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

## External links

### Tutorials

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

### Documentation