Direct function

A direct function (dfn, pronounced "dee fun") is an alternative way to define a function and operator (a <a href="/facts/Higher-order_function/VjnjGbpt">higher-order function</a>) in the programming language <a href="/facts/APL_(programming_language)/E2sb98gC">APL</a>. A direct operator can also be called a dop (pronounced "dee op"). They were invented by <a href="/facts/John_M._Scholes/LwUCgcBo">John Scholes</a> in 1996. They are a unique combination of <a href="/facts/Array_programming/gFx1SxIY">array programming</a>, higher-order function, and <a href="/facts/Functional_programming/cdxqPEIM">functional programming</a>, and are a major distinguishing advance of early 21st century APL over prior versions.
A dfn is a sequence of possibly <a href="/facts/Guard_(computer_science)/QsmS63NU">guarded expressions</a> (or just a guard) between { and }, separated by ⋄ or new-lines, wherein ⍺ denotes the left argument and ⍵ the right, and ∇ denotes <a href="/facts/Recursion_(computer_science)/2uXo18Gv">recursion</a> (function self-reference). For example, the function PT tests whether each row of ⍵ is a <a href="/facts/Pythagorean_triplet/I3IJgWhf">Pythagorean triplet</a> (by testing whether the sum of squares equals twice the square of the maximum).

 PT← {(+/⍵*2)=2×(⌈/⍵)*2}
 PT 3 4 5
1
 x
 4 5 3
 3 11 6
 5 13 12
17 16 8
11 12 4
17 15 8
 PT x
1 0 1 0 0 1

The <a href="/facts/Factorial/kkfy1Bwe">factorial</a> function as a dfn:

 fact← {0=⍵:1 ⋄ ⍵×∇ ⍵-1}
 fact 5
120
 fact¨ ⍳10 ⍝ fact applied to each element of 0 to 9
1 1 2 6 24 120 720 5040 40320 362880

Direct function open-in-new

Direct function