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 (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

Functions that have significant differences from APL equivalents or don't appear in APL are marked with an asterisk.

Modifiers

Combinators only control the application of functions. Because a non-function operand applies as a constant function, some combinators have extra meanings when passed a constant. For example, 0˜ is identical to 0˙—a constant function that always returns 0—and 0⊸< is the function that tests whether its right argument is greater than 0.

Choose isn't really a combinator since it calls the function ⊑, and Under is not a true combinator since it has an "undo" step at the end. This step might be implemented using the left operand's inverse (computational Under) or its structural properties (structural Under).

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