Specification: BQN literal notation

A literal is a single token that indicates a fixed character, number, or array. While literals indicate values of a data type, primitives indicate values of an operation type: function, 1-modifier, or 2-modifier.

Two types of literal deal with text. As the source code is considered to be a sequence of unicode code points ("characters"), and these code points are also used for BQN's character data type, the representation of a text literal is very similar to its value. In a text literal, the newline character is always represented using the ASCII line feed character, code point 10. A character literal is enclosed with single quotes ' and its value is identical to the single character between them. A string literal is enclosed in double quotes ", and any double quotes between them must come in pairs, as a lone double quote marks the end of the literal. The value of a string literal is a rank-1 array whose elements are the characters in between the enclosing quotes, after replacing each pair of double quotes with only one such quote. The null literal is the token @ and represents the null character, code point 0.

The format of a numeric literal is more complicated. From the tokenization rules, a numeric literal consists of a numeric character (one of ¯∞π.0123456789) followed by any number of numeric or alphabetic characters. Some numeric literals are valid and indicate a number, while others are invalid and cause an error. The grammar for valid numbers is given below in a BNF variant. The alphabetic character allowed is "e" or "E", which functions as in scientific notation. Not included in this grammar are underscores—they can be placed anywhere in a number, including after the last non-underscore character, and are ignored entirely.

number    = "¯"? ( "∞" | mantissa ( ( "e" | "E" ) exponent )? )
exponent  = "¯"? digit+
mantissa  = "π" | digit+ ( "." digit+ )?
digit     = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9"

The digits or arabic numerals correspond to the numbers from 0 to 9 in the conventional way (also, each corresponds to its code point value minus 48). A sequence of digits gives a natural number by evaluating it in base 10: the number is 0 for an empty sequence, and otherwise the last digit's numerical value plus ten times the number obtained from the remaining digits. The symbol indicates infinity and π indicates the ratio pi of a perfect circle's circumference to its diameter. The high minus symbol ¯ indicates that the number containing it is to be negated. When an exponent is provided (with e or E), the corresponding mantissa is multiplied by ten to that power, giving the value mantissa×10exponent.

The above specification describes exactly an extended real number. To obtain a BQN number, each component is rounded to its nearest representative by the rules of the number system used: for IEEE 754, smallest distance, with ties rounding to the option with even mantissa.