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A '''user-defined function''' (or '''tradfn''', pronounced "trad fun", for "traditional function", in [[Dyalog APL]]) is a function defined using a header that includes the function's name. Introduced in [[APL\360]], function definition was universally supported by APL dialects for much of the language's history, and is still commonly used in mainstream APLs. Since the 1990s other ways to [[Function styles|describe functions]] have appeared, with [[J]] and [[K]] rejecting function definition in favor of [[anonymous function]] description.
:''This page is about the function form typically written with the Del (<source lang=apl inline>∇</source>) character. See [[Function styles]] for an overview of all forms; in particular [[dfn]]s are considered a type of defined function in [[Dyalog APL]] and [[GNU APL]].''


The canonical representation form is equivalent to what the user would type into the [[line editor]] to define the function. An alternative representation consists of the entire [[session]] log transcript, including [[Del]]s (<source lang=apl inline>∇</source>) and line numbers, after having such a definition has been made.
A '''user-defined function''' (or '''tradfn''', pronounced "trad fun", for "traditional function", in [[Dyalog APL]]) is a function defined using a header that includes the function's name. Introduced in [[APL\360]], function definition was universally supported by APL dialects for much of the language's [[history]], and is still commonly used in mainstream APLs. Since the 1990s other ways to [[Function styles|describe functions]] have appeared, with [[J]] and [[K]] rejecting function definition in favor of [[anonymous function]] description.
 
{{Anchor|Representations}}The canonical representation form is equivalent to what the user would type into the [[line editor]] to define the function.<ref>[[Dyalog Ltd.]] Programming Reference Guide. [https://help.dyalog.com/latest/#Language/System%20Functions/cr.htm Canonical Representation].</ref> An alternative representation consists of the entire [[session]] log transcript, including [[Del]]s (<source lang=apl inline>∇</source>) and line numbers, after having such a definition has been made.<ref>[[Dyalog Ltd.]] Language Reference Guide. [https://help.dyalog.com/latest/#Language/System%20Functions/vr.htm Vector Representation].</ref> However, it should be noted that the <source lang=apl inline>∇</source>s are not part of the definition. Indeed, if using the [[Fix Definition]] (<source lang=apl inline>⎕FX</source>) [[system function]] to define the function, Dels need not (or must not, depending on implementation) be included.


Beginning in the 2010s [[Dyalog]]-based APL dialects including [[ngn/apl]], [[dzaima/APL]], and [[APL\iv]] have removed function definition in favor of [[dfn]]s. Wikipedia has a comparison of [[Wikipedia:Direct_function#Dfns_versus_tradfns|dfns versus tradfns]].
Beginning in the 2010s [[Dyalog]]-based APL dialects including [[ngn/apl]], [[dzaima/APL]], and [[APL\iv]] have removed function definition in favor of [[dfn]]s. Wikipedia has a comparison of [[Wikipedia:Direct_function#Dfns_versus_tradfns|dfns versus tradfns]].
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</source>
</source>
{{Works in|[[Dyalog APL]], [[APL2]], [[GNU APL]], [[NARS2000]], [[APLX]], and every older APL from [[APL\360]]}}
{{Works in|[[Dyalog APL]], [[APL2]], [[GNU APL]], [[NARS2000]], [[APLX]], and every older APL from [[APL\360]]}}
=== Semi-colons ===
Assignments are global by default. To keep a name local, it must be mentioned in the header, separated from the rest of the header by a semi-colon:
<source lang=apl>
      ∇ r←l Tradfn r;intermediate
        intermediate←l r
        r←intermediate intermediate
      ∇
</source>
{{Works in|[[Dyalog APL]], [[APL2]], [[GNU APL]], [[NARS2000]], [[APLX]], and every older APL from [[APL\360]]}}
=== Braces ===
=== Braces ===
An [[ambivalent function]] with an optional left argument, a conditional [[control structure]], one local variable, and a [[#Shyness|shy]] result:
An [[ambivalent function]] with an optional left argument, a conditional [[control structure]], one local variable, and a [[#Shyness|shy]] result:
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=== Brackets ===
=== Brackets ===
[[GNU APL]] allows functions and operators to accept an [[function axis|axis]] argument:<ref>[https://www.gnu.org/software/apl/apl.html#Section-3_002e2 3.2 Axis argument in defined functions] – GNU APL Manual</ref>
[[GNU APL]] allows functions and operators to accept an [[function axis|axis]] argument:<ref>[[GNU APL community]]. GNU APL Info Manual. [https://www.gnu.org/software/apl/apl.html#Section-3_002e2 Axis argument in defined functions].</ref>
<source lang=apl>
<source lang=apl>
       ∇ Z←Average[X] B
       ∇ Z←Average[X] B
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=== Dyalog APL extensions ===
=== Dyalog APL extensions ===
Dyalog APL's tradfns are enhanced in various ways compared to most other dialects.<ref>[[Dyalog Ltd.]] Programming Reference Guide. [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/Model%20Syntax.htm Model Syntax].</ref>
Dyalog APL's tradfns are enhanced in various ways compared to most other dialects.<ref>[[Dyalog Ltd.]] Programming Reference Guide. [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/TradFns/Model%20Syntax.htm Model Syntax].</ref>


