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.

Execution

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:

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.

Scripts

•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.

Files

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.

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.

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 '-'.

• 'f': File
• 'd': Directory
• 'l': Symlink
• 'p': Pipe (FIFO)
• 's': Socket
• 'b': Block device
• 'c': Character device

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.

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:

• Chars: BQN characters, or UTF-32. The file is assumed to be UTF-8 encoded.
• Lines: BQN strings. The file is decoded as with chars, then split into lines by CR, LR, or CRLF line endings.
• Bytes: Single-byte values, stored as BQN characters from @ to @+255.

The MapBytes function only takes one argument, a filename, and returns an array matching the result of Bytes. However, the array data should be memory-mapped allowing it to be loaded into memory on use. The array and arrays derived from it (such as slices) may change in value if the underlying file is modified after MapBytes is called.

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.

Open file object

Not yet specified.

Input and output

•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.

Terminal I/O

The system namespace •term gives fine-grained control of input and output when running in a terminal emulator or similar text-based interface.

Interface

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

Each function in this section is monadic.

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

•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, returning a list with a code giving what kind of structure it has followed by each of its components. Possible codes are listed in the table below according to the rule that forms the derived function—train or 2-modifier application. Non-function values, and some functions, can't be broken down. They are still classified with a code: -1 for a non-operation, 0 for a primitive, and 1 for other operations. "Other" includes blocks and system operations. The result is thus a list of length 2 to 4, and •Decompose cannot cause an error.

Time

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.

Math

System namespace •math contains mathematical utilities that are not easily implemented with basic arithmetic, analogous to C's math.h.

Constants ln10⇐⋆⁼10, ln2⇐⋆⁼2, log10e⇐÷⋆⁼10, log2e⇐÷⋆⁼2 computed in full precision.

Other correctly-rounded arithmetic: monadic Cbrt⇐3⊸√, Log2⇐2⋆⁼⊢, Log10⇐10⋆⁼⊢, Log1p⇐⋆⁼1⊸+, Expm1⇐1-˜⋆; dyadic Hypot⇐+⌾(ט).

Standard trigonometric functions Sin, Cos, Tan, Sinh, Cosh, Tanh, with inverses preceded by a (ASin, etc.) and accessable with ⁼. Additionally, the dyadic function ATan2 giving the angle of vector 𝕨‿𝕩 relative to 1‿0. All trig functions measure angles in radians.

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:

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 2⋆𝕩 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 2⋆32 must be supported (that is, a maximum integer result of (2⋆32)-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 2⋆53.

Bitwise operations

The system namespace •bits gives functions for efficiently applying bitwise and two's complement integer operations to arrays of data. These functions should compute result values with native CPU instructions, preferably SIMD if available.

An operation is exposed as a 1-modifier that takes up to four numbers for its operand.

• Operation width
• Result element width
• Right argument element width
• Left argument element width

The operand is extended to length 3 for monadic operations, and 4 for dyadic operations, by repeating the last element (like »⟜(4⥊⊢´)). It must be a number, or array of numbers with rank at most 1.

An example call is a 16‿1•bit._add b, to perform 16-bit additions on two boolean arrays with a boolean result.

To apply a bitwise operation, each argument is represented as a stream of bits based on the width given for it, then split into units whose width is the operation width. The operation is applied to these units. The result is again treated as a stream of bits and split according to the result width, with each unit forming a result element.

The operation width, along with the "Type" column above, determines what operation is performed. For bit operations it has no effect, except to constrain the argument sizes according to the shape rules below. Integer (meaning signed) and unsigned operations support widths of 8 and above, and should support higher values such as 128 if available.

Argument and result widths correspond to little-endian binary representations according to the following table (operation widths don't—see the "type" field in the table above). Here "boolean" indicates value 0 or 1, "signed integer" indicates two's complement representation, and "character" is a code point in an unsigned representation. Either type may be used for an argument, but the result will always use a primary type.

An argument must be an array of numbers or an array of characters. Its elements must fit into the appropriate type. The "cell size" is the length in bits of a 1-cell, that is, widthׯ1⊑1∾≢arg, and must be a multiple of the operation width. Both arguments must have the same cell size, and the same leading shape ¯1↓≢arg. The result shape is this leading shape followed by the cell size divided by the result element width.

Another tool is provided for performing direct conversions, with no operation applied. The 1-modifier •bit._cast takes a two-element operand and one argument, for example ⟨8,16‿'c'⟩•bit._cast ints to convert each pair of numbers in ints into a 2-byte character. Each element of 𝕗 is a number or number-character pair giving width and type. The argument is encoded according to the first and decoded according to the second.