# Dfn: Difference between revisions

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: ''"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 [[wikipedia:lexical scoping|lexical scoping]], in contrast to the dynamic scoping of [[tradfn]]s. In other words, a dfn cannot "see" locals of its caller, but can see locals of its definer. | ||

* [ | |||

Wikipedia includes a thorough treatment of [[Wikipedia:dfns|dfns]]. | |||

== Examples == | |||

<syntaxhighlight lang=apl> | |||

{⍵*0.5} 16 ⍝ square root | |||

4 | |||

3 {⍵*÷⍺} 27 ⍝ ⍺th root | |||

3</syntaxhighlight> | |||

=== Default left arguments === | |||

Assignment to <syntaxhighlight lang=apl inline>⍺</syntaxhighlight> is unusual in that the entire statement is only executed if the dfn is called monadically:<ref>[https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/DynamicFunctions/Default%20Left%20Argument.htm Default Left Argument] – Dyalog APL.</ref> | |||

<syntaxhighlight lang=apl> | |||

root←{ | |||

⍺←2 ⍝ square root by default | |||

⍵*÷⍺ ⍝ result | |||

}</syntaxhighlight> | |||

=== Guards === | |||

Guards provide dfns with support for basic flow control.<ref>[https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/DynamicFunctions/Guards.htm Guards] – Dyalog APL.</ref> This is a multiline dfn with a conditional result: | |||

<syntaxhighlight lang=apl> | |||

root←{ | |||

⍺=0:0 ⍝ return zero if zeroth root | |||

⍵*÷⍺ ⍝ result | |||

}</syntaxhighlight> | |||

=== Error-guards === | |||

Dyalog APL dfns support error-guards for processing errors by error codes.<ref>[https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/DynamicFunctions/Error%20Guards.htm Error Guards] – Dyalog APL.</ref> | |||

In the following example, there are two error-guards for the error code 11 (DOMAIN ERROR):<ref>[https://help.dyalog.com/latest/#Language/Errors/APL%20Errors.htm#APLErrors APL Error Messages and Codes] – Dyalog APL.</ref> | |||

<syntaxhighlight lang=apl> | |||

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 | |||

</syntaxhighlight> | |||

=== Shy results === | |||

[[Roger Hui]]'s <syntaxhighlight lang=apl inline>assert</syntaxhighlight> is a dfn that has become the de facto standard when it comes to test suites.<ref>Stefan Kruger. [https://www.dyalog.com/blog/2021/04/2020-problem-solving-competition-phase-ii-highlights/ 2020 Problem Solving Competition – Phase II highlights]. [[Dyalog Ltd.|Dyalog]] blog. April 30, 2021.</ref>. In it, Hui uses both a [[default left argument]] and a final assignment to make the dfn [[shy]]: | |||

<syntaxhighlight lang=apl> | |||

assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}</syntaxhighlight> | |||

== External links == | == External links == | ||

* [[ | * [[wikipedia:Direct function|Direct function]] | ||

* [[ | |||

=== Tutorials === | |||

* APL Cultivation: [https://chat.stackexchange.com/rooms/52405/conversation/lesson-2-diving-into-functions-in-apl Diving Into Functions in APL] | |||

* Mastering Dyalog: [https://www.dyalog.com/uploads/documents/MasteringDyalogAPL.pdf#page=174 page 174] | |||

=== Documentation === | |||

* [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/DynamicFunctions/Dynamic%20Functions%20and%20Operators.htm Dyalog] | |||

* [https://www.gnu.org/software/apl/apl.html#Section-3_002e7 GNU APL] | |||

== References == | |||

<references/> | |||

{{APL syntax}} | {{APL syntax}}[[Category:Kinds of functions]][[Category:Defining functions]] |

## Latest revision as of 22:11, 10 September 2022

*"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←{
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.^{[5]}. 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

### Tutorials

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

### Documentation

## References

- ↑ Default Left Argument – Dyalog APL.
- ↑ Guards – Dyalog APL.
- ↑ Error Guards – Dyalog APL.
- ↑ APL Error Messages and Codes – Dyalog APL.
- ↑ Stefan Kruger. 2020 Problem Solving Competition – Phase II highlights. Dyalog blog. April 30, 2021.