BQN primitives

Primitives are the basic functions and modifiers built into the language, written with individual glyphs (more about the concept here). The role of a primitive when written always matches its type (but you can use its value in other roles by assigning it, or other methods).

Primitives have no side effects other than errors, and can't perform infinite computations, except when a primitive modifier calls an operand function that does one of these things (and this can only happen when arguments are passed, as primitive modifiers are always deferred). Side effects here include both writing state such as variables or printed output, and reading any outside state, so that a function without them always returns the same result if passed the same arguments. Since trains and list notation have the same nice properties, tacit code written entirely with primitives, trains, and lists always describes finite, self-contained computations.

Recursion is the primary way to perform potentially infinite computations in BQN, and it can be packaged into control structures like While for ease of use. A given BQN implementation might also provide system values for "impure" tasks like file access or other I/O.

Functions

A function call with one argument (prefix) is called "monadic" and one with two arguments (infix) is "dyadic".

Modifiers

Combinators only control the application of functions, which are passed as operands. A data value such as a number or array can also be an operand and, as always, applies as a constant function.

The last three are combinators in spirit but go beyond the actual strict definition: Choose calls the function ⊑, Under has an "undo" step at the end, and Catch traps an error. The second definition for Under and the one for Catch are written in pseudo-BQN because they can't be expressed otherwise.

Other modifiers control array traversal and iteration. In three cases a simpler 1-modifier is paired with a generalized 2-modifier: for each of these the 1-modifier happens to be the same as the 2-modifier with a right operand of ¯1.