is mutable, and subsequent calls return this saved value. To avoid this and reload the file, pass a left argument of ⟨⟩.

•args is the arguments passed as the file was invoked, either from the command line or •Import. For command line calls it is a list of strings.

•path simply gives the path of the file in which it appears. It includes a trailing slash but not the name of the file itself.

•name gives the name, including the extension, of the file in which it appears. It doesn't include the path.

•wdpath returns the path of the current working directory, like the Unix pwd command, but including a trailing slash.

•Exit immediately terminates the running BQN process. If the argument is a valid return code (on Unix, an integer), it is returned; otherwise, the default return code (the one returned when the end of the program is reached) is used.


The system namespace value •file deals with file operations. For the purposes of •file, paths in the filesystem are always strings. As with •Import, file paths may be relative or absolute, and relative paths are relative to •path, except in •file.At which allows 𝕨 to specify an alternate base directory. The value •path used for a particular instance of •file is determined by the file that contains that instance.

When a •file function returns a file path or portion of a path, the path is always absolute and canonical, with . and .. components removed.

Possible fields of •file are given in the subsections below.

File paths

The following functions manipulate paths and don't access files. Each takes a relative or absolute path 𝕩, and At may also take a base directory 𝕨.

Name Summary
path Path of this source file, that is, •path
At Absolute path of file, with optional base 𝕨
Name File name including extension
Parent Path of the containing directory, with trailing backslash
BaseName File name, with dot and extension removed
Extension File extension, including leading dot
Parts List of parent, base name, and extension

File metadata

Metadata functions may query information about a file or directory but do not read to or write from it. Each takes a path 𝕩, and some functions also allow new data in 𝕨. The returned data in any case is the specified property.

Name Summary
Exists 1 if the file exists and 0 otherwise
Type A character indicating the file's type
Created Time created
Accessed Time of last access
Modified Time of last modification
Size Total size in bytes
Permissions Query or set file permissions
Owner Query or set owner user ID and group ID number

Times are Unix timestamps, that is, non-leap seconds since the Unix epoch, as used by time system values. File permissions on Unix are a three-element list of numbers giving the permissions for the owner, group, and other users. The file type is one of the following characters for the POSIX file types, matching Unix ls -l with 'f' instead of '-'.

File access

File access functions read or write files, either by manipulating files as a whole or interacting with the contents. Whole-file functions cannot overwrite target files: that is, Rename and Copy must give an error if a file exists at 𝕨, and CreateDir if a file exists at 𝕩, while Chars, Lines, and Bytes can overwrite the contents of an existing file 𝕨. However, these three functions must give an error if 𝕨 exists and is a directory.

Name Summary
Open Return an open file object based on 𝕩
Rename Rename file 𝕩 with path 𝕨
Copy Copy file 𝕩 to path 𝕨
CreateDir Create a directory at path 𝕩
Remove Delete file 𝕩
RemoveDir Recursively delete directory 𝕩 and all contents
List Return names of all files in directory 𝕩
Chars Read from or write to entire file, as characters
Lines Read from or write to entire file, as lines
Bytes Read from or write to entire file, as bytes

Rename, Copy, and CreateDir return the path of the new file. Remove and RemoveDir return 1 to indicate successful removal (and error otherwise).

List returns filenames only, without full paths. It lists all files and directories including hidden ones, but not the current and parent directory names . and ...

Functions Chars, Lines, and Bytes are all ambivalent. If only 𝕩 is given, then it is a filename, and the result is the contents of the file in the appropriate format. If there are two arguments, then 𝕨 is the filename and 𝕩 is the desired contents. These are written to the file, overwriting its contents, and the absolute filename 𝕨 is returned. The three formats are:

The following short names can also be provided for file access. They can be provided, and use the definitions from above even if •file is not provided.

Name Equivalent
•FChars •file.Chars
•FLines •file.Lines
•FBytes •file.Bytes

Open file object

Input and output

Name Summary
•Out Print argument string
•Show Print argument value
•Repr String representation of 𝕩, if possible
•Fmt Format value for printing

•Out prints a string to stdout, with a trailing newline. •Show displays a BQN value to the programmer (the representation is not specified, and does not need to be plain text). •Fmt returns a string (not a character table: lines are separated by linefeeds) indicating how 𝕩 would be printed by the interactive environment. Both •Show and •Fmt may take a left argument configuring how the value should be formatted.

•Repr attempts to return a string so that •BQN •Repr 𝕩 matches 𝕩. If 𝕩 contains any mutable values (operations or namespaces), this is not possible. However, if such a values is stateless, in the sense that they don't access variables outside of their own scopes, it is permissible for •Repr to return source code that would create a value with identical behavior.


