Hook: Difference between revisions

A '''hook''' is an asymmetrical form of function composition that first applies one of the composed functions to one argument, then applies the other function to one argument and the result. In [[J]], a 2-[[train]] is a hook, while [[I]] adds the mirror image to give two functions (I has first-class functions but no operators) hook (<code>h</code>) and backhook (<code>H</code>). [[BQN]] uses two [[operator]]s Before (<code>⊸</code>) and After (<code>⟜</code>), which also serve the purpose of the [[Bind]] operator.

The meaning of 2-train as hook was first proposed in [[Ken Iverson|Iverson]] and [[Eugene McDonnell|McDonnell]]'s paper ''Phrasal Forms'' introducing [[train]]s<ref>[[Ken Iverson]] and [[Eugene McDonnell]]. [http://www.jsoftware.com/papers/fork.htm Phrasal forms] at [[APL89]].</ref>, and soon included in [[J]]. This definition specifies that <source lang=j inline>(F G) y</source> is <source lang=j inline>y F G y</source> and <source lang=j inline>x (F G) y</source> is <source lang=j inline>x F G y</source>. However, [[Roger Hui]] later opined that this definition was better suited to a dyadic operator than an element of syntax,<ref>[[Roger Hui]]. [https://code.jsoftware.com/wiki/Essays/Hook_Conjunction%3F Hook Conjunction?]. J Wiki essays. 2006. Accessed 2021-02-08.</ref> and defined to 2-train to represent [[Atop]] instead when he led the introduction of trains to [[Dyalog APL]].

In [[I]] and [[BQN]], there are two hooks in order to maintain symmetry: for example, BQN defines Before (<code>⊸</code>) to be the dyadic operator <code>{(𝔽𝕨⊣𝕩)𝔾𝕩}</code> ("<code>𝔾</code>'s left argument comes from <code>𝔽</code>") and After (<code>⟜</code>) to be <code>{(𝕨⊣𝕩)𝔽𝔾𝕩}</code> ("<code>𝔽</code>'s right argument comes from <code>𝔾</code>"). In the dyadic case these functions are identical to [[Reverse Compose]] and [[Beside]] respectively, but in the monadic case they differ because the argument is used twice: the second function application takes it as an argument directly in addition to the result of the first function application.