# Difference between revisions of "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:[1]

root{
2           ⍝ square root by default
⍝ result
}

### Guards

Guards provide dfns with support for basic flow control.[2] 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.[3]

In the following example, there are two error-guards for the error code 11 (DOMAIN ERROR):[4]

Gravity{
G6.6743E¯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