Dfn

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 website.

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
      ⍝ Multiline dfn with optional left parameter
      root←{
          ⍺←2           ⍝ square root by default
          ⍵*÷⍺          ⍝ result
      }
      ⍝ Dfn with conditional result
      root←{
          ⍺←2           ⍝ square root by default
          ⍺=0:0         ⍝ zero if zeroth root
          ⍵*÷⍺          ⍝ result
      }

External links

• Direct function

Tutorials

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

Documentation

• Dyalog
• GNU APL