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: ''"dfns" redirects here. For the workspace by Scholes, see [[dfns workspace]].'' | |||
As of 2020, dfns are fully implemented in [[Dyalog APL]], [[NARS2000]], [[ngn/apl]], [[dzaima/APL]], and partially in [[GNU APL]]. | 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 == | |||
<source lang=apl> | |||
{⍵*0.5} 16 ⍝ square root | |||
4 | |||
3 {⍵*÷⍺} 27 ⍝ ⍺th root | |||
3</source> | |||
=== Default left arguments === | |||
Assignment to <source lang=apl inline>⍺</source> 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> | |||
<source lang=apl> | |||
root←{ | |||
⍺←2 ⍝ square root by default | |||
⍵*÷⍺ ⍝ result | |||
}</source> | |||
=== 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: | |||
<source lang=apl> | |||
root←{ | |||
⍺=0:0 ⍝ return zero if zeroth root | |||
⍵*÷⍺ ⍝ result | |||
}</source> | |||
=== 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> | |||
<source 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 | |||
</source> | |||
=== Shy results === | |||
[[Roger Hui]]'s <source lang=apl inline>assert</source> 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: | |||
<source lang=apl> | |||
assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}</source> | |||
== External links == | == External links == | ||
* [[ | * [[wikipedia:Direct function|Direct function]] | ||
* [[ | |||
{{APL syntax}} | === 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}}[[Category:Kinds of functions]][[Category:Defining functions]] |