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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").
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 [https://dfns.dyalog.com dfns website].
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.
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.
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== Examples ==
== Examples ==
<source lang=apl>
<syntaxhighlight lang=apl>
       {⍵*0.5} 16        ⍝ square root
       {⍵*0.5} 16        ⍝ square root
4
4
       3 {⍵*÷⍺} 27      ⍝ ⍺th root
       3 {⍵*÷⍺} 27      ⍝ ⍺th root
3
3</syntaxhighlight>
      ⍝ Multiline dfn with optional left parameter
=== 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←{
       root←{
           ⍺←2          ⍝ square root by default
           ⍺←2          ⍝ square root by default
           ⍵*÷⍺          ⍝ result
           ⍵*÷⍺          ⍝ result
       }
       }</syntaxhighlight>
      ⍝ Dfn with conditional result
=== 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←{
       root←{
          ⍺←2          ⍝ square root by default
           ⍺=0:0        ⍝ return zero if zeroth root
           ⍺=0:0        ⍝ zero if zeroth root
           ⍵*÷⍺          ⍝ result
           ⍵*÷⍺          ⍝ result
       }</source>
       }</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 ==
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* [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/DynamicFunctions/Dynamic%20Functions%20and%20Operators.htm Dyalog]
* [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]
* [https://www.gnu.org/software/apl/apl.html#Section-3_002e7 GNU APL]
== References ==
<references/>


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

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 mathematics ∙ Precedence ∙ Tacit programming (Train, Hook, Split composition)
Array Numeric literal ∙ String ∙ Strand notation ∙ Object literal ∙ Array notation (design considerations)
Function Argument ∙ Function valence ∙ Derived function ∙ Derived operator ∙ Niladic function ∙ Monadic function ∙ Dyadic function ∙ Ambivalent function ∙ Defined function (traditional) ∙ Dfn ∙ Function train
Operator Operand ∙ Operator valence ∙ Tradop ∙ Dop ∙ Derived operator
Assignment Multiple ∙ Indexed ∙ Selective ∙ Modified
Other Function axis ∙ Bracket indexing ∙ Branch ∙ Statement separator ∙ Quad name ∙ System command ∙ User command ∙ Keyword ∙ Dot notation ∙ Function-operator overloading ∙ Control structure ∙ Comment
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