Name Summary
•SH Execute shell command and return exitcodestdoutstderr

The argument to •SH is a list of strings giving the command and its arguments (for example "mv""old""new"). The command is executed synchronously, and the result is a list of three elements: the command's exit code, text written to stdout, and text written to stderr. In both cases the text is a plain string containing all text emitted by the program. Text is interpreted as UTF-8, with an error if it's not valid UTF-8.

Operation properties

Name Summary
•Type Return a number indicating type
•Glyph Return the glyph for a primitive
•Source Return the source of a block, as a string
•Decompose Show the parts of a compound function

Each function in this section is monadic.

•Type gives its argument's type, as a number from the table below:

Number Type
0 Array
1 Number
2 Character
3 Function
4 1-modifier
5 2-modifier
6 Namespace

•Glyph gives the glyph corresponding to a primitive as a single character, for example returning '+' given an argument matching +. It causes an error if the argument is not a primitive.

•Source gives a string containing a block's source, including the enclosing braces {}. It causes an error if the argument is not a block. In contrast to •Glyph, this function does not give full information about 𝕩 because the result cannot convey environment or mutable identity.

•Decompose breaks down one level of a compound function or modifier, returning a list with a code giving what kind of structure it has (as listed in the table below) followed by each of its components. "Other" includes blocks and system functions. Non-operations do not cause an error, but return code -1, then the argument as a single component. The result is thus a list of length 2 to 4, and •Decompose cannot cause an error.

Kind Code Components
Non-operation -1 𝕩
Primitive 0 𝕩
Other 1 𝕩
2-train 2 g,h
3-train 3 f,g,h
1-mod 4 𝕗,𝕣
2-mod 5 𝕗,𝕣,𝕘


Name Summary
•UnixTime Time between Unix epoch and function call
•MonoTime Monotonically-increasing time counter for relative measurement
•Delay Wait at least 𝕩 seconds, and return the actual wait time
•_timed Call 𝔽 on 𝕩 𝕨1 times, and return the average duration
•_maxTime_ Call 𝔽 on the arguments, but fail if it takes over 𝕨𝔾𝕩 seconds

All times are measured in seconds.

The Unix epoch is 1970-01-01 00:00:00 UTC, and Unix time is the number of seconds since this epoch, with adjustments for leap seconds. •UnixTime is intended for absolute time measurement and should use the source most accurate reflects Unix time when it's called. •MonoTime is intended for relative measurement and should use the method that gives the most precise time differences over the course of the program. Its return value must never decrease between calls.

•_timed returns the total time taken divided by the number of function calls (𝕨 if provided and 1 otherwise), including the overhead required for the outer loop that counts iterations (which will typically be negligible in comparison to the BQN code).

More accurately the modifier •_maxTime_ may fail if execution of 𝔽 takes over 𝕨𝔾𝕩 seconds, and should fail as quickly as it is practically able to. The most likely way to implement this modifier is to interrupt execution at the given time. If 𝔽 completes before the interrupt there is no need to measure the amount of time it actually took.

Random generation

•MakeRand initializes a deterministic pseudorandom number generator with seed value 𝕩. •rand, if it exists, is a globally accessible generator initialized at first use; this initialization should use randomness from an outside source if available. These random generators aren't required to be cryptographically secure and should always be treated as insecure. A random generator has the following member functions:

Name Summary
Range A number, or array of shape 𝕨, selected from 𝕩
Deal A simple random sample of 𝕨𝕩 elements of 𝕩
Subset A sorted SRS of 𝕩, with 𝕨 elements if given

For each of these functions, 𝕩 is a natural number. For Range, 𝕨 must be a valid shape (natural number, or list or unit array of natural numbers) if given, and for Deal and Subset it's a natural number less than or equal to 𝕩. All selections are made uniformly at random, that is, each possible result is equally likely. A simple random sample (SRS) of k elements from list s is a list of k distinct elements of s in any order. Both the choice of elements and their ordering must be uniformly random. Recommended algorithms for SRS selection are variants of a partial Knuth shuffle.

When 𝕨 isn't given, Deal's result contains all elements of 𝕩, making it a random shuffle of those values, or random permutation. In Subset, a random choice is made uniformly from the 2𝕩 subsets of 𝕩, so that a subset of any length may be returned.

In Range, 𝕩 may be 0. In this case the result consists of floating-point numbers in the unit interval from 0 to 1. The numbers should have an overall uniform distribution, but their precision and whether the endpoints 0 and 1 are possible may depend on the implementation.

Ranges up to 232 must be supported (that is, a maximum integer result of (232)-1) if the number system accommodates it. In implementations based on double-precision floats it's preferable but not required to support ranges up to 253.