Dfn: Difference between revisions
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== Examples == | == Examples == | ||
< | <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> | ||
=== Default left arguments === | === Default left arguments === | ||
Assignment to < | 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> | ||
=== 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: | ||
< | <syntaxhighlight lang=apl> | ||
root←{ | root←{ | ||
⍺=0:0 ⍝ return zero if zeroth root | ⍺=0:0 ⍝ return zero if zeroth root | ||
⍵*÷⍺ ⍝ result | ⍵*÷⍺ ⍝ result | ||
}</ | }</syntaxhighlight> | ||
=== Error-guards === | === Error-guards === | ||
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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> | 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←{ | Gravity←{ | ||
G←6.6743E¯11 ⍝ gravitational constant | G←6.6743E¯11 ⍝ gravitational constant | ||
| Line 49: | Line 49: | ||
Gravity 1.99e30 5.97e24 0 ⍝ trigger division by zero | Gravity 1.99e30 5.97e24 0 ⍝ trigger division by zero | ||
N/A | N/A | ||
</ | </syntaxhighlight> | ||
=== Shy results === | === Shy results === | ||
[[Roger Hui]]'s < | [[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}</ | assert ← {⍺←'assertion failure' ⋄ 0∊⍵:⍺ ⎕signal 8 ⋄ shy←0}</syntaxhighlight> | ||
== External links == | == External links == | ||
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.