==== Dynamic localisation ====
Names can be localised dynamically, while a tradfn is running, using the [[Shadow Name]] (<source lang=apl inline>⎕SHADOW</source>) [[system function]].<ref>[[Dyalog Ltd.]] Language Reference Guide. [https://help.dyalog.com/latest/#Language/System%20Functions/shadow.htm Shadow Name].</ref>
Names can be localised dynamically, while a tradfn is running, using the [[Shadow Name]] (<source lang=apl inline>⎕SHADOW</source>) [[system function]].<ref>[[Dyalog Ltd.]] Language Reference Guide. [https://help.dyalog.com/latest/#Language/System%20Functions/shadow.htm Shadow Name].</ref>
<source lang=apl>
<source lang=apl>
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</source>{{Works in|[[Dyalog APL]]}}
</source>{{Works in|[[Dyalog APL]]}}


Additional local names can also be declared on separate lines following the header line:<ref>[[Dyalog Ltd.]] Programming Reference Guide.  [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/Locals%20Lines.htm Locals Lines].</ref>
==== Locals lines ====
Additional local names can also be declared on separate lines following the header line:<ref>[[Dyalog Ltd.]] Programming Reference Guide.  [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/TradFns/Locals%20Lines.htm Locals Lines].</ref>
<source lang=apl>
<source lang=apl>
       name←1 2 3
       name←1 2 3
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</source>{{Works in|[[Dyalog APL]]}}
</source>{{Works in|[[Dyalog APL]]}}


==== Explicit ambivalence ====
The the header syntax can explicitly specify that a function is [[ambivalent]] by enclosing the left argument name in curly braces (for example <source lang=apl inline>result←{left} Function right</source>). Others dialects treat all functions that declare a left argument name as ambivalent and leave it up to the programmer to check for the presence of a value.
The the header syntax can explicitly specify that a function is [[ambivalent]] by enclosing the left argument name in curly braces (for example <source lang=apl inline>result←{left} Function right</source>). Others dialects treat all functions that declare a left argument name as ambivalent and leave it up to the programmer to check for the presence of a value.


==== Function results ====
A tradfn can return a function value as result. The returned function will replace the function and its arguments (if any) in the calling expression:
A tradfn can return a function value as result. The returned function will replace the function and its arguments (if any) in the calling expression:
<source lang=apl>
<source lang=apl>
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12
12
</source>{{Works in|[[Dyalog APL]]}}
</source>{{Works in|[[Dyalog APL]]}}
{{Anchor|Shyness}}
A tradfn can be declared as shy, that is, it exhibits the same behaviour as an assignment, in that by default, no result is printed when the function terminates, but attempting to use the result still succeeds. This declaration is done by putting curly braces around the result name (for example <source lang=apl inline>{result}←left Function right</source>).


The right argument and the result can be a name list instead of single name. The interpreter will unpack the right argument when the function is called, and collect the result when the function returns.<ref>[[Dyalog Ltd.]] Programming Reference Guide.  [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/Namelists.htm Namelists].</ref>
==== Shyness ====
By default, functions in APL will print their result to the session log even without using <source lang=apl inline>⎕←</source> unless their results are shy. Shy results are declared by putting curly braces around the result name (for example <source lang=apl inline>{result}←left Function right</source>). Assignment (<source lang=apl inline>name←array</source>) exhibits the same behaviour as a shy function in that, by default, no result is printed when the function terminates, but attempting to use the result still succeeds.
 
==== Namelists ====
The right argument and the result can be a name list instead of single name. The interpreter will unpack the right argument when the function is called, and collect the result when the function returns.<ref>[[Dyalog Ltd.]] Programming Reference Guide.  [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/TradFns/Namelists.htm Namelists].</ref>
<source lang=apl>
<source lang=apl>
       ∇ (c b a)←Rev(a b c)
       ∇ (c b a)←Rev(a b c)
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3 2 1
3 2 1
</source>{{Works in|[[Dyalog APL]]}}
</source>{{Works in|[[Dyalog APL]]}}
=== A+ differences===
=== A+ differences===
[[A+]] uses a reworked style of function and operator definition than maintains the principle of a header that matches the way the function will be used, but differs in many details:
[[A+]] uses a reworked style of function and operator definition than maintains the principle of a header that matches the way the function will be used, but differs in many details:
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=== Documentation ===
=== Documentation ===
* [https://help.dyalog.com/latest/#Language/Introduction/Functions.htm#Functions Dyalog – Introduction – Functions]
* Dyalog: [https://help.dyalog.com/latest/#Language/Introduction/Functions.htm Functions], [https://help.dyalog.com/latest/#Language/Introduction/Operators.htm Operators]
* [https://help.dyalog.com/latest/#Language/Defined%20Functions%20and%20Operators/Canonical%20Representation.htm#CanonicalRepresentation Dyalog – Defined Functions & Operators] <!-- links to Canonical Representation, but it's a bit confusing -->
* APLX: [http://microapl.com/apl_help/ch_020_010_070.htm User-defined Functions], [http://microapl.com/apl_help/ch_020_010_090.htm User-defined Operators]
* [http://microapl.com/apl_help/ch_020_010_070.htm APLX]


=== References ===
=== References ===
Retrieved from ‘https://aplwiki.com/wiki/Special:MobileDiff/5244...6989’

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