BQN–J dictionary

A guide to help users of J get up to speed with BQN quickly.

Terminology

Array model

BQN uses the based array model, which is fundamentally different from J's flat array model. BQN uses non-array values such as characters and numbers, called "atoms", while in J every noun is an array. A BQN array can contain any values in any mixture, while a J array must be uniformly numbers, characters, or boxes (BQN doesn't use boxes).

The J terms "atom" and "element" are used to mean different things by different authors. In BQN, an atom or rank-0 array is called a "unit", and the values contained in an array—which may or may not be arrays—are called "elements". Each element is contained in a 0-cell, or rank-0 subarray. BQN uses the term "major cell" for what J calls an "item" of an array: a cell with rank one less than that array. BQN shares the terms "list" and "table" for rank-1 and rank-2 arrays with J.

BQN uses "depth" rather than "boxing level". BQN gives atoms depth 0, so that the depth of a BQN array is one higher than the boxing level of the corresponding J array.

Roles

In J, the part of speech is an inherent property of a value, while in BQN it is determined by how the value is used in a particular expression, and can be different from the value's type. See context-free grammar.

Syntax

BQN's explicit functions and modifiers are called "blocks", and have a more sophisticated syntax than J; see the documentation. BQN uses lexical scope, and has no global variables. BQN also has a list notation using ⟨⟩.

For reading

J analogues of BQN primitive functions are given below. They are not always the same; usually this is because BQN has extra functionality relative to J, although in some cases it has less or different functionality.

Functions + - | < > are the same in both languages.

Most of BQN's combinators have J equivalents. The J equivalent "_ for ˙ assumes a noun operand, but ˙ makes a constant function for any operand. ◶ has arguments reversed relative to @., and uses an actual array of functions rather than gerunds. Besides these, BQN's ⟜ is like a J hook, that is, F⟜G is (F G), and ⊸ applies in the opposite direction.

For other modifiers the correspondence is looser. Here ⌜ shows the dyadic case and ´ the monadic case only.

For writing

J's primitive nouns are easily defined in BQN.

Functions + - | < > are the same in both languages.

Some other primitives are essentially the same in J and BQN, but with different spellings (but transpose behaves differently; J's dyadic |: is more like ⍉⁼):

Additionally, |.!.f is ⥊⟜f⊸« with a natural number left argument. Change « to » to rotate right instead of left.

The tables below give approximate implementations of J primitives. J has a whole lot of complicated primitives that no one uses (some of which are officially deprecated), so not everything is translated here.

Some J modifier expressions are translated below. BQN doesn't keep track of the rank of functions, so the "close" compositions @ & &. have no BQN equivalents: instead, specify a rank after composing.

BQN uses functions, not modifiers, for structural manipulation. The following table gives BQN functions corresponding to J's structural modifiers. The result is an array of arrays; use F¨ to apply a function to each of these, and >F¨ to apply a function and merge the results into a single array.