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Defined function (traditional) (view source)
Revision as of 21:29, 10 September 2022
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:''This page is about the function form typically written with the Del (< | :''This page is about the function form typically written with the Del (<syntaxhighlight 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]].'' | ||
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. | 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 (< | {{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 (<syntaxhighlight 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 <syntaxhighlight lang=apl inline>∇</source>s are not part of the definition. Indeed, if using the [[Fix Definition]] (<syntaxhighlight 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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=== Basics === | === Basics === | ||
A simple [[dyadic function]]: | A simple [[dyadic function]]: | ||
< | <syntaxhighlight lang=apl> | ||
∇ r←l Tradfn r | ∇ r←l Tradfn r | ||
⍝ ...do something | ⍝ ...do something | ||
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=== Semi-colons === | === 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: | 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: | ||
< | <syntaxhighlight lang=apl> | ||
∇ r←l Tradfn r;intermediate | ∇ r←l Tradfn r;intermediate | ||
intermediate←l r | intermediate←l r | ||
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=== 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: | ||
< | <syntaxhighlight lang=apl> | ||
∇ {res}←{left} AddMult2 right;local | ∇ {res}←{left} AddMult2 right;local | ||
:If 0=⎕NC'left' ⍝ if variable "left" is not defined already | :If 0=⎕NC'left' ⍝ if variable "left" is not defined already | ||
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=== Brackets === | === Brackets === | ||
[[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> | [[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> | ||
< | <syntaxhighlight lang=apl> | ||
∇ Z←Average[X] B | ∇ Z←Average[X] B | ||
Z←(+/[X]B) ÷ (⍴B)[X] | Z←(+/[X]B) ÷ (⍴B)[X] | ||
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=== Operators === | === Operators === | ||
A [[monadic operator]] and a [[dyadic operator]], both deriving [[monadic function]]s: | A [[monadic operator]] and a [[dyadic operator]], both deriving [[monadic function]]s: | ||
< | <syntaxhighlight lang=apl> | ||
∇ res←(Function SELF) right | ∇ res←(Function SELF) right | ||
res←right Function right | res←right Function right | ||
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{{Works in|[[Dyalog APL]], [[APL2]], [[GNU APL]], [[NARS2000]], [[APLX]]}} | {{Works in|[[Dyalog APL]], [[APL2]], [[GNU APL]], [[NARS2000]], [[APLX]]}} | ||
A monadic operator and a dyadic operator, both deriving [[dyadic function]]s: | A monadic operator and a dyadic operator, both deriving [[dyadic function]]s: | ||
< | <syntaxhighlight lang=apl> | ||
∇ res←left (Function SWAP) right | ∇ res←left (Function SWAP) right | ||
res←right Function left | res←right Function left | ||
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==== Dynamic localisation ==== | ==== Dynamic localisation ==== | ||
Names can be localised dynamically, while a tradfn is running, using the [[Shadow Name]] (< | Names can be localised dynamically, while a tradfn is running, using the [[Shadow Name]] (<syntaxhighlight 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> | ||
< | <syntaxhighlight lang=apl> | ||
name←1 2 3 | name←1 2 3 | ||
∇ res←Dummy | ∇ res←Dummy | ||
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==== Locals lines ==== | ==== 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> | 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> | ||
< | <syntaxhighlight lang=apl> | ||
name←1 2 3 | name←1 2 3 | ||
∇ res←Dummy | ∇ res←Dummy | ||
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==== Explicit ambivalence ==== | ==== 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 < | The the header syntax can explicitly specify that a function is [[ambivalent]] by enclosing the left argument name in curly braces (for example <syntaxhighlight 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 ==== | ==== 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: | ||
< | <syntaxhighlight lang=apl> | ||
∇ Fn←Apply name | ∇ Fn←Apply name | ||
:If name≡'plus' | :If name≡'plus' | ||
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==== Shyness ==== | ==== Shyness ==== | ||
By default, functions in APL will print their result to the session log even without using < | By default, functions in APL will print their result to the session log even without using <syntaxhighlight lang=apl inline>⎕←</source> unless their results are shy. Shy results are declared by putting curly braces around the result name (for example <syntaxhighlight lang=apl inline>{result}←left Function right</source>). Assignment (<syntaxhighlight 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 ==== | ==== 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> | 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> | ||
< | <syntaxhighlight lang=apl> | ||
∇ (c b a)←Rev(a b c) | ∇ (c b a)←Rev(a b c) | ||
∇ | ∇ | ||