Dfn: Difference between revisions

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m (Link to definition of "shy")
m (Text replacement - "</source>" to "</syntaxhighlight>")
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4
4
       3 {⍵*÷⍺} 27      ⍝ ⍺th root
       3 {⍵*÷⍺} 27      ⍝ ⍺th root
3</source>
3</syntaxhighlight>
=== Default left arguments ===
=== 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>  
Assignment to <source 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>  
<source lang=apl>
<source lang=apl>
       root←{
       root←{
           ⍺←2          ⍝ square root by default
           ⍺←2          ⍝ square root by default
           ⍵*÷⍺          ⍝ result
           ⍵*÷⍺          ⍝ result
       }</source>
       }</syntaxhighlight>
=== Guards ===
=== 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:
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:
Line 28: Line 28:
           ⍺=0:0        ⍝ return zero if zeroth root
           ⍺=0:0        ⍝ return zero if zeroth root
           ⍵*÷⍺          ⍝ result
           ⍵*÷⍺          ⍝ result
       }</source>
       }</syntaxhighlight>


=== Error-guards ===
=== Error-guards ===
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       Gravity 1.99e30 5.97e24 0  ⍝ trigger division by zero
       Gravity 1.99e30 5.97e24 0  ⍝ trigger division by zero
N/A
N/A
</source>
</syntaxhighlight>
=== Shy results ===
=== 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]]:
[[Roger Hui]]'s <source 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]]:
<source lang=apl>
<source lang=apl>
assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}</source>
assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}</syntaxhighlight>


== External links ==
== External links ==

Revision as of 21:45, 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

<source lang=apl>

     {⍵*0.5} 16        ⍝ square root

4

     3 {⍵*÷⍺} 27       ⍝ ⍺th root

3</syntaxhighlight>

Default left arguments

Assignment to <source lang=apl inline>⍺</syntaxhighlight> is unusual in that the entire statement is only executed if the dfn is called monadically:[1] <source lang=apl>

     root←{
         ⍺←2           ⍝ square root by default
         ⍵*÷⍺          ⍝ result
     }</syntaxhighlight>

Guards

Guards provide dfns with support for basic flow control.[2] This is a multiline dfn with a conditional result: <source 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.[3]

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

Shy results

Roger Hui's <source lang=apl inline>assert</syntaxhighlight> 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: <source lang=apl> assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}</syntaxhighlight>

External links

Tutorials

Documentation

References

  1. Default Left Argument – Dyalog APL.
  2. Guards – Dyalog APL.
  3. Error Guards – Dyalog APL.
  4. APL Error Messages and Codes – Dyalog APL.
  5. Stefan Kruger. 2020 Problem Solving Competition – Phase II highlights. Dyalog blog. April 30, 2021.


APL syntax [edit]
General Comparison with traditional mathematicsPrecedenceTacit programming (Train, Hook, Split composition)
Array Numeric literalStringStrand notationObject literalArray notation (design considerations)
Function ArgumentFunction valenceDerived functionDerived operatorNiladic functionMonadic functionDyadic functionAmbivalent functionDefined function (traditional)DfnFunction train
Operator OperandOperator valenceTradopDopDerived operator
Assignment MultipleIndexedSelectiveModified
Other Function axisBracket indexingBranchStatement separatorQuad nameSystem commandUser commandKeywordDot notationFunction-operator overloadingControl structure