Dfn

"dfns" redirects here. For the workspace by Scholes, see dfns workspace.

A dfn (contraction of direct function or dynamic function, pronounced "dee fun") is an alternative way to define a function and operator, invented by John Scholes. A dfn operator can also be called a dop (pronounced "dee op").

John Scholes was responsible for numerous presentations and publications on and about dfns, and until his passing he maintained the dfns workspace, a collection of dfns examples.

As of 2020, dfns are fully implemented in Dyalog APL, NARS2000, ngn/apl, dzaima/APL, and partially in GNU APL, although not all dialects implement lexical scoping, in contrast to the dynamic scoping of tradfns. In other words, a dfn cannot "see" locals of its caller, but can see locals of its definer.

Wikipedia includes a thorough treatment of dfns.

Examples

      {⍵*0.5} 16        ⍝ square root
4
      3 {⍵*÷⍺} 27       ⍝ ⍺th root
3

Default left arguments

Assignment to ⍺ is unusual in that the entire statement is only executed if the dfn is called monadically:

      root←{
          ⍺←2           ⍝ square root by default
          ⍵*÷⍺          ⍝ result
      }

Guards

Guards provide dfns with support for basic flow control. This is a multiline dfn with a conditional result:

      root←{
          ⍺=0:0         ⍝ return zero if zeroth root
          ⍵*÷⍺          ⍝ result
      }

Error-guards

Dyalog APL dfns support error-guards for processing errors by error codes.

In the following example, there are two error-guards for the error code 11 (DOMAIN ERROR):

Gravity←{
    G←6.6743E¯11       ⍝ gravitational constant
    11::'N/A'          ⍝ second DOMAIN ERROR: return 'N/A'
    11::∇⍎¨⍵           ⍝ first DOMAIN ERROR: maybe the argument is a vector of strings?
    G×⍵[1]×⍵[2]÷⍵[3]*2 ⍝ the argument is a vector of numbers
}

      ⍝ Calculate gravity force between the Earth and the Sun
      Gravity '1.99e30' '5.97e24' '1.50e11'
3.524119391E22
      Gravity 1.99e30 5.97e24 1.50e11
3.524119391E22
      Gravity 1.99e30 5.97e24 0   ⍝ trigger division by zero
N/A

Shy results

Roger Hui's assert is a dfn that has become the de facto standard when it comes to test suites.. In it, Hui uses both a default left argument and a final assignment to make the dfn shy:

assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}

External links

• Direct function

Tutorials

• APL Cultivation: Diving Into Functions in APL
• Mastering Dyalog: page 174

Documentation

• Dyalog
• GNU APL